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Time value of Money(Financial Management)

2012-07-06T03:05:00.001-07:00

Q. The following are exercise in future (terminal) values:

a) At the end of three years, how much is an initial deposit of $100 worth, assuming a compound annual interest rate of (i) 100 percent? (ii) 0 percent?

b) At the end of five years, how much is an initial $500 deposit followed by five year-end, annual $100 payments worth, assuming a compound annual interest rate of (i) 10 percent? (ii) 5 percent? (iii) 0 percent?

c) At the end of six years, how much is an initial $500 deposit followed by five year-end, annual $100 payments worth, assuming a compound annual interest rate of (i) 10 percent? (ii) 5 percent? (iii) 0 percent?

d) At the end of three years, how much is an initial $100 deposit worth, assuming a quarterly compounded annual interest rate of (i) 100 percent? (ii) 10 percent?

e) Why your answer to part (d) is differ from those to part (a)?

f) At the end of 10 years, how much is an initial $100 deposit worth, assuming an annual interest rate of 10 percent compounded (i) annually? (ii) Semiannually? (iii) Continuously?

Solution:

a) FV_n= P₀(1 + i)

(i) FV₃= $100(2.0)³=$100(8) = $800

(ii) FV₃= $100(1.10)³= $100(1.331)= $133.10

(iii) FV₃= $100(1.0)³= $100(1) = $100

b) FV_n = P₀(1 + i)ⁿ; FVA_n = R[([1 + i]n - 1)/i]

(i) FV₅ = $500(1.10)⁵ = $500(1.611) = $ 805.50

FVA₅ = $100[([1.10]⁵ - 1)/(.10)]

= $100(6.105) = 610.50

$1,416.00

(ii) FV₅ = $500(1.05)⁵ = $500(1.276) = $ 638.00

FVA₅ = $100[([1.05]⁵ - 1)/(.05)]

= $100(5.526) = 552.60

$1,190.60

(iii) FV₅ = $500(1.0)⁵ = $500(1) = $ 500.00

FVA₅ = $100(5)= 500.00

$ 1,000.00

c) FV_n= P0(1 + i)ⁿ; FVAD_n= R[([1 + i]n- 1)/i][1 + i]

(i) FV₆ = $500(1.10)⁶ = $500(1.772) = $ 886.50

FVA₅ = $100[([1.10]⁵ - 1)/(.10)]

= $100(6.105) (1.10) = 671.55

$1,557.55

(ii) FV₆ = $500(1.05)⁶ = $500(1.340) = $ 670.00

FVA₅ = $100[([1.05]⁵ - 1)/(.05)]

= $100(5.526) (1.10) = 580.23

$1,250.23

(iii) FV₆ = $500(1.0)⁶ = $500(1) = $ 500.00

FVA₅ = $100(5) = 500.00

$ 1,000.00

d) FV_n = PV₀(1 + [i/m])

(i) FV3= $100(1 + [1/4])₁₂= $100(14.552) = $1,455.20

(ii) FV3= $100(1 + [.10/4])₁₂= $100(1.345) = $ 134.50

e)

The more times a year interest is paid, the greater the future

value. It is particularly important when the interest rate is

high, as evidenced by the difference in solutions between

Parts 1.a) (i) and 1.d) (i).

f) FV_n= PV₀(1 + [i/m])^mn; FV_n = PV0(e)ⁱⁿ

(i) $100(1 + [.10/1])¹⁰ = $100(2.594) = $259.40

(ii) $100(1 + [.10/2])²⁰ = $100(2.653) = $265.30

(iii) $100(1 + [.10/4])⁴⁰= $100(2.685) = $268.50

(iv) $100(2.71828)1 = $271.83

2011-12-24T08:13:00.000-08:00

Inventories and the Cost of Goods Sold

Accountants may use an approach called Specific Identification, or they may adopt a cash flow assumption. Either of these approaches is acceptable. Once an approach has been selected, however, it should be applied consistently in accounting for sales of this particular type of merchandise.

Specific Identification:

The specific identification method can be used only when the actual costs of individual units of merchandise can be determined from the accounting records. The actual cost of this particular unit then is used in recording the cost of goods sold.

Cash Flow Assumption

If the items in inventory are homogeneous in nature, it is necessary for the seller to use the specific identification method. Rather, the seller may follow the more convenient practice of using a cost flow assumption. Using a cost follow assumption is particularly common where the company has a large number of identical inventory items that were purchased at different prices.

