Finance and Accounting(For ACCA, CIMA and other exams)

How to prepare for exams and profit from past papers

2020-10-27T09:36:00.001-07:00

These videos will explain how to profit from past papers while preparing for exams.

I had just prepared with out much preparation or editing, if it is of any use please use other wise just leave.

Video 1 introduction will give you the introduction of using exam resources

https://youtu.be/crdeTso5zcU

Video 2 reading question paper shows you to read examiners requirement

https://youtu.be/4dCZByvigzc

Video 3 planning and framing answer will provide answer

https://youtu.be/OWZy6T1qUEA

Video 4 other past paper addressing same issues, will show you how using past papers will help you to identify issues.

https://youtu.be/FONNiyN0BRU

Video 5 examiner remarks and marking scheme will show you how to use examiners remarks and marking scheme to identify issues.

https://youtu.be/IBq9vWVdd1o

VIDEOS ON LEARNING VARIANCE ANALYSIS

2019-10-10T07:35:00.001-07:00

Check the below mentioned blog post for complete theory, which was incorporated in the videos.

https://www.blogger.com/blogger.g?blogID=5984591937773450711#editor/target=post;postID=4798403123073469870;onPublishedMenu=posts;onClosedMenu=posts;postNum=71;src=postname

Basic knowledge required for variance analysis
https://youtu.be/JOULIrA3soQ

When variance becomes favorable and when adverse
https://youtu.be/HXnCe-DzW8o

Reason why we use standard rates in usage and actual usage in price variances
https://youtu.be/R1GcRdPZGWI

Knowing what is wrong with proof using single line variances
https://youtu.be/wapLwoht5oA

Material variances comprehensive example
https://youtu.be/OtMbWTvnmxM

Labour variances comprehensive example
https://youtu.be/YWCILUT-nbY

Variable overhead Variances
https://youtu.be/Cy8MdLwqU5g

Fixed overhead variances 1
https://youtu.be/kC8uC-CB_PA

Fixed overhead variances 2 comprehensive example
https://youtu.be/W9aJce5MpDA

Sales Sales margin variances
https://youtu.be/AAHizxFzB5M

Video on how to improve your professional level exam result

2019-10-04T15:46:00.002-07:00

https://youtu.be/MSdHDcReka0

Videos to Learn basic Accounting in an hour

2019-10-01T15:34:00.001-07:00

What is accounting why you need to learn the same
https://youtu.be/olNQ7y5Md34

Assumptions , elements and other basics required to learn accounting
https://youtu.be/0w2DFr3h8sM

basic knowledge required to learn accounting equation
https://youtu.be/weKMLtWphi4

Deriving accounting equation
https://youtu.be/Q7hvCvCNeCo

Recording entries in journal, ledger using accounting equation
https://youtu.be/fq2-cHXnUWw

Don't forget increase in assets debit.

The concept of double entry
https://youtu.be/L1wnvtAhsxY

Balancing ledger accounts
https://youtu.be/UzCg3exrUl0

preparing trial balance from ledger
https://youtu.be/OU7xG5WpiN0

Verifying accuracy of trial Balance
https://youtu.be/KN_cvHYOBq8

Preparing financial statements
https://youtu.be/rsO9w14_l2k

Preparing cash flow statement using accounting equation and financial statements
https://youtu.be/vIhZQkYjTME

How frauds are done using financial statements
https://youtu.be/xtv5zNCwoGE

Link to excel sheet
https://drive.google.com/file/d/1QZ16NJRvDx2fxmilJtK0F5FssyYZ_4LW/view?usp=sharing

Video of How to do Bank Reconciliation without knowledge of debits & credits

2019-09-26T03:54:00.000-07:00

Youtube link

https://youtu.be/EOxdbNN07MY

Video on Performing What if (sensitivity )Analysis using scenario manager, goal seek, data tables in excel

2019-01-20T06:23:00.000-08:00

Performing What if (sensitivity )Analysis using scenario manager, goal seek, data tables in excel

Performing what-if analysis also known as sensitivity or scenario analysis is of significant practical use to accountants and finance professionals.

Excel provides a useful tool to perform the same with ease.

As with any other tool, understanding for what purpose scenario manager, goal seek and data tables need to be used and their limitation was explained with simple examples of marginal costing and capital budgeting.

Even though the examples provided are simple, just to provide the flavor and steps necessary to arrive at correct solutions, you can arrive at complex scenarios for decision making with ease using these features.

Youtube link and data link

HTTPS://WWW.YOUTUBE.COM/WATCH?V=RPHEJLZEJG0

INPUT FILE CAN BE ACCESSED FROM

https://drive.google.com/file/d/1M_KudehQij8HE5U19cW3z3OO_AI763PV/view?usp=sharing

Videos of Excel basic training with practical applications

2019-01-05T04:01:00.000-08:00

Videos of Excel basic training with practical applications

data link

https://drive.google.com/file/d/1czi6YLpNrsNr66PjXhGE5TNkuRvEuLLV/view?usp=sharing

Often, I get emails asking how difficult the exams are at ACCA and CIMA professional levels, my reply is simple “it is very easy if you know the application”.

If you don’t know how to apply, it is just a waste of time and effort, I often say what is the use of learning if you don’t know about its application.

learning excel functions is just like learning various theories and models, at foundation and intermediate levels, but real life want applications, where knowledge doesn’t matter, what matters is application, that’s the reason professional exams provide you with real-life examples so that you can apply the theories you have studied during earlier stages, if you know application exams are cake walk otherwise disaster.

I am providing some videos, wherein you will learn how to apply Excel to some real-life examples.

My intention is just to remind you that knowing won’t help you much in exams or in life, what requires is an application.

Text Functions

Text functions are extremely useful to manipulate text, which will have wide-ranging benefits from audit to data mining.

1. TEXT FUNCTIONS, LEFT, RIGHT, LEN, MID, FIND

HTTPS://WWW.YOUTUBE.COM/WATCH?V=T2ZSC-JHGA4

2. FIND REPLACE LEN WITH FIND FUNCTION

HTTPS://WWW.YOUTUBE.COM/WATCH?V=STEFR4SAF04

3. APPLICATION AND INTEGRATION OF FIND WITH RIGHT, LEFT, AND MID-EXCEL FUNCTIONS

HTTPS://WWW.YOUTUBE.COM/WATCH?V=NW93ISYB32Y

4. UPPER, LOWER, PROPER EXCEL FUNCTIONS

HTTPS://WWW.YOUTUBE.COM/WATCH?V=7XLHDD-JNCA

5. TEXT TO COLUMNS

HTTPS://WWW.YOUTUBE.COM/WATCH?V=GPIC4CXIENM&T=2S

6. CONCATENATE

HTTPS://WWW.YOUTUBE.COM/WATCH?V=ITGJ_M6RFSG

Lookup Functions:

Lookup functions are extremely useful to extract information in other sheets, this is extremely useful in practice especially in audit finance and accounts.

7. VLOOKUP, TRANSPOSE, HLOOKUP

HTTPS://WWW.YOUTUBE.COM/WATCH?V=TQHKD-OZRCM

8. VLOOKUP PRACTICAL APPLICATION

HTTPS://WWW.YOUTUBE.COM/WATCH?V=9WMSJ36-JRQ

9. EXCEL INDEX AND MATCH FUNCTIONS

HTTPS://WWW.YOUTUBE.COM/WATCH?V=4CAN4ZUWT1G

Excel Logical functions, if, and, or

Logical functions are available in all programming languages, so learning them will always place you in a comfortable position when you need to extract information.

10. EXCEL IF WITH AND FUNCTION

HTTPS://WWW.YOUTUBE.COM/WATCH?V=MVD-RSWTBOY

This below video was made to show if with or function and error checking are added just to show complexity if you are unable to understand ignore.

11. COMPLEX IF FUNCTION WITH OR & AND WITH ERROR CHECKING

HTTPS://WWW.YOUTUBE.COM/WATCH?V=SE1BJLQMGLC

Excel for presentation, summarizing data

Excel is extremely useful to present &, summarize data, which can be done in multiple ways, some of the most powerful were shown below, we will also learn when to use what.

12. EXCEL SORT AND FILTER

HTTPS://WWW.YOUTUBE.COM/WATCH?V=PC3CC9QX4FS

13. EXCEL COUNTIF,COUNTIFS,SUMIF,SUMIFS,COUNTA

HTTPS://WWW.YOUTUBE.COM/WATCH?V=ABAOLMONUCW

14. EXCEL PIVOT TABLES

HTTPS://WWW.YOUTUBE.COM/WATCH?V=PXN0I1L6OHK

15. WHEN TO USE A FILTER, SORT, PIVOT TABLE AND FORMULA IN EXCEL

HTTPS://WWW.YOUTUBE.COM/WATCH?V=9WJ10TER_N8

Referencing and naming ranges

While watching above videos, there is something called absolute and relative referencing which we will see, we will further go and see the number of ways ranges can be named with its benefits and limitations.

16. EXCEL REFERENCING

HTTPS://WWW.YOUTUBE.COM/WATCH?V=4UA2NJLHJBG

17. EXCEL NAMING RANGES

HTTPS://WWW.YOUTUBE.COM/WATCH?V=AF0BFHDYALY

Excel features for accounts, audit, and finance

Below we will see some special features and functions which are very simple but powerful and can be used in the audit

18. EXCEL DATE FUNCTIONS FOR ACCOUNTS, AUDIT, AND FINANCE

HTTPS://WWW.YOUTUBE.COM/WATCH?V=KLGOXQ7NCXY

19. HOW TO SEARCH LINKED INFORMATION FROM OTHER SHEETS IN EXCEL

HTTPS://WWW.YOUTUBE.COM/WATCH?V=7LZXSBOQZG4

20. HOW TO VIEW FORMULAS IN EXCEL

HTTPS://WWW.YOUTUBE.COM/WATCH?V=VJK5HENBKPA

21. WHAT IF ANALYSIS, SCENARIO MANAGER, GOALSEEK, ONE-WAY & TWO-WAY DATA TABLES

HTTPS://WWW.YOUTUBE.COM/WATCH?V=RPHEJLZEJG0

INPUT FILE CAN BE ACCESSED FROM

https://drive.google.com/file/d/1M_KudehQij8HE5U19cW3z3OO_AI763PV/view?usp=sharing

Knowing vs. Applying

2018-03-08T06:42:00.001-08:00

Knowing vs. Applying

Even though many students know topics, they fail miserably at professional level exams; because many don’t understand the fact that, there is a considerable difference between knowing something and applying the same.

The biggest mistake many students make is, they feel that by studying more topics, they often be able to pass professional exams easily and often feel they have written exams excellently, but after seeing results blame the examiner for not passing them or study more to pass the exams, without understanding the real reason, which is inability to apply what they know to the case study question provided in the exam.

The real reason for deficiency in applying what we know is that we never ever trained ourselves for this. Many times, when we apply, we don’t even knowing the same. So by studying more, you know more and more, but to reap real benefits, what is necessary is the application of the knowledge to the real-life situations. Without which it is of no use, just like copying more and more movies into your hard drive, without seeing one or reading more and more cuisines without cooking one.

So how to learn this skill, simple, just by applying what you already know, frequently. This is something you can never attain by reading study text and textbooks, but by practicing previous question papers you can master this technique.

in our childhood days, we had learned in mathematics about, additions, subtractions, counting, division, multiplications etc, in biology about proteins, carbohydrates, fat etc, in geography about various continents, their climate and what they are famous for, we don’t know at that time, why we are studying all these things, but when someone gave gifts to use, we have counted, when someone giving us money we have added, when we gave money to someone we have subtracted, when we shared some thing, we have divided, from the childhood days we are applying, without ever knowing the fact that what we are doing is application of mathematical knowledge. This happens frequently, when the doctor says, about obesity and the reason is fat, this is something we have already studied but never applied.

We may not feel it as application, rather we feel it rather granted, but if you met someone who was uneducated, you know how difficult to do this simple tasks, you can easily cheat them, by paying them ten papers of $10 and saying you paid him $10000 as they don’t even know how to add and count, this is possible.

If you are using excel, you will know that same task can be done in multiple ways, so how you have achieved this, whenever you learned anything new, you thought about how it helps you to solve your present problems efficiently, your brain recognises and you find an application, but if you are satisfied with the present solution and does not think about applying the new method you have learned, you can’t find alternative application, which might be better and superior.

I will give a small example, quite often in audit, we need to look for duplication of data, this often becomes most important part of the audit.

So how can we find out duplicate figures in data, for example, cheque number or invoice number?

Let’s suppose, I am very new to excel, I learned about filtering, if I am having the inclination to find duplicates, I will filter and search each number appearing in filter to see duplicates, this may be inefficient way, but as I don’t know anything about excel, it works for me.

When you learn about sorting, and when you think about its application to your past problem you gain, you can now sort out and find out the difference between cheques or invoice number and able to find out duplicates in a much better way.

After some time you learned about remove duplicates, which you can readily apply to remove duplicates.

You learned about count and count if functions, you can apply the same.

You learned about pivot tables, you can now find out not only duplicate invoices and cheques but also go further.

You learned about macros, you will write a macro so that what you need is just to press a button so that you will get what you want and so on.

See, in all the above cases, what is helping you is not just knowing, but applying what you know to solve your problem, so unless you try to apply what you know to find out solution to your problem, you can’t get anything from your knowledge, it is as good as you don’t know anything and there is no difference between you and an individual who doesn’t know.

Now we will solve a question from ACCA P5 June 2012, question 4(I am very thankful to ACCA for allowing me to use their past papers), I had taken notes while reading the question, which I typed in the bracket.

Ganymede University (GU) is one of the three largest universities in Teeland, which has eight universities in total. All of the universities are in the public sector. GU obtains the vast majority of its revenue through government contracts for academic research and payments per head for teaching students. The economy of Teeland has been in recession in the last year and this has caused the government to cut funding for all the universities in the country.

In order to try to improve efficiency (the main objective of benchmarking, to help university when government cut funding due to recession), the chancellor of the university, who leads its executive board, has asked the head administrator to undertake an exercise to benchmark GU’s administration departments against the other two large universities in the country, AU and BU (sector/industry benchmarking). The government education ministry has supported this initiative and has required all three universities to cooperate by supplying information (information freely available hence benchmarking will help in finding results for poor performance and helps in improving performance).

The following information has been collected regarding administrative costs (benchmarking is done for administrative departments, reducing cost will help in improving efficiency)for the most recent academic year:

	GU	AU	BU
	$’000	$’000	$’000
Research
contract management	14,430	14,574	14,719
laboratory management	41,810	42,897	42,646
Teaching facilities management	26,993	27,263	26,723
Student support services	2,002	2,022	2,132
Teachers’ support services	4,005	4,100	4,441
Accounting	1,614	1,571	1,611
Human resources	1,236	1,203	1,559
IT management	6,471	6,187	6,013
General services	17,049	16,095	18,644

Total	1,15,610	1,15,912	1,18,488
Drivers:
Student numbers	28,394	22,783	29,061
Staff numbers	7,920	7,709	8,157
Research contract value $m	185	167	152

The key drivers of costs and revenues (CSF’s) have been assumed to be research contract values supported, student numbers and total staff numbers (examiner is helping us by providing drivers, previously he already stated that the data pertains to administrative cost and university wants to improve efficiency, thus, we need to calculate KPI’s based on this). The head administrator wants you to complete the benchmarking and make some preliminary comment on your results.

Required:

(b) Evaluate, as far as possible, Ganymede University’s benchmarked position. (9 marks)

The above question pertains to benchmarking, the examiner has not asked you about benchmarking, so if you write about benchmarking and its advantages and disadvantages, it will not help you to gain marks, what is required is the application of benchmarking to the question given.

So what we are asked is to evaluate the benchmarked position.

Benchmarking involves comparing with some preset standard or target using KPI’s, for CSF’s which helps in achieving organizational objectives.

In the present case, the objective is to increase revenue efficiency, by reducing administrative cost (CSF), by using various performance indicator (KPI’s), using drivers research contract values supported, student numbers and total staff numbers

The question has given both costs and drivers, so what is important is to identify correct cost driver, to calculate KPI or performance indicator. (This is some thing we will do in overhead allocation and activity based costing, where we assign costs based on related drivers)

How to establish a relationship between cost and driver, simple, we need to look at the correlation.

Let’s see now.

From the above, without doubt, we can relate and find out four ratios with ease
We can relate HR to staff, as more staff directly correlates with more HR cost, we can assign HR cost to a number of staff and find out HR cost per staff.

Student support services can be related with Student numbers and find out a ratio of student services cost per student for comparison.

We can find out research contract management and research laboratory management as a percentage of total research contract value, see the examiner is helping us to get pass marks, and also notice, we are using drivers as the denominator.

Now we will go further and look at teachers support services and teaching facilities management, teaching facilities management, is related directly with number of teachers, as we have no information on number of teachers, we need to find out which driver provided in the question correlates with number of teachers available , think for a minute the obvious answer is number of students, with more students we require more teachers and vice versa and it has nothing to do with staff or research contact value, so got the KPI’s teaching facilities management cost per student and teachers support services per student

Now, what remained are accounting, general services, and IT management, as these services are required by both staff and students and the question clearly states that GU obtains the vast majority of its revenue through payments per head for teaching students. Students become the most important driver to allocate costs, use number of students to allocate these three costs. If you want to use staff numbers, justify the same by stating that above services are more related to staff, hence it was allocated based on staff, or if you want, you can allocate the above costs to both staff and students stating, both require them, its simply your assumption.
I suggest you to go through the blog post, the link for the same is provided below,
http://cvdsomayajulu.blogspot.in/2017/06/how-to-use-correct-performance-measures.html
which helps to identify correct ratios, using predictive power or correlation, So in the above case if you assume accounting,IT and general services are more correlated with number of students, then it becomes the cost driver, if you assume, the above are more correlated with number of staff, then staff becomes cost driver.
Note: The examiner is least concerned with your workings, but he expects you to justify your answer, if your justification is right (this is very important), he will give marks, also note that you are able to calculate 4-5 ratios easily, which is more than enough to get high pass marks.

