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Prof. Q. Ma, HADM 2222 Fall 2009
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HADM 2222 Fall 2009, Prof. Q. Ma
Homework assignment
#4
[Due 11:59 a.m. Friday, October 16, 2009, Statler 435 drop box]
1.
What is the IRR of the following set of cash flows?
Year Cash
Flow
0
18,000
1
9,800
2
7,500
3
7,300
Solution:
The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the
IRR for this project is:
0 = –$18,000 + $9,800/(1+IRR) + $7,500/(1+IRR)
2
+ $7,300/(1+IRR)
3
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR
= 18.49%
2.
Bumble’s Bees, Inc., has identified the following two mutually exclusive projects:
Year
Cash Flow A
Cash Flow B
0
37,000
37,000
1
19,000
6,000
2
14,500
12,500
3
12,000
19,000
4
9,000
23,000
a. What is the IRR for each of these projects? Using the IRR decision rule, which project should the
company accept? Is this decision necessarily correct?
Solution:
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 = –$37,000 + $19,000/(1+IRR) + $14,500/(1+IRR)
2
+ $12,000/(1+IRR)
3
+ $9,000/(1+IRR)
4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR
= 20.30%
The equation for the IRR of Project B is:
0 = –$37,000 + $6,000/(1+IRR) + $12,500/(1+IRR)
2
+ $19,000/(1+IRR)
3
+ $23,000/(1+IRR)
4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR
= 18.55%
Examining the IRRs of the projects, we see that the IRRA is greater than the IRRB, 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.
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b. If the required return is 11 percent, what is the NPV for each of these projects? Which project will the
company choose if it applies the NPV decision rule?
Solution:
The NPV of Project A is:
NPVA = $6,588.52
NPVA = –$37,000 + $19,000/1.11+ $14,500/1.11
2
+ $12,000/1.11
3
+ $9,000/1.11
4
And the NPV of Project B is:
NPVB = $7,594.13
NPVB = –$37,000 + $6,000/1.11 + $12,500/1.11
2
+ $19,000/1.11
3
+ $23,000/1.11
4
The NPVB is greater than the NPVA, so we should accept Project B.
c. Over what range of discount rates would the company choose project A? Project B? At what discount
rate would the company be indifferent between these two projects? Explain.
Solution:
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