Chapter 26
Capital Investment Analysis
Study Guide Solutions
Fill-in-the-Blank Equations
1. Average investment
2. Average investment
3. Initial cost
4. Present value index
5. Equal annual net cash flows
Exercises
1. Management is considering the purchase of a new piece of equipment in five years and
the profitability of doing so. Which methods can management use to quickly calculate
and review the purchase of the building that do not use present values?
Average rate of return and cash payback methods
2. Assume that the building appears profitable using the methods described in Exercise 1,
but management is now considering the time value of money to determine the
equipment’s profitability. Which methods should management consider now?
Net present value and internal rate of return methods
3. Determine in each situation when capital investment analysis would be used.
a. Investment in short-term securities, which the company expects to hold three
months
No
b. Purchase of a new delivery truck, which has an estimated useful life of five years
Yes
c. Deciding which project would be more profitable if both will last at least seven
years
Yes
Strategy: Capital investment analysis is used for long-term projects and investments.
Average rate of return and cash payback methods do not use present values of cash
flows and do not consider the time value of money. The net present value method and
internal rate of return consider the time value of money to compare profitability.
1
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2
Chapter 26
4. West End Co. is considering a new project which will earn $450,000 of total income over
the next five years. The cost to start the project totals $500,000, and it will have a
$22,000 salvage value. Calculate the average rate of return for the project, rounding
percentages to the nearest whole percentage.
Estimated average annual income = $90,000 = $450,000/5 years
Average investment = $261,000 = ($500,000 + $22,000)/2
Average rate of return = 34% = $90,000/$261,000
5. The management at Mike’s Camping Supply would like to invest in a new project that
will generate $50,000 of income for the first three years and $70,000 for the seven years
afterwards. The cost of the project includes a $300,000 buy in and will have a residual
value of $15,000. Calculate the average rate of return for the project, rounding
percentages to the nearest whole percentage.
Estimated average annual income = $64,000 = $640,000/10 years
Average investment = $157,500 = ($300,000 + $15,000)/2
Average rate of return = 41% = $64,000/$157,500
6. Bass Corporation would like to generate an average rate of return of 20% for a new
project that has an initial cost of $500,000 and $40,000 residual value. Determine the
average annual income required to meet the desired rate of return.
Average investment = $270,000 = ($500,000 + $40,000)/2
Estimated average annual income = $54,000 = $270,000 × 20%
Strategy: The average rate of return gives the average percentage of income, or return,
a company will receive for its investment in the project. The average rate of return is
calculated by dividing the average annual income by the average investment. The
average investment is equal to the average of the initial cost and the residual value,
which is the average book value of the project, since the residual value is the project’s
worth at the end of its useful life.
7. West End Co. is considering an investment in a new project. The project would have an
initial start-up fee of $260,000. The company will incur $20,000 of additional cash
expenses each year due to the project, but will earn income of $42,000. Calculate the
cash payback period, rounding answers to two decimal places.
Cash payback period = 11.82 years = $260,000/($42,000 – $20,000)
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Capital Investment Analysis 3
8. Mike’s Camping Supply is considering the purchase of new equipment for $750,000. The
equipment will allow the company to generate additional cash revenues of $180,000
each year. The company will incur total expenses of $64,000 from the machine each
year, including $7,000 related to depreciation. Calculate the cash payback period,
rounding answers to two decimal places.
Net cash inflow per year = $123,000 = $180,000 – ($64,000 – $7,000)
Cash payback period = 6.10 years = $750,000/$123,000
9. Management at Bass Corporation is considering investing in a new project. The project
will have an initial cost of $500,000 and generate additional cash revenues of $95,000.
Expenses each year will total $25,000. Calculate the cash payback period for the project,
rounding answers to two decimal places.
Cash payback period = 7.14 years = $500,000/$70,000
Strategy: The cash payback period provides the amount of time a project will take to
return the company’s initial cost of the investment or pay the company back. To
calculate, divide the initial investment by the annual net cash inflow. The net cash inflow
is the revenues generated less expenses incurred due to the project.
10. Use the table shown below to calculate the present value of $40,000 received five years
from now. Assume a 10% interest rate.
