Question

We have two independent and mutually exclusive projects, A and B. Project A requires an initial investment of $1000, and will yield $500 of cash inflows for the next three years. Project B requires an initial investment of $3,500, and will yield $1,000 of cash inflows for the next five years. The required return on both projects is 10%.                                                                                                   (13 marks total)

a.  What are the net present values of Project A and Project B?               (2 marks)

b.  What is the problem with using the NPV investment criterion in this case? What alternative criterion should be used?                                        (1 mark)

c.  Which project should be chosen?                                                 (2 marks)

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?       (1 mark)

e.  What are the real cash flows from Project A and Project B?                (2 marks)

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.)                                    (2 marks)

g.  Which project should be chosen based on the real cash flows and real rate of return?                                                                              (3 marks)

Answer 1

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Answer:

Project A Initial cost of investment = $1,000 Annual cash inflows = $500 Term = 3 Years Average annual cash inflows = (Even annual cash inflow * Term) / Term = $500 * 3/3 = $500 Real rate of return of Project A (Average rate of return) = Average annual cash inflows / Cost of investment = $500 / $1,000 = 0.50 = 50% Required rate of return = 10% NPV = Present value of cash inflows - Present value of cash outflows = Annual cash inflows * PVIFARR, n) - Initial cost of investment = $500 * PVIFA(10%, 3) - $1,000 = $500 * 2.4868 - $1,000 = $243.4 Project B Initial cost of investment = $3,500 Annual cash inflows = $1,000 Term = 5 Years Average annual cash inflows = (Even annual cash inflow * Term ) / Term = $1,000 * 5/5 = $1.000 Real rate of return of Project B = $1,000 / $3,500 = 0.2857143 = 28.57% Required rate of return = 10% NPV = $1,000 * PVIFA(10%, 5) - $3,500 = $1,000 * 3.7908 - $3,500 = $290.8 As per real rate of return we should select Project A and as per NPV basis we should select Project B. However both the projects have different lifes and cost of investment, it is better to select project on the basis of real rate of return. Hence we should select Project A