12) For a project that has an initial cash outflow followed by cash inflows, the profitability index (PI) is
equal to the present value of cash inflows divided by the cost of capital.
13) Economic value added is the difference between an investment’s net operating profit after taxes and
the accounting profit.
14) The NPV of a project is the difference between an investment’s net operating profit after taxes and the
cost of funds used to finance the investment, which is found by multiplying the dollar amount of the
funds used to finance the investment by the firm’s weighted average cost of capital.
15) Which of the following is an advantage of NPV?
A) It measures the risk exposure.
B) It takes into account the time value of investors’ money.
C) It is highly sensitive to the discount rates.
D) It measures how quickly a firm can breakeven.
16) The return that must be earned on a project in order to leave the firm’s value unchanged is ________.
A) the internal rate of return
B) the interest rate
C) the cost of capital
D) the compound rate
17) Thinking in terms of the goal of wealth maximization, a project breaks even for shareholders,
meaning that it neither creates nor destroys value, if ________.
A) its NPV equals 0
B) its IRR equals 0
C) its net profit after taxes equals 0
D) its payback period is one year or less
18) A firm can accept a project with a net present value of zero because ________.
A) the project would maintain the wealth of the firm’s owners
B) the project would enhance the wealth of the firm’s owners
C) the project would maintain the earnings of the firm
D) the project would enhance the earnings of the firm
19) A firm is evaluating an investment proposal which has an initial investment of $5,000 and cash flows
presently valued at $4,000. The net present value of the investment is ________.
A) -$1,000
B) $9,000
C) $4,000
D) -$4,000
20) What is the NPV for a project whose cost of capital is 15 percent and initial after-tax cost is $5,000,000
and is expected to provide after-tax operating cash inflows of $1,800,000 in year 1, $1,900,000 in year 2,
$1,700,000 in year 3, and $1,300,000 in year 4?
A) $1,700,000
B) $371,764
C) -$137,053
D) -$4,862,947
21) What is the NPV for a project if its cost of capital is 0 percent and its initial after-tax cost is $5,000,000
and it is expected to provide after-tax operating cash inflows of $1,800,000 in year 1, $1,900,000 in year 2,
$1,700,000 in year 3, and $1,300,000 in year 4?
A) $1,700,000
B) $371,764
C) $137,053
D) $6,700,000
22) What is the NPV for a project if its cost of capital is 12 percent and its initial after-tax cost is $5,000,000
and it is expected to provide after-tax operating cash flows of $1,800,000 in year 1, $1,900,000 in year 2,
$1,700,000 in year 3, and ($1,300,000) in year 4?
A) -$1,494,336
B) $158,011
C) -$158,011
D) $3,505,664
23) A firm is evaluating three capital projects. The net present values for the projects are as follows:
The firm should ________.
A) accept Projects 1 and 2, and reject Project 3
B) accept Projects 1 and 3, and reject Project 2
C) accept Project 3, and reject Projects 1 and 2
D) accept all projects
24) What is the profitability index of a project that has an initial cash outflow of $600, an inflow of $250
for the next 3 years and a cost of capital of 10 percent?
A) 0.667
B) 2.036
C) 1.036
D) 2.739
Table 10.1
25) Given the information in Table 10.1 and 15 percent cost of capital,
(a) compute the net present value.
(b) should the project be accepted?
Table 10.2
26) Given the information in Table 10.2 and 15 percent cost of capital,
(a) compute the net present value.
(b) should the project be accepted?
10.4 Internal rate of return (IRR)
1) The internal rate of return (IRR) is defined as the discount rate that equates the net present value with
the initial investment associated with a project.
2) The IRR is the discount rate that equates the NPV of an investment opportunity with $0.
3) The IRR is the compounded annual rate of return that a firm will earn if it invests in a project and
receives the estimated cash inflows.
4) An internal rate of return greater than the cost of capital guarantees that the firm will earn at least its
required return.
5) A capital budgeting technique that can be computed by solving for the discount rate that equates the
present value of a project’s inflows to the present value of its outflows is called net present value.
6) A capital budgeting technique that can be computed by solving for the discount rate that equates the
present value of a project’s inflows to the present value of its outflows is called internal rate of return.
7) If a project’s IRR is greater than 0 percent, the project should be accepted.
8) If a project’s IRR is greater than the cost of capital, the project should be rejected.
9) What is the IRR for the following project if its initial after-tax cost is $5,000,000 and it is expected to
provide after-tax operating cash inflows of $1,800,000 in year 1, $1,900,000 in year 2, $1,700,000 in year 3,
and $1,300,000 in year 4?
