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10-19 a. The project’s expected cash flows are as follows (in millions of dollars):
Time Net Cash Flow
We can construct the following NPV profile:
Discount Rate NPV
0% ($1,700,000)
9 (29,156)
10 120,661
Answers and Solutions: 10 - 1
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
N P V ( M i l l i o n s o f D o l l a r s )
M a x i m u m
N P V a t 8 0 . 5 %
D i s c o u n t
R a t e ( % )
I R R
1
= 9 . 2 %
I R R
2
= 4 2 0 %
N P V a p p r o a c h e s - $ 4 . 4 a s
t h e c o s t o f c a p i t a l
a p p r o a c h e s
3
2
- 4
1
- 2
1 0
- 3
- 1
- 4 . 4
2 0
8 0 . 5
4 2 0
The table above was constructed using a financial calculator with the following
c. Other possible projects with multiple rates of return could be nuclear power plants
d. Here is the MIRR for the project when r = 8%:
Now, MIRR is the discount rate that forces the PV of the TV of $29,916,000 over 2
At r = 14%, MIRR for the project is calculated as follows:
Answers and Solutions: 10 - 2
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
Yes. The MIRR method leads to the same conclusion as the NPV method. Reject the
b. The PV of costs for the conveyor system is ($911,067), while the PV of costs for the
Financial calculator solution:
10-21 a. Payback A (cash flows in thousands):
Annual
Period Cash Flows Cumulative
0 ($25,000) ($25,000)
1 5,000 (20,000)
Answers and Solutions: 10 - 3
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
Payback B (cash flows in thousands):
Annual
Period Cash Flows Cumulative
0 ($25,000) ($25,000)
b. Discounted Payback A (cash flows in thousands):
Annual Discounted @10%
Period Cash Flows Cash Flows Cumulative
0 ($25,000) ($25,000.00) ($25,000.00)
1 5,000 4,545.45 (20,454.55)
Discounted Payback B (cash flows in thousands):
Annual Discounted @10%
Period Cash Flows Cash Flows Cumulative
0 ($25,000) ($25,000.00) ($25,000.00)
Both projects have positive NPVs, so both projects should be undertaken.
Answers and Solutions: 10 - 4
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
At a discount rate of 5%, Project A has the higher NPV; consequently, it should be
accepted.
At a discount rate of 15%, Project B has the higher NPV; consequently, it should be
accepted.
f. Project ∆ =
Year CFA – CFB
0 $ 0
g. Use 3 steps to calculate MIRRA @ r = 10%:
Step 1: Calculate the NPV of the uneven cash inflow stream, so its FV can then be
Step 2: Calculate the FV of the cash inflow stream as follows:
Step 3: Calculate MIRRA as follows:
Use 3 steps to calculate MIRRB @ r = 10%:
Step 1: Calculate the NPV of the uneven cash inflow stream, so its FV can then be
Answers and Solutions: 10 - 5
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
Step 2: Calculate the FV of the cash flow stream as follows:
Step 3: Calculate MIRRB as follows:
According to the MIRR approach, if the 2 projects were mutually exclusive, Project A
would be chosen because it has the higher MIRR. This is consistent with the NPV
approach.
10-22 a. NPV of termination after Year t:
b. No. Salvage possibilities could only raise NPV and IRR. The value of the firm is
maximized by terminating the project after Year 3.
SOLUTION TO SPREADSHEET PROBLEM
Answers and Solutions: 10 - 6
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website, in whole or in part.
10-23 The detailed solution for the problem is available in the file Solution for Ch10 P23 Build
a Model.xlsx at the textbook’s Web site.
Answers and Solutions: 10 - 7
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
MINI CASE
You have just graduated from the MBA program of a large university, and one of your
favorite courses was “Today’s Entrepreneurs.” In fact, you enjoyed it so much you have
decided you want to “be your own boss.” While you were in the master’s program, your
grandfather died and left you $1 million to do with as you please. You are not an inventor
and you do not have a trade skill that you can market; however, you have decided that you
would like to purchase at least one established franchise in the fast-foods area, maybe two
(if profitable). The problem is that you have never been one to stay with any project for too
long, so you figure that your time frame is three years. After three years you will sell off
your investment and go on to something else.
You have narrowed your selection down to two choices; (1) Franchise L, Lisa’s Soups,
Salads, & Stuff and (2) Franchise S, Sam’s Fabulous Fried Chicken. The net cash flows
shown below include the price you would receive for selling the franchise in Year 3 and the
forecast of how each franchise will do over the three-year period. Franchise L’s cash flows
will start off slowly but will increase rather quickly as people become more health
conscious, while Franchise S’s cash flows will start off high but will trail off as other
chicken competitors enter the marketplace and as people become more health conscious
and avoid fried foods. Franchise L serves breakfast and lunch, while Franchise S serves
only dinner, so it is possible for you to invest in both franchises. You see these franchises as
perfect complements to one another: You could attract both the lunch and dinner crowds
and the health conscious and not so health conscious crowds without the franchises directly
competing against one another.
Here are the net cash flows (in thousands of dollars):
Expected Net Cash Flows
Year Franchise L Franchise S
0 ($100) ($100)
1 10 70
2 60 50
3 80 20
Depreciation, salvage values, net working capital requirements, and tax effects are all
included in these cash flows.
You also have made subjective risk assessments of each franchise, and concluded that
both franchises have risk characteristics that require a return of 10%. You must now
determine whether one or both of the franchises should be accepted.
Answers and Solutions: 10 - 8
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
website, in whole or in part.
a. What is capital budgeting?
Answer: Capital budgeting is the process of analyzing additions to fixed assets. Capital
budgeting is important because, more than anything else, fixed asset investment
3. Determine the appropriate discount rate, based on the riskiness of the cash flows
b. What is the difference between independent and mutually exclusive projects?
Answer: Projects are independent if the cash flows of one are not affected by the acceptance of
the other. Conversely, two projects are mutually exclusive if acceptance of one
c. 1. Define the term net present value (NPV). What is each franchise’s NPV?
Answer: The net present value (NPV) is simply the sum of the present values of a project’s
cash flows:
Franchise L’s NPV is $18.79:
0123
||||
NPVs are easy to determine using a calculator with an NPV function. Enter the cash
c. 2. What is the rationale behind the NPV method? According to NPV, which
franchise or franchises should be accepted if they are independent? Mutually
exclusive?
Answer: The rationale behind the NPV method is straightforward: if a project has NPV = $0,
then the project generates exactly enough cash flows (1) to recover the cost of the
Consider Franchise L’s cash inflows, which total $150. They are sufficient (1) to
return the $100 initial investment, (2) to provide investors with their 10% aggregate
If Franchises L and S are independent, then both should be accepted, because they
Answers and Solutions: 10 - 10
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website, in whole or in part.
10%