Three cost flow assumption are in widespread use:

· Average cost:

· First-In-First-Out(FIFO)

· Last-In-First-Out(LIFO)

The cost flow assumption selected by a company need not correspond to the actual physical movement of the company’s inventory. When units are identical, it does not matter which units are delivered to the customers in a particular sales transaction. Therefore in measuring the income of a business that sells units of identical merchandise, assumption considers the flow of costs to be more important that the physical flow of the merchandise.

Average Cost Method

When using average cost, assign the average cost of the goods available for sale to cost of goods sold. The average cost is determined by dividing the cost of goods available for sale by the units on hand.

Example:

On August 1^st and 3^rd, TBC purchases inventory. On August 14^th, they sell 20 bikes for 130 each.

First, TBC needs to compute the average cost of the items in inventory. They do this by dividing the cost of goods available for sale of $2,500 by the total units in inventory of 25. The average cost per unit is $100.

Then, to determine the Cost of Goods Sold for August 14^th, multiply the number of units sold by the average cost. This calculation determines that the Cost of Goods Sold for August 14^th is $2,000.

Entries will be:

After this sale, TBC has 5 units in inventory at an average cost of $100 each.

First-In-First-Out Method

The first in first out method, often called FIFO, is based on the assumption that the first merchandise purchased is the first merchandise sold.

Example:

TBC makes 2 purchases on August 17^th and August 28^th. On August 31^st, TBC sells 23 bikes.

To determine the cost of goods sold on August 31^st using FIFO, TBC takes the cost of the 5 remaining units from the August 3^rd purchase at $106 each. Then, they move down to the next purchase on August 17^th and take the cost of 18 units at $115 dollars each. The Cost of Goods Sold for August 31^st is $2,600.

Entry will be:

After the August 31^st sale, TBC has 12 units in inventory: 2 units at $115 each and 10 units at $119 each.

Last-In-First-Out Method

When using the Last-in, First-out (LIFO) method, we assign the most recent costs to the units sold. That leaves the older costs to be used to value ending inventory.

Example:

TBC makes two purchases on August 17^th and August 28^th. On August 31^st, TBC sells 23 bikes.

Using LIFO, TBC takes the cost of the 10 units from the most recent purchase on August 28^th at $119 each. Then, they move up to the next most recent purchase on August 17^th and take the cost of 13 units at $115 each. The Cost of Goods Sold for August 31^st is $2,685.

Entry will be:

After the August 31^st sale, TBC has 12 units in inventory: 5 units at $91 each and 7 units at $115 each.

2011-12-04T03:42:00.000-08:00

.ADJUSTING ENTRIES

Adjusting entries are journal entries made at the end of the accounting period to allocate revenue and expenses to the period in which they actually are applicable. Certain transaction affect the revenue or expenses of two or more accounting periods. The purpose of adjusting entries is to assign to each accounting period appropriate amounts of revenue and expense.

The Need For Adjusting Entries

For the purpose of measuring income and preparing financial statement, the life of a business is divided into a series of accounting periods. This practice enables decisions makers to compare the financial statement of successive periods and to identify significant trends.

Types Of Adjusting Entries

The number of adjusting needed at an end of each accounting period entirely upon the nature of the company’s business activates. However, most adjusting entries fall into one of four categories

1. Converting Assets into Expenses

A cash expenditure (or cost) that will benefit more than one accounting period usually is recorded by debiting an Asset account and by crediting Cash account. Entry will be as given below;

Here and asset purchased with cash $3,000.

The assets account created actually represents the deferral of an expense. In each future period tat benefits from the use of this asset, an adjusting entry is made to allocate a portion of the asset’s cost from the balance sheet to the income statement as an expense. This adjusting entry is recorded by debiting the appropriate expense account a crediting the related asset account. So an adjusting entry will be as below;

In above given example an asset account is decreased with$ 1,000 which was consumed in whole month and office supplies of remaining amount with $2,000 will be consumed in future time period.

Here an Asset is converting into an Expense.

2.Converting Liabilities into Revenue

A business may collect cash in advance for services to be rendered in future accounting periods. Transaction of this nature is usually recorded by debiting Cash and by crediting a liability account may be called Unearned Revenue.

