Chapter 15 – Capital investment decisions
TRUE/FALSE
1. The accounting rate of return (ARR) is a traditional method of project evaluation, which involves
dividing either the average net profit by the average book value of the investment, or the average
net profit by the total initial investment value.
2. The payback period is a method used to assist in making decisions about capital investments, and
looks at the time required to recover the initial investment.
3. The payback period provides some assessment of risk, with a longer payback period indicating a
lower risk for the project.
4. Capital investment decisions include mutually exclusive projects where the acceptance of one
project results in the rejection of another project or projects.
5. An entity is contemplating investing in a long-term project. A comparison of two mutually
exclusive projects reveals that Project A involves an initial outlay of $6000 with cash inflows of
$2600 for years 1–5, whereas Project B requires a cash outlay of $4500 with cash inflows of $1300
for years 1–5. Based on this information, the IRR for Project A is higher than the IRR for Project
B.
6. An alternative approach to using the algebraic equation for calculating the internal rate of return is
to use trial and error.
7. The internal rate of return is the rate of return that discounts the cash flows of a project so that the
present value of cash inflows equals the present value of expected profits.
8. A common characteristic of the internal rate of return and the accounting rate of return is that both
use the concept of a rate of return.
9. A problem with calculating the internal rate of return is that it relies on the estimation of future
cash flows, which can be inaccurate, thus making the IRR less reliable.
10. For a project that has an initial outflow of $10,000 and equal inflows of $3400 for four years, the
NPV at a minimum rate of return of 20% will be $(1198) and should not be accepted.
11. For mutually exclusive projects, the IRR and NPV can give different rankings, but for independent
conventional cash flow projects the rankings will be the same.
12. Where two projects have the same investment outlays and project lives but different net cash inflows,
the IRR and NPV may give different rankings.
MULTIPLE CHOICE
1. In which of the following situations would it not be useful to apply the concepts and techniques
used in capital investment decisions?
A.
A company is considering the purchase of a new machine that would reduce the cost of
direct labour in the production process.
B.
A company is comparing the profitability and capital investments of two district offices to
determine which one has the best current return on investment.
C.
A company is reviewing the past performance of two investment projects to determine
which project had the best five-year return on the investment made.
D.
A company is evaluating the potential investment in research and development expenses
to develop a new product line.
2. Which of the following does not affect a capital investment decision?
A.
Cash flows
B.
Accrual-basis net profit
C.
Risk
D.
All of the above affect capital investment decisions.
3. What is a disadvantage of using the accounting rate of return?
A.
It links long-term decision making to profit as the measure of success.
B.
It is easy to understand.
C.
It uses accounting measures of profit rather than cash flows.
D.
None of the above.
4. Which of the following is not an advantage of the accounting rate of return method?
A.
It is easy to understand.
B.
It includes the time value of money.
C.
It is simple to calculate.
D.
The profit ratio is familiar to managers.
5. The accounting rate of return does not consider:
A.
cost of investment.
B.
profitability.
C.
the time value of money.
D.
depreciation.
6. Guerdon Ltd is reviewing a project that has an initial outlay of $3m. The project will generate a
cash inflow of $2m per annum. The project is expected to have a useful life of six years and a zero
salvage value. This company uses straight-line depreciation. What is the accounting rate of return
on the total investment?
A.
15%
B.
20%
C.
33%
D.
50%
7. What is the accounting rate of return on the total investment?
A.
10%
B.
20%
C.
60%
D.
70%
8. What is the accounting rate of return based on the average book value of the investment?
A.
40%
B.
60%
C.
100%
D.
120%
9. Based on the following information, what is the payback period for the two investment projects?
Select the best combination.
Year
Project A
0
$(18,000)
1–3
$2000 per annum
4–6
$5000 per annum
Payback period Payback period
Project A Project B
A.
6.4 years 5.6 years
B.
5.4 years 4.6 years
C.
6.5 years 5.5 years
D.
5.4 years 5.6 years
10. The payback period is:
A.
the length of time required for cash inflows from the project to recover the initial
investment.
B.
the length of time required for profits from the project to equal the original cash outlay.
C.
the length of time required for the cash flows from the project to be expressed as a
percentage of the original capital.
D.
none of the above.
11. Ridge NL is considering investing in a new project. Given the following information, which
project would Ridge choose if a maximum payback period of 5.8 years is set?
Project A
Project B
Initial investment
$160,000
$180,000
Cash flows
Year 1
25,000
25,000
Year 2
25,000
30,000
Year 3
25,000
35,000
Year 4
25,000
30,000
Year 5
25,000
25,000
Year 6
25,000
20,000
Year 7
25,000
15,000
A.
Project B, as the payback period is less than 5.8 years.
B.
Both projects, as the payback periods are less than 5.8 years.
C.
Project A, as the payback period is less than 5.8 years.
D.
Neither project, as both payback periods exceed 5.8 years.
12. Guerdon Ltd is reviewing a project that has an initial outlay of $3m. The project will generate a
cash inflow of $2m per annum. The project is expected to have a useful life of six years and a zero
salvage value. This company uses straight-line depreciation. What is the payback period?
A.
0.67 years
B.
1.5 years
C.
2.0 years
D.
6 years
13. Which of the methods of evaluating capital investment projects does not consider all of the future
cash flows related to a project?
A.
Net present value (NPV).
B.
Internal rate of return (IRR).
C.
Payback method.
D.
All are correct.
14. What is an advantage of the payback method of reviewing capital investments?
A.
It is based on accounting information.
B.
It considers the timing of all cash flows.
C.
It is based on non-cash flow information.
D.
It provides some assessment of risk.
