11. NPV versus IRR – consider the following cash flows on two mutually exclusive projects for the Bahamas Recreation Corporation (BRC). Both projects requires an annual return of 14 percent.
| year | Deepwater Fishing | New Submarine Ride |
| 0 | -$750000 | -$2100000 |
| 1 | 310000 | 1200000 |
| 2 | 430000 | 760000 |
| 3 | 330000 | 850000 |
As financial analyst for BRC, you are asked the following questions:
a. If your decision rule is to accept the project with the greater IRR, which project should you choose?
b. Because you are fully aware of the IRR rule’s scale problem, you calculate the incremental IRR for the cash flows. Based on your computation, which project should you choose?
c. To be prudent, you compute the NPV for both projects. Which project should you choose? Is it consistent with the incremental IRR rule?
Answer:
a. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR for each project is:
Deepwater Fishing IRR:
0 = C0 + C1 /(1+IRR) + C2/(1+IRR)2 + C3/(1+IRR)3
0 = -$750,000 + 310,000/(1+IRR) + 430,000/(1+IRR)2 + 330,000/(1+IRR)3
IRR =
New Submarine Ride IRR:
0 = C0 + C1 /(1+IRR) + C2/(1+IRR)2 + C3/(1+IRR)3
0 = -$2,100,000 + 1,200,000/(1+IRR) + 760,000/(1+IRR)2 + 850,000/(1+IRR)3
IRR =
a. To calculate the incremental IRR, we subtract the smaller project cash flows from the larger project’s cash flows. In this case, we subtract the Deepwater Fishing Cash flows from the Sub Marine Ride cash flows. The incremental IRR is the IRR of these incremental cash flows. So, the incremental cash flows of the sub marine ride are:
| | year 0 | year 1 | year 2 | year 3 |
| Submarine Ride | ($2100000) | 1200000 | 760000 | 850000 |
| Deep water Fishing | ($750000) | 310000 | 430000 | 330000 |
| Submarine - Fishing | ($1350000) | 890000 | 330000 | 520000 |
Setting the present value of these incremental cash flows equal to zero, we find the incremental IRR is:
0 = C0 + C1 /(1+IRR) + C2/(1+IRR)2 + C3/(1+IRR)3
0 = -$1350000 + 890000/(1+IRR) + 330000/(1+IRR)2 + 520000/(1+IRR)3
Incremental IRR = 15.78%
a. The NPV is the sum of the present value of the cash flows from the project, so the NPV of each project will be:
Deepwater Fishing:
NPV = -$750,000 + $310,000/ 1.14 + $430,000/(1.14)2 +$330,000/(1.14)3
NPV = $75 548.08
Submarine Ride:
NPV = -$2,100,000 + $1,200,000/1.14 + $760,000/1.142 + $850,000/1.143
NPV = $111 169.72
Reference: Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition. Chapter 5, questions number 11, page 164.
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