The Moore Corporation is considering the acquisition of a new machine. The machine can be purchased for $90,000; it will cost $6,000 to transport
to Moore’s plant and $9,000 to install. It is estimated that the machine will last 10 years, and it is
expected to have an estimated salvage value of $5,000. Over its 10-year life, the machine is expected to
produce 2,000 units per year with a selling price of $500 and combined material and labor costs of $450
per unit. Federal tax regulations permit machines of this type to be depreciated using the straight-line
method over 5 years with no estimated salvage value. Moore has a marginal tax rate of 40%.
What is the net cash outflow at the beginning of the first year that Moore Corporation should
use in a capital budgeting analysis?
Detailed Answer
Correct answer: (D)
The net cash outflow, or net investment, includes not only the cost of the machine itself, but also the
costs of shipping and installation. The purchase price of the machine is $90,000; it will cost $6,000 to
transport to Moore’s plant and $9,000 to install, for a total of $105,000.
2
Yipann Corporation is reviewing an
investment proposal. The initial cost and other relevant data for each year are presented in the schedule
below. All cash flows are assumed to take place at the end of the year. The salvage value of the
investment at the end of each year is equal to its net book value, and there will be no salvage value at
the end of the investment’s life.
Year
Initial Cost and Book Value
Annual Net After-Tax Cash Flows
Annual Net Income
0
$105,000
$ 0
$ 0
1
70,000
50,000
15,000
2
42,000
45,000
17,000
3
21,000
40,000
19,000
4
7,000
35,000
21,000
5
0
30,000
23,000
Yipann uses a 24% after-tax target rate of return for new investment proposals. The discount factors for a
24% rate of return are given below.
Year
Present Value of $1.00 Received at the End of Period
Present Value of an Annuity of $1.00 Received at the End of each Period
1
0.81
0.81
2
0.65
1.46
3
0.52
1.98
4
0.42
2.40
5
0.34
2.74
6
0.28
3.02
7
0.22
3.24
The average annual cash inflow at which Yipann would be indifferent to the investment
(rounded to the nearest dollar) is:
Detailed Answer
Correct answer: (C)
This question is asking for an average annual after-tax cash flow amount that will result in a net
present value of zero for the project, because that will be the average annual cash flow at which Yipann will
be indifferent to the investment. This is a present value of an annuity problem, because since we are looking
for an average annual cash flow amount, all the annual cash flow amounts after Year 0 must be the same
average amount. The annual cash flows given in the problem are irrelevant to calculating the answer to this
question.
Since the initial investment is $105,000 and the project’s life is 5 years, we need to know what annuity
amount will produce a present value of $105,000 when discounted at 24% for 5 years. The present value of
an annuity is the annuity amount multiplied by the PV of an annuity factor. The PV of an annuity factor for
24% for 5 years is given in the question: 2.74. The present value needed is the amount of the initial
investment, which is $105,000. Using the present value and the present value factor, we can calculate the
annuity amount. The annuity amount is $105,000 ÷ 2.74, which is equal to $38,321.
Therefore, if the 5 annual after-tax cash flows are all the same and they are each $38,321, the NPV of the
investment will be zero and Yipann will be indifferent to whether or not it makes the investment. If it makes
the investment, the investment will provide no additional value to the shareholders and the shareholders will
gain nothing. If Yipann does not make the investment, the shareholders will lose nothing.
3
Yipann Corporation is reviewing an
investment proposal. The initial cost and other relevant data for each year are presented in the schedule
below. All cash flows are assumed to take place at the end of the year. The salvage value of the
investment at the end of each year is equal to its net book value, and there will be no salvage value at
the end of the investment’s life.
Year
Initial Cost and Book Value
Annual Net After-Tax Cash Flows
Annual Net Income
0
$105,000
$ 0
$ 0
1
70,000
50,000
15,000
2
42,000
45,000
17,000
3
21,000
40,000
19,000
4
7,000
35,000
21,000
5
0
30,000
23,000
Yipann uses a 24% after-tax target rate of return for new investment proposals. The discount factors for a
24% rate of return are given below.