For the above question , studying about benchmarking from various study texts and text books will only help you in knowing what benchmarking is all about, but will not help much in solving above question, but applying what we studied about correlation, CSF’s, KPI’s , and cause and effect relation between cost’s and drivers while studying overhead allocation or activity based costing,will help us to solve this.

In examination you need to analyze and explain the figures which you have calculated, which I am leaving for you.

How identifying CSF's & KPI's help us in performing Benchmarking (useful to ACCA P5)

2018-03-07T08:16:00.004-08:00

How identifying CSF's & KPI's help us in performing Benchmarking

Benchmarking simply implies comparing with some preset target or standard, so as to evaluate and improve the performance of the organization.

So benchmarking is used not only to evaluate, but to improve, so if we set poor standards, the performance evaluation will show that we are performing brilliantly, but without much improvement, which is reflected in our CSF’s and measured by KPI’s.

So benchmarking involves identifying objectives we need to improve by comparing with preset standards, identifying CSF’s which we want to compare with preset standards to improve objectives and measuring CSF’s using KPI ’s and comparing the same with preset standards to know whether we have improved our performance in achieving objectives.

As benchmarking involves comparing with some preset standards, so how can we preset the standard? this depends on the availability of information, if there is no information available we need to compare with just our selves, (our historical performance), and if the information is freely available we can compare with competitors and if possible with best organizations operating in other industries.

Internal benchmarking or historical benchmarking

When an organization is operating in a new industry, or when information becomes a comparative advantage and everybody wants to protect the same, one can set standards using historical data, this is something done in practice using variance analysis and budgetary control.

Example: Suppose a student wants to succeed in exams, he is from remote village, as there is no one to measure performance he needs to compare with his historical performance, in this case, success in exams becomes objective, CSF is to study better to succeed in exams and KPI is the marks, note in this case even if his not studying in remote village if his colleges are very competitive and they don’t want to share any information he has no other option left except to compare with his own historical information.

Another example, an individual weight 170 Kgs, to improve health, his doctor suggests to reduce weight, as there is no one with similar weight, he starts to compare with himself over a period of one year and after 1 year weights 153 kgs, yes there is improvement, but that does not reduce his health risk, which is the main objective. (see, the objective is to improve health, the CSF is to reduce weight, which helps in achieving the objective of improved health, and KPI is the weight measured in Kgs)

Industry/sector benchmarking, functional /competitive benchmarking

When industry evolves, organisations can obtain information pertaining to other organisations through industry journals etc, or through exchange programmes where organisations share best practices to obtain superior performance which may help all who are participating; this can happen in the same industry or sector, which helps in setting standards for benchmark, here too, the standards should be set in the areas where the organisation can improve the performance.

Example: The student studying in a remote village at the time of writing exams meets a college and both agreed to exchange information so that one can compare his performance with another, thus helping to evaluate their own performance and if possible exchange information which will benefit the other, thus helping them both. Suppose even if one doesn't want to share, still by comparing with someone who has performed better and knowing how he has done will help to improve the performance.

Another example, The person who wants to reduce his weight of 170 Kgs, finds some one on internet who weights 185 kgs, they want to collaborate and share information and meet after six month,s one reduces weight by 10 Kgs another by 30 Kgs, now they share how they are able to reduce weight with one another, and both will get new techniques if they are following different weight losing programmes and helps both to reduce weight in future, in this case, if they don’t want to share weight losing programmes, still it gives hint to another that there exists something if followed will help in reducing weight, so he will try to figure it out.

Strategic benchmarking, best in class benchmarking

The last and much better is to look for and try to adopt great standards where ever you find one. This ultimately brings great success.

Example, A student who is studying taxation, notice that doctors operate and study at the same time, he also observes that painters and musicians will not only take classes and notes but also practice a lot, so he wants to emulate them and start applying taxation to help organisations and individuals to reduce their tax liabilities, here he is not just learning, but started applying which him a lot in his professional life

Another example, The person who wants to reduce his weight of 170 Kgs, sees a sports man, so he starts exercising and after 1 year weights 150 kgs, but he knows that to be fit like a sports star, he should be around 65-70 kgs, yes there is improvement, but that does not make him fit like a sports star, he knows that he needs to improve a lot and tries to improve, see compared with first two cases, this drives him to improve more as he set very high standards of performance.

Now we will apply to organisational setting, zero defects, TQM, just in time, Kaizen or continuous improvement, which evolved in manufacturing industry, that too in car manufacturing industry, developed at Toyota, a car manufacturing company, when adopted by other car manufactures is an example of sector benchmarking, functional /competitive benchmarking.

When it was adopted by other manufacturing industries, this becomes the case of Industry benchmarking,

When those concepts penetrated and adopted by other companies in other industries which are nowhere related to manufacturing like, like information technology, healthcare, banking etc, they become strategic benchmarking or best in class benchmarking

ACCA 2012 Q.no 2 (I am very thankful to ACCA for allowing me to use their past papers)

While reading question Comments are added to identify objectives, CSF’s and KPI’s and get it connected with other subject areas which one might have studied before writing the P5 exam, this is something which helps us, identifying, whether we are able to apply our knowledge and to connect answer with questions asked by examiner.

Amal Airline (Amal) is the national airline of Jayland. It was originally owned by the government but was listed on the local stock exchange when sold to private investors more than 20 years ago. The airline’s objective is to be the best premium global airline. (differentiation, Michael Porter)

Amal provides long- and short-haul services all over the world and is based at its hub at Jay city airport. Amal has been hit by a worldwide reduction in air travel due to poor economic conditions. The most recent financial results show a loss (reason given above) and this has caused the board to reconsider its position and take action to address the changing environment.

Amal has cut its dividend in order to conserve cash and it is trying to rebuild profitability by reducing costs by 14%. (objective for benchmarking, premium airlines vs cost cutting)

The airline is capital intensive (any capital-intensive industry requires economies of scale, so we need to look into this aspect while evaluating CSF’s and KPI”s) as it requires to maintain a large fleet of modern aircraft. The two major costs for the airline are staff and fuel. (CSF”s to reduce cost, it wants to reduce cost by 14%, so it can focus on staff and fuel), In trying to renegotiate working conditions and pay, (to reduce staff costs), the management has angered the unionized workforce (obvious, I too don’t want to increase work with a reduced pay). There has already been some strike action by the unions representing the aircraft crew and ground staff and more are threatened. They are upset about changes to pension provisions which will require them to make larger contributions (this automatically reduces staff costs, as it is defined contribution plan, compared with earlier defined benefit plan ) and also, a reduction in the number of crew on each aircraft (we need to see how many are employed by other players in the industry a benchmarking KPI) which they believe will require them to work harder and so they want a compensating pay-rise (reasonable demand, as more work, requires more pay, but we need to compare this with other players in the industry another KPI to look for)

Additionally, the board is pushing forward a large project to improve the design of the company website in order to increase the number of passengers who check-in online and so would not require as much assistance at the airport. (this certainly reduces cost but requires a tradeoff between investment vs. cost reduction)

The new design is also aiming to increase the number of passengers who book their tickets through the company’s website rather than other resellers’ websites or at booking agents.( this increases revenue as it reduces commission and brokerage) The project is currently two months behind schedule due to one of the main software suppliers becoming insolvent. (Project management, time overruns increases cost).

Finally, the board has been considering taking advantage of new technology in aircraft engines by making a large investment ($450m) in new low-noise, fuel-efficient aircraft in an effort to reduce the environmental complaints surrounding air travel and also cut costs. (fuel efficient aircraft reduces cost).

Given all of the issues and projects affecting Amal, the CEO has tried to find a unifying view that will explain the airline’s performance. She has heard that the performance prism may provide such a framework.

As further background, the CEO has supplied the data below on Amal and two of its main competitors. Kayland Air is a government-owned and runs airline in the neighboring country of Kayland. It has a similar mix of business to Amal and targets a similar market.(sector benchmarking, both are same, so it becomes apple in one country vs apple in another country) Cheapo Air is currently one of the most successful (best in the class, but will not represent the air line industry) of the new privately-owned airlines that have gained significant market share over the last 15 years by offering a cheap but basic short-haul service to customers in and around Jayland.(cost differentiation, Michael porter) Cheapo Air subcontracts many of their activities in order to remain flexible.(subcontracting obviously reduces costs, but it has its own risks) The CEO wants you to calculate some suitable performance measures and explain the results.

Data provided by the CEO:

Data for the most recent calendar year
	Amal	Kayland Air	Cheapo Air
Passengers (’000s)	23,649	38,272	35,624
Passenger kilometres (millions)	79,618	82,554	40,973
Revenue $m	5,430	7,350	2,170
Costs
Fuel $m	1,480	1,823	535
Staff $m	1,560	2,998	238
Staff numbers	32,501	56,065	5,372
Operating profit $m	630	54	127
Number of aircraft	182	361	143
Average aircraft size (seats)	195	163	125
Seat kilometres (millions)	1,00,654	1,05,974	46,934
Note: A seat kilometer is generated for every one kilometer flown by an available seat on the company’s aircraft.

We can directly compare Amal vs Kayland Air, what KPI’s to use, it depends on our CSF’s, which further depends on our objective.

The objective is to increase profitability by reducing costs.

CSF’s, Capacity utilization, reduction of fuel and staff costs, thus increasing profitability (all given in the question)

KPI’s,

For capacity utilization, we need to calculate how much aircraft was used? as question has given number of aircraft and average seat size, we can get total number of seats available, but some flights may never fly, and some may fly for long distances, and some may fly for short distances, thus distance travelled matters, this makes the above calculation useless, but as ever the examiner helps us by providing information in the question itself giving Passenger kilometres (millions), and Passenger kilometres (millions), so by dividing Passenger kilometres (millions) with Seat kilometres (millions) one can ascertain capacity utilisation. It was not straightforward, but you are wringing ACCA P5, the professional exam, and you are expected to know this.

If you want, you can give other utilization ratios such as staff or fuel cost per Passenger kilometers or seat kilometer, while seat kilometer is the total capacity, the passenger kilometer is the utilized capacity.

Using passenger kilometer will take into account how efficiently the airline is running, Efficiency depends on several other external factors like, size of the craft, the fuel efficiency of aircraft, how well it is maintained, the age of the aircraft etc, as the airlines has less control over external factors, so it is better to compare with seat kilometers, which is within the control of management.
(Why using seat kilometer is better predictor of fuel cost than using passenger kilometer was discussed in this blog post, the link is provided below
http://cvdsomayajulu.blogspot.in/2017/06/how-to-use-correct-performance-measures.html)

The other CSF’s given were fuel and staff.

When revenue and costs are given, one can use cost to revenue ratio’s like, cost of fuel and staff as a percentage of revenue, you can also use per units for example like revenue generated by each unit (member) of staff, revenue generated by each unit of fuel etc.

To see the CSF of profitability, we need to look at profitability ratios.

Thus we are able to get the following table

	Amal	Kayland Air	Cheapo Air
Capacity utilisation	0.7910068	0.779002397	0.8729919
Efficiency Passenger kilometres (millions) / Seat kilometres (millions)	79.10%	77.90%	87.30%
fuel as % of revenue	27.26%	24.80%	24.65%
staff cost as % of revenue	28.73%	40.79%	10.97%
Operating profit as % of Revenue	11.60%	0.73%	5.85%
Average staff costs (total staff cost / number of staff)	47998.52	53473.65	44303.80
Revenue generated per staff	167071.78	131097.83	403946.39
Fuel cost per seat kilometres	14703.837	17202.33265	11398.986
staff cost per seat kilometers	15498.639	28289.95791	5070.9507

The question states that CEO wants you to calculate some suitable performance measures and explain the results, so writing about benchmarking will not give any marks.

Now what is important is analysis, why Cheapo Air is performing so better, whether Amal airline is really performing badly.

While writing answer provides a reference to what is given in the question.

Amal is a premium airline, thus comparing it with low-cost airline like Cheapo is not fair, but it can be used as best of class benchmark to learn how it is performing efficiently, to ascertain correct performance it is better to compare Amal with Kayland Air, which is government company but having similar operations in different country, hence becomes sector/industry benchmarking.

To be fair, Amal is performing far better than its peer Kayland Air in another country, the Amal ’s operating profit as % of revenue is far better than both Kayland Air and Cheapo, this may be due to operating in a premium segment.

As management is concerned about profitability and its poor financial result and it is planning to reduce fuel and staff costs to improve profitability, we need to look at how others are doing in this aspect, this helps us to identify reasons for better performance and implement the same in Amal to improve profitability.

Cheapo Air utilisation rate is higher at 87.30%, is performing better, which helps in reduction of fuel cost and staff costs, the question states that Cheapo is offering a cheap but basic short-haul service to customers and it outsources some of its operations thus having possibility of reducing labour costs, but when we look at average staff costs, the cheapo’s staff cost of 44303.80 is not having much difference with Amal’s 47998.52, as airlines are a competitive industry, staff need to be paid competitively, hence not a huge difference, but when we come to staff costs per seat kilometre it is nearly 1/3^rd of Amal’s and 1/6^th of Kayland Air, thus showing it is not only paying staff competitively, but using them more efficiently.

Comparing Amal with Cheapo Air is not fair, as one is operating in premium long-haul segment , while other is operating in a cheap but basic short- haul segment, to judge real performance we need to compare Amal with Kayland Air, with respect to Kayland Air, the Amal is performing far better, its staff costs to revenue and staff costs per seat kilometres are 50% of Kayland Air and also having high revenue generated per staff.

Amal’s operating profit to revenue is superior to both Kayland Air and Cheapo, as it is operating in premium segment it is expected , but revenue generated per staff is much lower compared with Cheapo, which shows there is a possibility of improvement, Cheapo’s fuel cost per seat kilometers is less, as management is considering decision to purchase fuel-efficient aircraft in future, this factor needs to be studied further.(Note, I am using seat kilometer, which is controllable, while passenger kilometer is not)

You can also state that in future the cost of staff will be reduced due to introduction of new defined contribution scheme, instead of defined benefit scheme followed now, by this you are relating P2 to P5

Yield to maturity

2018-02-02T07:14:00.000-08:00

Yield to maturity

Bonds are debt obligations, wherein bondholder lends money in return for interest paid on face value also called par, in some cases the amount paid will not be redeemed, which we call irredeemable or perpetual and many times they are redeemable or convertible after some time into specific instrument, which can be either equity or preferential shares.

Bonds are tradeable; hence their market value changes with demand and supply, which affects the rate of interest receivable on the amount paid to purchase the bond.

Bonds can be issued at par, premium, and discount and they can be redeemed at par, premium, and discount.

So from the above, we can say that bonds come in different flavors, depending not only on duration but also on issued or redeemable at par, discount or premium, so the Yield to maturity becomes a most important factor, in comparing different bonds having a similar credit rating.

We will go through small example BCA co-issued a bond at par for$100 with a coupon rate of 6 percent, which will be redeemable at par in three years time, the present market price is $91, and the coupon is 6 percent.

Coupon rate is the rate of interest payable on bond, so in the above example, the coupon interest receivable or just interest received by bondholder is 6% x$100 =$60

So interest receivable is = coupon rate x par value of the bond

The above formula can be used to calculate both par value and coupon rate, provided other two values were given for example if we have to calculate coupon rate, it will be interesting receivable/par value of the bond

As $100 bond was sold for $91, this bond was sold at discount of $9.

So what is the rate of return for bondholder who purchased bond for $91

His rate of return will be $6/$91, which comes to 0.065 or 6.59%, this rate is called income yield or interest yield, which is nothing but interest received/price paid at market value for bond, if bondholder has to pay income tax on this income, he can call it gross yield before income tax and net yield after income tax.

Note: coupon rate depends on par value, whereas yield depends on market price, so if the market price of the bond is less than par value, or if the bond is quoted at discount, then the yield will be more than coupon rate and vice versa.

In the above example the bondholder has purchased the bond at discount for $91, which at the time of redemption will provide him $100 as it is redeemable at par, so he is getting not only 6.59% return, but also additional benefit of $9, which is nowhere reflected in the yield we have calculated above.

This is where comes in to picture the concept of Yield to maturity, which takes into account not only Yield but also capital appreciation.

Total capital appreciation = Amount available for redemption – Price paid/Price paid

= 9/91 = 0.0989 or 9.89%

As it is redeemable in three years time, capital appreciation per year = total capital appreciation/number of years left for redemption = 9.89%/3 = 3.3%

So the Yield to maturity or redemption yield = actual yield per year + % of capital appreciation per year

= 6.59% + 3.3% = 9.89%, this is just an appropriate estimate, as it is not taking into account time value of money, so if you want to get the accurate rate you need to consider the time value of money using present values and calculate the internal rate of return.

So how to calculate Yield to maturity accurately, for that you need to understand what yield to maturity is all about, it is the discount rate at which the present value of all the cash inflows from the bond (interest plus principal in the form of redeemable amount) is equal to the present value of cash outflows from bond (purchase price of bond at current market price)

This rate is called the internal rate of return.

In the above example

$91 = 6/(1+kb)¹ + 6/(1+kb)² + 106/(1+kb)³

Solving for kb, using internal rate of return will give us, the rate of return 9.6%, this 9.6%, is called yield to maturity, with has taken into consideration not only yield, but also capital appreciation.

