Business Consulting

Profit Maximization in Perfect Competition

2012-01-20T07:19:00.000-08:00

Profit Maximization in Perfect Competition Market

Producing and selling at profit maximization output at particular price is very important to ensure our resource and capital are utilized at optimum level. Economic theory say that in perfect competition market in long run Price=demand function=Marginal Revenue=Marginal Cost. This is because the efficient market condition that allow easy entry and out.

1.0 Question No. 1

The Green company produces chemicals in a perfectly

competitive market. The current market price is $40;

the firm’s total cost is C=100 + 4Q + Q2.

a. Determine the firm’s profit –maximizing output.

More generally, write down the equation for the firm’s supply curve in terms of price P.

b. Complying with more stringent environmental

regulations increases the firm’s fixed cost from 100

to 144. Would this affect the firm’s output?

Its supply curve?

2.0 Question No. 2

Suppose that the manager of a firm operating in a

competitive market has estimated the firm’s average

variable cost function to be

AVC = 10 – 0.03Q + 0.00005Q2

Total fixed cost is $600.

a. What is the corresponding marginal cost function?

b. At what output is AVC at its minimum?

c. What is the minimum value for AVC?

If the forecasted price of the firm’s output is $10 per unit:

d. How much output will the firm produce in the short run?

e. How much profit (loss) will the firm earn?

If the forecasted price of the firm’s output is $7 per unit:

f. How much output will the firm produce in the short run?

g. How much profit (loss) will the firm earn? If the forecasted price is $5 per unit:

If the forecasted price is $5 per unit:

h. How much output will the firm produce in the short run?

i. How much profit (loss) will the firm earn?

1.0 Question 1

Solution 1(a)

Total cost C= 100 + 4Q + Q²

Fixed Cost (FC) = 100

Variable Cost (VC) = 4Q + Q²

Marginal Cost (MC) = 4 + 2Q

Average Cost (AC)	=	100	+	4Q	+	Q²
		Q

	=	100	+	4	+	Q
		Q

Average Variable Cost (AVC)	=	4Q	+	Q²
		Q

	=	4	+	Q

The current market price is $40. To solve the Q, the firm will set the P = MC to maximise profits.

(P)	40	=	4	+	2Q	(MC)

	2Q	=	40	-	4

	Q	=	36 / 2

	Q	=	18

AVC	=	4 + Q

	=	4 + 18

	=	$22

ATC	=	(100 / Q) + 4 + Q

	=	(100 / 18) + 4 + 18

	=	$27.55

Profit = TR – TC

= (PxQ) – (FC + VC)

= (PxQ) – (100 + 4Q + Q²)

= (40 x 18) – (100 + 4(18) + 18²)

= 720 – 100 – 72 – 324

= $224

From here we can see at the market price $40, the company will produce 18 unit of outputs more than cover its Total Cost (FC & VC). Thus, the Green Company makes a profit as shown in Figure 1.

Solution 1(b)

If the fixed cost increases from 100 to 144?

ATC	=	(144 / Q) + 4 + Q

	=	(100 / 18) + 4 + 18

	=	$30

Profit = TR – TC

= (PxQ) – (FC + VC)

= (PxQ) – (144 + 4Q + Q²)

= (40 x 18) – (144 + 4(18) + 18²)

= 720 – 144 – 72 – 324

= $180

As the input price given of $40 and output of 18 units is fix, an increase in Fixed Cost from $100 to $144 wouldn’t have any effect on the supply curve. The company just recorded less profit as the Total Revenue earned need to cover slightly higher Total Cost from $27.5 to $30. The company still making profit at $180 which less than $224 previously.

