Question

In: Finance

We have two independent and mutually exclusive projects, A and B. Project A requires an initial...

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?

Solutions

Expert Solution

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%


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