A) 15.57%
B) 0.00%
C) 13.57%
D) 12.25%
10) What is the IRR for the following project if its initial after-tax cost is $5,000,000 and it is expected to
provide an after-tax operating cash outflow of ($1,800,000) in year 1, followed by inflows of $2,900,000 in
year 2, $2,700,000 in year 3, and $2,300,000 in year 4?
A) 5.83%
B) 9.67%
C) 11.44%
D) 31.53%
11) The ________ is the discount rate that equates the present value of the cash inflows with the initial
investment.
A) payback period
B) net present value
C) cost of capital
D) internal rate of return
12) The ________ is the compound annual rate of return that a firm will earn if it invests in the project and
receives the given cash inflows.
A) risk-free rate
B) internal rate of return
C) opportunity cost
D) cost of capital
13) A firm with a cost of capital of 13.5 percent is evaluating three capital projects. The internal rates of
return are as follows:
The firm should ________.
A) accept Project 1 and 2, and reject Project 3
B) accept Project 2, and reject Projects 1 and 3
C) accept Project 1, and reject Projects 2 and 3
D) accept Project 3, and reject Projects 1 and 2
14) An insurance company specializes in selling warranties for consumer electronics products. For selling
these warranties they receive cash up front, but later they must pay out cash for policyholders who file
claims. Suppose a particular product they sell brings in $1 million in cash right away but requires them to
pay $1.2 million in claims a year later. The firm’s cost of capital is 10%. Calculate the IRR that the firm
earns on the product and comment on whether it is a good investment.
10.5 Comparing NPV and IRR techniques
1) A project’s net present value profile is a graph that plots a project’s NPV for various discount rates.
2) A project’s net present value profile is a graph that plots a project’s IRR for various discount rates.
3) Projects A and B both require an initial investment of $100,000. Project A produces $200,000 in cash
flows in the subsequent 5 years. Project B produces cash flow of $400,000 next year, $300,000 in year 2,
$200,000 in year 3, and $50,000 in years 4 and 5. Which of the following is true?
A) The NPV of project A will be more sensitive to changes in the cost of capital compared to the NPV of
project B.
B) The NPV of project B will be more sensitive to changes in the cost of capital compared to the NPV of
project A.
C) The two projects have NPVs that are equally sensitive to changes in the cost of capital.
D) Neither project’s NPV is sensitive to changes in the cost of capital.
4) Net present value profiles are most useful when selecting among independent projects.
5) For conventional projects, both NPV and IRR techniques will always generate the same accept-reject
decision.
6) Net present value profiles are most useful when selecting among mutually exclusive projects.
7) Consider the following projects, X and Y, where the firm can only choose one. Project X costs $600 and
has cash flows of $400 in each of the next 2 years. Project Y also costs $600, and generates cash flows of
$500 and $275 for the next 2 years, respectively. Which investment should the firm choose if the cost of
capital is 10 percent?
A) Project X, since it has a higher NPV than Project Y
B) Project Y, since it has a higher NPV than Project X
C) Project X, since it has a lower NPV than Project Y
D) Project Y, since it has a lower NPV than Project X
8) Consider the following projects, X and Y where the firm can only choose one. Project X costs $600 and
has cash flows of $400 in each of the next 2 years. Project Y also costs $600, and generates cash flows of
$500 and $275 for the next 2 years, respectively. Which investment should the firm choose if the cost of
capital is 25 percent?
A) Project X, since it has a higher NPV than Project Y
B) Project Y, since it has a higher NPV than Project X
C) neither, since both the projects have negative NPV
D) neither, since both the projects have positive NPV
9) Which of the following is true regarding an NPV profile?
A) It is used for evaluating and comparing independent projects when conflicting ranking exists.
B) It is a graph that illustrates a project’s IRR against various values of NPV.
C) It shows an inverse relationship between a project’s IRR and NPV.
D) It charts the net present value of a project as a function of the cost of capital.
10) Tangshan Mining Company is considering investing in a new mining project. The firm’s cost of
capital is 12 percent and the project is expected to have an initial after-tax cost of $5,000,000. Furthermore,
the project is expected to provide after-tax operating cash flows of $2,500,000 in year 1, $2,300,000 in year
2, $2,200,000 in year 3, and ($1,300,000) in year 4?
(a) Calculate the project’s NPV.
(b) Calculate the project’s IRR.
(c) Should the firm make the investment?