2.0 Question 2

Solution 2(a) – What is the corresponding marginal cost function

AVC = 10-0.03Q+0.00005Q²

VC = 10Q-0.03Q²+0.00005Q³(multiply by Q)

TC = 600+10Q-0.03Q²+0.00005Q³

MC = 10-0.06Q+0.00015Q²

Solution 2(b)–Minimum Output for AVC

10-0.03Q+0.00005Q²= 10-0.06Q+0.00015Q²

0.03Q+0.00010Q²= 0

Q(0.03+0.00010Q)= 0

Q = 0, or Q = 0.03/0.00010 = 300 units

Solution 2(c) - Minimum value for AVC

At Q = 300, AVC = 10-0.03(300)+0.00005(300²)

= $5.5 (minimum)

To get AVC at its minimum can be found by setting AVC = MC. At Q = 300, AVC = $5.5 and is a minimum. So Q=300 is where the AVC at its minimum. So, in the short run firm will not produce if price are less than $5.5.

Solution 2(d) - If P = $10 per unit

P=MC

$10 = 10-0.06Q+0.00015Q²

0.06Q - 0.00015Q²= 0

Q(0.06 - 0.00015Q) = 0

Q = 0, or Q = 0.06/0.00015 =400 units

At Q = 400, AVC = 10-0.03(400) +0.00005(400²)

= $6 (minimum)

In the short run, firm will only produce 400 outputs at the price of $6 in the short run since it’s the minimum AVC.

Solution 2(e) - Profit / Loss

Profit = TR – TC

= (PxQ) – (FC + VC)

= (PxQ) – (600+10Q-0.03Q²+0.00005Q³)

= (10 x 400) – (600+10(400)-0.03(400²)+0.00005(400³)

= 4000 - 3000

= $1000 (Profit)

Solution 2(f) - If P = $7 per unit

P=MC

$7 = 10-0.06Q+0.00015Q²

0.06Q - 0.00015Q²+ 3= 0

6000Q-15Q²+300000 = 0(round the number)

We solve the Q using quadratic formula below:

Q = 58.57 @ 59unit ; or Q = 341.43 @ 341units

At Q = 341, AVC = 10-0.03(341)+0.00005(341)²

= $5.58 (Minimum)

In the short run, firm will only produce 341 outputs at the price of $5.58.

Solution 2(g) - Profit / Loss

Profit = TR – TC

= (PxQ) – (FC + VC)

= (PxQ) – (600+10Q-0.03Q²+0.00005Q³)

= (7 x 341) – (600+10(341)-0.03(341²)+0.00005(341³)

= 2387 - 2504

= - $117 (Loss)

Even though the firm loss at RM117, it still less than fixed cost of RM600 (FC > Loss), as such the firm can still continue operating in the short run.

Solution 2(h) - If P = $5 per unit

P=MC

$5 = 10-0.06Q+0.00015Q²

0.06Q - 0.00015Q²+5= 0

6000Q-15Q²+500000 = 0(round the number)

We solve the Q using quadratic formula below:

Q = 118.35 @ 118 units ; or Q = 281.65 @ 282units

At Q = 282, AVC = 10-0.03(282)+0.00005(282)²

= $5.51 (Minimum)

In the short run, firm will only produce 282 outputs at the price of $5.51.

Solution 2(i) - Profit / Loss

Profit = TR – TC

= (PxQ) – (FC + VC)

= (PxQ) – (600+10Q-0.03Q²+0.00005Q³)

= (7 x 282) – (600+10(282)-0.03(282²)+0.00005(282³)

= 1974–2155.60

= - $181.60 (Loss)

Even though the firm loss at RM181.60, it still less than fixed cost of RM600 (FC > Loss), as such the firm can still continue operating in the short run.

Statement of Financial Position (Balance Sheet) & Business

2012-01-20T06:20:00.000-08:00

What information does a Statement of Financial Position (Balance Sheet) reports about a Business?

1.0 Introduction

The Statement of Financial Position or Balance Sheet is simply a statement of the assets, liabilities and capital of a business at a particular time / period. It is nothing more than a detailed representation of the accounting equation of asset, liabilities and owner equity. Statement of Financial Position does not provide information about Revenue and Expense.

