Question

A company is considering an investment proposal to install new milling controls. The project will cost Kes50,000. The facility has a life expectancy of five years and no salvage value. The company’s tax rate is 40%. The estimated cash flows from the proposed investment proposal are as follows:

Year CF
1 10,000
2 11,000
3 14,000
4 15,000
5 25,000

Compute:
a. Accounting Rate of Return and advise management if the required rate of return is 6 %

b. Traditional Payback period and advise management on the feasibility of the project

c. Discounted payback period at 6% discounting factor

d. Net present value at 6% discounting factor and advise management on the project’s feasibility

e. Net present value at 15% discounting factor and advise management on the project’s feasibility

f. Internal rate of return and explain its significance to the firm

g. Profitability Index at 10% discounting factor

Answer 1

First we will calculate the NPV of the project.

a) NPV of the project with 6% required rate of return:

Particulars
Cash Outflow	-50000
Cash inflow at Year 1	10000
Cash inflow at Year 2	11000
Cash inflow at Year 3	14000
Cash inflow at Year 4	15000
Cash inflow at Year 5	25000
Cost of capital	6.00%
Present value of cash flows	₹ 61,541.45
Net present value of cash flow	₹ 11,541.45

Internal Rate of Return

12.95%

we have used the NPV and IRR formula in excel to get the above values. The accounting rate of return is the return of un-discounted cash inflows over the cash outflows

= (10000 + 11000 + 14000 + 15000 + 25000)/50000

= 50%

b) Payback period = 4 years. The initial investment of Cash Outflows will be recovered in 4 years by the un-discounted cash inflows. (10000 + 11000 + 14000 + 15000 = 50000)

c) Discounted payback period: This needs to be calculated as the time taken to recover the cash outflow by discounting the cash inflow at 6%)

Particulars	Amount	Discount Rate	Discounted amount	Amount recovered
Cash Outflow	-50000
Cash inflow at Year 1	10000	1.060	9433.96	-40566.04
Cash inflow at Year 2	11000	1.123	9795.19	-30770.85
Cash inflow at Year 3	14000	1.191	11754.83	-19016.02
Cash inflow at Year 4	15000	1.262	11885.90	-7130.12
Cash inflow at Year 5	25000	1.338	18684.60	11554.48

It takes 4.382 years to recover the initial cash outflow of the project.

d) NPV is calculated above, please find the calculations below:

Particulars
Cash Outflow	-50000
Cash inflow at Year 1	10000
Cash inflow at Year 2	11000
Cash inflow at Year 3	14000
Cash inflow at Year 4	15000
Cash inflow at Year 5	25000
Cost of capital	6.00%
Present value of cash flows	₹ 61,541.45
Net present value of cash flow	₹ 11,541.45

Internal Rate of Return

12.95%

e) NPV at 15% discounting factor

Particulars
Cash Outflow	-50000
Cash inflow at Year 1	10000
Cash inflow at Year 2	11000
Cash inflow at Year 3	14000
Cash inflow at Year 4	15000
Cash inflow at Year 5	25000
Cost of capital	15.00%
Present value of cash flows	₹ 47,224.18
Net present value of cash flow	₹ -2,775.82

The project is not feasible as the NPV of the project is negative so the management should not take this project if the discounting factor is 15%

f) IRR is the rate of return which measures the return in the percentage terms if the NPV of the project is Zero. The IRR of the above project is 12.95% It is useful to compare the rate of return from one project to the other. For eg: if the IRR of the project is greater than the discounting factor then we can accept the project and if its less than the discounting factor then we can accept the project. For our project in the example above when the discounting factor is 6% we can accept the project and when it increases to 15% the NPV becomes negative. So the IRR is important to asses the project returns.

g) profitability index: its calculated as the Present value of future the cash flows/initial investment

PV of future cash flows = 61,541.45

Initial Investment = 50,000

Profitability Index: 61,541.45/50,000

= 1.23