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Sample of Finance Assignment Illustrations and Solutions:

Illustration: 1 Assume that a deposit is to be made at year zero into an account that

will earn 8% compounded annually. It is desired to withdraw $ 5,000 three years from

now and $ 7,000 six years from now. What is the size of the year zero deposit that will

produce these future payments.

Solution:

Let the initial deposit be sum of the present values of the two later withdrawals by using

the present value table.

PV = FV × PVF(r,n)

PV = $ 5,000 × PVF(8%,3) + $ 7,000 × PVF(8%,6)

PV = $ 5,000 (.794) + $7,000 (.630)

PV = $ 3,970 + $ 4,410

PV = $ 8,380

The amount of $ 8,380 grows to a value of $ 10,559 in three years ; $ 5,000 is

withdrawn then, leaving $ 7,000. Therefore, an amount of $ 8,380 deposited today will

result in the desired withdrawals.

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Illustration: 2 Assume that a $ 20,00,000 plant expansion is to be financed as follows

: The firm makes a 15% down payment and borrows the remainder at 9% interest rate.

The loan is to be repaid in 8 equal annual installments beginning 4 years from now.

What is the size of the required annual loan payments.

Solution:

The firm borrows $ 17,00,000 (85%). Compound interest occurs over the entire 11

years of the life of the loan. In order obtain the required annual loan payment., two

additional points have to be remembered : (1) the loan repayment will be computed by

using a present –value annuity table; and (2) the present value of an annuity located

one year before the first payment.

To compute the size of the annual payment, first compute the amount owed at the end

of year 3 (one year before the first payment). By compounding $ 17,00,000 for three

years at 9%,

FV = PV (1 + 𝒓)𝒏

FV = $ 17,00,000 (1 + .𝟎𝟗)𝟑

FV = $ 22,01,550

Now the FV becomes the present value of the 8-payment annuity discounted at 9%. So,

compute the equal yearly payment by using Equation 2.2B

PV = Annuity Amount 𝑃𝑉𝐴𝐹(𝑟 ,𝑛)

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PV = Annuity Amount × 𝑃𝑉𝐴𝐹(𝟗% 𝟖)

$ 22,01,500 = Annuity Amount × (5.535)(𝟗% 𝟖)

Annuity Amount = $ 3,97,750.

The plant expansion financing plan can be summarized as follows :- Down payment at

year zero of $ 3,00,000; the balance borrowed at 9% interest. Eight yearly loan

repayments of $ 3,97,750 are to be made beginning at the end of year 4.

Illustration: 3 A 10-year savings annuity of $ 2,000 per year is beginning at the end

of current year. The payment of retirement annuity is to begin 16 years from now (the

first payment is to be received at the end of year 16) and will continue to provide a 20-

year payment annuity. If this plan is arranged through a savings bank that pays interest

@ 7% per year on the deposited funds, what is the size of the yearly retirement annuity

that will result.

Solution :

Obtain the compounded amount of the 10-payment savings annuity of $ 2,000

corresponding to 10 payments and 7%

FV = Annuity Amount × 𝐶𝑉𝐴𝐹(𝑡 ,𝑛)

FV = $ 2,000 × CVA𝐹(7%10)

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FV = 2,000 (13.816)

FV = $ 27,632

The amount of $ 27,632 is available immediately after the last payment. Now, compound

the amount of $ 27,632 for 5 years as a single payment at 7%. This will give the total

cumulative value in the beginning of year 16.

FV = PV × CV𝐹(𝑟 ,𝑛)

FV = PV × CV𝐹(7% 5)

FV = 27,632 (1,403)

FV = $ 38.768

Finally, obtain the size of the equal retirement annuity payment by using the amount of

$ 38,768 as the present value of the retirement annuity, Substitute the values

corresponding to 20 payments and 7% as follows :

PV = Annuity Amount × 𝑃𝑉𝐴𝐹(𝑟 ,𝑛)

PV = Annuity Amount × 𝑃𝑉𝐴𝐹(7%,5)

$ 38.768 = Annuity Amount (10.594)

Annuity Amount = $ 3,659

Thus, the savings annuity of $ 2,000 for 10 years will produce a 20 years retirement

annuity of $ 3,659 per year starting at the end of 16 years from now.

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