Present Value of $1 at Compound Interest
Year
10%
12%
15%
1
0.909
0.893
0.870
2
0.826
0.797
0.756
3
0.751
0.721
0.658
4
0.683
0.636
0.572
5
0.621
0.567
0.497
6
0.564
0.507
0.432
7
0.513
0.452
0.376
8
0.467
0.404
0.327
9
0.424
0.361
0.284
10
0.386
0.322
0.247
Present value = $24,840 = $40,000 × 0.621
11. Use the table shown in Exercise 10 to calculate the present value of $22,000 received
ten years from now, assuming an interest rate of 15%.
Present value = $5,434 = $22,000 × 0.247
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4
Chapter 26
12. A company expects to generate cash revenues of $20,000 over the next five years.
Calculate the present value of the earnings using the table below if there is a 10%
interest rate.
Present Value of an Annuity of $1 at Compound Interest
Year
10%
12%
15%
1
0.909
0.893
0.870
2
1.736
1.690
1.626
3
2.487
2.402
2.283
4
3.170
3.037
2.855
5
3.791
3.605
3.353
6
4.355
4.111
3.785
7
4.868
4.564
4.160
8
5.335
4.968
4.487
9
5.759
5.328
4.772
10
6.145
5.650
5.019
Present value = $75,820 = $20,000 × 3.791
Strategy: Using a present value table, find the present value factor that is associated
with the number of years the cash flow will occur and the interest rate given. Multiply
the present value factor by the cash flow to determine the present value of the cash
flow.
13. West End Co. is looking into a new project. The cost to begin the project will be
$150,000. The company requires a 12% rate of return. The project is expected to
generate $30,000 of revenue the first year, $50,000 the second year, $75,000 the third
year, and $45,000 in the last year. Use the present vale table in Exercise 10 to find the
net present value of the investment.
Year Present Value of $1
1
0.893
2
0.797
3
0.721
4
0.636
Total
Less amount to be invested
Net present value
Net Cash Flow
$30,000
50,000
75,000
45,000
Present Value of
Net Cash Flow
$ 26,790
39,850
54,075
28,620
$149,335
150,000
$ (665)
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Capital Investment Analysis 5
14. Use the information in Exercise 13 to calculate the present value index of the project,
Alternative 1, for West End Co. Round answers to three decimal places. If Alternative 2
has a present value index of 1.212, in which project should the company invest?
Present value index = 0.996 = $149,335/$150,000
The company should invest in Alternative 2.
15. Mike’s Camping Supply is considering the purchase of a new piece of equipment, which
will cost $140,000. The equipment will generate additional cash revenues of $50,000 for
the first two years, $85,000 in the third year, and $80,000 in its last year. The
equipment, which the company plans to sell at the end of the fourth year, will also have
a $10,000 salvage value. Use the present value table in Exercise 10 to determine the net
present value of the investment. Should the company invest in the new piece of
equipment if it requires a 15% rate of return?
Year Present Value of $1 Net Cash Flow
1
0.870
$50,000
2
0.756
50,000
3
0.658
85,000
4
0.572
80,000
Total
Less amount to be invested
Net present value
Present Value of
Net Cash Flow
$ 43,500
37,800
55,930
45,760
$182,990
140,000
$ 42,990
The company should invest in the new piece of equipment.
16. Mike’s Camping Supply is deciding between the equipment, the Automatic Fabricator, in
Exercise 15 or the Deluxe Fabricator, which has a present value index of 1.06. Calculate
the present value index of the Automatic Fabricator to determine which piece of
machinery the company should purchase. Round answers to two decimal places.
Present value index = 1.31 = $182,990/$140,000
The company should purchase the Automatic Fabricator.
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6
Chapter 26
17. Bass Corporation requires a 10% rate of return for all investments. Management is
considering a project that will initially cost $75,000. The company expects to generate
$12,000 of revenue in the first year, $25,000 in the second year, and $20,000 for the last
two years of the project. Use the table in Exercise 10 to calculate the net present value
of the project and determine if the company should make the investment.
Year Present Value of $1 Net Cash Flow
1
0.909
$12,000
2
0.826
25,000
3
0.751
20,000
4
0.683
20,000
Total
Less amount to be invested
Net present value
Present Value of
Net Cash Flow
$10,908
20,650
15,020
13,660
$60,238
75,000
$(14,762)
Since the project has a negative net present value, Bass Corporation should not invest in
it.
