An organization is using capital budgeting techniques to
compare two independent projects. It could accept one, both, or
neither of the projects. Which of the following statements is true
about the use of net present value (NPV) and internal rate of
return (IRR) methods for evaluating these two projects?
Detailed Answer
(a) The requirement is to compare NPV and IRR. Answer
(a) is correct because NPV and IRR criteria will always lead
to the same accept or reject decision. Answer (b) is incorrect
because if the second project’s internal rate of return is higher
than the first project’s, the organization would accept the second
project based on IRR.
2
An organization has four investment proposals with the following
costs and expected cash inflows:
Expected Cash Inflows
Project
Cost
End of year 1
End of year 2
End of year 3
A
Unknown
$10,000
$10,000
$10,000
B
$20,000
5,000
10,000
15,000
C
25,000
15,000
10,000
5,000
D
30,000
20,000
Unknown
20,000
Additional information
Discount rate
Number of periods
Present value of $1 due at the end of n periods [PVIF]
Present value of an annuity of $1 per period for n periods [PVIFA]
5%
1
0.9524
0.9524
5%
2
0.9070
1.8594
5%
3
0.8638
2.7232
10%
1
0.9091
0.9091
10%
2
0.8264
1.7355
10%
3
0.7513
2.4869
15%
1
0.8696
0.8696
15%
2
0.7561
1.6257
15%
3
0.6575
2.2832
If Project A has an internal rate of return (IRR) of 15%, then
it has a cost of
Detailed Answer
(b) The requirement is to calculate the cost of the project
from its cash flow information. Answer (b) is correct. The
internal rate of return is the discount rate that sets the net present
value of the project to zero, so the present value of the costs
equals the present value of the cash inflows. The cost of Project
A can be calculated by determining the present value of the annual
annuity of $10,000 cash flows discounted at 15%. Therefore,
the cost of the investment is $22,832 ($10,000 × 2.2832).
Answer (a) is incorrect because this solution uses the present
value interest factor of 15%, one period rather than the present
value interest factor for an annuity. Answer (c) is incorrect because
this solution is obtained using a 10% rather than a 15% discount
rate. Answer (d) is incorrect because this solution is obtained
using a 5% rather than a 15% discount rate.
3
An organization has four investment proposals with the following
costs and expected cash inflows:
Expected Cash Inflows
Project
Cost
End of year 1
End of year 2
End of year 3
A
Unknown
$10,000
$10,000
$10,000
B
$20,000
5,000
10,000
15,000
C
25,000
15,000
10,000
5,000
D
30,000
20,000
Unknown
20,000
Additional information
Discount rate
Number of periods
Present value of $1 due at the end of n periods [PVIF]
Present value of an annuity of $1 per period for n periods [PVIFA]
5%
1
0.9524
0.9524
5%
2
0.9070
1.8594
5%
3
0.8638
2.7232
10%
1
0.9091
0.9091
10%
2
0.8264
1.7355
10%
3
0.7513
2.4869
15%
1
0.8696
0.8696
15%
2
0.7561
1.6257
15%
3
0.6575
2.2832
If the discount rate is 10%, the net present value (NPV) of
Project B is
Detailed Answer
(a) The requirement is to calculate the net present value
of Project B. Answer (a) is correct because the net present value
is the present value of the cash inflows less the cost of the project.
The net present value of the future inflows is $24,079 [($5,000 ×
.9091) + ($10,000 × .8264) + ($15,000 × .7513)]. Therefore,
the net present value of the project is $4,079 ($24,079 –
$20,000). Answer (b) is incorrect because this solution is obtained
using a 5%, rather than a 10%, discount rate. Answer (c) is
incorrect because this is the net present value of Project A at a
10% discount rate. Answer (d) is incorrect because this solution
is obtained using the present value interest factor for annuities.
4
An organization has four investment proposals with the following
costs and expected cash inflows:
Expected Cash Inflows
Project
Cost
End of year 1
End of year 2
End of year 3
A
Unknown
$10,000
$10,000
$10,000
B
$20,000
5,000
10,000
15,000
C
25,000
15,000
10,000
5,000
D
30,000
20,000
Unknown
20,000
Additional information
Discount rate
Number of periods
Present value of $1 due at the end of n periods [PVIF]
Present value of an annuity of $1 per period for n periods [PVIFA]
5%
1
0.9524
0.9524
5%
2
0.9070
1.8594
5%
3
0.8638
2.7232
10%
1
0.9091
0.9091
10%
2
0.8264
1.7355
10%
3
0.7513
2.4869
15%
1
0.8696
0.8696
15%
2
0.7561
1.6257
15%
3
0.6575
2.2832
The payback period of Project C is
Detailed Answer
(c) The requirement is to calculate the payback period
of Project C. Answer (c) is correct because after two years, the
cumulative cash inflows for Project C are exactly equal to the
initial investment outlay, $25,000 ($15,000 + 10,000). Answer
(a) is incorrect because the payback period would be zero only if
a project had no cost or provided immediate cash inflows in excess
of the investment outlay. Project C does not provide an
immediate payback of its investment cost. Answer (b) is incorrect
because after one year, the cumulative cash inflows for Project
C are only $15,000 versus an initial investment outlay of
$25,000. The project has not yet recovered its costs. Answer (d)
is incorrect because Project C pays back its initial investment
outlay in only two years.
