CHAPTER 9
B-169
NPV is the PV of the outflows minus the PV of the inflows, so the NPV is:
NPV of the project = –$1,400,000 + 1,214,285.71 = –$185,714.29
The NPV is negative, so we would reject the project.
b.
Here we want to know the minimum growth rate in cash flows necessary to accept the project. The
minimum growth rate is the growth rate at which we would have a zero NPV. The equation for a
zero NPV, using the equation for the PV of a growing perpetuity is:
0 = –$1,400,000 + $85,000/(.13 –
g
)
Solving for
g
, we get:
g
= .0693 or 6.93%
26.
The IRR of the project is:
$58,000 = $34,000/(1+IRR) + $45,000/(1+IRR)
2
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR = 22.14%
At an interest rate of 12 percent, the NPV is:
NPV = $58,000 – $34,000/1.12 – $45,000/1.12
2
NPV = –$8,230.87
At an interest rate of zero percent, we can add cash flows, so the NPV is:
NPV = $58,000 – $34,000 – $45,000
NPV = –$21,000.00
And at an interest rate of 24 percent, the NPV is:
NPV = $58,000 – $34,000/1.24 – $45,000/1.24
2
NPV = +$1,314.26
The cash flows for the project are unconventional. Since the initial cash flow is positive and the