Year
Present Value of $1.00 Received at the End of Period
Present Value of an Annuity of $1.00 Received at the End of each Period
1
0.81
0.81
2
0.65
1.46
3
0.52
1.98
4
0.42
2.40
5
0.34
2.74
6
0.28
3.02
7
0.22
3.24
The accounting rate of return for the investment proposal over its life using the initial value
of the investment is:
Detailed Answer
Correct answer: (B)
The accounting rate of return is the average annual after-tax net income attributable to the project
divided by the net initial investment. The average of the five annual net income amounts given is $19,000
([$15,000 + $17,000 + $19,000 + $21,000 + $23,000] ÷ 5 = $19,000.) $19,000 ÷ $105,000 = 0.18095 or
18.1%. (Note: sometimes the average of the initial investment over the life of the project is used to calculate
the accounting rate of return. The average of the initial investment over the life of the project is calculated as
the initial investment divided by 2. However, this question specifies to use the initial value of the investment,
not the average investment.)
4
Yipann Corporation is reviewing an
investment proposal. The initial cost and other relevant data for each year are presented in the schedule
below. All cash flows are assumed to take place at the end of the year. The salvage value of the
investment at the end of each year is equal to its net book value, and there will be no salvage value at
the end of the investment’s life.
Year
Initial Cost and Book Value
Annual Net After-Tax Cash Flows
Annual Net Income
0
$105,000
$ 0
$ 0
1
70,000
50,000
15,000
2
42,000
45,000
17,000
3
21,000
40,000
19,000
4
7,000
35,000
21,000
5
0
30,000
23,000
Yipann uses a 24% after-tax target rate of return for new investment proposals. The discount factors for a
24% rate of return are given below.
Year
Present Value of $1.00 Received at the End of Period
Present Value of an Annuity of $1.00 Received at the End of each Period
1
0.81
0.81
2
0.65
1.46
3
0.52
1.98
4
0.42
2.40
5
0.34
2.74
6
0.28
3.02
7
0.22
3.24
The traditional payback period for the investment proposal is:
Detailed Answer
Correct answer: (C)
The cash flow analysis is as follows:
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Initial Investment in Equipment
(105,000)
After-Tax Cash Flow
50,000
45,000
40,000
35,000
30,000
Total After-Tax Cash Flows
(105,000)
50,000
45,000
40,000
35,000
30,000
Cumulative Cash Flow
(105,000)
(55,000)
(10,000)
30,000
65,000
95,000
The cumulative cash flow from the project becomes positive during Year 3. Assuming that the cash flows
occur evenly throughout the year, the payback period is 2.25 years, calculated as follows:
Number of the project year in the final year when cash flow is negative: 2
Plus: a fraction consisting of
ï‚Ÿ Numerator = the positive value of the negative cumulative inflow amount from the final negative year,
which is 10,000
ï‚Ÿ Denominator = cash flow for the following year, which is 40,000
or: 2 + (10,000 ÷ 40,000) = 2.25
Note that the present value factors given are irrelevant to answering this question, because the payback
method is not a discounted cash flow technique.
5
Yipann Corporation is reviewing an
investment proposal. The initial cost and other relevant data for each year are presented in the schedule
below. All cash flows are assumed to take place at the end of the year. The salvage value of the
investment at the end of each year is equal to its net book value, and there will be no salvage value at
the end of the investment’s life.
Year
Initial Cost and Book Value
Annual Net After-Tax Cash Flows
Annual Net Income
0
$105,000
$ 0
$ 0
1
70,000
50,000
15,000
2
42,000
45,000
17,000
3
21,000
40,000
19,000
4
7,000
35,000
21,000
5
0
30,000
23,000
Yipann uses a 24% after-tax target rate of return for new investment proposals. The discount factors for a
24% rate of return are given below.
Year
Present Value of $1.00 Received at the End of Period
Present Value of an Annuity of $1.00 Received at the End of each Period
1
0.81
0.81
2
0.65
1.46
3
0.52
1.98
4
0.42
2.40
5
0.34
2.74
6
0.28
3.02
7
0.22
3.24
The net present value of the investment proposal is:
Detailed Answer
Correct answer: (B)
To calculate the NPV, we simply need to multiply each annual after tax cash flow amount by the
appropriate present value of $1 factor, sum them, and subtract the initial investment. All of these amounts
are given to us, which means that our work is simply mathematical.