11) Conflicting rankings in the case of mutually exclusive projects using NPV and IRR often result from
differences in the magnitude and/or timing of cash flows.
12) Projects having higher cash inflows in the early years tend to be less sensitive to changes in the cost of
capital and are therefore often acceptable at higher discount rates compared to projects with higher cash
inflows that occur in the later years.
13) In general, projects with similar-sized investments and lower cash inflows in the early years tend to
be preferred at higher discount rates.
14) In general, the greater the difference between the magnitude and/or timing of cash inflows, the
greater the likelihood of conflicting ranking between NPV and IRR.
15) Certain mathematical properties may cause a project with a nonconventional cash flow pattern to
have multiple IRRs; this problem does not occur with the NPV approach.
16) On a purely theoretical basis, NPV is a better approach when selecting among two mutually exclusive
projects.
17) On a purely theoretical basis, IRR is a better approach when selecting among two mutually exclusive
projects.
18) The appeal of the IRR technique is due to the general disposition of business people to think in terms
of rates of return rather than actual dollar returns.
Table 10.3
A firm is evaluating two projects that are mutually exclusive with initial investments and cash flows as
follows:
19) If the firm in Table 10.3 has a required payback of two years, it should ________.
A) accept Project A and Project B
B) accept Project A and reject Project B
C) reject Project A and accept Project B
D) reject both the projects
20) The new financial analyst does not like the payback approach (Table 10.3) and determines that the
firm’s required rate of return is 15 percent. Based on IRR, his recommendation would be to ________.
A) accept both the projects
B) accept Project A and reject Project B
C) reject Project A and accept Project B
D) reject both the projects
Table 10.4
A firm must choose from six capital budgeting proposals outlined below. The firm is subject to capital
rationing and has a capital budget of $1,000,000; the firm’s cost of capital is 15 percent.
21) Using the internal rate of return approach to ranking projects, which project(s) should the firm accept?
(See Table 10.4)
A) 1, 2, 3, 4, and 5
B) 1, 2, 3, and 5
C) 2, 3, 4, and 6
D) 1, 3, 4, and 6
22) Using the net present value approach to ranking projects, which projects should the firm accept? (See
Table 10.4)
A) 1, 2, 3, 4, and 5
B) 1, 3, 5, and 6
C) 2, 3, 4, and 5
D) 1, 3, 4, 5, and 6
23) When the net present value is negative, the internal rate of return is ________ the cost of capital.
A) greater than
B) greater than or equal to
C) less than
D) equal to
24) A firm with a cost of capital of 15% is evaluating two independent projects utilizing the internal rate
of return technique. Project X has an initial investment of $80,000 and cash inflows at the end of each of
the next five years of $25,000. Project Z has an initial investment of $120,000 and cash inflows at the end
of each of the next four years of $40,000. The firm should ________.
A) accept both the projects because they have equal IRR
B) accept Project X and reject project Z
C) accept Project Z because its IRR is higher than Project X
D) reject both the projects because they have negative IRR
25) Comparing net present value and internal rate of return ________.
A) always results in the same ranking of projects
B) always results in the same accept-reject decision
C) may give different accept-reject decisions
D) is only necessary on independent projects
26) Which capital budgeting method is most useful for evaluating a project that has an initial after-tax
cost of $5,000,000 and is expected to provide after–tax operating cash flows of $1,800,000 in year 1,
($2,900,000) in year 2, $2,700,000 in year 3, and $2,300,000 in year 4?
A) net present value
B) internal rate of return
C) payback
D) accounting rate of return
27) Which of the following is a reason that makes NPV a better approach to capital budgeting on a purely
theoretical basis?
A) It measures the benefits relative to the amount invested.
B) It measures the actual value created by an investment.
C) Financial decision makers are inclined to higher rates of return.
D) Interest rates are expressed as annual rates of return.
28) In comparing the internal rate of return and net present value methods of evaluation, ________.
A) internal rate of return is theoretically superior, but financial managers prefer net present value
B) net present value is theoretically superior, but financial managers often prefer to use internal rate of
return
C) financial managers prefer net present value, because it is presented as a rate of return
D) financial managers prefer net present value, because it measures benefits relative to the amount
invested
29) Consider the following projects, X and Y where the firm can only choose one. Project X costs $600 and
has cash flows of $400 in each of the next 2 years. Project Y also costs $600, and generates cash flows of
$500 and $275 for the next 2 years, respectively. Sketch a net present value profile for each of these
projects. Which project should the firm choose if the cost of capital is 10 percent? What if the cost of
capital is 25 percent? Show all work.