Answer to Question #157010 in Financial Math for Wachira Ann Wangari

Question

a) Martin is setting up a business ABC and his estimated cash flows are as follows: his initial capital was kshs 60,000. He projects a loss of kshs 10,000 then a profit of kshs 15,000 the following year and the preceding three years a constant profit of kshs20,000 respectively. His required rate of return is 15%. Calculate

I) payback period

II) NPV

III) Comment on the above methods

b) Suppose a loan of kshs 5,000,000 is to be repaid over 5-year period. If an interest rate of 8% per year is charged annually on the unpaid balance ,prepare an amortization schedule for the loan.

Answer 1

Question 1a,

Year cashflow cumulative cashflow

kshs kshs

0 (60,000) (60,000)

1 (10,000) (70,000)

2 15000 (55,000)

3 20000 (35,000)

4 20000 (15,000)

5 20000 5,000

Payback period= 4years + ((kshs 1500/kshs 20000) * 12 months)

Therefore, PBP = 4 years and 9 month.

Question 1b,

Year cashflow Dcf(15%) present value

kshs kshs

0 (60,000) 1.0000 (60,000)

1 (10,000) 0.8696 (8696)

2 15,000 0.7561 11341.5

3 20,000 0.6575 13150

4 20,000 0.5718 11436

5 20,000 0.4972 9944

Total=(22,824.5)

DCF means discounted cashflow

Figures in bracket denote negative number.

The final answer of NPV i.e *Figure in bracket* was obtained by using the DCF to discounting all future cash flow from the capital investment project and then subtracting the initial cost of project.

Question 1c,

Commenting on Payback period

From the computation in 1a above, it is observed that the calculated payback period is 4 years and 9 month i.e 57 months. This means that the project is viable since it takes the original cost of the project to be recovered from the proposed 5 years earnings of the project. The earnings of the project represent the cash inflow from years 1 to year 5.

Commenting on Net present value result,

The project should be rejected because the NPV calculated represents an immediate increase in the wealth of an organization, if the project is acceptable.

However, the result above, it can be concluded that the firm's wealth will decrease by kshs 22824.5, if it is acceptable.

Question 2,

Determination of Instalment payment;

$P=\frac{A{(1-(1+r)^-n)}}{r}$

P= loan borrowed

A= Annual Installment

r= interest rate

n= number of years

$5000000=\frac{A{(1-(1+0.08)^-5)}}{0.08}$

A= kshs 1, 252, 282.27

Amortization schedule table is presented in jpeg format