For understanding concept of internal rate of return, you can go to the following link

https://www.blogger.com/blogger.g?blogID=5984591937773450711#editor/target=post;postID=539881542899895523;onPublishedMenu=allposts;onClosedMenu=allposts;postNum=35;src=postname

Relationship between Performance Measurement, Evaluation, Management, Mission, CSF & KPI

2018-01-21T05:21:00.002-08:00

Relationship between Performance Measurement, Evaluation, Management, Mission, CSF & KPI

What is meant by performance measurement?

What is meant by performance evaluation/assessment?

What is meant by performance management?

How they relate to Mission, CSF (Critical success factors) & KPI (Key performance indicators)?

What is the difference?

What models or techniques we need to use for performance measurement, evaluation, management, mission CSF & KPI.

To be frank, these words are fancy words, you are already doing this, but you don’t know this, I will show this with out using any financial jargon like profits, wealth maximization, ROI etc.

Let's take small example of yourself.

As a student, your school wants to produce good responsible citizens by providing you and other students with good quality education and to check your progress in studies, it has conducted a maths exam (for that matter, any class and any subject, I took this one only as an example) you got 50%, your two best friends have also written , one got 25% and another got 90%.

These marks are measuring yours and your friend's performance, so 50%, 25% & 90% marks are performance measures, so I am using % of marks as a performance measure.

Your teacher was asked to grade the students according to their performance, for which she uses marks; the grading system followed is A grade for more than 75% marks, B grade for marks between 35%-75%, and C grade for marks below 35% marks.

So you got grade B and one of your friends, who got 90%, got grade A and another who got 25% got grade C.

See the same marks are used to classify students to evaluate/assess them, where A shows good B shows average and C shows below average.

If the management of the school decides to use these marks or grades to improve the performance of those who scored less, the same marks are now being used as performance management tool, to plan, organize and control scarce resources( teachers attention time) to improve student performance.

See, the same marks are used to measure, evaluate and manage student performance, you are not using any model or tool, when marks are used as a score or measure it became performance measurement tool, when it is used to evaluate or assess the performance of one student against other, the same marks are becoming performance evaluation tool, when marks are used to help students to improve their performance, it is becoming performance management tool.

See in the above example, first, there is a measurement, and then one uses this measurement to evaluate/assess to manage.

So, there will no management without measurement, whenever you want to manage something, you must measure first, so the measurement is inherent in management.

The Mission of school is to produce good responsible citizens by providing good quality education, as it defines its business, objective and purpose, for that matter its very existence and the performance of the student in studies is the critical success factor, as students perform better in studies, it shows the organisation is providing good quality education otherwise not and how this better in studies is measured, yes by using marks & grades so it becomes the Key performance indicator, which shows how he is performing in studies to become a good citizen.

This is something given in every performance management case study, asking you to link performance measures, with a mission statement, or asking you about the weakness of present performance measures or KPI’s, or how CSF’s and KPI’s relate to the mission statement.

This is not a space science, if you can understand above example, you already know a lot..

Whenever you study something especially in social sciences, never ever believe it right, there are always two sides, if one view supports it there will be another opposing the same.

So, what the examiner is expecting from you, is to study using this critical aspect

(I can quote number of questions in ACCA P5 paper setting, where in examiner gives mission as creating wealth and quotes performance measures which are not wealth creating like ROI, and expects you to criticize as it is not creating wealth, the recent example is March/June 2017 paper,)

In the above example, the mission of the school is to produce good responsible citizens, by making students study and secure good grades and marks.

Is it correct?

Note carefully, whether studies only make good responsible citizens, not so, if it is true, then we might have avoided whole financial crises, started in 2008, which involves some of the best brains in finance.

Next teacher is assessing the performance of students based on one measurement criteria of subject marks, student C may be excellent in dance, music, literature,coding or sports but that criteria doesn’t help here, this is what examiner expects you in exams, to tell about deficiencies of present performance measures, note every performance measure will have some strengths and some weakness, you must know both and use in exam hall to critically question the measures when asked for.

So we can make relationship between, mission, CSF’s, KPI’s, Performance measures, evaluation and management

Performance measures and KPI’s are the marks & grades

Performance of the student in studies is the CSF, which itself is judged by marks

If a student is not performing well in studies, provided by low marks and grades, is used to evaluate and manage, thus helping in performance evaluation and management.

Good performance of the student in studies helps in achieving Mission of producing Good responsible citizens

See I am using only one measure Marks for measurement, evaluation and Management.

What about models:

Even before Balance scorecard, performance pyramid, building blocks models were developed, the performance used to be measured and managed and some majestic structures like great pyramids were built.

Long before the above models were developed, there are measures like profit, cost, ROI etc which are used to measure, assess, evaluate and manage the performance. With each stage, the measures gets broader, so that people can't cheat, for example if profit is the parameter people start to increase profit,by cutting desired long term expenses like research and development, if ROI is used, people started reducing long term investments to improve ROI, thus arrived wealth maximization, but which is difficult as we require discount factor and future returns, which are difficult to measure.

Then arrived models like balance score card, performance prism etc, which are much broader, and takes into account both financial and non financial measures or simply speaking they are multi-dimensional.

As they are multi-dimensional, they are going to be much broader and difficult to manipulate.

For example if performance of student is based not only on studies, (Worst if his performance is effected due to his inability to score in a single subject), but also on others aspects of development like sports, drawing, music etc, it truly helps in making student a good responsible citizen.

Conclusion: There will be no assessment/evaluation without measurement, and there will be no management without measurement and assessment/evaluation, the measures used to assess performance becomes KPI’s, which help in assessing CSF’s, which help in performance management, which ultimately helps in achieving the mission.

Just one measurement may be enough, but it may not be able to provide complete picture, hence we require other measures especially relative measures and balance scorecards which measure diverse parameters.

In organisations, when profit maximization becomes mission,, profit may be enough to measure performance of manager at operational level, and the same profit can be used as assessment tool to judge performance of divisions at tactical level or managerial level and the same profit is used to take strategic level decisions by top level management like closure of products, departments etc. see just one measure, here profit can be used, but you must also know its implications and limitations.

Now are you able to write to this question given in ACCA P5 June 2012 exam question No.1

(iii) Assess how the quote ‘What gets measured, gets done’ could apply to Metis. (10 marks)

You may also be able to link KPI's with Mission and CSF's, if you can try the latest paper

ACCA P5 March/June 2017 Question no 1 (i) Evaluate the links between the current key performance indicators at DS in Appendix 1 and its mission.(8 marks).

(I am very thankful to ACCA for allowing me to use their past papers)

Links to some interesting videos on block chain technology and bit coin

2018-01-13T22:45:00.002-08:00

Blockchain: Massively Simplified | Richie Etwaru | TEDxMorristown

https://www.youtube.com/watch?v=k53LUZxUF50

Whiteboard Session: How Does Blockchain Work?

https://hbr.org/video/5582134272001/whiteboard-session-how-does-blockchain-work

What the #?!* is Bitcoin? | Jeremy Rubin | TEDxBeaconStreet

https://www.youtube.com/watch?v=Vzjtvt77mgc

Are you able to relate this article to your Finance studies.

2018-01-13T09:06:00.002-08:00

After reading this article you must be able to relate, write and score some marks for the question asked in ACCA P4 question no 4 of March/June 2017 – Sample Questions.

http://www.accaglobal.com/in/en/student/exam-support-resources/professional-exams-study-resources/p4/past-exam-papers.html

For answer see at the end of this blog post. I strongly recommend you to subscribe to Economist, so that you can read at least 3 free articles per week, which I do.
Use this link

https://www.economist.com/news/briefing/21729988-low-interest-rates-have-made-more-or-less-all-investments-expensive-bubble-without-any-fizz

Or,

Search google for

Economist article Asset Prices The bubble without any fizz

Low interest rates have made more or less all investments expensive

The article says that " when the price of a risky bond rises, relative to the price of a safe benchmark, the credit spread narrows, the question says about the credit spread, which is the difference between , rate of return on risky bond and safe bond, in general the rate of return on safe bond will be less compared with risky bonk, due to risk vs return relationship, with reduction in rating, the risk on the investment increases, which effects its return, and as rate of return on debt increases, it effects overall cost of capital, which takes into account weighted average cost of debt, equity and other sources of capital, as it is used to discount cash flows, it reduces value of the enterprise and return and wealth of shareholders.

I am sure, if you are able to read and analyse this article correctly, you can easily score pass marks to the third bit of the question " Discuss the impact of the fall in Toltuck Co’s credit rating on its ability to raise financial capital and on its shareholders’ return"

I am very thankful for ACCA for allowing me to use their past papers.

How to learn R easy way

2018-01-13T08:22:00.001-08:00

How to learn R, easy way

R is a free software environment for statistical computing and graphics, widely used by data miners for data analysis.
To learn more about R, see the link provided below
https://en.wikipedia.org/wiki/R_(programming_language)

Mastering R is difficult, but learning to do some basic statistics and analysis so as to use the same in audit and other applications is easy., especially if you know how to copy and paste.

If you are able to get R script and understand code, you can apply the same to other data sources just by changing the file name and variable names in the file and doing copy and paste.
Once you have been able to generate code, just by changing file names and variable names, you can apply the same to other files..

One can get code from internet by searching for R scripts, and by copying and pasting the commands, you can see the output.

I suggest you to install R studio in addition to R, and practice on your own data files after going through this blog post once.

I am going to provide some code and explain how to apply the same using copy and paste

If you understand basics like how to use file name, field names or column names, you can easily apply to other files, just forget about technical terms like vectors etc, once you build up confidence, you can move further..

As a example I am covering overheads and its relationship to machine hours, but if you are able to understand the logic you can apply the same to finding out relation ship between demand and supply, price of a stock with respect to stock index, marketing expenditure and its impact on generating demand, increase in profits in relation to increase in sales volume or value etc.
I am not going for advanced commands, I just want to give flavor of what R is compared with Excel, so that you can move forward to enjoy the journey, if you like the flavor.

First, we will do some simple data calculations or simple mathematical calculations.

Multiplication: Type in R: 8*6 you will get answer 48
Note Type in R implies Type in R studio also.

Power: Type in R: 2^16 you will get answer 65536

Square root: Type in R: sqrt(2)you will get answer 1.414214

Absolute value: Type in R: abs(-65)you will get answer 65

To get help on particular command: Type in R: ?sqrt you will get help on the function sqrt or square root as follows sqrt(x) computes the (principal) square root of x, √{x}.

Storing information in a variable: Type in R: SquareRoot5 = sqrt(5), it calculates square root of 5 and stores in the variable SquareRoot5, not to get the value

Type in R: SquareRoot5, the answer will be 2.236068

To know what variables we used Type in R: ls()you will get answer "SquareRoot5", which is the only variable we have used.

Type in R: seq(0,10) , the answer will be 0 1 2 3 4 5 6 7 8 9 10

Type in R: Sequence = seq(0,10,2) , the sequence from 0-10 with a difference of 2 is stored in a variable Sequence

Type in R: Sequence, the answer will be 0 2 4 6 8 10

Vectors is the name given, to combine group of values and store data.

Type in R: c(2,3,5,8,13) , the answer will be 2 3 5 8 13, the values are stored

Type in R: Country = c("Brazil", "China", "India","Switzerland","USA")

Type in R: Country , the answer will be "Brazil" "China" "India" "Switzerland" "USA"

Type in R: LifeExpectancy = c(74,76,65,83,79)

Type in R: LifeExpectancy, the answer will be 74 76 65 83 79, so the numbers are stored in the variable lifeexpectancy

As these are stored in a variable, we can do some manipulation.

Type in R: LifeExpectancy[2], the answer will be 76, as it is the second value in the lifeexpectancy.

Now we will do some real things, we have data of country, region it belongs to and its population, the file name is pop and the variables country, region and population is given

First copy the file in the directory, then load the CSV file using the following command

Loading CSV files, after they copied in the directory of R, or you can change the directory of R where the working files have been stored,to know where is the directory see the pictures below, which help to locate directory or change directory, in R and R Studio

Or you can use the following command line

setwd("D:/r")

Where D is the disk name and r is the folder name, in which CSV files have been stored

The links to both files used in this blog was provided below and the same was copied at the end of the blog

https://drive.google.com/open?id=1G5Ok5Bxc-9z4AlvPeCwVuSqvdPtpUINZ

https://drive.google.com/file/d/1G5Ok5Bxc-9z4AlvPeCwVuSqvdPtpUINZ/view?usp=sharing

https://drive.google.com/open?id=18I5j-eDbnaDbuOUpVhbWNReKoSytFRAC

https://drive.google.com/file/d/1G5Ok5Bxc-9z4AlvPeCwVuSqvdPtpUINZ/view?usp=sharing

After locating files read the CSV file using the following in R

popula = read.csv("pop.csv")

I am storing the data of the pop CSV file in the variable popula, you can use any name here, so that I can manipulate data using popula

First thing we need to do in data analysis is to know about the structure of the data, whether it is a text file, date file, or numeric file, for that we use str command

Copy and paste in R or type in R str(popula)

It states that integer was stored in population data and other two are text values, and it provides information that there are 194 observations of these there are 6 levels in the region, which implies that region is divided into six segments.

Copy and paste in R or type in R summary(popula)

as these are text fields , you will get summary information on the data which shows 6 countries and says there are 188 other countries, which amounts to 194 countries, which tallies with above data, it also shows the data of how these 194 countries are split into 6 regions and number of countries in each region, , as population is numeric field, it will provide Min. 1st Qu. Median Mean 3rd Qu. Max.

To subgroup how many countries are there in Europe

Copy and paste in R or type in R country_Europe = subset(popula, region == "Europe")

In the above command, popula is the CSV file name, region is the column name with six regions and Europe is one of the entries in the region column, and you want to extract information for that region,country_Europe is the variable in which we are storing the data, so that we can do some analysis.

Now if you type

str(country_Europe)

you will see that there are 53 observations which tally with earlier data.

Writing CSV files

Copy and paste in R or type in R write.csv(country_Europe, " country_Europe.csv")

Now if you look at your working directory you will see country_Europe CSV file, which consists of all data pertaining to the region of Europe

If you want to remove the variable country_Europe from R

Copy and paste in R or type in R rm(country_Europe)

mean(popula$population), popula is the variable where we have stored the file pop and population is the column name for which we require average, the answer will be 36359.97, which is same as the mean of the population we have calculated in the summary of popula

to know which country is having a minimum population

Copy and paste in R or type in R which.min(popula$population)

The answer will be 126, so it is in 126^th cell, now we need to know, which country it is

Copy and paste in R or type in R popula$country[126]

The answer is Niue

to know which country is having maximum population

Copy and paste in R or type in R which.max(popula$population)

The answer is 36

Now we can get the country name by using the same code as above

Copy and paste in R or type in R popula$country[36]

The answer is China

Note: you can check the above two codes by sorting out the data either in ascending or descending order, and you get the answer.

Now we will do some real analysis pertaining to overheads

The CSV file is overhead, it consists of year and overheads and we need to analyze, what is effecting overheads, whether overheads are effected by machine hours, batch size, no of batches etc

So first thing is we need to read overhead file, as there is a column named overhead, we will read to ohead

Ohead=read.csv("Ohead.csv")

I am not using Overhead as we have to perform correlation and regression on the overhead column, so it might be confusing, you can store in any file, like ovehea etc, but it needs to be called back, whenever you want to perform operations on this.

summary(Ohead), to get summary of data

now calculate the standard deviation

Copy and paste in R or type in R sd(Ohead$overhead)

The answer is 28991.4

Ohead is the file name which we have stored in a variable Ohead and overhead is the column head for which we want to find out variance

Now we will do some graphs to understand the relationship between overheads and other variables.

One most important graph to understand relationship between two variables is scatter plot

Copy and paste in R or type in R plot(Ohead$overhead, Ohead$machrs)

You will see graph, which shows there is a positive correlation between these variables. Remember Ohead is the file name we have stored in a variable Ohead and machrs and overhead are column headings for which we are calculating relationship.

Before going further we just want to know what type of distribution is overhead, so we will go for histograms

Copy and paste in R or type in R hist(Ohead$overhead)

It shows the distribution is normally distributed.

As we are discussing graphs, we will go for one more, the boxplot

For single variable

Copy and paste in R or type in R boxplot(Ohead$overhead)

For two variables

Copy and paste in R or type in R boxplot(Ohead$overhead, Ohead$machrs)

This you can extend to “n” number of variables, just by giving comma.

Now we will see how to calculate boxplot to understand the correlation between two variables.

Copy and paste in R or type in R boxplot(Ohead$overhead~Ohead$machrs)

In the above symbol, ~ denotes correlation.

Now we will perform some correlation

Copy and paste in R or type in R cor(Ohead$overhead, Ohead$machrs)

The answer is 0.8609357, which shows there is a high positive correlation between overheads and machine hours.

Instead of finding out correlation for each variable on other, R provides us with a function so that, we can know the correlation of one variable with another variable.

Copy and paste in R or type in R    cor(Ohead)

It shows there is high relationship between machine hours and overhead, which was already proved above with a value of 0.860935717

The next comes batches with 0.480956086, and there is a negative relationship between overheads and batch size -0.399136847

As any correlation less than 50% is considered weak, we will use the same, while framing model to predict overheads.

We can also use the graph to see the relationship.

Copy and paste in R or type in R    pairs(Ohead)

The picture clearly shows a positive relationship between machine hours and overheads and negative relationship between overheads and batch size.

To get the same on a log scale.

Copy and paste in R or type in R   pairs(Ohead,log = "xy")

Now we will do some regression,lm is used for regression

Copy and paste in R or type in R    reg = lm(overhead~machrs, data= Ohead)

The above line is saying lm means perform regression on overhead column ~ is saying with respect to machine hours, by using data contained in Ohead which stores Ohead.csv file, if CSV file is stored in Overheadreg, then data=Overheadreg.