5
An organization has four investment proposals with the following
costs and expected cash inflows:
Expected Cash Inflows
Project
Cost
End of year 1
End of year 2
End of year 3
A
Unknown
$10,000
$10,000
$10,000
B
$20,000
5,000
10,000
15,000
C
25,000
15,000
10,000
5,000
D
30,000
20,000
Unknown
20,000
Additional information
Discount rate
Number of periods
Present value of $1 due at the end of n periods [PVIF]
Present value of an annuity of $1 per period for n periods [PVIFA]
5%
1
0.9524
0.9524
5%
2
0.9070
1.8594
5%
3
0.8638
2.7232
10%
1
0.9091
0.9091
10%
2
0.8264
1.7355
10%
3
0.7513
2.4869
15%
1
0.8696
0.8696
15%
2
0.7561
1.6257
15%
3
0.6575
2.2832
If the discount rate is 5% and the discounted payback period
of Project D is exactly two years, then the year two cash inflow for
Project D is
Detailed Answer
(c) The requirement is to calculate the year 2 cash inflow
for Project D. Answer (c) is correct. The discounted payback
period is the length of time required for discounted cash
flows to recover the cost of the investment. The year two cash
inflow for Project D that is consistent with a discounted payback
period of 2 years can be calculated as follows:
Investment cost = present value of year 1 and 2
cash inflows $30,000 = $20,000 × (.9524) + year 2
cash inflow × (0.9070) Year 2 cash inflow =
[$30,000 – ($20,000 × .9524)] ÷ 0.9070 =
$12,075.
Answer (c) is incorrect because this solution is obtained using
the present value interest factor for annuities. Answer (b) is incorrect
because this solution is based on the regular payback
period. Since the cash inflow in year 1 is $20,000, Project D pays
back its $30,000 cost in two years if the cash inflow in year 2 is
$10,000. Answer (d) is incorrect because this solution is obtained
using a 10%, rather than a 5%, discount rate.
6
Tam Co. is negotiating for the purchase of equipment that
would cost $100,000, with the expectation that $20,000 per year
could be saved in after-tax cash costs if the equipment were acquired.
The equipment’s estimated useful life is ten years, with no residual value, and would be depreciated by the straight-line
method. Tam’s predetermined minimum desired rate of return is
12%. Present value of an annuity of 1 at 12% for ten periods is
5.65. Present value of 1 due in ten periods at 12% is .322. In
estimating the internal rate of return, the factors in the table of
present values of an annuity should be taken from the columns
closest to
Detailed Answer
(c) The internal rate of return (IRR) determines the
rate of discount at which the present value of the future cash
flows will exactly equal the investment outlay. It is computed by
setting up the following equation
Initial investment = TVMF X Cash flows
and solving for the time value of money factor (TVMF). The
IRR can then be found by locating the TVMF for (n) periods in
the present value of an ordinary annuity table and tracing to the
top of that column to find the rate of return. The problem asks
for the TVMF for the IRR of the equipment, which is calculated
as follows:
$100,000 = TVMF X $20,000
5.00 = TVMF
In estimating the IRR, the factors in the table of present values of
an annuity should be taken from the columns closest to 5.00.
7
How are the following used in the calculation of the internal
rate of return of a proposed project? Ignore income tax considerations.
Residual sales value of project . . . .Depreciation expense
Detailed Answer
(d) The internal rate of return of a proposed project
includes the residual sales value of a project but not the depreciation
expense. This is true because the residual sales value represents
a future cash flow whereas depreciation expense (ignoring
income tax considerations) provides no cash inflow or outflow.
8
Neu Co. is considering the purchase of an investment that
has a positive net present value based on Neu’s 12% hurdle rate.
The internal rate of return would be
Detailed Answer
(c) The relationship between the NPV method and the
IRR method can be summarized as follows:
NPV IRR
NPV > 0 IRR > Discount rate
NPV = 0 IRR = Discount rate
NPV < 0 IRR < Discount rate
Since the problem states that Neu Co. has a positive net present
value on the investment, then the internal rate of return would be
> 12%.
9
Bennet Inc. uses the net present value method to evaluate
capital projects. Bennet’s required rate of return is 10%. Bennet
is considering two mutually exclusive projects for its manufacturing
business. Both projects require an initial outlay of
$120,000 and are expected to have a useful life of four years. The
projected after-tax cash flows associated with these projects are as
follows:
Year
Project X
Project Y
1
$40,000
$10,000
2
40,000
20,000
3
40,000
60,000
4
40,000
80,000
Total
$160,000
$170,000
Assuming adequate funds are available, which of the following
project options would you recommend that Bennet’s management
undertake?
Detailed Answer
(a) The requirement is to determine which mutually
exclusive investment should be accepted. Answer (a) is correct
because Project X has the higher net present value as calculated
below.
Net present value of Project X= $6,800= ($40,000 x 3.170) - $120,000
Net present value of Project Y= $5,310= [($10,000 x 0.909) +($20,000
x 0.826) + ($60,000 x 0.751) +
($80,000 x 0.683)] - $120,000
10
Capital Invest Inc. uses a 12% hurdle rate for all capital expenditures
and has done the following analysis for four projects for the
upcoming year.
Project 1
Project 2
Project 3
Project 4
Initial capital outlay
$200,000
$298,000
$248,000
$272,000
Annual net cash inflows
Year1
$65,000
$100,000
$80,000
$95,000
Year 2
70,000
135,000
95,000
125,000
Year 3
80,000
90,000
90,000
90,000
Year 4
40,000
65,000
80,000
60,000
Net present value
(3,798)
4,276
14,064
14,662
Profitability index
98%
101%
106%
105%
Internal rate of return
11%
13%
14%
15%
Which project(s) should Capital Invest Inc. undertake
during the upcoming year assuming it has no budget restrictions?
Detailed Answer
(c) The requirement is to select the projects that should
be undertaken assuming no budget constraints. Answer (c) is
correct because the company should undertake all projects with a
positive net present value. This would include Projects 2, 3, and
4. Answers (a), (b), and (d) are incorrect because Project 1 has a
negative net present value and should not be undertaken.
