Question

You are interested in an investment project that costs $ 46125 initially. The investment has a 5​-year horizon and promises future​ end-of-year cash inflows of $ 12300​, $ 12915​, $ 11685​, $ 9225​, and $ 8610​, respectively. Your current opportunity cost is 6.84 % per year.​ However, the Fed has stated that inflation may rise by 1.5 % or may fall by the same amount over the next 5 years.

Assume a direct positive impact of inflation on the prevailing rates​ (Fisher effect) and answer the following​ questions: (Assume that inflation has an impact on the opportunity​ cost, but that cash flows are contractually fixed and are not affected by​ inflation.)

a. What is the net present value​ (NPV) of the investment under the current required rate of​ return?

b. What is the net present value​ (NPV) of the investment under a period of rising​ inflation?

c. What is the net present value​ (NPV) of the investment under a period of falling​ inflation?

Answer 1

PV = Original value/(1+Opportunity cost)^t

NPV = Sum of all PV

Using the above formulae

a) Opportunity cost = 6.84%

Year	0	1	2	3	4	5
Initial Investment	-46,125
Cash inflows		12,300	12,915	11,685	9,225	8,610
PV of Net Cash Flow	-46,125	11,512.54	11,314.27	9,581.36	7,079.96	6,184.92
Opportunity cost	6.84%
NPV	-451.95

b) Inflation rise by 1.5%

1 + Nominal IR = (1+ Real IR)(1 + Inflation)

1 + NIR = (1+0.0684)(1+ 0.015)

NIR = 1.0844 - 1 = 8.44%

Year	0	1	2	3	4	5
Initial Investment	-46,125
Cash inflows		12,300	12,915	11,685	9,225	8,610
PV of Net Cash Flow	-46,125	11,342.68	10,982.86	9,163.47	6,671.27	5,741.90
Opportunity cost	8.44%
NPV	-2,222.82

b) Inflation fall by 1.5%

1 + Nominal IR = (1+ Real IR)(1 + Inflation)

1 + NIR = (1+0.0684)(1- 0.015)

NIR = 1.0524 - 1 = 5.24%

Year	0	1	2	3	4	5
Initial Investment	-46,125
Cash inflows		12,300	12,915	11,685	9,225	8,610
PV of Net Cash Flow	-46,125	11,687.57	11,660.92	10,025.04	7,520.44	6,669.59
Opportunity cost	5.24%
NPV	1,438.55

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