Copy and paste in R or type in R summary(reg)

Residuals:

     Min       1Q   Median       3Q      Max

-30803.4 -11275.9    901.6  13796.2  20356.1

Coefficients:

             Estimate Std. Error t value Pr(>|t|)

(Intercept) 83703.683  14485.703   5.778 3.33e-06 ***

machrs         29.134      3.253   8.955 1.04e-09 ***

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 15010 on 28 degrees of freedom

Multiple R-squared:  0.7412,           Adjusted R-squared:  0.732

F-statistic:  80.2 on 1 and 28 DF,  p-value: 1.037e-09

See the t-value is available for each, but there is only one F-statistic and P-value.

The most important is adjusted R-squared if we add additional variable if it increases, the variable added will help us in better predicting the output, otherwise not.

It penalises for every additional independent variable taken to predict dependent variable

The t statistic is compared with student t distribution to determine P values.

In regression equation, the null hypothesis that the coefficients are zero, or there will be only intercepted and other variables will have no effect on dependent variable or there will be no independent variable.

The high value of R-squared, the high value of the F-statistic at 28 degrees of freedom, and low value of p will not support the null hypothesis, hence we can conclude that change in overheads can be attributed to machine hours. This was further proved by significance codes given at the bottom ***, which means it is highly significant.

Now we will see how R-squared is calculated, even though it is not necessary

First, we will calculate Sum of Squared Errors

Copy and paste in R or type in R    reg$residuals, it will find out errors or residuals

Next, calculate the sum of the square of residuals.

Copy and paste in R or type in R    SSE = sum(reg$residuals^2)

Copy and paste in R or type in R SSE  you will get the answer 6307877833

Now we will calculate Sum of square of Total

Copy and paste in R or type in R SST = sum((Ohead$overhead - mean(Ohead$overhead))^2)

Copy and paste in R or type in R Rsquared= 1 - SSE/SST

Copy and paste in R or type in Rsquared = 0.7412103

Which is same as what has calculated above.

(remember SST = SSR +SSE, Where SST is the overheads given, and SSR is calculated by using regression line from the data calculated above and difference between becomes SSE, the error or residual, taking graph of residuals helps in finding whether they are normal or not and how they are scattered

As we have seen some correlation between batch size, and number of batches, we will use the same in regression and see how adjusted R-squared will be

Copy and paste in R or type in R    reg = lm(overhead~machrs+batchsize, data= Ohead)

Copy and paste in R or type in R summary(reg)

See Adjusted R-squared:  0.9152, which is a significant improvement over the last one.

Now we will see with batches, before doing with both

Copy and paste in R or type in R    reg = lm(overhead~machrs+Batches, data= Ohead)

Copy and paste in R or type in R summary(reg)

Adjusted R-squared: 0.948, which is a significant improvement, so batches is much better to batch size, now we will incorporate both into the model and see adjusted R-squared

Copy and paste in R or type in R    reg =lm(formula = overhead ~ machrs + batchsize + Batches, data = Ohead)

Copy and paste in R or type in R  summary(reg)

Adjusted R-squared:  0.9485, which is a marginal improvement over, taking batches alone, so compared with batch size, number of batches is much better.

The above analysis can also be proved if you study regression relation between overhead and batches and batchsize. The Adjusted R-squared is high and P values are low in batches compared with batch size.

Now you can frame a regression equation by taking into account batchsize and batches.

Residuals:

     Min       1Q   Median       3Q      Max

-14251.4  -4542.6   -152.8   3642.7  13929.8

Coefficients:

             Estimate Std. Error t value Pr(>|t|)

(Intercept) 52650.051  17421.588   3.022 0.005577 **

machrs         28.901      1.434  20.155  < 2e-16 ***

batchsize     -42.954     37.652  -1.141 0.264350

Batches       601.863    139.993   4.299 0.000213 ***

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6576 on 26 degrees of freedom

Multiple R-squared:  0.9539,           Adjusted R-squared:  0.9485

F-statistic: 179.2 on 3 and 26 DF,  p-value: < 2.2e-16

Overheads = 52650.051(intercept)+28.901 x machine hours + 601.863 x Batches

As batchsize is not a significant variable, I had not considered the same in the above equation.

I suggest you to try other variables, but with the addition of other variables, like sales value, a number of packages etc, the R-squared values reduces and results in less F-statistic value and more p-value showing their insignificance.

pop file copy

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Albania	Europe	3162
Algeria	Africa	38482
Andorra	Europe	78
Angola	Africa	20821
Antigua and Barbuda	Americas	89
Argentina	Americas	41087
Armenia	Europe	2969
Australia	Western Pacific	23050
Austria	Europe	8464
Azerbaijan	Europe	9309
Bahamas	Americas	372
Bahrain	Eastern Mediterranean	1318
Bangladesh	South-East Asia	155000
Barbados	Americas	283
Belarus	Europe	9405
Belgium	Europe	11060
Belize	Americas	324
Benin	Africa	10051
Bhutan	South-East Asia	742
Bolivia (Plurinational State of)	Americas	10496
Bosnia and Herzegovina	Europe	3834
Botswana	Africa	2004
Brazil	Americas	199000
Brunei Darussalam	Western Pacific	412
Bulgaria	Europe	7278
Burkina Faso	Africa	16460
Burundi	Africa	9850
Cambodia	Western Pacific	14865
Cameroon	Africa	21700
Canada	Americas	34838
Cape Verde	Africa	494
Central African Republic	Africa	4525
Chad	Africa	12448
Chile	Americas	17465
China	Western Pacific	1390000
Colombia	Americas	47704
Comoros	Africa	718
Congo	Africa	4337
Cook Islands	Western Pacific	21
Costa Rica	Americas	4805
Ivory Coast	Africa	19840
Croatia	Europe	4307
Cuba	Americas	11271
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Poland	Europe	38211
Portugal	Europe	10604
Qatar	Eastern Mediterranean	2051
Republic of Korea	Western Pacific	49003
Republic of Moldova	Europe	3514
Romania	Europe	21755
Russian Federation	Europe	143000
Rwanda	Africa	11458
Saint Kitts and Nevis	Americas	54
Saint Lucia	Americas	181
Saint Vincent and the Grenadines	Americas	109
Samoa	Western Pacific	189
San Marino	Europe	31
Sao Tome and Principe	Africa	188
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Sudan	Eastern Mediterranean	37195
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United Kingdom	Europe	62783
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Vanuatu	Western Pacific	247
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Viet Nam	Western Pacific	90796
Yemen	Eastern Mediterranean	23852
Zambia	Africa	14075
Zimbabwe	Africa	13724

Ohead file copy

Year	overhead	machrs	batchsize	Batches	Labourhrs	Production	salesunits	Numpackags	salesvalue	Totprodcost
1988	230001	5316	194	62	58260	12028	14141	587	1131280	989870
1989	221034	5460	360	44	62773	15840	12586	784	1132740	1107568
1990	240423	4902	190	78	55432	14820	12939	933	1164510	1138632
1991	185955	3018	198	80	65011	15840	15847	579	1188525	982514
1992	218055	4149	165	78	56052	12870	12948	949	1165320	1139424
1993	263025	5871	184	82	57174	15088	14657	642	1172560	1025990
1994	235350	4683	132	96	65496	12672	13625	761	1158125	1090000
1995	211902	4392	219	68	62130	14892	14250	634	1140000	997500
1996	190251	4635	284	50	58675	14200	12884	674	1159560	1133792
1997	168171	3357	203	58	60213	11774	15118	859	1133850	937316
1998	202338	4146	147	70	57057	10290	12881	787	1159290	1133528
1999	216306	3960	112	94	65241	10528	12595	702	1133550	1108360
2000	205599	3792	162	98	58483	15876	15881	893	1191075	984622
2001	207237	4032	251	58	64684	14558	15359	761	1151925	952258
2002	256650	5409	122	96	64406	11712	12316	935	1108440	1083808
2003	174591	3066	198	76	65049	15048	14962	868	1196960	1047340
2004	184878	4530	342	42	55476	14364	15385	516	1153875	953870
2005	242067	5379	239	58	56042	13862	13660	507	1161100	1092800
2006	174768	3447	189	54	63012	10206	15563	776	1167225	964906
2007	166011	3465	289	44	60074	12716	13551	870	1151835	1084080
2008	255324	5541	138	76	58761	10488	14742	789	1179360	1031940
2009	229455	5496	318	46	56868	14628	13830	832	1175550	1106400
2010	203349	3408	184	84	64223	15456	15659	657	1174425	970858
2011	169194	3408	278	44	64055	12232	12819	766	1153710	1128072
2012	199866	3990	206	66	57115	13596	14522	533	1161760	1016540
2013	190482	4074	288	52	57652	14976	14309	995	1144720	1001630
2014	268248	5646	121	90	61140	10890	15824	828	1186800	981088
2015	202554	3522	144	90	57754	12960	13293	944	1129905	1063440
2016	221040	4929	231	62	61644	14322	13425	991	1141125	1074000
2017	198396	4143	209	52	58027	10868	15191	648	1139325	941842

Periodic and continuous compounding and calculation of present values.

2017-12-13T06:01:00.000-08:00

Periodic and continuous compounding and calculation of present values

In financial management, students frequently encounter questions in various flavors, pertaining to periodic interest payments based on monthly, weekly, quarterly, half-yearly etc. Students often find it difficult to remember the formula, so we will address this issue so that student will never ever find difficult to answer this type of questions.

Basic Logic behind compounding:

Let us understand the basic idea behind compounding. If P is the initial investment (the principal) and r is the interest rate per period (expressed as percentage), the amount one will get after completion of a period is equal to P + r x P = (P x 1) + (r x P) = P(1+r) (taking P common)

From the above it is clear that to compute the balance at the end of the period, you will multiply balance at the beginning of the period with (1+r), where multiplying 1 with principal will give the principal amount and multiplying principal with interest rate r will give interest amount.

If we extend the above logic, and would like to compute interest for the second period,

As initial amount or principal at the start of the second period is P (1+r), the interest on it will be r(P(1+r)), so the total amount after completion of second period is P (1+r) (the principal at the beginning of second period) + r(P(1+r)) (the interest earned for second period), which can be rewritten as 1x P(1+r) (the principal at the beginning of second period) + r x P(1+r) (the interest on the principal at the beginning of second period), as (1+r ) is common in both equations we can write the same as P(1+r)x(1+r) = P(1+r)²

Now we will understand logic and formulate formula:

So if the amount earned after the first period is P(1+r)¹ and amount earned after the second period is P(1+r)², note that the period is coming as power, so we can generalise the above and say that if you have to receive amount after “n” periods, the amount will be P(1+r)ⁿ

In the above equation P is the principal at the beginning of the period “0”, and r is the rate of interest per period and n is the number of periods for which interest is payable.

Periodic interest:

From our childhood days we are using the above formula, by taking a year as a period, and interest rate per annum as rate, to calculate compound interest for first, second,........n years.

We can use the same logic for calculating payment of interest for smaller periods, for example, if interest payment is done semi-annually, quarterly, monthly, weekly, daily, hourly etc, but the only change is the rate of interest, which needs to be calculated for divided periods of days, months, quarters etc.

For example, if the annual interest rate is given and we need to calculate interest for semi-annually, we need to recalculate rate of interest for semi-annually, as r/2.

If one needs to calculate quarterly and monthly interest rate from annual rate, we need to recalculate the same as r/4 for quarterly and r/12 for the monthly interest rate.

So what we are doing here, we are arriving at an interest rate per period, ie, per month, quarter etc from annual interest, by dividing annual interest rate by a number of periods per annum as the interest rate is given per annum.

Thus we can write the same as r/k, where k is the number of periods in a year.

Now we want to rewrite the above formula P(1+r)ⁿas P (1+r/k)ⁿ

Where “k” is a number of periods for which interest is paid in a year.

Now, let’s try this to understand the concept

First, in order to avoid confusion, with r, the rate of interest per annum, we will use “r/k”, as discussed earlier, as“i", the periodic interest rate, so that i= r/2 for semi-annual and r/4 for quarterly.

Semi-annually:

Staring period = principal

End of first half of year = principal + interest = P+Pi or P(1+i)

End of year = (principal + interest earned in first half) + interest on (principal + interest earned in first half) = thus becomes P(1+i)² annually, applying same logic if it is done for two years the amount at the end of the second year will be P(1+i)⁴

If you observe closely as it is half-yearly, the interest rate is divided by 2 and at the same time at the end of one year the power increased by 2 and at the end of two years the power is 2 years x 2, we will try to make an equation or formula out of this, but before that we will look further at quarterly payments and cross verify our above conclusion.

Quarterly payments:

Return i = r/4, where r is the annual rate of interest.

Staring period = principal

End of first quarter = principal + interest = P(1+i),

End of second quarter = (principal + interest earned in first quarter) + interest on (principal + interest earned in first quarter) = P(1+i)², see interest is earned not only on principal but also on interest earned during first quarter.

So this process repeats, the interest at the end of third quarter is calculated on the amount at the beginning of third quarter or end of second quarter, hence becomes P(1+i)³

And finally interest at the end of fourth quarter becomes P (1+i)⁴, which is nothing but the amount earned after 1 year, so when it goes to next year end it will be P(1+r)⁸ as two years involves 8 quarters

Now we can formulate the same as formula or equation

When there are periodic payments, if there are “k” periods for which interest is paid in a year and annual interest rate of r is given,, then i, the interest rate for the period is arrived at r/k and the amount earned in the first year is P (1+i)⁴ or P (1+r/k)⁴ or P (1+r/4)⁴

As k=4 and power is 4, I can rewrite the above equation as P (1+r/k)^k

Now we will go further,

But if I repeat the same for the second year, it is P (1+i)⁸ or P (1+r/k)⁸ or P (1+r/4)⁸ as k=4 and power is 8, I can rewrite the above equation as P (1+r/k)^{kx 2} for the second year

Now we have found the logic to derive a formula

In case of periodic payments, made within a year, the amount received after 1^st year is P (1+r/k)^kx1 and the amount received after 2^nd year is P (1+r/k)^{kx 2}, so the amount received after t years is P (1+r/k)^{kx t}

Now we have two equations

P(1+r)ⁿ and P (1+r/k)^kx
t, which formula to use?

Both, as they are same, but for periodic payments, you need to convert r as r/k and n as kxt

What will happen if we use the formula P (1+r/k)^kx
t involving no periodic payments, for example, to calculate annual interest rate, in which case it will automatically transform itself to P(1+r)ⁿ, let's see

If it is an annual payment, there will be only one interest payment so k =1, as we are calculating interest for 1 year, t = 1, so both equations will give the same answer P(1+r)¹ = P (1+r/1)^1x
1 = P(1+r)

What will happen if we use P(1+r)ⁿ for periodic payments, then you need to recalculate r as r/k and n=k x t, where t is the years for which interest needs to be paid, k is the periodic payments you will make in a year.

I compiled a small variation of questions, that may appear in exams, just see how given r, the variables n,k,t and i are changing

Variation	Rate r% per annum	number of periods for which interest is paid in a year k	Interest rate per period i	Number of years after which you receive principal t	Number of periods n
Principal after 1 year, given 12% annum	12% annum	1 per annum	12% (r/k)	1	1 x1(t x k)
Principal after 2 years, given 12% annum	12% annum	1 per annum	12% (r/k)	2	2x1(t x k)
Principal after 6 months, given 12% annum	12% annum	2 per annum	6% (r/k)	6/12 or half year	1= 6/12x2 (t x k)
Principal after one month, given 12% annum	12% annum	12 per annum	1% (r/k)	1/12 or one month	1= 1/12x12 (t x k)
Principal after 2 years, given 12% biannual	6% annum	1 per two years or ½ or 0.5 per annum	6%/0.5 (r/k) =12%	2	1=2 x 1/2 (t x k)
Principal after 3 years, given 18% triannual	6% annum	1 per three years or 1/3 per annum	6%/(1/3) (r/k) = 18%	3	1=3 x 1/3 (t x k)
Principal after 6 months, given 6% half yearly	12% annum	2 per annum	6% (r/k)	6/12	1= 6/12x2 (t x k)
Principal after one month, given 1% monthly	12% annum	12 per annum	1% (r/k)	1/12	1= 1/12x12 (t x k)
Principal after 6 months, given 3% quarterly	12% annum	4 per annum	3%(r/k)	6/12	2= 6/12x4 (t x k)
Principal after 6 months, given 1% monthly	12% annum	12 per annum	1% (r/k)	6/12	6= 6/12x12 (t x k)

Now we will solve an example:

We will first use the formula P (1+r)ⁿ

Example:

Suppose $10,000 is invested at an annual interest rate of 12%. Compute the balance after 10 years if the interest is compounded

a. Quarterly b. Monthly c. Daily

Ans:

Quarterly:

P =$10,000 given, n, the number of periods for which interest needs to be computed=4 quarters in one year x 10 years = 40 periods or quarters, r= return per period, as it is quarterly, as annual return of 12% is given we need to convert the same to quarterly return = 12%/4 = 3% per quarter

P (1+r)ⁿ = $10000 (1+3%)⁴⁰ = $32620

Monthly

P =$10,000 given, n, the number of periods for which interest needs to be computed=12 Months in one year x 10 years = 120 periods or months, r= return per period, as it is monthly, as annual return of 12% is given we need to convert the same to monthly return = 12%/12 = 1% per month

P (1+r)ⁿ = $10000 (1+1%)¹²⁰ = $10000 x 3.300387 = $33003.87

Daily

P =$10,000 given, n, the number of periods for which interest needs to be computed=365 days in one year x 10 years = 3650 periods or days, r= return per period, as it is daily, as annual return of 12% is given, we need to convert the same to daily return = 12%/365 = 0.032877 % per day

P (1+r)ⁿ =$10000 (1+0.032877 %)³⁶⁵⁰ = $10000 x 3.319462 = $33194.62

Now we will redo the above question using the formula P (1+r/k)^kt

Quarterly:

K = quarters, which are 4 in a year, the number of years interest is paid, for (t) 10 years, interest is paid for k x t times, 10 x 4 = 40 times, so kt = 40, Rate of return per quarter = rate of return per year / number of quarters in year= r/k= 12%/4 quarters in a year, the interest rate per period = 3% per quarter and P = $10000

P (1+r/k)^kt = $10000 (1+3%)⁴⁰ = $32620

Monthly

K = months, which are 12 in a year, the number of years interest is paid, for (t) =10 years, interest is paid for k x t times, 10 x 12 = 120 times, so kt = 120, Rate of return per month = rate of return per year / number of months in a year= r/k= 12%/12 quarters in a year, the interest rate per period = 1% per month and P = $10000

P (1+r/k)^kt = $10000 (1+1%)¹²⁰ = $10000 x 3.300387 = $33003.87

Daily

K = days, which are 365 in a year, the number of years interest is paid, for (t) =10 years, interest is paid for k x t times, 10 x 365 = 3650 times, so kt = 3650, Rate of return per month = rate of return per year / number of months in a year= r/k= 12%/365 days in a year, the interest rate per period = 0.032877 % per day and P = $10000

P (1+r/k)^kt = $10000 (1+0.032877 %)³⁶⁵⁰ = $10000 x 3.319462= $33194.62

Notes:

Whether you use P (1+r)ⁿ or P (1+r/k)^kt , the answer will be same, if you understand logic and reason behind using them.

