CHAPTER 5 –
25. First, we need to find the future value of the cash flows for the one year in which they are blocked by
the government. So, reinvesting each cash inflow for one year, we find:
So, the NPV of the project is:
And the IRR of the project is:
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find
that:
IRR = 10.92%
While this may look like a MIRR calculation, it is not a MIRR, rather it is a standard IRR
26. a. We can apply the growing perpetuity formula to find the PV of Stream A. The perpetuity
formula values the stream as of one year before the first payment. Therefore, the growing
perpetuity formula values the stream of cash flows as of Year 2. Next, discount the PV as of the
end of Year 2 back two years to find the PV as of today, Year 0. Doing so, we find:
We can apply the perpetuity formula to find the PV of Stream B. The perpetuity formula
discounts the stream back to Year 1, one period prior to the first cash flow. Discount the PV as
of the end of Year 1 back one year to find the PV as of today, Year 0. Doing so, we find:
b. If we combine the cash flow streams to form Project C, we get:
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CHAPTER 5 –
Project C = Project A + Project B
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we
find that:
c. The correct decision rule for an investing-type project is to accept the project if the discount
rate is below the IRR. Since there is one IRR, a decision can be made. At a point in the future,
the cash flows from Project A will be greater than those from Project B. Therefore, although
27. To answer this question, we need to examine the incremental cash flows. To make the projects
equally attractive, Project Billion must have a larger initial investment. We know this because the
subsequent cash flows from Project Billion are larger than the subsequent cash flows from Project
Million. So, subtracting the Project Million cash flows from the Project Billion cash flows, we find
the incremental cash flows are:
Incremental
Year cash flows
Now we can find the present value of the subsequent incremental cash flows at the discount rate, 12
percent. The present value of the incremental cash flows is:
28. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR of the
project is:
Even though it appears there are two IRRs, a spreadsheet, financial calculator, or trial and error will
not give an answer. The reason is that there is no real IRR for this set of cash flows. If you examine
the IRR equation, what we are really doing is solving for the roots of the equation. Going back to
high school algebra, in this problem we are solving a quadratic equation. In case you don’t
remember, the quadratic equation is:
2
CHAPTER 5 –
x =
−b±
√
b2−4ac
2a
In this case, the equation is:
x =
−(−26 ,000 )±
√
(−26 ,000 )2−4(20 ,000 )(13 ,000 )
2(20 ,000 )
The square root term works out to be:
676,000,000 – 1,040,000,000 = –364,000,000
The square root of a negative number is a complex number, so there is no real number solution,
meaning the project has no real IRR.
Calculator Solutions
1. b. Project A
CFo–$20,000 CFo–$24,000
C01 $13,200 C01 $14,100
F01 1F01 1
5.
CFo–$24,000
C01 $9,700
F01 1
6. Project A Project B
CFo–$5,700 CFo–$3,450
C01 $2,750 C01 $1,380
F01 1F01 1
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7.
CFo0
C01 $59,000
F01 7
I = 13%
10.
CFo$9,400
C01 –$4,500
F01 1
C02 –$3,100
F02 1
CFo$9,400 CFo$9,400
C01 –$4,500 C01 –$4,500
F01 1F01 1
11. a. Deepwater fishing Submarine ride
CFo–$850,000 CFo–$1,650,000
C01 $320,000 C01 $810,000
F01 1F01 1
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CHAPTER 5 –
b.
CFo–$800,000
C01 $490,000
F01 1
c. Deepwater fishing Submarine ride
CFo–$850,000 CFo–$1,650,000
C01 $320,000 C01 $810,000
F01 1F01 1
12. Project I
CFo$0 CFo–$35,000
C01 $19,800 C01 $19,800
F01 3F01 3
I = 10% I = 10%
Project II
CFo$0 CFo–$16,000
C01 $9,400 C01 $9,400
F01 3F01 3
I = 10% I = 10%
13.
CFo–$78,000,000 CFo–$78,000,000
C01 $110,000,000 C01 $110,000,000
F01 1F01 1
5
CHAPTER 5 –
$11,256,198.35
Financial calculators will only give you one IRR, even if there are multiple IRRs. Using trial and
14. b. Board game DVD
CFo–$950 CFo–$2,100
C01 $700 C01 $1,500
F01 1F01 1
c. Board game DVD
CFo–$950 CFo–$2,100
C01 $700 C01 $1,500
F01 1F01 1
d.
CFo–$1,150
C01 $800
F01 1
15. a. CDMA G4 Wi-Fi
CFo0CFo0CFo0
C01 $22,000,000 C01 $20,000,000 C01 $36,000,000
F01 1F01 1F01 1
C02 $15,00,000 C02 $50,000,000 C02 $64,000,000
6
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PICDMA = $36,153,268.22 / $16,000,000 = 2.26
b. CDMA G4 Wi-Fi
CFo–$16,000,000 CFo–$24,000,000 CFo–$40,000,000
C01 $22,000,000 C01 $20,000,000 C01 $36,000,000
F01 1F01 1F01 1
16. b. AZM AZF
CFo–$495,000 CFo–$960,000
C01 $352,000 C01 $385,000
F01 1F01 1
C02 $198,000 C02 $464,000
c. AZM AZF
CFo–$495,000 CFo–$960,000
C01 $352,000 C01 $385,000
F01 1F01 1
17. a. Project A Project B Project C
CFo0CFo0CFo0
C01 $165,000 C01 $300,000 C01 $180,000
F01 1F01 1F01 1
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b. Project A Project B Project C
CFo–$225,000 CFo–$450,000 CFo–$225,000
C01 $165,000 C01 $300,000 C01 $180,000
F01 1F01 1F01 1
18. b. Dry prepeg Solvent prepeg
CFo–$1,700,000 CFo–$750,000
C01 $1,100,000 C01 $375,000
F01 1F01 1
C02 $900,000 C02 $600,000
c. Dry prepeg Solvent prepeg
CFo–$1,700,000 CFo–$750,000
C01 $1,100,000 C01 $375,000
F01 1F01 1
d.
CFo–$950,000
C01 $725,000
F01 1
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19. b. NP-30 NX-20
CFo–$660,000 CFo–$420,000
C01 $222,000 C01 $120,000
F01 5F01 1
C02 C02 $132,000
F02 F02 1
c. NP-30 NX-20
CFo0CFo0
C01 $222,000 C01 $120,000
F01 5F01 1
C02 C02 $132,000
F02 F02 1
d. NP-30 NX-20
CFo–$660,000 CFo–$420,000
C01 $222,000 C01 $120,000
F01 5F01 1
C02 C02 $132,000
F02 F02 1
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28.
CFo$20,000
C01 –$26,000
F01 1
10