Strategy: When determining the net present value, first determine the present value of
the future cash flows. Subtract the amount of the investment from the sum of the
present value of the cash flows to find the net present value. If a project has a positive
net present value, the company will generate more cash flows that invested, making the
project profitable. However, if the project has a negative net present value, it will not be
profitable because the company invested more dollars today than the value of the
income to be received at the beginning of the project.
18. Calculate the present value index of Project 1 (information in Exercise 17) for Bass
Corporation, rounding answers to two decimal places. If Project 2 has a present value
index of 1.15, in which project should the company invest?
Present value index = 0.80 = $60,238/$75,000
The company should invest in Project 2.
Strategy: The present value index provides the relation of the present value of the cash
flows to the cost of the investment. The index is calculated by dividing the sum of the
present value of net cash flows by the amount to be invested. Investments with a higher
present value index represent investments with a higher profitability. A present value
index less than one indicates a negative net present value, since the present value of the
net cash flows are less than the amount to be invested.
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Capital Investment Analysis 7
19. West End Co. plans to invest $103,662 in a new project that will produce annual net
cash flows of $18,000 for 9 years. Determine the internal rate of return for the project,
using the table in Exercise 12.
Present value factor for an annuity of $1 = 5.759 = $103,662/$18,000
Internal rate of return = 10%
20. Mike’s Camping Supply plans to invest $28,824 in a new project that will produce annual
net cash flows of $12,000 for 3 years. Determine the internal rate of return for the
project, using the table in Exercise 12.
Present value factor for an annuity of $1 = 2.402 = $28,824/$12,000
Internal rate of return = 12%
21. Bass Corporation plans to invest $20,547 in a new project that will produce annual net
cash flows of $9,000 for 3 years. Determine the internal rate of return for the project,
using the table in Exercise 12.
Present value factor for an annuity of $1 = 2.283 = $20,547/$9,000
Internal rate of return = 15%
Strategy: When determining the internal rate of return for an investment, first calculate
the present value factor by dividing the amount to be invested by the annual net cash
flows. Next, look to a present value of an annuity of $1 table to find the internal rate of
return by finding the present value factor calculated for the time period the cash flows
will occur.
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8
Chapter 26
22. West End Co. is deciding between two projects. Use the information shown below and
the table in Exercise 10 to calculate and compare the net present value for each at the
end of four years and determine which would be more profitable. Assume that Project 1
can be disposed of for $28,000 at the end of the fifth year.
Project 1
Project 2
Cost
$100,000 Cost
$55,000
Minimum desired rate of return
10% Minimum desired rate of return
10%
Expected useful life
7 years Expected useful life
5 years
Yearly cash flows to be received:
Yearly cash flows to be received:
Year 1
$ 20,000
Year 1
$ 15,000
Year 2
24,000
Year 2
18,000
Year 3
28,000
Year 3
21,000
Year 4
32,000
Year 4
24,000
Year 5
36,000
Year 5
27,000
Year 6
40,000 Total
$105,000
Year 7
44,000
Total
$224,000
Project 1
Year Present Value of $1 Net Cash Flow
1
0.909
$20,000
2
0.826
24,000
3
0.751
28,000
4
0.683
32,000
5
0.621
64,000
Total
Less amount to be invested
Net present value
Project 2
Year Present Value of $1 Net Cash Flow
1
0.909
$15,000
2
0.826
18,000
3
0.751
21,000
4
0.683
24,000
5
0.621
27,000
Total
Less amount to be invested
Net present value
Present Value of
Net Cash Flow
$ 18,180
19,824
21,028
21,856
39,744
$120,632
100,000
$ 20,632
Present Value of
Net Cash Flow
$13,635
14,868
15,771
16,392
16,767
$77,433
55,000
$22,433
Project 2 would be more profitable for the company.
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Capital Investment Analysis 9
23. Using the table in Exercise 10, calculate the net present value for each project shown below
at the end of six years and determine which would be the better decision for Mike’s
Camping Supply. Assume that Project 1 can be sold for $15,000 at the end of the sixth year.