Assets = Liabilities + Owner Equity / Capital

As what it name is, Statement of Financial Position suggest that it provide information about financial position of a business. In its simplest format the Statement of Financial Position (balance sheet) is presented horizontally with assets being shown on the left and liabilities and capital being shown on the right. As a result the total of each side of the Statement of Financial Position (balance sheet) will be the same, hence the balance sheet balances. Even in other format the two side of accounting equation must balances. If you are a shareholder of a company, or you are user of a financial statement provided, it is important that you understand how the balance sheet is structured, how to analyse it and how to read it. To better understand of what information a Statement of Financial Position provides about a business, firstly we have to know the content of Statement of Financial Position.

Exhibit 1. Example of horizontal Statement of Financial Position (Balance Sheet)

Exhibit 2. Example of Vertical Statement of Financial Position (Balance Sheet)

1.1 Content of Statement of Financial Position (Balance Sheet)

1.1.1 Assets

When we prepare Statement of Financial Position, assets are divided into two categories; fixed asset and current assets.

i. Fixed assets are defined as any asset acquired for retention by an entity for the purpose of providing service to the business, and not held for resale in normal course of trading. In other words a fixed asset is a resource acquired by an organisation with the intention of using it to earn income for a long period of time. Examples of fixed assets include land, building, motor vehicles, machinery and equipment.

ii. Current Assets are defined as Cash or other asset; e.g stock, debtors, and short term investment held for conversion into cash in the normal course of trading. In other words, a current asset is one which either already is cash, or will be converted into cash within a short period of time. Current assets are listed based on its order of liquidity. It is listed from the most liquid to the least liquid. Liquidity is the measure of closeness of assets to being cash

1.1.2 Liabilities

Similar to assets, liabilities are divided into two categories as; current liabilities and long term liabilities, reflecting the time between the Statement of Financial Position date and the date by which the liabilities should be settled. For the liabilities, the accounts are organized from short to long-term borrowings and other obligations.

i. Current liabilities – liabilities which fall due for payment within one year.

ii. Long term liabilities are those which due for repayment more than one year after the Statement of Financial Position date.

1.1.3 Capital / Shareholder Equity

Preferred stock, common stock, additional paid-in-capital, retained earnings, and treasury stock are all reported on the balance sheet in the stockholders' equity section. Information regarding the par value, authorized shares, issued shares, and outstanding shares must be disclosed for each type of stock. If a company has preferred stock, it is listed first in the stockholders' equity section due to its preference in dividends and during liquidation.

Capital / Shareholder Equity could be described as the amount which a business owes to its owner, i.e we see the business as separate entity from owner. It is the amount of money initially invested into the company plus any retained earning, and it represents a source of funding for the business. In other words, it is amount of owner’s money used to finance the business.

The items within these groups do not alter whether different presentation format is used; it is simply a case of moving the groups around and calculating some additional sub-totals.

1.2 What information does Statement of Financial Position reports about a Business?

By understanding type of data in Statement of Financial Position we could derive some business information that could give status and position of a business entity. Analyse and interpret data in Statement of Financial Position for more meaningful information regarding a business is very important for all users, for example an investor would consider an investment (acquire share) in a company that have high debt equity ratio and current ratio as high risk investment. The investor might not able to recover his investment if the company unable to meet its debt’s obligation and as result going under liquidation. The information that Statement of Financial Position could provide about a business is as follow:

1.2.1 Nature of Business

Item contain in Balance Sheet could give you a glimpse of a company nature of business. A service oriented or consultancy and professional company might not have item inventory in their Statement of Financial Position which is different from a trading company. Depending on the company, the exact makeup of the inventory account will differ. For example, a manufacturing firm will carry a large amount of raw materials, while a retail firm caries none. The makeup of a retailer's inventory typically consists of goods purchased from manufacturers and wholesalers.

