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CHAPTER 9
B161
12.
a.
The IRR is the interest rate that makes the NPV of the project equal to zero. The equation for the IRR of
Project A is:
0 = –$43,000 + $23,000/(1+IRR) + $17,900/(1+IRR)
2
+ $12,400/(1+IRR)
3
+ $9,400/(1+IRR)
4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR = 20.44%
The equation for the IRR of Project B is:
0 = –$43,000 + $7,000/(1+IRR) + $13,800/(1+IRR)
2
+ $24,000/(1+IRR)
3
+ $26,000/(1+IRR)
4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR = 18.84%
Examining the IRRs of the projects, we see that the IRR
A
is greater than the IRR
B
, so IRR decision
rule implies accepting project A. This may not be a correct decision; however, because the IRR
criterion has a ranking problem for mutually exclusive projects. To see if the IRR decision rule is
correct or not, we need to evaluate the project NPVs.
b.
The NPV of Project A is:
NPV
A
= –$43,000 + $23,000/1.11+ $17,900/1.11
2
+ $12,400/1.11
3
+ $9,400/1.11
4
NPV
A
= $7,507.61
And the NPV of Project B is:
NPV
B
= –$43,000 + $7,000/1.11 + $13,800/1.11
2
+ $24,000/1.11
3
+ $26,000/1.11
4
NPV
B
= $9,182.29
The NPV
B
is greater than the NPV
A
, so we should accept Project B.
c.
To find the crossover rate, we subtract the cash flows from one project from the cash flows of the
other project. Here, we will subtract the cash flows for Project B from the cash flows of Project A.
Once we find these differential cash flows, we find the IRR. The equation for the crossover rate is:
Crossover rate: 0 = $16,000/(1+R) + $4,100/(1+R)
2
– $11,600/(1+R)
3
– $16,600/(1+R)
4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
R = 15.30%
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This document was uploaded on 10/31/2011 for the course FIN 3403 at University of Florida.
 Spring '06
 Tapley
 Finance, Interest, Interest Rate

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