But you need to understand what r, i,n,k, and t stand for, r is rate of interest per annum, k is the number of times interest is paid in a year, t is the number of years for which interest is paid, n the total periods for which interest is paid, n= k x t and i=r/k

Continuous compounding

The most important aspect of second formula is that, with increase in periods, the rate of return per period will start reducing in the equation or formula itself, so, when we do continuous compounding, as with every increase in “k” the above formula approaches Pe^rt, where “e” is the exponential function with the value 2.718281...................

So when one needs to do continuous compounding, we can’t use the formula P (1+r/k)^ktinstead we use Pe^rt, where r is the rate of return per annum, and t= number of years.

Note: in continuous compounding, the “k” becomes so small that it is altogether disappearing from the equation.

In the above equation r and t are same as we discussed earlier, r is the rate of return per year and t is a number of years, but if continuous compounding is done for the quarter, month, day, we need to convert "r" as a monthly return, quarterly return, daily return etc.

How can we do this, yes, as we have done before, by dividing r by k, where k is a number of periods, if r is divided by k, then we have seen that n=kt, then t becomes n/k.

Proof:

We won’t derive formula, as it can be done using calculus, stating as derivative function or limit, when, k approaches infinity, but, lack of knowledge in calculus won’t deny us to use logic to see how we got “e”, with value of e=2.718281..................., you may ask how r started appearing as power for which see the proof provided below.

Let’s assume x (you take any figure a,b,c,z etc, still you will get the same answer) = k/r, k=xr (cross multiplication), using these we can rewrite the equation P (1+r/k)^kt as P (1+1/x)^xrt, below I will show how increasing the value of x from 1 to 31536000, will change the value of (1+1/x)^x to e=2.718281..................., so I can substitute e for (1+1/x)^x, so the equation P (1+1/x)^xrt changes to Pe^rt, where e=2.718281................... calculated by using (1+1/x)^x

Now try this either manually or In excel, by increasing the value of x in the equation, (1+1/x)^x and you can see the equation approaches, 2.718281... which is nothing but “e”, you can easily do this, either by changing single cell, or by copying the formula in multiple cells, and increase the values of x in each cell.

How to do it in excel:

Incorporate the following formula in any cell in excel =(1+(1/A2))^A2, and try to increase input value in cell A2 from 1 to 365, if possible you can even divide the day into hours and seconds, with every increase in the period of time the equation approaches the value e=2.718281...................

Period	x	Value	formula used
Year	1	2.00000000	(1+(1/B2))^B2
Semi-Annual	2	2.25000000	(1+(1/B3))^B3
Quarterly	4	2.44140625	(1+(1/B4))^B4
Bymonthly	6	2.52162637	(1+(1/B5))^B5
Monthly	12	2.61303529	(1+(1/B6))^B6
Days	365	2.71456748	(1+(1/B7))^B7
Hours	8760	2.71812669	(1+(1/B8))^B8
Minutes	525600	2.71827924	(1+(1/B9))^B9
Seconds	31536000	2.71828178	(1+(1/B10))^B10

Now we will do the above example using continuous compounding

Suppose $10,000 is invested at an annual interest rate of 12%. Compute the balance after 10 years if the interest is compounded, Continuously

Continuous compounding

The formula is Pe^rt

where

P = $10000, r = rate of return per year =12% and t = number of years=10 years

Pe^rt= $10000x (e^{12% x
10}) = $10000 x 3.320117 = $33201.17

Notes: to check, whether your answer is right or wrong, you can compare interest or amount you got at the end of the period using various compounding, as interest is paid on principal + interest earned during the previous period, interest earned on continuous basis is always more than interest earned on second, which is more than interest earned on hours basis, which is more than interest earned on hourly basis, which is more than interest earned on daily basis, which is more than interest earned on monthly basis, which is more than interest earned on bi-monthly basis, which is more than interest earned on quarterly basis, which is more than interest earned on semi- annual basis, which is more than interest earned on yearly basis, which is more than interest earned on bi-annual basis etc.

Effective interest rate

Simply speaking effective interest rate is the conversion of daily, monthly, quarterly, half-yearly etc, interest to annual interest. So that you can compare normal annual rates with effective interest rates. It should be noted that effective interest rate differs and increases with increase in time intervals, for example, the effective interest rate on daily interest payments will be more than, monthly interest payments, which is more than quarterly interest payments etc.

					Matured amount	Matured amount - Principal
	Principal	k	n	r	P (1+r/k)^kn	Effective interest	Effective interest rate
Yearly	10000	1	1	12%	11200	1200	12.000%
Semi-annually	10000	2	1	12%	11236	1236	12.360%
Quarterly	10000	4	1	12%	11255.0881	1255.0881	12.551%
Monthly	10000	12	1	12%	11268.2503	1268.250301	12.683%
Daily	10000	365	1	12%	11274.74616	1274.746156	12.747%
Continuous	10000		1	12%	11274.96852	1274.968516	12.750%

The above table shows how effective interest rate is calculated, but we will derive the formula.

Deriving Formula:

We don’t know what the effective interest rate is, so let's assume it be X, the unknown (you can use A, a, k, Z for that matter any alphabet, number of figure for unknown)

As it an annual interest rate we can use the formula P (1+r)ⁿ, so it will be P(1+X)¹, P(1+X).

In case of periodic payments we have used the formula P (1+r/k)^kt, where we have used r/k = I, and let’s further simplify by taking a period as a year so t and n are both one year

Now equate both, one with annual payment and one with periodic payments, as both are for one year period, both should give the same result, this is something we have already proved previously.

P (1+X) = P (1+i)^k, as P is there on both sides, cancel it first, which gives

1+X = (1+i)^k now calculate r by deducting 1 from both sides.

we will be able to arrive at effective interest rate X = (1+i)^k - 1, where i =r/k

Note: Effective interest rate should always be equal or more than normal interest rates, if it is less, there is something wrong with the answer.

Now I am recalculating effective interest rate using the formula derived above, in the table as an additional column, the answer will be same.

					Matured amount	Matured amount - Principal		X = (1+i)^k - 1,where i =r/k
	Principal	k	n	r	P (1+r/k)^kn	Effective interest	Effective interest rate
Yearly	10000	1	1	12%	11200	1200	12.000%	12.000%
Semi-annually	10000	2	1	12%	11236	1236	12.360%	12.360%
Quarterly	10000	4	1	12%	11255.0881	1255.0881	12.551%	12.551%
Monthly	10000	12	1	12%	11268.2503	1268.250301	12.683%	12.683%
Daily	10000	365	1	12%	11274.74616	1274.746156	12.747%	12.747%

For continuous compounding, the effective rate is e^r -1, where r is the rate of return per annum.

Example:

Which is better, an investment that earns 12.50% compounded quarterly, one that earns 12% compounded monthly, or one that earns 11.50% compounded continuously?

Quarterly:

X = (1+i)^k - 1,where i =r/k , r=12.50%,k=4, i=12.50%/4 = 3.125%, effective interest rate r = (1+0.03125)⁴ -1 = 1.130982399 -1 = 13.098%

Monthly:

X = (1+i)^k - 1,where i =r/k , r=12%,k=12, i=12%/12 = 1%, effective interest rate r = (1+0.01)¹² -1 = 1.12682503-1 = 12.68%

Continuous compounding:

e^r -1 where r=11.5% , 1.121873438-1 = 12.18%

Decision: as effective interest rate of 13.098% is more, quarterly compounding is more beneficial.

How to calculate present values

Use this simple maths formula if A x B = 1, B = 1/A¹ or A^-1 also called A inverse, when denominator comes to the numerator, the power becomes negative. If you understand the above logic applies the same to the future value we have calculated above to get present values.

If future value FV = P(1+r)ⁿ , where P is the present value,

We can easily calculate present value P = FV x (1+r)^-n

If you use future value FV = P (1+r/k)^kt , where P is the present value,

We can easily calculate present value P = FV x (1+r/k)^-kt

The same thing holds true for continuous compounding using exponential equation

FV= Pe^rt, where P is the present value,

We can easily calculate present value P = FV x e^-rt

Example:

Mr. X is about to enter employment and 4 years from now, he wants to take his dream vacation which costs him an estimate of $5,00,000. How much should he invest now at 7% to have enough for the trip if interest is compounded:

a. Quarterly b. Continuously

Quarterly:

P = FV x (1+r/k)^-kt , where FV = $5,00,000 r =7%,k=4(quarterly), t= number of years=4

Present value = $5,00,000 x (1+(7%/4))^{-4
x 4} = $378808.2

Proof: FV = $5,00,000 = $378808.2 x (1+(7%/4))^{4 x 4}

Continuously:

P = FV x e^-rt

$5,00,000 x e^-7%x4 = $5,00,000 x 0.755784 = $377891.9

Proof:

FV = $500000 = $377891.9 x e^7%x4 = $377891.9 X 1.32313 =$500000

Another example, this time from finance:

The following table gives Treasury zero rates and cash flows on a Treasury bond with a face value of $1000 and pays a coupon of 2% per annum semi-annually

Maturity (years	Zero rate
0.5	2.0%
1.0	2.3%
1.5	2.7%
2.0	3.2%

Zero rates are continuously compounded, what is the bond’s theoretical price?

The bond’s theoretical price is

20×e^-0.02×0.5+20×e^-0.023×1+20×e^-0.027×1.5+1020×e^-0.032×2 = 1015.32.

Notes 2% on $1000, is 20, as zero rates are given for 6 months, 1 year, 1.5 years and 2 years, then t, the number of years will be, 0.5,1,1.5&2 years respectively.

In professional exams you won’t get questions in a straightforward way, but rather as a part of total question, try the question no 3(a), of ACCA P4 June 2009 exam sitting, he uses discount factor, which is nothing but calculating present value, as discount rates are given for month, t, the part of the year becomes 1/12, as it is a present value question, the power becomes negative. He uses continuous compounding, but you can use monthly periodic payment calculation.

If you are unable to get the same, the links to question and answer were provided below as picture file. I am very thankful to ACCA for allowing me to use their past papers.

After reading this article are you able to see any performance measure useful for your exams

2017-07-02T05:42:00.000-07:00

Read the article first on economist website then go to the end of this post to see relevant paragraph and the performance measure

http://www.economist.com/news/business/21722880-even-industry-where-computer-crashes-are-increasingly-common-british-airways-botches-its

or search google for

Computer says no

British Airways botches its response to its latest technical woes

Even in an industry where computer crashes are increasingly common

In many P5 questions, one of the important ratio to remember is cost to revenue, if you look at past papers and note, this ratio often appears in questions, and you can get some easy marks not only on quoting this ratio, but also mentioning how dangerous it is if organisation concentrates on this ratio to increase short term profits at the cost of long term erosion of goodwill, thus value due to this Performance measure,
This you can even use if you are writing any thing from risk management point of view, which is most often the case with CIMA exams.
Now see the relevant paragraph from the article in economist "The first lesson from such painful experiences is to refrain from pruning investment in IT too far, as some airlines may have in their desperate efforts to fend off budget competitors. “Legacy carriers like BA saw spending on this as an overhead,” says Henry Harteveldt of Atmosphere Research, a consultancy. “But it should be seen as a cost of doing business.” In 2015 airlines spent 2.7% of their revenues on IT, half the norm across all industries and a lower share even than hotels."

How to use correct performance measures - useful for ACCA P5

2017-06-01T09:10:00.001-07:00

Before reading this I suggest you to look at the following post

http://cvdsomayajulu.blogspot.in/2017/05/acca-p5-use-correct-ratios-as.html

Most of the case study exams use some form of performance measures. Students often fail to quote correct performance measures and the result is a failure.

How to quote correct performance measure, what we need to do if we not found one, it is something we will discuss here.

Let’s try to understand the same using examples.

A company has produced 10000 units, some portion of the cost is $100000, this cost does not change, even when the production increased to 12000 units or for that matter 150000 units.

So if the question says, what is the above cost for 2500000 units and 150 units?

We know, from our studies that the above portion of the cost is called, the fixed cost, which does not change with the number of units produced or sold, so the cost will be same, $100000, for both 2500000 units and 150 units

Let’s take another example

Some portion of Cost of a product is $100000 for 10000 units, it is $120000 for 12000 units and $1500000 for 150000 units, and so what is the cost of the same for 2500000 units and 150 units.

As the cost is changing at $10 for each unit, we call this variable cost and the cost of 2500000 units will be $25000000 and cost of 150 units is $1500

So what we have learned from the above, fixed cost remains same irrespective of production/sales and variable cost changes with production/sales.

So given information about the cost of the particular output, you will be able to predict the cost at different levels of output.

How you are able to predict the cost because you are able to establish cause and effect relationships.

This is something you are required to do while writing performance measures, whether they are showing cause and effect relationship which can be used to predict things.

Let’s take another example, which shows sales in units and volume of sales in $ for the past two years

Details	1st year	2nd year	Current year
sales (units)	10000	12000	14000
sales (value) $	1000000	1140000

From the above information are you able to predict sales in units provided sales of $ for the current year?

The answer is no, if we analyse data from above table (shown below), it is clearly seen that with 20% increase in sales in units there is only 14% increase in sales in value, the reason is the increase in sales (units) is achieved by reducing the price, by 5%, so, to achieve 40% increase in sales (units), we need to reduce price, this is what we already know, but how much is something we don’t know.

	Details	1st year	2nd year	The increase from the previous year
1	sales (units)	10000	12000	1.2
2	sales (value) $	1000000	1140000	1.14
	Sales price/unit= 2/1	$100	$95

This is where assumptions come in, we may assume that for every increase of sales (units) by 20%, the price needs to be reduced by 5%, thus to achieve sales (units) of 14000, the price per unit should be $95 x 0.95% = $90.25, so the sales (value) $ will be 14000 x $90.25 = $1263500

See what you have done above, you have established a cause and effect relationship between sales (units) and sales (value) thus able to predict the sales value at 14000 units, for which you made some assumptions, which are reasonable.

So to make your performance measures effective you require

· To establish a relationship which must be reasonable, if it is not reasonable to reject it

· The relationship should show cause and effect

· The relationship must be able to predict things if necessary

One of the frequent parts of exam question is, the objective of the organization is to maximize the wealth of its shareholders, and it is using ROI (return on investment) as a measure to do the same.

If we apply what we have observed above, there is no relationship between ROI and wealth maximization, the relationship is somewhat unreasonable, RI (Residual Income) or EVA etc. are better measures of wealth maximization.

Let’s try question no 2(a), worth 12 Marks from ACCA 2012 June P5 exam.

Search google or you can read both questions and answer using the link provided above at the start of this blog post, which I discussed in another post.

I want you to analyze the question using the above approach

The first ratio we will discuss is operating profit/sales ratio, is it reasonable, yes, if it is so is there any cause and effect between two, yes, as increase in sales generally increases operating profits, next, given sales whether we can use the same to predict future operating profits, yes, we can do the same, if operating profit % is more than competitors or our historic sales, it clearly shows we are operating efficiently compared with competitors or with our previous years, when compared with competitors, it also shows we are able to charge premium using differentiation. Hence we can say the ratio is reasonable.

The second ratio we will discuss is revenue per passenger, we can reject the ratio, why, as aircraft is traveling both long and short distances and a competitor only short distance, it is not a reasonable ratio, as kilometers traveled is nowhere reflected in the ratio.

Even if by mistake you assumed the same as reasonable, is there any cause and effect, no, revenue is nowhere related to the passenger, but related to distance traveled by a passenger, hence we can reject this ratio.

Let’s look at another ratio, calculate fuel cost per number of passengers, is it reasonable, no, we can’t use due to the reason discussed above.