1.2.2 Type of Business

Different business type such as sole proprietor, partnership, Sendirian Berhad Company and Public Listed would have different format of Statement of Financial Position presentation. Type of account and information disclosed in capital section of Statement of Financial Position would give us information the type of business that the Statement of Financial Position is prepared for.

1.2.3 Accounting period

Statement of Financial Position is prepared based on accounting period of the business. Thus information provided is only limited for that period of time. Bear in mind that any change after the accounting period will not reflected in the Statement of Financial Position even though the change might be significant.

1.2.4 Business practice/policy

Like Magical Meals business practice which does not give its customer credit term for the services provided will explain why Magical Meals do not have account receivable. Same as business policy of a company that do not seek it funding through debt will have higher shareholder equity value compare to its long term debt.

1.2.5 Value of the business

Information contain in Statement of Financial Position could be used to value a business. This is important especially for valuation of a company worth during takeover and liquidation. There are several factors to take into consideration in valuation of a business worth for takeover such as;

i. Futures performance / future financial return expectation

ii. Future cash flow

iii. Technology transfer

iv. Human expertise

v. Value of total assets

vi. Debts & liabilities.

There several methods to value a business. Methods that could be used using available information in Statement of Financial Position are;

i. Assets valuation based – company net worth which is equal to assets minus liabilities as what is shown in the Statement of Financial Position. This is used especially when the buyer interested in its asset and not taking over as going concern.

ii. Market capitalization – using amount of issued share available times with the company’s share market price. Amount of share issued and authorized could be obtained from Statement of Financial Position. If price per share is used for private company valuation, value of net asset divide over number of share could be used as basis to compare price per share.

During liquidation however what important is tangible assets and liabilities

1.2.6 Source of funding / financing

How the business is financed? We could derive from Statement of Financial Position on Statement on how company financed their business. There several form of financing such as debt and equity. We could get this information of sources of a company funding through item in long term liabilities and capital. Ratio of financing fixed asset through shareholder fund /owner equity measures the extent to which owner's equity (capital) has been invested in plant and equipment (fixed assets). A lower ratio indicates a proportionately smaller investment in fixed assets in relation to owner equity and a better cushion for creditors in case of liquidation. Similarly, a higher ratio would indicate the opposite situation. The presence of substantial leased fixed assets (not shown on the balance sheet) may deceptively lower this ratio.

Net Fixed Assets

Owner Equity

How much capital is being used? In a Statement of Financial Position of a public listed company will provide information of how much of its authorised share capital and type of share capital approved. How much amount of share capital being issued also will be disclosed.

1.2.7 Level of Financial Leverage

How much is the long term liabilities over owner equity? Information on a business long term liability is disclosed in Statement of Financial Position. This information could be used to measure its ability to meet financial obligations by using several financial leverage ratios. One ratio formula that could be used using available information in Statement of Financial Position is Debt Equity ratio. Based on this information we could determine level of company leverage. This leverage could be measured through Debt Equity Ratio;

Debt Equity ratio : Total Liabilities

Owner or Shareholders Equity

This ratio expresses the relationship between capital contributed by creditors and that contributed by owners. It expresses the degree of protection provided by the owners for the creditors. The higher the ratio, the greater the risk being assumed by creditors. The lower the ratio, the greater the long-term financial safety. A firm with a low debt/worth ratio usually has greater flexibility to borrow in the future. A more highly leveraged company has a more limited debt capacity.

A high debt/equity ratio generally means that a company has been aggressive in financing its growth with debt. This can result in volatile earnings as a result of the additional interest expense. A company may potentially increase revenue by seeking funding through outside debt. For example a company might not able to undertake a potentially profitable expensive project without enough capital could alternative seek funding through debt. However, the cost of this debt financing may outweigh the return that the company generates on the debt through investment and business activities and become too much for the company to handle. This can lead to bankruptcy, which would leave shareholders with nothing.

This can give investors an idea of how financially stable the company is and how the company finances itself.

