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Solutions to Problems
P10-1 Payback period (LG 2; Basic)
b. The company should accept the project because payback period (7.23 years) is less than the
maximum acceptable period (8 years).
P10-2 Payback comparisons (LG 2; Intermediate)
b,c. The maximum acceptable payback period is 5 years. Only Machine 1 has a faster payback, so
Nova should accept only that project.
d. Yes, Machine 2 has returns that last 20 years while Machine 1 has only 7 years of returns. The
P10-3 Choosing between two projects with acceptable payback periods (LG 2; Intermediate)
a.
Both projects have payback periods of exactly 4 years.
b. Based on the maximum acceptable payback period of 4 years set by John Shell, both projects
are equally attractive. If the projects are mutually exclusive projects, John should accept B.
c. Project B is preferred because it offers larger cash flows in the early years. [Note: By the end of
P10-4 Personal finance: Long-term investment decisions, payback period (LG 2; Intermediate)
a. and b. Project A Project B
Year Annual
Cash Flow Cumulative
Cash Flow Annual
Cash Flow Cumulative
Cash Flow
1 $2,200 $2,200 $1,500 $1,500
2 2,500 4,700 1,500 3,000
c. Project A is more attractive than project B because of its shorter payback period.
d. One shortcoming of the payback method is its disregard of total cash flows over project life.
Here, for example, project A generates $11,000 in total cash flows (implying an NPV at a zero
discount rate of $2,000), while total cash flows for project B equal $12,000, implying an NPV
P10-5 NPV (LG 3; Basic)
NPV Present value of cash inflows from project Initial investment. All projects have 15-year
inflows is:
a. Annual cash inflows = $150,000, so present value = PV(.09, 15, -150000) = $1,209,103.26
NPV $2,942,151.28 $3,000,000 = $ NPV is negative, so project should be
rejected.
P10-6 NPV for varying cost of capital (LG 3; Basic)
NPV Present value of cash inflows from project Initial investment. All projects have 8-year
lives, an initial cost of $360,000, and annual cash inflows of $62,650. The Excel command for
a. Cost of capital = 6%, so present value of cash inflows = PV(0.06,8,62650) = $389,043.58.
b. Cost of capital = 8%, so the present value of cash inflows = PV(0.08,8,62650) = $360,026.93.
amount).
P10-7 NPV: Independent projects (LG 3; Intermediate)
All cash flows in thousands. NPV = Present value of all cash outflows and inflows.
Year
Cash Flows Discounted Cash Flows Discounted Cash Flows Discounted Cash Flows Discounted Cash Flows Discounted
0 (250)$ (250)$ (375)$ (375)$ (550)$ (550)$ (750)$ (750)$ (1,150)$ (1,150)$
1 50$ 45.45$ 45$ 40.91$ 350$ 318.18$ 200$ 182$ 80$ 72.73$
2 90$ 74.38$ 55$ 45.45$ 210$ 173.55$ 235$ 194$ 135$ 111.57$
3 140$ 105.18$ 65$ 48.84$ 165$ 123.97$ 250$ 188$ 190$ 142.75$
4 80$ 54.64$ 55$ 37.57$ 55$ 37.57$ 265$ 181$ 255$ 174.17$
5
NPV = 29.66$
45$ 27.94$ 45$ 27.94$ 100$ 62$ 315$ 195.59$
6 35$ 19.76$ 10$ 5.64$ 50$ 28$ 380$ 214.50$
7 25$ 12.83$
NPV = 136.85$ NPV = 85.18$
275$ 141.12$
8 15$ 7.00$ 100$ 46.65$
9 5$ 2.12$ 45$ 19.08$
10
NPV = (132.59)$
25$ 9.64$
NPV = (22.20)$
Project E
ACCEPT
ACCEPT
ACCEPT
ACCEPT
REJECT
Project A
Project B
Project C
Project D
P10-8 NPV (LG 3; Challenge)
a. In Excel, the present value of a 5-year, $385,000 annuity (paid at year-end), discounted at 9%
is:
present-value terms than the one-time immediate payment of $1.5 million.
b. In Excel, the series of year-end payments over 5 years with a present value of $1.5 million is:
c. The payment stream is now $385,000 today and 4 end-of-year payments of $385,000. In
Excel, the present value of the 4 end-of-year payments is:
Now, Simes would prefer the one-time immediate payment of $1.5 million because it is less
than the present value of five, beginning of year payments of $385,000.
d. The present value of the cash inflows expected from the solar-powered toy car is given by:
Simes should choose the payment option with the lowest present value.