Then what about fuel cost per aircraft, It looks reasonable, but if you examine, it does not looks great ratio to calculate as fuel consumption depends on size, number, distance travelled, and their fuel efficient engines none are reflected in above ratio, so the better measure is something which involves distance, as distance travelled is directly related to fuel, so passenger kilometers or seat kilometers is the better measure, if we consider seat kilometers we will get fuel cost per seat kilometer and if we consider passenger kilometers we get fuel cost per passenger kilometer, both are comparable, so which is better, here comes predictability into picture.
Are you able to predict fuel cost next year given seat kilometer or passenger kilometer, I think seat kilometer, because passenger kilometer will depend on number of passengers.
You can also think in this angle, whether fuel cost is changes with increase or decrease in number of passengers or seats, obviously seats, the number of seats determines the size of the aircraft hence its engine capacity and fuel consumption, hence we are better able to predict fuel cost using seat kilometers rather than passenger kilometers, hence it is used.
Finally if you are able to divide fuel cost per passenger kilometer with fuel cost per seat kilometer, you will get how efficiently the aircraft is running, which is nothing but capacity utilisation, note fuel cost gets cancelled in both numerator and denominator hence the ratio is passenger kilometers/seat kilometers.

Now we will look at another paper, this is from ACCA P5 2015 September / December sitting; I had taken a relevant portion from question no 1

Iron Chicken (IC) is a multinational business which manufactures commercial building control systems. Building control systems include heating and air-conditioning systems, lighting controls, power and water monitoring and security systems (e.g. keypad access, alarms and CCTV).

IC’s manufacturing takes place at a number of factory sites where some products have a long product life and are simple and mass-produced while other products are complex and have a short product life due to changing technologies. IC’s mission statement is ‘to create value for shareholders through control products which improve productivity, save energy and increase comfort and safety’.

The CEO believes that the poor performance of the company can be addressed by ensuring that the mission statement flows down into the performance management of the business. To that end, the following critical success factors (CSFs) have been identified and the CEO wants you to suggest additional key performance indicators (KPIs)for these.

CSF Associated	current KPI
1. Greater staff productivity	Units produced per labor hour
2. Reduction of wastage in production	Power consumed per unit produced
3. The greater innovation of products	Number of new products launched

Your suggestions should be in addition to these current KPIs.

Third, in order to improve performance, the CEO plans to implement initiatives associated with ‘lean’ manufacturing.

Specifically, there are three projects which have been suggested and the CEO needs your advice on these:

1. Move to just-in-time manufacturing

2. Use kaizen costing

3. Examine the costs of quality in achieving a ‘zero defects’ approach to manufacturing The CEO has stated, ‘I need to know briefly how the improvement projects will meet the three CSFs and also how they will impact on the existing three KPIs.’

Required:

(ii) For each of the three critical success factors at IC, briefly explain a weakness of the current KPI associated with that CSF and then provide a justified alternative KPI. (6 marks)

(iii) Explain what the three improvement projects are, how they will help to meet the CSFs at IC and comment on the impact of each project on the existing three KPIs. (15 marks)

Note, the examiner has given you three CSF’s and the associated KPI’s and required you to explain the weakness of the current KPI associated with the CSF and need to provide a justified alternative.

CSF Associated	current KPI
1. Greater staff productivity	Units produced per labor hour
2. Reduction of wastage in production	Power consumed per unit produced
3. The greater innovation of products	Number of new products launched

Note: I am giving some alternative answers to what the examiner has given in the question, in the examination, if you are able to justify, it’s ok

1. 1^st CSF given is Greater staff productivity, what is productivity, the standard definition is output/input, for staff, it will be output per labour hour, so units produced per labour hour seems excellent measure to measure staff productivity, and it is reasonable, and next we will ask is a cause and effect relationship, and you can use this to predict staff productivity, but hear is the twist, see the question carefully, it is stated in the question that” some products have a long product life and are simple and mass-produced while other products are complex and have a short product life due to changing technologies”. (if you have don previous exam questions as practice, it something similar to above question, where different aircraft will be of different sizes and ages) The productivity measure of units produced per labour hour is good if units are uniform, but in a multi-product company with each having different products life’s this measure is not appropriate, so which measure is more appropriate, yes value of output / value of input for staff seems appropriate, as it takes into account revenue of all products produced by staff, see the cause and effect relationship and the ratio can be used to predict value provided labour hours are given. You can also use value added per unit of labor, which is calculated as Total sales less labor cost/staff cost.

Note: You can use the same approach to answer the rest of the question, now I am giving additional analysis to arrive at alternative solutions and for the third part, I am providing analysis to arrive answer similar to examiners.

2. 2^nd CSF given is Reduction of wastage in production; what is waste, you might have studied waste and scrap, anything which increases cost without increasing revenue is called waste (remember the word waste fellow), examples include any non value added activities like, Waste arising from delays, defects, excess production etc. the current KPI of power consumed per unit is taking into account only one factor of production, and there are number of factors like excess usage of material, labour and other expenses, which this ratio is not considering, hence the ratio does not look reasonable and look at question which states that ” some products have a long product life and are simple and mass-produced while other products are complex and have a short product life due to changing technologies”.

So how can we measure waste, if the standard is $100 and actual is $105, the $5 is the excess cost incurred, but if it results in excess profits through value addition it is justifiable otherwise we will consider it as waste. One ratio is the calculation of sales / total cost or total cost/sales and compare the same with some other period to know the waste or we can use standard cost and compare actual cost with standard cost, to find out waste, but if increase in cost is justifiable and it is helping us to increase revenues, then how can we call it as waste.

So the better measure is to use sales to cost or cost to sales ratio or use total sales margin variance to measure wastage. It should also be noted that as technology is changing, anything produced in excess will become waste if there is a change in technology, this was not considered in present KPI, what the examiner is given as obsolescence is nothing but product becomes useless due to change in technology (if you observe closely, with the introduction of new mobile phones, the demand for old ones will be reduced

3. 2^rd CSF given is a Greater innovation of products; the present measure is Number of new products launched, is it really a measure of innovation, no, there is no real relationship between a number of products launched and innovation. The exact relationship exists only when it is patented, but patent talks about only innovation, Chinese file lot of patents, but it is the USA which launches innovative products, there are many who produced product like iPod before apple, but it is Apple who was successful in marketing, how you can say it is successful and great product, because it is able to commercially exploit the opportunity.

So what is important criteria is a number of products introduced which are commercially successful, not the number of products produced to justify the criteria to be a greater innovation of products.

Use correct ratios to evaluate performance/ measurement/management to pass exams - useful for ACCA P5

2017-05-29T06:58:00.000-07:00

In exams the questions pertaining to the evaluation of performance/ measurement/management comes in different flavors, some of them may require you to apply models like Balance scorecard, performance prism, performance pyramid, Building blocks model etc.

While some questions require you to provide suitable performance measures, while others may provide you with performance measures and request you to evaluate the same.

In many cases, you don’t require any models, applying appropriate ratios will solve the problem. If you carefully observe each model like balance score card, they will all end up with some ratios, like ROI or increase in sales/cost/profit for financial performance, defects per process for evaluating internal processes etc.

In every case, if used properly, ratios will help you to score reasonable marks to pass exams.

Why we require ratios: Simply we require ratios because we need to compare things (we always like to compare apples with apples, remember this sentence, we will use this frequently, so as to avoid mistakes)

What is required to calculate ratios: We need two figures (note the two figures can relate to the same unit like sales/cost/profit of two periods, or relating to two different units, like cost, sales, profit etc.)

Why we need to compare: Simply to evaluate performance.

If you got two figures and calculated some ratio, you will not get marks, in order to get marks the ratio needs to be able to evaluate the performance i.e., you must be able to link ratio to objectives provided in the question.

Take some small examples here, one person is lifting 115 kilograms, another 200 kilograms, who is the better weightlifter, the second one right, who is lifting 200 kilograms.

But until I know, other things like who they are, i.e., their gender and age, I can’t evaluate their performance in the right perspective.

This is what is required in exams, just don’t go on calculate some ratios, if information is not available, you need to suggest the same, for example in the above case based on the information provided, assuming gender and age are same, we can say that the person lifting 200 kilograms is performing better compared to one lifting 115 kilograms of weight.

What will happen if one is male and another female, we can’t compare, as we need apple to compare apple? The same is true if one belongs to 20 years age group and another 30 years.

Now we will take another example, this time from movies, I am listing revenues from two great movies, “Gone with the Wind” and “Avatar”, just tell me which is better in terms of revenues. “Gone with the Wind” earned revenue worth $390 million, while “Avatar” earned revenue worth $2.78 billion (The above figures are taken from Wikipedia on 29/05/2017).

We can’t compare millions with billions, so we need to convert the same into the uniform denominator, i.e., either billions or millions so that we can compare apple to apple.( We are not actually comparing apples to apples, but one fruit with another, why it is you will know later)

Converting “Avatar” revenues into millions will give $2780 million (1 billion = 1000 million), so “Avatar “got nearly 7 times ($2780 million / $390), more revenues than Gone with the wind.

Whether our performance evaluation of the movie “Gone with the Wind” is correct?

No , just comparing revenues is not correct, “Gone with the Wind” is very old movie, it is released in 1939, while Avatar is quite new, released in 2009, so we need to take into account inflation, as this information is not available, we can’t evaluate the performance of the movie “Gone with the Wind” properly, hence we are not actually comparing apples to apples.

But if cost/Budget is provided we can compare apple with apple by comparing the cost of revenue.

The Cost/ Budget of the movie “Gone with the Wind” is $3.85 million, while the cost of the movie Avatar is $246 million, so from additional information of cost we can easily, calculate the profit and find out returns on sales by dividing profit by revenues or we can also say that the movie “Gone with the Wind” has collected 100times more than its cost while Avatar collected 10 times more, hence the performance of the movie “Gone with the Wind” is best compared to Avatar.

Still, we can quote stating that comparison of the performance of movies between two periods is difficult, but comparing revenues as % of cost or profit as % of revenues is a better performance indicator, then comparing just costs or revenues. (The above figures are taken from Wikipedia on 29/05/2017)

Top 10 Highest-grossing films of all time taken from Wikipedia on 29/5/2017 was provided below, do you think you are comparing apples with apples

Highest-grossing films[13]

Rank

Title

Worldwide gross

Year

Avatar

2,78,79,65,087

2009

Titanic

2,18,67,72,302

1997

Star Wars: The Force Awakens

2,06,82,23,624

2015

Jurassic World

1,67,17,13,208

2015

The Avengers

1,51,88,12,988

2012

Furious 7

1,51,60,45,911

2015

Avengers: Age of Ultron

1,40,54,03,694

2015

Harry Potter and the Deathly Hallows – Part 2

1,34,15,11,219

2011

Frozen

1,28,70,00,000

2013

Beauty and the Beast

1,23,25,63,435

2017

I can give you, a lot of real life examples, but I feel I have given you enough flavor, in exams whenever you are calculating ratios, just asking a simple question, whether it able to evaluate performance correctly or not, will help you a lot in providing the correct answer. For example P5 examiner repeatedly asks the question stating that, the objective of management is to maximise shareholders value and provides information that the management is evaluating performance using ROI, so you must state that the better measure to evaluate maximising shareholders values is Residual Income (RI) or EVA (Economic value added) rather than Return on Investment (ROI). This is a question in ACCA P5.

Now we will take another question ACCA 2012 June question no 2(a), worth 12 Marks, I want to thank ACCA for allowing me to use its past papers.

Note: I underlined with italics and bold, to note important points, which I use in my answer

Amal Airline (Amal) is the national airline of Jayland. It was originally owned by the government but was listed on the local stock exchange when sold to private investors more than 20 years ago. The airline’s objective is to be the best premium global airline(My own notes: Is it able to differentiate, if yes is it reflecting in revenues, we need to calculate revenue per passenger)

Amal provides long- and short-haul services all over the world and is based at its hub at Jay City airport. Amal has been hit by a worldwide reduction in air travel due to poor economic conditions. The most recent financial results show a loss and this has caused the board to reconsider its position and take action to address the changed environment.

Amal has cut its dividend in order to conserve cash and it is trying to rebuild profitability by reducing costs by 14%.

The airline is capital intensive. (My own notes: so capacity utilization becomes important) as it requires to maintain a large fleet of modern aircraft. The two major costs for the airline are staff and fuel. In trying to renegotiate working conditions and pay, (My own notes: why because the staff is one of the two major costs), the management have angered the unionised workforce. There has already been some strike action by the unions representing the aircraft crew and ground staff and more is threatened. They are upset about changes to pension provisions which will require them to make larger contributions and also, a reduction in the number of crew on each aircraft which they believe will require them to work harder and so they want a compensating pay-rise.

Additionally, the board is pushing forward a large project to improve the design of the company website in order to increase the number of passengers who check-in on-line and so would not require as much assistance at the airport.

The new design is also aiming to increase the number of passengers who book their tickets through the company’s website rather than other resellers’ websites or at booking agents. The project is currently two months behind schedule due to one of the main software suppliers becoming insolvent.

Finally, the board has been considering taking advantage of new technology in aircraft engines by making a large investment ($450m) in new low-noise, fuel-efficient aircraft in an effort to reduce the environmental complaints surrounding air travel and also cut costs.

Given all of the issues and projects affecting Amal, the CEO has tried to find a unifying view that will explain the airline’s performance. She has heard that the performance prism may provide such a framework. As further background, the CEO has supplied the data below on Amal and two of its main competitors. Kayland Air is a government owned and runs airline in the neighboring country of Kayland. It has a similar mix of business to Amal and targets a similar market. (My own notes: This is not still useful to say comparing apples with apples as Amal is privatized and listed, while Kayland Air is still in government hands ), Cheapo Air is currently one of the most successful of the new privately-owned airlines that have gained significant market share over the last 15 years by offering a cheap but basic short-haul service to customers in and around Jayland. (My own notes: But Amal provides both long and short-haul services, so we are not comparing apple to apple, we require certain other measures), Cheapo Air subcontracts many of their activities. (My own notes: so this may help to reduce costs, we will study the same in P3), in order to remain flexible. The CEO wants you to calculate some suitable performance measures and explain the results.

Data provided by the CEO: Data for the most recent calendar year

	Amal	Kayland Air	Cheapo Air
Passengers(’000s)	23,649	38,272	35,624
Passenger kilometres(millions)	79,618	82,554	40,973
Revenue $m	5,430	7,350	2,170
Costs
Fuel $m	1,480	1,823	535
Staff $m	1,560	2,998	238
Staff numbers	32,501	56,065	5,372
Operating profit $m	630	54	127
Number of aircraft	182	361	143
Average aircraft size (seats)	195	163	125
Seat kilometres (millions)	1,00,654	1,05,974	46,934

Note: A seat kilometer is generated for every one kilometer flown by an available seat on the company’s aircraft.

Required :( a) Using the data provided, analyse the three airlines using appropriate performance indicators and comment on your results. (12 marks)

What ratios we can use here, the question states that Amal is running in loss, as net profit figures is not given, we can go for operating profit, as we can’t compare it from one to another we need to calculate appropriate measure for comparison, how can we do it, yes by comparing operating profit with sales, we can compare. It is quite easy.

As it want to become premium airline, it is better to calculate revenue per passenger, but as Amal covers both long and short distances, the appropriate measure is the revenue per passenger kilometres, please note that revenue per passenger is not appropriate as it is not helping us to compare apples with apples, as distance covered by other airlines may be different, so the appropriate measure is revenue per passenger kilometre and not revenue per passenger, which will show whether it is able to charge premium or not.
(Why we use passenger kilometer, rather than Seat kilometer is discussed in the following post
https://www.blogger.com/blogger.gblogID=5984591937773450711#editor/target=post;postID=9102857826615634407;onPublishedMenu=allposts;onClosedMenu=allposts;postNum=11;src=link)

The question says fuel and staff costs are high, so comparing staff cost per staff as a number of staff is provided, we are able to compare how much each airline is paying for each staff.

What about fuel, fuel is used for distance travelled, and the distance travelled is given as passengers and seat kilometres, so which is better option, to measure performance of aircraft we use seat kilometres and to evaluate the performance of Amal it is better to use passenger kilometres and you can compare both to see efficiency.

There is another measure we can use comparing costs with revenues, this is quite easy as we don’t know the net profit, this is also appropriate measure we can use to compare different airlines.

Finally as it is clearly given in the question that the airline industry is a capital-intensive industry, it is always better to calculate capacity utilisation, how to do this, we have been given seat kilometres, which is the installed capacity, and passenger kilometres, which is the actual capacity, so the capacity utilisation is calculated as passenger kilometres/ seat kilometres.

Note: we are not using the figures, the number of aircraft and average aircraft size, as they won’t provide any appropriate measures, always remember the word “compare apple with apple”, it will help you a lot to answer these type of questions.

Why we are not using a number of aircraft, or average aircraft size, each aircraft is different in size, using number is inappropriate and vice versa.

so why it has been given in addition to number of passengers, just to confuse you, so that if you don't know you will use wrong performance measures, which has no relevance , see the purpose of the examiner, at professional levels he is not making you to calculate a lot, but he himself is providing some calculations and you need to use correct measures and analyse the same to arrive at correct decisions, if the same question is given at intermediate stage, you might have been asked to calculate passenger kilometres or seat kilometres, and capacity using the same.
After completing this post I suggest you to look at the following post for further analysis.
http://cvdsomayajulu.blogspot.in/2017/06/how-to-use-correct-performance-measures.html

How to select ACCA optional papers, for that matter any qualification

2017-05-27T03:47:00.000-07:00

Even though the main purpose of this post is to select option papers at ACCA professional exams options paper stage, you can use the same approach to select various qualifications.

Many students get stuck at professional level especially while doing option papers, feel bad about selecting wrong paper.

As they have other options, whenever they fail, they feel they have made a wrong decision.

Before, entering option papers, even if they fail, they don’t feel bad about it, as it is not in their control because they have no other option but to pass. But at options level, whenever they fail, they feel doubt about their option and think that if they might have selected other paper, they might have passed it comfortably. The main problem with this approach is that if you fail once or twice, you start questioning your own selection, this only harms you, as you are questioning your own strengths, because I am sure you are selected papers only after serious filtering and selected only those papers, which you felt comfortable with.