1.2.8 Company's short-term financial health (solvency).

Information of a company ability to pay off its short term obligation through its own operation could be measured by using Working Capital ratio;

Working Capital = Current Assets – Current Liabilities

Positive working capital means that the company is able to pay off its short-term liabilities. Current liabilities will provide information of how much the business owe from its operation activities. Negative working capital means that a company currently is unable to meet its short-term liabilities with its current assets (cash, accounts receivable and inventory).

Other applicable ratio using information provided on Statement of Financial Position is Current Ratio;

Current Ratio = Current Assets

Current Liabilities

The current ratio is a rough indication of a firm's ability to service its current obligations. Generally, the higher the current ratio, the greater the cushion between current obligations and a firm's ability to pay them. The stronger ratio reflects a numerical superiority of current assets over current liabilities.

3.2.9 Business liquidity

How liquid its assets are - how much is in the form of cash or can be easily converted into cash, i.e. Inventory and Receivable. Current assets are those assets which will mature into cash during the next twelve months. They are a measure of the liquidity of a company, which is the amount of time it takes for an asset to be converted into cash.

This time period is referred to as the Operating Cycle. In other words, a company begins with cash, purchases inventory with the cash, sells the inventory which creates a receivable, and then collects the receivable which generates the cash. The cash is then used to purchase additional inventory and the cycle begins again. In terms of liquidity, cash is the highest quality current asset and inventory is the lowest quality. Whereas cash is immediately available to pay obligations, inventory must be converted into cash (through the operating cycle), before it is available to pay bills. Take note that money that is tied up in inventory or money that customers still owe to the company cannot be used to pay off any of the company's obligations.

The composition and quality of current assets is a critical factor in the analysis of an individual firm's liquidity.

Quick Ratio = Current Asset – Inventory – Prepaid Expense

Current Liabilities

Also known as the "acid test" ratio, this is a refinement of the current ratio and is a more conservative measure of liquidity. The quick ratio expresses the degree to which a company's current liabilities are covered by the most liquid current assets. Generally, any value of less than 1 to 1 implies a reciprocal dependency on inventory or other current assets to liquidate short-term debt.

1.2.10 Other Analysis

i. Horizontal Analysis – Statement of Financial Position for two year could be combined together in vertical format as in Exhibit 2. By doing so comparison between 2 accounting period could be made and analysed. Thus users of Statement of Financial position could interpret data in Statement of Financial position in more meaningful and interpretation. This will give information of change on each of Statement of Financial Position’s item between these two accounting period. The output could be presented in percentage change or monetary value to give various interpretation of the information.

ii. Estimation – using data in Statement of Financial Position such amount closing balance of Trade Debtor or Trade Creditor, we could estimate roughly amount of credit sale and credit purchase. For example, this could be obtained by dividing amount trade debtor with trade debtor’s number of cycle in a year. If a company give its client 3 month credit term to pay their invoices then it will be 4 cycle of trade debtor (12month / 3month credit term = 4 cycles). Amount of trade debtor as in Statement of Financial Position times with 4 cycles with gives roughly amount of credit sales for the company in a year. This kind of information is useful for user such as auditor to use it as a sign of irregularities in the Statement of Financial Position.

iii. Performance Analysis – Normally Statement of Financial Position will only show closing balance amount of Account Retained Earning. If Statement of Financial Position present Account Retained Earning in detail which show amount of net profit for the period. Then we could analyze the performance of a business through these ratios;

Return on Assets=[Net Income+Interest (1-tax rate)/Total Assets

An indicator of how profitable a company is relative to its total assets. ROA gives an idea as to how efficient management is at using its assets to generate earnings. Calculated by dividing a company's annual earnings by its total assets, ROA is displayed as a percentage. Sometime this is referred to as “return on investment”.

Return on Equity = Net Income / Owner’s Equity

Return on Equity (ROE) is an indicator of company's profitability by measuring how much profit the company generates with the money invested by ordinary share owners.