Chapter 9: Net Present Value and Other Investment Criteria
Page 294-295 Questions: 14, 15, 16, 17 19
14.
a.
The equation for the NPV of the project is:
NPV = –$45,000,000 + $78,000,000/1.1 – $14,000,000/1.1
2
= $13,482,142.86
The NPV is greater than 0, so we would accept the project.
b.
The equation for the IRR of the project is:
0 = –$45,000,000 + $78,000,000/(1+IRR) – $14,000,000/(1+IRR)
2
From Descartes rule of signs, we know there are potentially two IRRs since the cash
flows change signs twice. From trial and error, the two IRRs are:
IRR = 53.00%, –79.67%
When there are multiple IRRs, the IRR decision rule is ambiguous. Both IRRs
are correct, that is, both interest rates make the NPV of the project equal to zero.
If we are evaluating whether or not to accept this project, we would not want to
use the IRR to make our decision.
15.
The profitability index is defined as the PV of the cash inflows divided by the PV of
the cash outflows. The equation for the profitability index at a required return of 10
percent is:
PI = [$7,300/1.1 + $6,900/1.1
2
+ $5,700/1.1
3
] / $14,000 = 1.187
The equation for the profitability index at a required return of 15 percent is:
PI = [$7,300/1.15 + $6,900/1.15
2
+ $5,700/1.15
3
] / $14,000 = 1.094
The equation for the profitability index at a required return of 22 percent is:
PI = [$7,300/1.22 + $6,900/1.22
2
+ $5,700/1.22
3
] / $14,000 = 0.983
We would accept the project if the required return were 10 percent or 15 percent
since the PI is greater than one. We would reject the project if the required return
were 22 percent since the PI is less than one.
16.