Question

We have two independent and mutually exclusive projects, A and B. Project A requires an initial investment of $1500, and will yield $800 of cash inflows for the next three years. Project B requires an initial investment of $5000, and will yield $1,500 of cash inflows for the next five years. The required return on each project is 10%.

a. What are the net present values of Project A and Project B?

b. What is the problem with using the NPV investment criterion in this case? What alternative criterion should be used?

c. Which project should be chosen?

The cash flows and required return given are all in nominal terms. Given that the inflation rate is 3%, answer the following questions:

d. What is the real rate of return based on the exact Fisher equation?

e. What are the real cash flows from Project A and Project B?

f.   What are the real net present values of Project A and Project B? (Hint: The real NPV should be the same as the nominal NPV.)    

g.       Which project should be chosen based on the real cash flows and real rate of return?

Answer 1

a)

Statement showing NPV for project A

Year	Cash flow	PVIF @ 10%	PV
	A	B	C = A x B
1	800.00	0.9091	727.27
2	800.00	0.8264	661.16
3	800.00	0.7513	601.05
Total of PV of cash inflow	1989.48
Less : Initial Investment	1500.00
NPV	489.48

Thus NPV of project A = $489.48

Statement showing NPV of project B

Year	Cash flow	PVIF @ 10%	PV
	A	B	C = A x B
1	1500.00	0.9091	1363.64
2	1500.00	0.8264	1239.67
3	1500.00	0.7513	1126.97
4	1500.00	0.6830	1024.52
5	1500.00	0.6209	931.38
Total of PV of cash inflow	5686.18
Less : Initial Investment	5000.00
NPV	686.18

Thus NPV of project B = $686.18

b) Here project A and project B have different life and thus not comparatble.Hence NPV method might not provide us with proper solution. Alternatively we should find Equivalent annual benefit of both the project to select which project should be undertaken

c) Equivalent annual benefit of project A = NPV/PVIFA(10%,3years)

=489.48/(0.9091 + 0.8264 + 0.7513)

= 489.48 / 2.4869

= 196.83 $

Equivalent annual benefit of project B = NPV/PVIFA(10%,5years)

= 686.18 / (0.9091 + 0.8264 + 0.7513 + 0.6830 + 0.6209)

= 686.18 / 3.7908

= 181.01 $

Thus on basis of Equivalent annual benefit project A should be selected

d) Real rate of return = (1+ Nominal rate of return) / (+ Inflation rate) -

= (1+10%)/(1+3%) - 1

= (1+0.1)/(1+0.03) - 1

= 1.1/1.03 - 1

= 1.068 - 1

= 0.068

i.e 6.8%