CHAPTER 9
NET PRESENT VALUE AND OTHER
INVESTMENT CRITERIA
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps.
Due to space and readability constraints, when these intermediate steps are included in this solutions
manual, rounding may appear to have occurred. However, the final answer for each problem is found
without rounding during any step in the problem.
Basic
13.
The IRR is the interest rate that makes the NPV of the project equal to zero. The equation to calculate
the IRR of Project X is:
0 = –$15,000 + $8,150/(1+IRR) + $5,050/(1+IRR)
2
+ $6,800/(1+IRR)
3
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR = 16.57%
For Project Y, the equation to find the IRR is:
0 = –$15,000 + $7,700/(1+IRR) + $5,150/(1+IRR)
2
+ $7,250/(1+IRR)
3
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR = 16.45%
To find the crossover rate, we subtract the cash flows from one project from the cash flows of the other
project, and find the IRR of the differential cash flows. We will subtract the cash flows from Project Y
from the cash flows from Project X. It is irrelevant which cash flows we subtract from the other.
Subtracting the cash flows, the equation to calculate the IRR for these differential cash flows is:
Crossover rate: 0 = $450/(1+R) – $100/(1+R)
2
– $450/(1+R)
3
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
R = 11.73%
The table below shows the NPV of each project for different required returns. Notice that Project Y
always has a higher NPV for discount rates below 11.73 percent, and always has a lower NPV for
discount rates above 11.73 percent.
R