P10-9 NPV and maximum return (LG 3; Challenge)
a. NPV = Present value of cash inflows – initial investment ($150,000). In Excel, present value
of cash inflows =PV(0.10,4,44400) = $140,742.03.
figure, NPV will be positive, and project should be accepted.
P10-10 NPV: Mutually exclusive projects (LG 3; Intermediate)
a.,b., c, d and e.
Cash flows in thousands. Negative numbers are outflows; positive inflows. Profitability Index
P10-11 Personal finance: Long-term investment decisions, NPV method (LG 3; Intermediate)
Upfront cost of MBA program $100,000
($50,000 for tuition and $50,000 for lost earnings)
Incremental benefit (higher salary per year) $20,000
P10-12 Payback and NPV (LG 2, 3; Intermediate)
a.
Project Payback Period Payback Rank
A $40,000 $13,000 3.08 years 2
b.
c. With a 16% cost of capital, Project C offers the highest NPV and the shortest payback period.
Project C has relatively high cash flows in the early years; indeed, 87.5% of project cost is
important criterion is NPV because of its connection to shareholder wealth maximization.
P10-13 NPV and EVA (LG 3; Intermediate)
a. NPV = Present value of cash inflows – Initial outlay ($2.5 million). Because cash inflows are a
b. Annual EVA Annual cash inflow – Annual opportunity cost of capital
c. Overall EVA Present value of annual EVA, discounted at the cost of capital = $15,000
same.
P10-14 Internal rate of return (LG 4; Intermediate)
For a given set of cash flows, IRR is the interest rate that makes project NPV = 0:
To obtain IRR in Excel , start by arranging the cash inflows in adjacent cells in a row or column
beginning with the cash outflow in year 0. For example, if the cash flows for project A are placed in
IRR.
P10-15 Internal rate of return (LG 4; Intermediate)
For Peach of Mind, inc. (PMI), offering extended warranties is profitable only if the
marginal benefit (price customer pays) exceeds the marginal cost (present value of outlays
costs, so PMI should offer extended warranties.
Another approach is to compute the
compare that IRR to the 7% cost of
capital:
Project IRR is only 4%. Usually, when the cost of capital exceeds IRR, the firm should
reject the project. Here, however, cash flows have the opposite sign from usual (i.e., there
P10-16 IRR: Mutually exclusive projects (LG 4; Intermediate)
a. and b.
Annual project cash outflows and
inflows appear in the columns under
the project heading.
P10-17 Personal Finance: Long-term investment decisions, IRR method (LG 4; Intermediate)
a.
b. IRR is the discount rate such that NPV = 0. Here, project NPV = 0 for discount rates of 0%,
10%, 20%, and 30%—implying IRR can take all four values. The unconventional cash-flow
pattern (multiple sign changes) explains the multiple IRRs. With multiple IRRs, it is not clear
c. The largest cash outflow (–$602.6) occurs in year 3. Other things equal, a change in the
discount rate will have a larger impact on present value when the outflow or inflow occurs
P10-18 IRR, investment life, and cash inflows (LG 4; Challenge)
a. In Excel, arrange the one cash outflow (–$61,450) and 10 cash inflows ($10,000) in 11
b. To find the number of years $10,000 would have to be received to make the project acceptable
by the IRR decision rule, use the NPER command in Excel. The proper syntax is:
c. To find the minimum cash inflows over 10 years that would make the project acceptable, use
the PMT command in Excel. The proper syntax is:
P10-19 NPV and IRR (LG 3, 4; Intermediate)
a. NPV = Present value of cash inflows – Initial investment ($18,250). In Excel, the present value of cash
inflows = PV(0.10,7,-4000) = $19,473.68. So, NPV = $19,473.68 – $18,250 = $1,223.68.
b. To find IRR in Excel, place the one cash outflow (-18250) and 7 cash inflows (4000) in
P10-20 NPV, with rankings (LG 3, 4; Intermediate)
Note: IRR was obtained in Excel and the following syntax (cash flows arranged in the first four
9.7%.