Here the liability account created represents the deferral of a revenue.

In the period that services are actually rendered an adjusting entry is made to allocate a portion a of the liability to the income. By recognize the revenue earned during the period.

Here adjusted entry recorded by debiting the Liability and crediting Revenue Earned for the value of services.

3. Accuring Unpaid Expenses

Expenses may be incurred in current accounting period even though no cash payment will occur until future period. These accrued expenses are recorded by an adjusting entry made at the end of each accounting period. The adjusting entry is recorded by debiting the appropriate account and crediting the related liability.

Normally in all business salaries are paid at the start of months so here salaries are earned by employees, this is business expense and expense is still payable so it will be recorded as liability.

4. Accruing Uncollected Revenue

Revenue may be earned during the current period, even though the collection of cash will occur until a future period. Unrecorded earned revenue, for which no cash has been received, requires an adjusting entry at the end of the accounting period. The adjusting entry is recorded by Debiting the appropriate asset account and by crediting the appropriate revenue account.

2011-11-05T04:36:00.000-07:00

Q4. A researcher estimated that the price elasticity of demand for automobiles in the United States is -1.2, while the income elasticity of demand is 3.0. Next year U.S auto makers intend to increase the average price of automobiles by 5% and they expect the consumers’ disposable income to increase by 3%.

a) If sales of domestically produced automobiles are 8 million this year, how many automobiles do you expect U.S auto makers to sell next year?

b) By how much should domestic automakers increase the price of automobiles if they wish to increase sales by 5% next year?

SOLUTION

(a)

Qx’ = Qx + Qx(dpx/px)Ep + Qx(dI/I) EI

Qx’ = 8 + 8(0.05)X-1.2 + 8(0.03) x 3

Qx’ = 8 + 8(-0.06) + 8(0.09)

Qx’ = 8(1 – 0.06 + 0.09)

Qx’ = 8.24 Million

(b)

If we intend to increase 5% sales then sales becomes 8.4 Million, The equation becomes

8.4 = 8+8+(dpx/px)(-1.2)+2(0.03)(3)

8.4 = 8.72+(-9.6)(dpx/px)

8.4 – 8.72 =(-9.6)(dpx/px)

(dpx/px) = 0.32/9.6

dpx/px) = 0.0333

There should be 3.33% increase in price if company want to increase 5% sales.

Mangerial Economics(solution of Assignment 2)

2011-11-05T04:22:00.000-07:00

Managerial Economics

Assignment 2

Q1. The demand equation faced by DuMont Electronics for its personal computers is given by

P = 10,000 – 4Q

SOLUTION:

a) Write the marginal revenue equation.

We know that

TR = P x Q

TR = (10,000-4Q) x Q

TR = 10,000Q-4Q²

Now taking derivative of TR

dTR/dQ = 10,000Q-4Q²

MR = 10,000-8Q

b) At what price and quantity will marginal revenue be zero?

MR = 0

10,000 – 8Q = 0

10,000 = 8Q

Q = 1000/8

Q = 1,250

Putting the value in Price equation,

P = 10,000 – 4(1250)

P = 5,000

c) If the price is increased from 6,000 to 7,000, what will be the effect on total revenue? What does this imply about price elasticity?

When p = 6,000, then Q will be

6,000 = 10,000 – 4Q

4Q = 10,000 – 6,000

Q = 1,000

TR will be

TR = 10,000(1,000) – 4(1,000)²

TR = 10000000 -4000000

TR = 6,000,000

When p = 7,000, then Q will be

7,000 = 10,000 – 4Q

4Q = 10,000 – 7,000

Q = 750

TR will be

TR = 10,000(750) – 4(750)²

TR = 7500000-2220000

TR = 5,250,000

It tells that there is elastic price elasticity of demand

Q2. The Inquiry club at Jefferson University has compiled a book that exposes the private lives of many of the professors on campus. Economics majors in the club estimate that total revenue from sales of the book is given by the equation

TR = 120Q – 0.1Q³

SOLUTION:

a) Over what output range is demand elastic?