.......Cash Inflow.. PV of $1 factor
Year 1 $50,000 × .81 = $ 40,500
Year 2 45,000 × .65 = 29,250
Year 3 40,000 × .52 = 20,800
Year 4 35,000 × .42 = 14,700
Year 5 30,000 × .34 = 10,200
..PV of Cash Inflows = $115,450
The NPV is $115,450 − the initial investment of $105,000, or $10,450.
6
Kern Co. is planning to invest in a two-year project that is expected to yield cash flows from operations, net of income taxes, of $50,000 in the first year and $80,000 in the second year. Kern requires an internal rate of return of 15%. The present value of $1 for one period at 15% is 0.870 and for two periods at 15% is 0.756. The future value of $1 for one period at 15% is 1.150 and for two periods at 15% is 1.323. The maximum that Kern should invest immediately is
Detailed Answer
Correct answer: (B)
The maximum amount that Kern Co. should invest
now to obtain a 15% internal rate of return is the present value of the project’s total net cash flows as computed below.
Year .. Net cash flows .. Present value of an ord. annuity .. Present value of net cash flows
1 $50,000 × .870 = $43,500
2 $80,000 × .756 = $60,480
Total present value $103,980
7
Pole Co. is investing in a machine with a three-year life. The machine is expected to reduce annual cash operating costs by $30,000 in each of the first two years and by $20,000 in year three. Present values of an annuity of $1 at 14% are
Period 1 - 0.88; 2 - 1.65; 3 - 2.32
Using a 14% cost of capital, what is the present value of
these future savings?
Detailed Answer
Correct answer: (C)
The requirement is to determine the present value of the future cash savings resulting from purchase of the new machine. The present value of the $30,000 savings per year for the first two years is calculated using the present value of an annuity for two periods. Since the amount of the cash savings drops to $20,000 in year three, this amount must be calculated separately. The PV of an annuity for three periods minus the PV of an annuity for two periods, equals the PV of an amount to be received three years in the future. The total present value of the cash savings is calculated as follows:
PV of $30,000 for 2 periods = $30,000 × 1.65 = $49,500
PV of $20,000 in period 3 = $20,000 × (2.32 - 1.65) = 13,400
Total present value of cash savings $62,900
Alternatively, $20,000 could have been treated as an
annuity for three years and an additional $10,000 for two
years.
8
For the next two years, a lease is estimated to have
an operating net cash inflow of $7,500 per annum, before
adjusting for $5,000 per annum tax basis lease amortization, and a 40% tax rate. The present value of an ordinary annuity of $1 per year at 10% for two years is 1.74. What is the lease’s after-tax present value using a 10% discount factor?
Detailed Answer
Correct answer: (D)
The net present value of a project equals
NPV = (PV future cash flows) - (Investment)
Since this problem involves a lease requiring only annual
payments there is no initial investment in this case. Lease
amortization must be subtracted from cash inflows to
determine income tax expense.
$7,500 Annual cash inflow - 5,000 Tax basis lease amortization $2,500 Taxable lease income
× 40%
$1,000 Tax expense per year
However, lease amortization is not a cash outflow and is thus excluded from the calculation of NPV. The after-tax present value of the lease equals:
$ 7,500 Annual cash inflow - 1,000 Cash outflow for taxes
$6,500 × 1.74 PV factor for two years at 10% =
$11,310
9
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
Correct 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.
10
A firm, with an 18% cost of capital, is considering the
following projects (on January 1, 2011):
Jan. 1, 2011, Cash outflow (000’s omitted)
Dec. 31, 2015, Cash inflow (000’s omitted)
Project internal rate of return
Project A $3,500 $7,400 15%
Project B 4,000 9,950 ?
Present Value of $1 Due at End of "N" Periods
N 12% 14% 15% 16% 18% 20% 22%
4 .6355 .5921 .5718 .5523 .5158 .4823 .4230
5 .5674 .5194 .4972 .4761 .4371 .4019 .3411
6 .5066 .4556 .4323 .4104 .3704 .3349 .2751
Using the net present value method, Project A’s net
present value is
Detailed Answer
Correct answer: (C)
The requirement is to calculate the net present value of Project A. Answer (c) is correct. The December 31, 2015 cash inflow is five years from the present cash outflow, and the net present value method uses the firm’s cost of capital of 18%. The present value factor for 18% for 5 years is .4371, and $7,400,000 times .4371 equals $3,234,540, which is $265,460 less than the present cash outflow of $3,500,000.
