Time value of Money(Financial Management)

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

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.

.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.

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.