By taking derivative of TR

dTR/dQ=120Q-0.1Q3

0 = 120 – 0.3Q²

120 = 0.3Q²

Q² = 120/0.3

Q² = 400

Q = 20

We know that

TR = PxQ

P = TR/Q

P = 120 – 0.1Q²

P = 120 – 0.1(20)²

P = 120 – 0.1(400)

P = 120 - 40

P = 80

Q = 20 demand is elast

b) Initially, the price is set at $71.6. To maximize total revenue should the price be increased or decreased? Explain

If price is 80, then TR

TR = 120(20) – 0.1(20)²

TR = 2,400 – 800

TR = 1,600

If price is set to 71.6, then TR becomes

TR = 20 x 71.6

TR = 143

2This clearly indicate that price should be increased from 71.6 to 80 in order to get maximum Total revenue

Q3. The coefficient of income in a regression of quantity demanded of commodity on price, income and other variables is 10.

SOLUTION:

a) Calculate the income elasticity of demand for this commodity at income of 10,000 and sales of 80, 000 units. Interpret your answer.

The income elasticity of demand is

E I =dQ/dI X I/Q

So we have

dQ/dI= 10

So by putting its value in E I, we get

E I = 10 X 10,000/80,000

E I = 1.25

Interpretation:

1% increase the Quantity will lead to 1.25% increase . Keeping other thing constant

b) What would be the income elasticity of demand if sales increased from 80,000 to 90,000 units and income rose from 10, 000 to 11,000? What type of good is this commodity?

E I =Q_2-Q₁/I₂-I₁ X I₂+I₁/Q₂+Q₁

E I =90,000-80,000/11,000 X 11,000+10,000/90,000+80,000

E I = 1.24

Value is positive and greater than 1, so goods are luxurious.

]

Q5. The coefficient of the price of gasoline in the regression of the quantity demanded of automobiles (in millions of units) on the price of gasoline (in dollars) and other variables is -14.

SOLUTION:

a) Calculate the cross price elasticity of demand between automobiles and gasoline at the gasoline price of $1per gallon and sales of automobiles of 8 (million units). Interpret your answer

The cross elasticity of demand is

Exy = dQ_x/dP_yX P_y/Q_x

Wher

dQ_x/dP_y= -14

Then

Exy = -14( 1/8)

Exy = -1.75

1 % increase in price of automobiles would result the 1.75% decrease in gasoline

b) What would be the cross price elasticity of demand between automobiles and gasoline if sales of automobiles decline from 8 to 6 with an increase in gasoline price from $1 to $1.20 per gallon? Interpret you answer.,

Exy = Q_x1–Q_x1 /P_y2-P_y1 X P_y2+P_y1/Q_x2+Q_x1

Exy = 6-8/1.2-1 X 1.2 +1/6+8

Exy = -1.57

So Exy is –ve and the goods are complimentary

Q6. The Profit function of a firm selling two products is

Π = 50 Q₁ – Q₁² + 100Q₂ – 4Q₂²

where Q1 and Q2 represent the output rates of product 1 and product 2, respectively. Determine the profit maximizing output rates for the two products and the profit associated with the two output rates.

SOLUTION:

First taking partial derivative w.r.t Q₁, and equate the equation to zero

∂∏/∂Q₁= 50Q₁-Q₁²+100Q₂-4Q₂²

0 = 50 – 2Q₁

Q₁ = 25

Now taking derivative w.r.t Q₂ and equate the equation to zero

∂∏/∂Q₂ =50Q₁-Q₁²+100Q₂-4Q₂²

0 = 100 – 8Q₂

Q₂ = 12.5

Profit will maximum when it sell 25 units of product 1 and 12.5 units of product 2.

Putting the value of Q₁ and Q₂ in profit equation,

Π = 50 (25) – (25⁾² + 100(12.5) – 4(12.5)₂

Π = 1,250

So firm will earn 1250 by producing 25 units of product 1 and 12.5 units of product 2

Q7. Given the Total Cost function

TC = 100Q – Q² +0.3Q³

SOLUTION:

a) The marginal and average cost functions

MC Function

MC =

dTC/dQ = 100Q – Q² +0.3Q³

MC = 100 – 2Q + 0.9Q²

AC = TC/Q

AC = 100Q – Q² +0.3Q³

AC = 100 – Q + 0.3Q²

b) The rate of output that results in minimum average cost.

AC = 100 – Q + 0.3Q²

Taking derivative

dAC/dQ = 100 – Q + 0.3Q²

0 = -1 +0.6Q

1 = 0.6Q

Q = 1.667

Average cost will be min at the rate of output of 1.667 units