So my first suggestion is, select papers based on some objective criteria, for example, selection based on your strengths or weaknesses, which helps you a lot when you analyse your failure and prepare for future exams, I also request you not to select papers based on some subjective criteria, for example someone close to you were studying the same paper etc., which doesn’t help you very much whenever you want to analyse your future failure.

There are two approaches to selecting option papers, one is a positive approach based on using your strength, and another is the negative approach, based on using your weakness.

Positive approach: If you use this approach, you are selecting a paper based on your strengths, as papers you are dealing at option level, P4, P5, P6, and P7, are the papers which you dealt at intermediate stage in the form of F9, F5, F6, F8, your performance in these papers will help you a lot in selecting option papers based on how much you enjoyed studying the same and how much confidence you are.

For example:

If you feel F9 Financial management as easy and scored heavily and you enjoy the same while studying, then P4, Advanced Financial Management, should be your option.

If you feel F5 Performance management as easy and scored heavily and you enjoy the same while studying, then P5, Advanced performance management, should be your option.

If you feel F6 Taxation as easy and scored heavily and you enjoy the same while studying, then P6, Advanced Taxation, should be your option.

If you feel F8 Audit and Assurance as easy and scored heavily and you enjoy the same while studying, then P7, Advanced Audit, and Assurance should be your option.

If you want to go into audit side then your options get reduced, as you need to pass P7 Advanced Audit and Assurance to become an auditor, and you need to take one out of other three, if you want to go into practice, then Taxation becomes more useful.

If you are an international student, and your domestic taxation paper is not there in ACCA syllabus, but if you want to practice international taxation, which you enjoy very much then, you are left with three options for selecting one more paper.

If you enjoy financial management and want to practice as a consultant then P5 is the better option.

Negative approach:

Here we are selecting papers not on strengths, but based on weakness, the negative side.

If you are selecting papers based on strengths, passing becomes easy, even if you fail, it will not impact you much as you are sure that you are going to pass, but if you hate all papers, then you need to select the same based on weakness and you must be very careful with this approach, as every failure will have negative impact, and shows your weakness and makes you feel doubt about yourself. So whenever you fail and starting to doubt your selection, just by asking why you have selected the paper in the first place helps you to gain confidence.

Example

The approach goes like this, if you really hate some papers, then most hated should come last, then comes less hated than most hated, so by taking this approach, if you are hating all 4 papers, then least hated, should form part of your option papers, but the question is how we can pass if you start hating the same from day one, from the stage of selection itself, hence I don’t recommend this approach, but if you really hate all papers, then this is the only approach recommended.so If you don’t enjoy and hate audit and taxation most, then you are left with no other option but to take P4 and P5 even though you may not like them, but may not hate them most and vice versa.

So what to do: Just start in advance to select option papers, even before you have seen the same, by trying them during leisure time after passing relevant papers, to check to what extent we are able to cope at final level papers.

If possible after passing following papers, try the relevant papers at options level.

Passing	Try
F9	P4
F5	P5
F6	P6
F8	P7

If you are good at all papers, and interested in all papers, which is rare, then your option becomes difficult, but otherwise, it is straightforward.

Before selecting optional papers, look for two things

Your interest, and ability to enjoy the studies. By looking at past papers for over a period of time will help you to solve this problem.

If some papers interests you, which make you enjoy your studies then go for that paper.

What to do when I am in doubt or when some failure occurs:

When you are in doubt, use this approach, If your selection is based on negative approach, then if you ask a simple question, how much it is possible for me to pass the paper which I hate most compared with present choice, this will give lot of confidence and comfort that your selection is right, if you have selected other paper, then you might have failed in that paper too and it might have brought more misery.

If you have used a positive approach, then it is straight forward if you are failing in paper which you have enjoyed studying, then what about a paper, which you don’t enjoy much, I am 100% sure that you might have made yourself more miserable.

The final conclusion is that in order to pass, you need to enjoy the syllabus or hate them the least, so take the decision at intermediate stage itself, and plan accordingly, once selected stick to that never ever doubt your selection based on exam results or some other criteria. Just by stepping into shoes of your own performance if you might have written the paper you have hated most will solve your all doubts and queries.

Note: If you are evaluating multiple qualifications, for example, CIMA vs ICAEW vs ACCA you can use the same approach, if you like taxation and audit very much then ICAEW or ACCA may be a better option, but if you hate them most then CIMA may be the better option.

How to choose an investment including your professional or academic qualification.

2017-05-20T09:10:00.003-07:00

Many people will face dilemma , while making investment decisions, whether it may involve investing time and money in professional qualifications or in equity, but my answer is , to succeed in any investment decisions, you must have lot of

1. Patience, if you don’t have patience you are certainly going to fail, as every investment involves some element of failure and not everyone is not so fortune of 100% success, it is your patience and understanding your psychology, that makes investments tick.

2. Understanding your psychology, always remember that you are unique and completely different from anyone living in this universe. So if you try to copy others, you will certainly go to fail, you need to make strategies according to your own psychology.

3. Taking into account the opportunity cost, the opportunity cost is the cost of next best opportunity or alternative, which you are missing if you are continuing with your current investment.

Before making any investment, just be patient and observe the same for some time, and see whether your interest in it is same or differed over a period of time, for example, if you want to study some professional qualification (this is also an investment as it increases your returns in terms of higher salary and savings) or invest in some stocks, just don’t do it on the basis of your instant or someone close to you is doing or succeeded. If someone succeeds doesn’t mean that you will succeed, but you are certainly going to fail if you can’t align yourself with the same.

To align investments with yourself takes time, that’s where patience and understanding your psychology is required, you need to study yourself and understand your needs and aspirations in order to get the maximum out of your investment decisions.

If you studied your psychology well, you will enjoy the journey of investment, irrespective of its success or failure, as a failure are an integral part, you will not get disappointed, rather take this as an opportunity to learn and try to profit from the same in future.

If you start enjoying the beauty of investment, you will be positive irrespective of your success. If you succeed you will get a return and if you fail, you will get experience, which shows a way which you need to avoid in future to succeed.

This quote from Thomas . A. Edison is worth noting here, “I have not failed. I've just found 10,000 ways that won't work.”

Always start your investment with small amount and test the same before making it big, of course if you want to acquire equity as investment, you can easily invest small amounts and test your strategy, how to do the same for acquiring professional qualification, you can read the syllabus and take the papers which you feel quite easy to do, and try to download past papers and write answers and test the same with the examiners answers. If you fail don’t worry, reassess yourself, if you are still confident, go ahead, if not stop it.

Always take into account opportunity cost into consideration, while making investment decisions. For example if you are studying, you are actually missing job, thus earnings, if you don’t have any job or you have been fired and have no alternatives, then opportunity cost is zero, then go and acquire qualification, but if you have job, the effort you are making to succeed in acquiring qualification, will reduce your time to enjoy other joys of life, which you may have to delay for some time, or you may not try for those jobs which may pay you a bit more but also expects you to give lot of time, in this case, the lost joys or salary is the opportunity cost.

When you want to quit or exit the investment, if your opportunity cost is increasing with time of holding, it is better to exit from the investment.

For example if you are in final examinations and need to pass one or two papers, you have already travelled a lot, and your opportunity cost of leaving the qualification is more than opportunity cost of acquiring the same, so better spend time in acquiring, but if you have passed 4 papers out of 10 papers, then with passage of time, it is better to leave as with passage of time, the papers becomes more and more difficult hence it is suggested to exit.

What about equities, in the case of equities, you already know about the risk-free rate, the rate offered by the government for your deposits, which will provide you with a benchmark rate to be used as an opportunity cost to rate your equity investment decisions. If your rate is less than the rate offered by government securities, it is better to quit and invest the same in risk-free government bonds. If your rate of return is more than the rate offered by risk-free government bonds, you can always continue with your investment journey.

This benchmark also provides the opportunity cost against which you can measure your returns, and take decisions like build, hold or exit, if you are patient enough and able to acquire a single stock at a very low price, note it should not be the lowest price, low than current prices is enough, you can always profit from the same.

Some important excel functions

2017-05-14T07:46:00.000-07:00

CIMA and ACCA examiners always say that there are multiple ways to arrive at a solution,

The same is true with excel, you can arrive at the same with multiple ways, if you know more functions you are able save a lot of time, for example to know about duplicates, I can use sort function, duplicates function and Pivot function, all three shows there are duplicates, but if I know pivot table well, I can know quickly how many duplicates are there in the data and how many times each of the data was duplicated.

I am not explaining the functions, as I don't want to reinvent the wheel, you can search You tube and learn the same, if you already know about a particular function just leave the same and go to other, whenever I encounter some new function I will try to add the same to the list over a period of time.

RRANGE NAMES

• LOOKUP

• VLOOKUP

• HLOOKUP

• INDEX

• MATCH

• COMBINING INDEX WITH MATCH, THIS IS SOMEWHAT TOUGH FUNCTION, IF YOU ARE ABLE TO MASTER IT YOU DOESN’T REQUIRE VLOOKUP.

• LEFT

• RIGHT

• MID

• TRIM

• LEN

• FIND

• CONVERTING TEXT TO COLUMNS USING DATA-DATA TOOLS-TEXT TO COLUMNS

• SEARCH

• REPT

• CONCATENATE OR &

• REPLACE

• VALUE

• UPPER

• LOWER

• PROPER

• CHAR

• CLEAN

• SUBSTITUTE

• USE THE CLEAN AND SUBSTITUTE FUNCTIONS TO REMOVE UNPRINTABLE CHARACTERS

• IF STATEMENTS

• NOW()

• TODAY()

• TIME(HOUR,MINUTE,SECOND)

• TIMEVALUE FUNCTION TO CONVERT A TEXT STRING TO A TIME

• HOUR,

• MINUTE

• SECOND

• INDIRECT

• MACROS: DIVIDE THE TOTAL INTO SMALL STEPS, USE VIEW MACROS TO RECORD MACRO AND SUM THEM ALL USING ONE MACRO OR COMBINING THEM

• PIVOTTABLES

• DATA CONSOLIDATE

• DATA MODEL

• POWERPIVOT

• OFFSET FUNCTION

• FORMULAS TAB ON THE RIBBON AND THEN VIEW THE FORMULA AUDITING

• DATA TABLES FOR SENSITIVITY ANALYSIS

• GOAL SEEK

• SCENARIO MANAGER

• COUNTIF

• COUNTIFS,

• COUNT,

• COUNTA,

• AND COUNTBLANK FUNCTIONS

• SUMIF,

• AVERAGEIF,

• SUMIFS

• AVERAGEIFS

• INDIRECT

• CONDITIONAL FORMATTING

• SORTING

• TABLES

• OPTIMIZATION WITH EXCEL SOLVER (LOOK AT THIS ARTICLE FROM CIMA USING SOLVER TO SOLVE LINEAR PROGRAMMING QUESTION OR SEARCH GOOGLE FOR LINEAR FINAL GRAHAME STEVEN CIMA) FOR THE SAME LINK IS PROVIDED BELOW
, http://www.cimaglobal.com/Documents/ImportedDocuments/ci_dec_01_p20-23.pdf

• IMPORTING DATA FROM A TEXT FILE OR DOCUMENT

• IMPORTING DATA FROM THE INTERNET

• DATA VALIDATION

• SUMMARIZING DATA BY USING DESCRIPTIVE STATISTICS USING EXCEL ADD-INS

• USING PIVOTTABLES AND SLICERS, INSERT-TABLES-PIVOT TABLES

• FILTERING DATA AND

• REMOVING DUPLICATES USING DATA-DATA TOOLS-REMOVE DUPLICATES

• CREATING SUBTOTALS DATA SUBTOTALS

• ARRAY FORMULAS

Make books your companion either through reading or listening

2017-05-14T07:29:00.001-07:00

“The man who does not read has no advantage over the man who cannot read.”

"I have never let my schooling interfere with my education"
― Mark Twain
Reading books in addition to your study texts will provide you with practical examples and limitations inherent in the topics we are studying in the real world.

These limitations help you a lot when you actually enter the job market and see the difference between what you have studied is completely different from what you are doing at work.

The passing of exams will certify that you are eligible as a professional, but in order to shine in your profession you require more than what you have studied.

As a saying goes, fools learn from their own mistakes, while wise learn from others, hence reading books helps you a lot, as it is written by persons, who has discovered something new or thriving after facing lot of problems in real life, which provides you with opportunity to learn from their lives.

So what you achieving by reading a good book, you are saving a lot of life, which is scarce and precise as it is a limited resource and by doing so you are optimizing your life, thus you are not trying to reinvent the wheel.

For example, Isaac Newton, one of the greatest brains lived on earth, has spent nearly 10 years to discover calculus, thus by learning calculus you are saving 10 years of great brain.

But how to know what to read, and whether a book is worth reading or not, it depends on what you are looking for, sometimes you get the same at the end of the chapter in study texts as reference books, sometimes when you are reading one book you get some others as reference from the author, sometime while reading any book the author will quote about other books which will provide as reference.

You don’t need to read the entire book, just read what interests you and feel useful to you as an example I am mentioning some below.

If you reading financial management, and efficient market hypothesis, you will come across the book called “A random walk down wall street”, once you read first few chapters, you started to know what is wrong with valuation techniques which we study for exams, whether markets are efficient or not etc.

If you are studying management accounting, you will come across the concept called Theory of constraints, so go and read a book “The Goal”, which is usually the reference, from which the concept was originated, you know about “TOC”, and its application in real world.

If you read “The Black swan” or “Thinking fast and slow”, you will start seeing risks and look at bias in your decision making.

Start with any book; for which you don’t have to purchase a book; you can actually rent the same or read from public libraries.

once you make the habit of reading, it will take you a long way and become your companion of your life time, (every one may leave you, with the passage of age, but you have to leave books, they will never ever leave you, so they are the life’s great buddies), if you don’t have time to read, then at least listen, using audio books, there are several sites available which provides audio books free of cost (search Google for free audio books or you can also search youtube.com stating audio books and convert the video of the same using any software which converts videos in you tube to MP3)

You can also use TED talks, talks at Google, search google for the same to get talks from the authors themselves.

To convert YouTube videos to MP3 you can use the link below which I usually use to convert the same, or search Google.

http://convert2mp3.net/en/

Some Talks at Google

Daniel Kahneman: "Thinking, Fast and Slow" | Talks at Google

https://www.youtube.com/watch?v=CjVQJdIrDJ0

Aswath Damodaran: "The Value of Stories in Business" | Talks at Google

https://www.youtube.com/watch?v=uH-ffKIgb38

Aswath Damodaran: "Valuation: Four Lessons to Take Away" | Talks at Google

https://www.youtube.com/watch?v=Z5chrxMuBoo

Some TED talks

How to speak so that people want to listen | Julian Treasure

https://www.youtube.com/watch?v=eIho2S0ZahI

To find work you love, don't follow your passion | Benjamin Todd

https://www.youtube.com/watch?v=MKlx1DLa9EA

How to gain control of your free time | Laura Vanderkam

https://www.youtube.com/watch?v=n3kNlFMXslo

The Goal-Business Novel Part 1 of 9 -Free Download((accessed from India in 14^th May 2017 from You tube), all nine are available, I provided link for the first, so if you are able to connect, you can do for others.

https://www.youtube.com/watch?v=osbaztmBkKI

Estimating costs using Regression and Residual analysis

2017-05-05T09:01:00.002-07:00

The objective of this post is to how we can estimate costs using regression and residual analysis using excel add-ins, assuming there is a linear relationship between overhead cost and basis used to absorb costs.

How to add excel add in and using P values is already discussed in the following blog, please refer to the same.
http://cvdsomayajulu.blogspot.in/2017/04/simple-linear-regression-and-multiple.html

Costs consists of three components

Material, labour and expenses.

These are further divided into direct and indirect.

Direct costs are identifiable with the product and we can establish perfect cause and effect relationship, hence there is no problem, you can directly attribute the same to final product.

The indirect costs portion also known as an overhead poses the problem as we can’t identify the same with final product.

So what we will do, as we can’t relate costs to final product, we need to first allocate the same to some cost centre or cost pool then assign the same to final product.

there are two approaches here one is the Activity based costing, where overheads are collected according to cost pools and then activities are identified which help to assign those costs based on activates consumed, for example all maintenance costs are collected and allocated to those who ever uses these maintenance services.

The other one is more traditional one which uses cost allocation, cost apportion and cost absorption

Cost allocation: Allocation is used if you are able to identify cost which can be attributed to a particular cost centre, which can be either a production department or a service department. For example, depreciation on machinery is directly assigned to the department which is using that machinery.

Note here we can establish direct cause and effect between costs with cost centers/ pools or objects, but not with final products, for example maintenance cost of a particular machine can be directly allocated to machine, in the same way insurance cost of a particular machine can be attributed to a particular machine, here machine is the cost centre/ pool against which we are collecting cost.

Cost Apportionment: Sometime you may not see direct cause and effect, as there are more than one cost centre using the activity, so here you need to apportion or giving a share of cost to or proportion of cost to each cost centre on some equitable basis.

How we determine equitable basis, this depends on facts, for example electricity used by three machines, which are nothing but cost centers can be apportioned based on KWH. In the same way maintenance expenditure incurred needs to be apportioned based on hours of maintenance taken by each cost centre, it looks subjective but you can use correlation and see if there is any real relation between the basis used for apportionment.

What is primary and secondary distribution of overheads:

If you observe closely, in the above case, while talking about allocation we said that cost of maintenance needs to be collected under maintenance department, which is nothing but a cost centre or cost pool, while in second case while apportioning costs of maintenance, we discussed about apportioning the same to other cost centre.

