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Lesson 5 Homework Solution
100 Points
Chapter 9
Q1: Describe how NPV is calculated, and describe the information this measure provides about a
sequence of cash flows. What is the NPV criterion decision rule?
Example for Question 2: Calculating IRR: A firm evaluates all of its projects by applying the IRR rule. If
the required return is 14 percent, should the firm accept the following project?
Yea
r Cash Flow
0
1
2
3
−$34,000
15,000
17,000
13,000
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 = –$34,000 + $15,000/(1+IRR) + $17,000/(1+IRR)2 + $13,000/(1+IRR)3
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR = 15.80%
Since the IRR is greater than the required return, we would accept the project.
(Please also see Homework 5 Excel Examples for computation on Excel)
Q2: Calculating IRR: A firm evaluates all of its projects by applying the IRR rule. If the required return is
12.5 percent, should the firm accept the following project?
Yea
r Cash Flow
0
1
2
3
−$42,000
12,000
18,000
28,000
(Please follow above example to solve this question)
Example for Question 3: NPV versus IRR: Bruin, Inc., has identified the following two mutually exclusive
projects:
Year
Cash Flow
(A) Cash Flow (B)
0
1
2
3
4
−$37,500
17,300
16,200
13,800
7,600
−$37,500
5,700
12,900
16,300
27,500
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?
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:
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 = –$37,500 + $17,300/(1+IRR) + $16,200/(1+IRR)2 + $13,800/(1+IRR)3 + $7,600/(1+IRR)4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find
that:
IRR = 19.71%
The equation for the IRR of Project B is:
0 = –$37,500 + $5,700/(1+IRR) + $12,900/(1+IRR)2 + $16,300/(1+IRR)3 + $27,500/(1+IRR)4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find
that:
IRR = 18.76%
Examining the IRRs of the projects, we see that IRRA is greater than IRRB, so the 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:
NPVA = –$37,500 + $17,300/1.11+ $16,200/1.112 + $13,800/1.113 + $7,600/1.114
NPVA = $6,330.67
And the NPV of Project B is:
NPVB = –$37,500 + $5,700/1.11 + $12,900/1.112 + $16,300/1.113 + $27,500/1.114
NPVB = $8,138.59
The NPVB is greater than the NPVA, so we should accept Project B.
(Please also see Homework 5 Excel Examples for computation on Excel)
Q3: NPV versus IRR: Bruin, Inc., has identified the following two mutually exclusive projects:
Year
Cash Flow
(A) Cash Flow (B)
0
1
2
3
4
−$40,500
18,000
16,000
14,800
10,600
−$40,500
6,000
12,700
16,000
30,500
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?
b. If the required return is 12 percent, what is the NPV for each of these projects? Which project will
the company choose if it applies the NPV decision rule?
(Please follow above example to solve this question)
Chapter 10
Q4: In the context of capital budgeting, what is an opportunity cost?
Example for Question 5: Calculating Project Cash Flow from Assets: In the previous problem, suppose
the project requires an initial investment in net working capital of $250,000, and the fixed asset will
have a market value of $180,000 at the end of the project. What is the project’s Year 0 net cash flow?
Year 1? Year 2? Year 3? What is the new NPV?
Solution: The cash outflow at the beginning of the project will increase because of the spending on NWC.
At the end of the project, the company will recover the NWC, so it will be a cash inflow. The sale of
the equipment will result in a cash inflow, but we also must account for the taxes that will be paid on
this sale. So, the cash flows for each year of the project will be:
Year Cash Flow
0 –$2,570,000 = –$2,320,000 – 250,000
1 1,019,550
2 1,019,550
3 1,411,750 = $1,019,550 + 250,000 + 180,000 + ($0 – 180,000)(.21)
And the NPV of the project is:
NPV = –$2,570,000 + $1,019,550(PVIFA12%,2) + ($1,411,750/1.123)
NPV = $157,947.28
(Please also see Homework 5 Excel Examples for computation on Excel)
Q5: Calculating Project Cash Flow from Assets: In the previous problem, suppose the project requires
an initial investment in net working capital of $200,000, and the fixed asset will have a market value of
$175,000 at the end of the project. What is the project’s Year 0 net cash flow? Year 1? Year 2? Year 3?
What is the new NPV?
Please follow above example to solve this question)
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