Project 1
Project 2
Cost
$160,000 Cost
$150,000
Minimum desired rate of return
12% Minimum desired rate of return
12%
Expected useful life
7 years Expected useful life
6 years
Yearly cash flows to be received:
Yearly cash flows to be received:
Year 1
$ 40,000
Year 1
$ 40,000
Year 2
44,000
Year 2
42,000
Year 3
41,000
Year 3
46,000
Year 4
42,000
Year 4
41,000
Year 5
45,000
Year 5
45,000
Year 6
48,000
Year 6
47,500
Year 7
18,000 Total
$261,500
Total
$278,000
Project 1
Year Present Value of $1 Net Cash Flow
1
0.893
$40,000
2
0.797
44,000
3
0.721
41,000
4
0.636
42,000
5
0.567
45,000
6
0.507
63,000
Total
Less amount to be invested
Net present value
Project 2
Year Present Value of $1 Net Cash Flow
1
0.893
$40,000
2
0.797
42,000
3
0.721
46,000
4
0.636
41,000
5
0.567
45,000
6
0.507
47,500
Total
Less amount to be invested
Net present value
Present Value of
Net Cash Flow
$ 35,720
35,068
29,561
26,712
25,515
31,941
$184,517
160,000
$ 24,517
Present Value of
Net Cash Flow
$ 35,720
33,474
33,166
26,076
25,515
24,083
$178,034
150,000
$ 28,034
The company should undertake Project 2, which would be more profitable.
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10
Chapter 26
24. Use the information shown below and the table in Exercise 10 to determine which
project has a higher net present value at the end of three years for Bass Corporation. At
the end of Year 3, Project 2 can be sold for $45,000.
Project 1
Cost
$85,000
Minimum desired rate of return
15%
Expected useful life
3 years
Yearly cash flows to be received:
Year 1
$ 40,000
Year 2
48,000
Year 3
50,000
Total
$138,000
Project 2
Cost
$80,000
Minimum desired rate of return
15%
Expected useful life
6 years
Yearly cash flows to be received:
Year 1
$ 30,000
Year 2
22,000
Year 3
28,000
Year 4
18,000
Year 5
12,000
Year 6
15,000
Total
$125,000
Project 1
Year Present Value of $1 Net Cash Flow
1
0.870
$40,000
2
0.756
48,000
3
0.658
50,000
Total
Less amount to be invested
Net present value
Project 2
Year Present Value of $1 Net Cash Flow
1
0.870
$30,000
2
0.756
22,000
3
0.658
73,000
Total
Less amount to be invested
Net present value
Present Value of
Net Cash Flow
$ 34,800
36,288
32,900
$103,988
85,000
$ 18,988
Present Value of
Net Cash Flow
$26,100
16,632
48,034
$90,766
80,000
$10,766
Bass Corporation should choose Project 1, which has a higher net present value at the
end of Year 3.
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Capital Investment Analysis 11
Strategy: If one project has a shorter life than another, the cash flows after its useful life
will be zero for each year, making it incomparable. The projects should be compared
using the same time frame. To do so, calculate the net present value of the shorter
project as normal. Then, calculate the net present value of the longer project as normal,
but adjusted to the correct time frame, which is usually equal to the life of the shorter
project. For the last year of the time frame, the net cash flow of the longer project should
also include the selling price at that time to reflect the value until the end of the project’s
life.
25. If a capital investment proposal meets the net present value and internal rate of return
standard, what does management analyze next?
Management should next look at the qualitative considerations.
26. Assume that a manager is reviewing a rejected capital investment proposal and the
qualitative considerations that the company should include. If the qualitative
considerations do change the decision, what should management do next?
If qualitative considerations change the decision, management should accept the
proposal.
27. After accepting a number of proposals, what is the next step that management should
consider and perform an analysis of?
Management should rank the proposals and consider the amount of capital funds
available.
Strategy: First, the minimum cash payback and average rate of return standards should
be considered since they do not consider the time value of money concept and are simple
to calculate. If the proposal meets the standards, management should next determine if
the net present value and internal rate of return standards are met, which consider the
time value of money. All proposals, including previously rejected proposals, should be
reviewed for the impact of qualitative considerations on the decision to accept. If a
proposal has been previously rejected but qualitative considerations cause it to be a
good decision, it should be accepted. If the proposal has been accepted previously but
qualitative considerations change the decision, it should be rejected. All accepted
proposals should be ranked next and funds allocated to the ones with highest priority.
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