The primary distribution consists of assigning costs (both allocation and apportion) to both production and service cost centre, whereas secondary distribution consists of apportioning cost of service cost centre to production cost centre.

On what basis: Yes, you need to correlate the basis of distribution with costs.

There are three basis we can use for secondary distribution

I. Repeated Distribution Method II. Trial & Error Method III. Simultaneous Equation Method

Now comes the last, absorption of overheads:

After allocation and apportionment, we need to absorb the cost of a cost centre and need to relate the same to final product, this is what absorption of overheads is all about.

For example if machine is the cost centre, which produces single output then the cost assigned to machine/ number of units produced will give cost of output, but if it produces different products each take different times, then time taken becomes the basis on which we need to absorb the costs, so we calculate cost per machine hour as cost incurred on machine / no of machine hours , then we arrive at product cost using number of machine hours required to produce a product x cost per machine hour.

Simply stated, overheads absorbed = overhead absorption rate x unit used to absorb overhead or overhead absorption rate = overheads absorbed / unit used to absorb overhead (which differs from case to case)

How we know which unit to be used to absorb overhead:

Hear we can use both correlation and if possible regression if you see you can absorb overhead based on multiple criteria, and as discussed in the earlier blog if you are able to generate higher Adjusted R square, with low P value, the additional variable used in regression equation will significantly improve the absorption of overheads hence helps us to cost our products fairly.

See excel sheet attached for calculations.

https://drive.google.com/file/d/0B8zFXP_e-bWtMUhhX0QybEZMOWc/view?usp=sharing

https://drive.google.com/open?id=0B8zFXP_e-bWtMUhhX0QybEZMOWc

The Problem is provided below, which you can directly copy and test in excel sheet or use the question in the excel sheet itself.

overhead	mac hrs	batch size	Batches	Labour hours	Production	sales in units	Number of packags	sales in value	Total production cost
230001	5316	194	62	58260	12028	14141	587	1131280	989870
221034	5460	360	44	62773	15840	12586	784	1132740	1107568
240423	4902	190	78	55432	14820	12939	933	1164510	1138632
185955	3018	198	80	65011	15840	15847	579	1188525	982514
218055	4149	165	78	56052	12870	12948	949	1165320	1139424
263025	5871	184	82	57174	15088	14657	642	1172560	1025990
235350	4683	132	96	65496	12672	13625	761	1158125	1090000
211902	4392	219	68	62130	14892	14250	634	1140000	997500
190251	4635	284	50	58675	14200	12884	674	1159560	1133792
168171	3357	203	58	60213	11774	15118	859	1133850	937316
202338	4146	147	70	57057	10290	12881	787	1159290	1133528
216306	3960	112	94	65241	10528	12595	702	1133550	1108360
205599	3792	162	98	58483	15876	15881	893	1191075	984622
207237	4032	251	58	64684	14558	15359	761	1151925	952258
256650	5409	122	96	64406	11712	12316	935	1108440	1083808
174591	3066	198	76	65049	15048	14962	868	1196960	1047340
184878	4530	342	42	55476	14364	15385	516	1153875	953870
242067	5379	239	58	56042	13862	13660	507	1161100	1092800
174768	3447	189	54	63012	10206	15563	776	1167225	964906
166011	3465	289	44	60074	12716	13551	870	1151835	1084080
255324	5541	138	76	58761	10488	14742	789	1179360	1031940
229455	5496	318	46	56868	14628	13830	832	1175550	1106400
203349	3408	184	84	64223	15456	15659	657	1174425	970858
169194	3408	278	44	64055	12232	12819	766	1153710	1128072
199866	3990	206	66	57115	13596	14522	533	1161760	1016540
190482	4074	288	52	57652	14976	14309	995	1144720	1001630
268248	5646	121	90	61140	10890	15824	828	1186800	981088
202554	3522	144	90	57754	12960	13293	944	1129905	1063440
221040	4929	231	62	61644	14322	13425	991	1141125	1074000
198396	4143	209	52	58027	10868	15191	648	1139325	941842

We have been provided with data pertaining to manufacturing overheads incurred by a company, note that it needs to be absorbed based on some basis, we have been given machine hours, batch size, number of batches, labour hours production in units, sales in units, number of packages, sales in value and production cost.

From the firsthand experience, if you know something about costing you are tempted to use machine hours as basis of absorption as it is a manufacturing overheads and you see no value in sales in units or sales in value, this was proved by correlation analysis and regression analysis done on manufacturing overheads with sales value and units.

As P value is more when we performed simple linier regression between overheads and other variables, we arrive at final wherein we are able to relate manufacturing overheads costs with machine hours, but the R squared improved significantly by taking into account batches, but by including one more variable batch size, we are able to improve R square, but the P value of the same is insignificant.

It should be noted that if taken individually both batch size and number of batches are showing very low P values, but number of batches is having more R square than batch size. So, what to do whether we include batch size in our regression model or not, here comes the residual analysis.

Residual vs error: Error is used for population whereas residual is used for sample, when we talk about regression equation, we write the same as

Y = a+b1x1+b2x2+-------------+bnxn+ e, where e is error.

You already know that Y is the dependent variable, a is the slope and b1 to bn are coefficients of x1 to xn, so if you know slope and coefficients b1 - ----bn, you are able to predict the value of Y.

Once you come with predicted values, you need to check whether the prediction is right or not , here comes into the residual into picture, which is nothing but actual data less predicted data using actual data variables x1 to xn.

If you picture the residual data which is available as an ready made in excel, with calculations for prediction and residual, if you find some pattern like liner or curve you are in problem, but if the graph looks haphazard which does not find any meaning, then you are able to say that the regression equation is able to predict with accuracy.

If you see the graphs and residual analysis in the excel sheets which was provided below

https://drive.google.com/file/d/0B8zFXP_e-bWtcnQ0bDlLNkNHOVE/view?usp=sharing

https://drive.google.com/open?id=0B8zFXP_e-bWtcnQ0bDlLNkNHOVE

Manufacturing overheads with machine hours and compare the same with batch size and batches the picture becomes more random

Graph in mc hrs batch size and batches looks quite similar to graph in mac hrs batches as P value of batch size is high it becomes insignificant, even it increases R square marginally from 0.9479 to 0.9485. but if we look at just with machine hours and batch size, where R square is 0.9152.

So, as batch size P value is high it is not increasing R square much and the residual graph looks similar, it is better to predict regression equation using machine hours and number of batches, which increases adjusted R square significantly from 0.7319 to 0.9479

Regression equation for predicting overheads at 230001 using machine hours and batches is given by equation

34862.78(intercept)+ 28.72 (machine hours coefficient) x machine hours (5316)+ 741.40(batches coefficient) x number of batches (62) which gives value of 233552.15, (it will not be exactly as I rounded up to two decimals, but if you take the coefficients and intercept from excel you will get the same, which I had shown for in residuals excel file “mac hrs batches”. (showing calculated values with excel generated values, which will come below as residual output.

Residual is nothing but actual 230001- prediction 233552.15 = -3551.15

Screen shots to generate predicted values with residuals and residual graph.

Data – data analysis – regression.

Click ok

Select y range the dependent variable in this case it is overheads column, and x range which is machine hours and batches column select labels if you include labels in above range of x and y, the you need to select output range and tick residuals and residual plots, and you have done and get residual output with graph.

What type of Manager you are and want to work with: Professional advice

2017-05-04T06:54:00.001-07:00

When you join in your job, either doing professional education or after doing the same, you come across people who can be categorized into four categories based on heart and brain, which in a spectrum will range from god to devil. I also request you to categorize yourself on this spectrum and try to be human if not god.

Note: Note persons in cells 2 and 3 may become god, and may actually be one, but if your wave length doesn’t match with them, it is always better to leave. For example in cell 2, a person may have great heart, but he may be expert in tax and you want to be expert in audit, he may be having both great brain and heart from tax point of view, but you are unable to much get benefit, as you want to be an audit expert rather than tax expert, so get as much as you can which is useful to your audit and look for better opportunities in your field, in the same way the person in cell 3, may be pushing you to your limits, which in the short run may seem unkindly, but he is actually helping you in long run. So the cells 2 and 3 depends on circumstances, but you can definitely identify persons in cell 1 and cell 4

	Heart
Brain		*Great*	*Not Great*
	*Great*	1. Excellent and Heaven to work with, never ever leave	3. Exploit knowledge as quickly as possible and get out to explore new knowledge.
	*Not Great*	2. If possible help them with your knowledge, and use their help to gain qualification, but never stay for long especially at the beginning of your career.	4. Worst, will show what the hell looks like on earth, kick on their ass and leave, if possible run as fast as possible.

1. Great brains with great hearts (Gods):

You rarely come across people who have both great brains and heart, who shows you what is called heaven on earth, you can learn a lot from them, they support you on your strengths, and knows your weakness, and tries to help you to overcome weakness and at the same time use your strengths in work, to a maximum extent possible, so that in future when he left you, for whatever reason it might have been, you will miss him a lot. If you work under him for a period of 5 years you may overcome most of your weakness and develop great strengths, which help you a lot in your professional career. These people are really what we call leaders, never ever leave them, if possible follow them if they go to other organisation.

Professional advice: Never ever leave the Manager if you are working with this type of persons, irrespective of the stage in your professional career especially for a marginal increase in salary. If possible try to be one if you can make it, you can bring change to lot of life’s, that’s what we are born as human beings.

2. Great hearts but Not great brains (Humans):

These people are basically good but in many cases they may require you to cover-up their weakness with respect to knowledge, we can’t call these people gods as they don’t help much in your career progression as you can’t gain much from them.

Professional advice: if you are still pursuing your professional career, it is always advantage to work with this kind of people as they help you a lot to complete your exams by granting leave etc., even though it is tempting to stay for a long, it is not good to your professional career so it is better not to stay too long with this kind of people as you may not be able to develop sufficient skills, if you get better opportunities it is always advised to leave these type of Managers, but with cordial relationships.

3. Great brains but Not great hearts (Humans):

These persons have great brains, and you will always feel envy about their knowledge, as great brains are compensated with less hearts, we can still categorise them as human, because if you are smart enough you can gain a lot from their knowledge, which can boost your career path, so they are indirectly helping you.

Professional advice: If you are at initial stages of your career, these persons are great to work with, as you acquire more exposure by working with these people, you become more professional and confident, but once you are confident enough and got necessary exposure you can dump and jump to another Manager, you get lot of these people in your professional career, and you need to learn and dump whenever you see better career prospects.

4. Neither great heart nor great brain:

Sometimes you come across these persons; they neither have great brains nor great heart, they will show you what the hell looks like on earth. These persons are sadistic, psychopaths and devilish. As they know they don’t have brain, they want to dominate others using power.

Professional advice: these people are hazardous to health and wealth as you can’t learn anything from them you are blocking your career prospects by working with them. So, once you know what they are, just run away and if possible as fast as you can. If you are daring, you can scold him in public (because it gives happiness to others, who are unable to do the same due to some personal/family problems) and if possible kick on his ass in private (as kicking will be a criminal offence, do it privately, as it is an shameful event, he won’t say this to any one) and resign when he needs you most, as he is no brainier, he has to beat his head against wall in your absence, and may have to resign for his poor performance.

How management can benefit from using confidence intervals along with P values in hypothesis testing

2017-04-27T07:59:00.000-07:00

Before this I request you to go through this blog to get basic understanding about hypothesis testing, which was covered in detail the link of which is provided below.

http://cvdsomayajulu.blogspot.in/2017/04/logic-behind-hypothesis-testinghow-much.html

There are three ways of testing hypothesis.

1. Critical value approach or method

2. P value approach or method and

3. Confidence interval level approach or method

Critical value approach or method:

This involves calculating the test statistic appropriate for a particular data and comparing same with the value available at confidence level for that test, you may call it statistic at α, if test statistic is less than statistic at α, we reject null hypothesis otherwise we doesn’t reject the null hypothesis.

For example if number of observations are more than 30 and standard deviation is know we will do Z test.

For this we will find out Z statistic using formula and find the value of the same, let’s call it Z

Then given the confidence level we will find out Z value, we will call it Zα, anything less than this will fall in critical region and needs to be rejected, so Zα is critical or you may call standard against which we need to compare test statistic so as to reject or not to reject null hypothesis.

So if Z< Zα, we reject null hypothesis otherwise not.

For example the Z statistic calculated using the formula is 2.55, if you want to test the same at 99% confidence level or α of 1%, assuming one tailed test the value of Zα from z table gives the value 2.33. as 2.55 is >2.33 , we don’t reject null hypothesis, let’s assume to be left side test the value of Z statistic calculated is -2.55 , which we need to compare against Zα of -2.33, but in this case as -2.55 is less than th value of Zα -2.33, it falls into the critical region, hence we reject null hypothesis.

Significance of this approach: except how close it is to the critical value, it doesn’t have much significance in management decision making, except rejecting or not rejecting null hypothesis.

P Value approach or method: In this approach α becomes critical or standard against which we measure P value, it simply states that if P value is less than or equal to α, we reject null hypothesis as P value is falling in critical region and vice versa.

It should be noted that P value is derived using value we got form test statistic calculated above. For example , for example if calculation of Z statistic provided a value of -2.67 for single tailed test, , the P value will be 0.0038, if we measure the same at 99% confidence level or α of 1% or 0.01, as 0.0038≤ 0.01, we reject null hypothesis.

Significance of this approach: For example if P value is 2.61% and we are testing at 95% confidence level or α of 5%, as P value is less than α, we reject the same at α of 5%, but if we test the same at 99% confidence level, we may accept the same as we can’t reject null hypothesis level, so we can test the P value at different confidence levels.

This becomes particularly useful while doing multiple regression, any independent variable whose P value is very low becomes significant independent variable, which helps regression equation better predictor with the addition of this independent variable. We can directly reject null hypothesis which states that the prediction power of independent variable on dependent variable is zero.

Confidence interval level approach or method:

While defining null hypothesis we define population parameter, for example if we are testing for population mean, it will be defined as H0: µ = 25, so if this population parameter value of 25 falls within confidence intervals we will not reject null hypothesis and vice versa.

For example, in the above example if the confidence intervals are 10 to 60 as 25 falls within this interval we don’t reject null hypothesis, let’s assume another confidence interval 24 to 27, as 25 falls between this we don’t reject null hypothesis. This is very important aspect of confidence interval’s, if you want to quote a price for a tender, if confidence interval is wide, you may quote less and may lose chance to gain extra profit, but if you quote high, you may lost bid itself.

Significance of this approach: Management should be very careful while using confidence intervals to reject or not to reject null hypothesis. As increase in confidence level increases the width, which brings more problems than answers and less confidence level my reduce width, which may not be able to highlight the true picture, but using confidence intervels along with P values may bring more benefit .

If the confidence intervals range is very broad as in first case 10 to 60, compared with second case of 24 to 27, the management has to think twice while making important decisions.
lets take an example here management studies relationship between production and cost at 95% confidence level and arrives the confidence interval of cost between 22 to 38, this is to state that we expect that 95% of the confidence intervals constructed in this manner will contain the true value of the coefficient of production.
See how it effects decision making here, if industry standard is 23 dollars, but our actual cost is 33 dollars, both are within the range, so if you start accepting jobs based on industry standard of 23 dollars, the jobs are not profitable, hence you need to look at P value here, if it is showing significant relationship by having minute value like 0.000023, then it shows significant relationship and you need to redo using more data.

If you want to know more about regression analysis see the link below

http://cvdsomayajulu.blogspot.in/2017/04/simple-linear-regression-and-multiple.html

Lets take an example of regression analysis with is given by the equation Y= b+bx+b1x1+b2x2+- - - - + bnxn + e, the equation for simple liner regression is given by Y = b + bx +e

If this is the equation what the confidence intervals will tell us about.

Taking into effect of other variables (for multiple regression it may be x1, x2 etc), for each increase of one unit of X, Y is estimated to increase by at least one unit of lower confidence interval level but no more than one unit of higher confidence interval level, this provides immense information for management decision making.

Null hypothesis for regression equation assumes that there exists no relationship between dependent and independent variables, simply speaking H0: x or x1 = 0

For example, you have solved a question on regression and arrived at following simple regression equation Y=0.96 + 1.66X, at 99% confidence level obtained the lower confidence interval level of 1.33 and higher confidence interval level of 2.01, you can assume y be any dependent variable like sales and x the independent variable like cost of advertising. It can be interpreted as follows for each 1 unit increase of advertisement expenditure, the sales is estimated to be increased by at least 1.33units but not more than 2.01 units

Not let’s do the same for multiple regression

For example, you have solved a question on regression and arrived at following multiple regression equation Y=580-53.21X + 7X1, Where Y is the sales (Dependent variable), which is depended on X ( the price) and X1 (the advertisement expenditure). Let’s assume the lower and upper confidence limits for price are -69 and -39.

The above confidence interval limits states that assuming the effect of advertisement expenditure, for every increase in one unit of price the sales will reduce between 39 to 69 units, see the fluctuation here nearly 30 units which is huge.

See the beauty hear your decision of increase in price may ruin your company if you increase price by a unit, the sales may fall by 69 units instead of 39 units. So if the confidence intervals are wide, the decision making becomes more difficult.

If for advertisement expenditure if it just as above 1.33 to 2.01, assuming the effect of price., each unit of expenditure on advertising will increase sales between 1.33 to 2.01 units.

So if you are in management position studying and interpreting confidence intervals provides huge advantage in make decisions especially if independent units are measured in same units, for example in the above case if price and advertisement expenditure is expressed in dollars, reducing the price is more beneficial than increase of advertisement expenditure, and will get much push if it is backed by a data which provides P values which conforms that price and advertisement expenses have significant effect on sales.