P10-21 All techniques, conflicting rankings (LG 2, 3, 4: Intermediate)
a., b., c., and d.
Project NPVs
At a 0% discount rate, each year’s discounted cash flow equals the undiscounted cash flow. so:
NPVA Present value of cash flows ($270,000) – Initial outlay ($150,000) $120,000.
Project IRRs
To find IRR in Excel, place cash flows in adjacent cells in a row or column starting with
project cost expressed as a negative number, and use the IRR command. Answers appear in the
table.
e. Project Rankings by Various Approaches to Capital Budgeting:
Project Payback NPV IRR
Nicholson Roofing should use the NPV ranking (and choose project A) because NPV is more closely tied to
maximizing shareholder wealth. Indeed, NPV indicates exactly how much a project will benefit shareholders.
f. Project NPVs (at a 12% rate):
the NPV of both projects but had a smaller impact on project B’s NPV because a larger
percentage of the project annual cash flows occur in the early years.
P10-22 Payback, NPV, and IRR (LG 2, 3, 4; Intermediate)
a. Payback period:
b. NPV computation
(12% discount rate):
Another approach is to use the NPV command in Excel. This command is misleading in that it
generates the present value of an unequal stream of cash inflows, not actual NPV. To obtain
project NPV, the initial outlay must be subtracted from the figured generated by the NPV
c. To find IRR in Excel, arrange cash outflows and inflows in adjacent cells in a row or column
and use IRR command. If, for example, CF0 ($95,000) is in A1; CF1 ($20,000) is in A2; CF2
d. NPV approach: NPV , so project should be accepted.
The project should be undertaken because it satisfies the decision criteria for both NPV and
IRR approaches to capital budgeting.
P10-23 NPV, IRR, and NPV profiles (LG 3, 4, 5; Challenge)
a. and b.
Project A
NPV: In Excel, put CF1 (25000) in A1; CF2 (35000) in A2; CF3 (45000) in A3; CF4 (50000) in
A4; and CF5 (55000) in A5. Then, use the NPV command to obtain the present value of
decision criterion, project A should be accepted.
IRR: In Excel, put cash flows in adjacent cells starting with project cost (expressed as a
negative number because it is an outflow). If, for example, cash flows appear in the first
six rows of column A with CF0 (-130000) in A1, CF1 (25000) in A2, CF2 (35000) in A3,
Project B
NPV: In Excel, put 40000 in A1, 35000 in A2, 30000 in A3, 10000 in A4, and 5000 in A5.
Then, use the NPV command to obtain the present value of these inflows; proper
NPV > 0, so project B should be accepted.
IRR: In Excel, put cash flows in adjacent cells starting with project cost (expressed as a
negative number because it is an outflow). If, for example, cash flows appear in the first
c. To draw NPV profiles for projects A and B, find NPVs for both projects over a range of
discount rates. Start with the NPV for both projects at a 0% discount rate (which is simply the
Note the two projects have
NPVs of roughly $4,532
when the discount rate is
14.777%.
d. IRR ranking: IRRA = 16.06% and IRRB = 17.75%, so project B is always preferred.
NPV ranking: Project A has a positive NPV for discount rates below 16.06%, and project B
e. The change in rankings above and below 15% stems from the different cash-flow patterns of
the two projects. Total undiscounted cash inflows are $80,000from project A and $35,000
from project B. But 50% of project A’s undiscounted cash inflows occur in the last two years
