10-18 Cash flow time line for Machine 190-3:
0 1 2 3
| | | |
-190,000 87,000 87,000 87,000
Using a financial calculator, input the following data: CF0 = -190000; CF1-3 = 87000;
I/YR = 14; and solve for NPV190-3 = $11,982 (for 3 years).
Cash flow time line for Machine 360-6:
0 1 2 3 4 5 6
| | | | | | |
-360,000 98,300 98,300 98,300 98,300 98,300 98,300
Using a financial calculator, input the following data: CF0 = -360000; CF1-6 = 98300;
I/YR = 14; and solve for NPV360-6 = $22,256 (for 6 years).
14%
14%
10-19 a. The project’s expected cash flows are as follows (in millions of dollars):
Time Net Cash Flow
0 ($ 4.4)
1 27.7
2 (25.0)
We can construct the following NPV profile:
Discount Rate NPV
0% ($1,700,000)
9 (29,156)
10 120,661
50 2,955,556
100 3,200,000
200 2,055,556
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
3
2
1
The table above was constructed using a financial calculator with the following inputs:
CF0 = -4400000, CF1 = 27700000, CF2 = –25000000, and I/YR = discount rate to solve
for the NPV.
c. Other possible projects with multiple rates of return could be nuclear power plants
where disposal of radioactive wastes is required at the end of the project’s life, or
leveraged leases where the borrowed funds are repaid at the end of the lease life. (See
Chapter 18 of Financial Management, 13th edition for more information on leases.)
Now, MIRR is the discount rate that forces the PV of the TV of $29,916,000 over 2
years to equal $25,833,470.51:
$25,833,470.51 = $29,916,000(PVIFr,2).
Inputs 2 -25833470.51 0 29916000
Output = 7.61
N
I/YR
FV
PMT
PV
Inputs 2 -23636688.21 0 31578000
Output = 15.58
MIRR = 15.58%.
Yes. The MIRR method leads to the same conclusion as the NPV method. Reject the
project if r = 8%, which is greater than the corresponding MIRR of 7.61%, and accept
the project if r = 14%, which is less than the corresponding MIRR of 15.58%.
10-20 a. The IRRs of the two alternatives are undefined. To calculate an IRR, the cash flow
stream must include both cash inflows and outflows.
10-21 a. Payback A (cash flows in thousands):
Annual
Period Cash Flows Cumulative
0 ($25,000) ($25,000)
1 5,000 (20,000)
N
I/YR
FV
PMT
PV
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)
2 10,000 8,264.46 (12,190.08)
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)
1 20,000 18,181.82 (6,818.18)
2 10,000 8,264.46 1,446.28
3 8,000 6,010.52 7,456.80
4 6,000 4,098.08 11,554.88
Discounted PaybackB = 1 + $6,818.18/$8,264.46 = 1.825 years.
d. At a discount rate of 5%, NPVA = $18,243,813.
At a discount rate of 5%, NPVB = $14,964,829.
At a discount rate of 5%, Project A has the higher NPV; consequently, it should be
accepted.
f. Project ∆ =
Year CFA – CFB
0 $ 0
1 (15)
2 0
3 7
4 14
IRR∆ = Crossover rate = 13.5254% ≈ 13.53%.
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
calculated. With a financial calculator, enter the cash inflow stream into the
cash flow registers being sure to enter 0 for CF0, then enter I/YR = 10, and
solve for NPV = $37,739,908.
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
calculated. With a financial calculator, enter the cash inflow stream into the
cash flow registers being sure to enter 0 for CF0, then enter I/YR = 10, and
solve for NPV = $36,554,880.
Step 2: Calculate the FV of the cash flow stream as follows:
Enter N = 4, I/YR = 10, PV = -36554880, and PMT = 0 to solve for FV =
$53,520,000.
10-22 a. NPV of termination after Year t:
NPV0 = -$22,500 + $22,500 = 0.
Using a financial calculator, input the following: CF0 = -22500, CF1 = 23750, and I/YR
= 10 to solve for NPV1 = –$909.09 ≈ -$909.
Using a financial calculator, input the following: CF0 = -22500, CF1 = 6250, CF2 =
20250, and I/YR = 10 to solve for NPV2 = –$82.64 ≈ -$83.
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
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.
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.
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.
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
decisions chart a company’s course for the future. Conceptually, the capital budgeting
process is identical to the decision process used by individuals making investment
decisions. These steps are involved:
1. Estimate the cash flows—interest and maturity value or dividends in the case of
bonds and stocks, operating cash flows in the case of capital projects.
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 impacts
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:
0 1 2 3
| | | |
(100.00) 10 60 80
9.09
49.59
60.11
18.79 = NPVL
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
investment and (2) to enable investors to earn their required rates of return (the
opportunity cost of capital). If NPV = $0, then in a financial (but not an accounting)
c. 3. Would the NPVs change if the cost of capital changed?
Answer: The NPV of a project is dependent on the cost of capital used. Thus, if the cost of capital
10%
d. 1. Define the term internal rate of return (IRR). What is each franchise’s IRR?
Answer: The internal rate of return (IRR) is the discount rate that forces the NPV of a project to
equal zero:
0 1 2 3
| | | |
CF0 CF1 CF2 CF3
Franchise L’s IRR is 18.1%:
0 1 2 3
| | | |
-100.00 10 60 80
8.47
43.02
48.57
$ 0.06 ≈ $0 if IRRL = 18.1% is used as the discount rate.
IRR
18.1%
d. 2. How is the IRR on a project related to the YTM on a bond? For example, suppose
the initial cost of a project is $100 and it has cash flows of $40 at Years 1, 2, and
3. What is its IRR? Use the Excel RATE function as though the project were a
bond.
Answer: The IRR is the discount rate that forces the PV of a project’s expected future cash flows
to equal the initial cash flow. This is analogous to a bond’s yield because a bond’s yield
is the discount rate that forces the present value of a bonds coupons and maturity value
to equal the price of the bond.
Using the RATE function: IRR = RATE(3,40,-100) = 9.7%
The time line solution is:
d. 3. What is the logic behind the IRR method? According to IRR, which franchises
should be accepted if they are independent? Mutually exclusive?
Answer: IRR measures a project’s profitability in the rate of return sense: If a project’s IRR
equals its cost of capital, then its cash flows are just sufficient to provide investors with
d. 4. Would the franchises’ IRRs change if the cost of capital changed?
Answer: IRRs are independent of the cost of capital. Therefore, neither IRRS nor IRRL would
e. 1. Draw NPV profiles for Franchises L and S. At what discount rate do the profiles
cross?
Answer: The NPV profiles are plotted in the figure below.
Note the following points:
1. The Y-intercept is the project’s NPV when r = 0%. This is $50 for L and $40 for
S.