15. The ____ value of an amount is the value of that amount at a later date.
A.
Present
B.
Fair
C.
Future
D.
Prospective
16. What is the internal rate of return for a project that has an initial outlay of $65,000 and expected
cash inflows of $9456 per year for eight years?
A.
3%
B.
3.5%
C.
4%
D.
6.8%
17. Using the tables provided, calculate or estimate the internal rates of return (IRR) that are the
closest to those listed for the two projects.
Year
Project A
Project B
0
$(25,000)
$(80,000)
1
$ 14,405
$ 47,334
2
$ 14,405
$ 47,334
Present value of $1 to be received after N periods:
N periods
Interest rate
1
2
7%
$0.9346
$0.8734
8%
.9259
.8573
9%
.9174
.8417
10%
.9091
.8264
11%
.9009
.8116
12%
.8929
.7972
13%
.8850
.7831
IRR IRR
Project A Project B
A.
0.0% 11.5%
B.
11.5% 12.0%
C.
10.0% 12.0%
D.
11.0% 13.5%
18. Using the tables provided, calculate the IRR of two investments and select the best combination of
answers.
Year
Project A
Project B
0
$(120,000)
$(50,000)
1
$ 130,800
$57,250
Present value of $1 to be received after N periods:
N periods
Interest rate
1
2
7%
$0.9346
$0.8734
8%
.9259
.8573
9%
.9174
.8417
10%
.9091
.8264
11%
.9009
.8116
12%
.8929
.7972
13%
.8850
.7831
14% .8733 .7695
IRR IRR
Project A Project B
A.
9% 12%
B.
9% 7%
C.
9% 14%
D.
0.10% 0.12%
19. Which of the following is not an advantage of IRR?
A.
It uses the concept of a rate of return, which is familiar to many managers.
B.
It incorporates the time value of money by not treating cash received in different years as
equal.
C.
There is only one IRR for every investment.
D.
It uses cash flows and not profits, and the payment of cash outflows is more closely
aligned with cash inflows than profits would be.
20. Net present value (NPV) is an important concept used to analyse capital investment projects. NPV
can best be described as:
A.
the amount that should be used to discount the future cash flows to the present, and then
compared with the current investment.
B.
the amount that must be invested now to earn a particular future value.
C.
the difference between the future cash inflows and the discounted cost of the investment.
D.
the difference between the discounted future cash inflows and the cost of the investment.
21. A positive net present value indicates that:
A.
the IRR is less than the discount rate.
B.
the cost of capital is greater than the present value of the future cash inflows.
C.
the projected return on the investment is expected to exceed the cost of capital plus the
cost of the initial investment.
D.
the IRR is less than the cost of capital.
22. Companies evaluating capital investment projects frequently use net present value analysis to make
decisions about which projects are likely to be the most profitable. Cash flows are projected for
future periods and then discounted to the present. A common rate to use when discounting these
cash flows is the:
A.
internal rate of return.
B.
weighted cost of capital.
C.
prime rate of interest.
D.
accounting rate of return.
23. Phil’s Fish Shack Ltd wants to purchase machinery costing $20,000. The machinery is expected to
have a life of two years and a zero residual value at the end of that time. The company uses a
discount rate of 10%. The net cash inflows for each year are forecast to be:
Year 1 $12,000
Year 2 $16,000
N periods
Interest rate
1
2
7%
$0.9346
$0.8734
8%
.9259
.8573
9%
.9174
.8417
10%
.9091
.8264
What is the approximate net present value of the investment?
A.
$4131
B.
$5452
C.
$8000
D.
$20,000
24. Which of the following statements is true concerning the future value of an investment?
A.
The difference between the future and present values of an investment is the annuity.
B.
The future value of an investment is expected to be larger than its present value.
C.
The future value of an investment is expected to be smaller than its present value.
D.
The future value of an investment is always smaller than its present value.
25. Which of the following statements is true concerning the present value of an investment?
A.
The difference between the future and present values of an investment is the annuity.
B.
The present value of an investment is expected to be larger than its future value.
C.
The present value of an investment is expected to be smaller than its future value.
D.
The present value of an investment is always larger than its future value.
26. The difference between future value and present value is:
A.
cost.
B.
annuity.
C.
apportionment.
D.
interest.
27. The Orgonne Milling Company is contemplating the purchase of new equipment. The machinery is
expected to generate increased sales of $50,000 per year over its five-year life. Excluding the cost
of the machinery, additional costs are expected to be $15,000 per year. If the firm requires a
minimum 12% return on its investment, what is the maximum price the company can pay for this
equipment? (PV annuity at 12% for five years is 3.604)
A.
$180,200
B.
$175,000
C.
$126,140
D.
$54,072
28. The Sparks Sailboat Company has just acquired new manufacturing equipment. No down payment
was made, but four year-end payments of $2400 will be required to pay for the machine. If 8% is
the appropriate rate, at what amount should Sparks Sailboat Company record the new equipment
on its books? (PV annuity at 8% for four years is 3.312, five years is 3.992)
A.
$7056
B.
$7949
C.
$9581
D.
$13,060
29. The ____ value of an amount is the value of that amount on a particular date prior to the time the
amount is paid or received.
A.
present
B.
current
C.
contemporary
D.
coetaneous
30. Using the tables provided, calculate the net present value (NPV) of each of the following projects
and select the best answer from the choices given. The applicable discount rate is 11%.
Year
Project A
Project B
0
$(25,000)
$(80,000)
1
8000
30,000
2
8000
30,000
3
8000
30,000
4
8000
30,000
Present value of $1 to be received after N periods:
N periods
Interest rate
1
2
3
4
10%
$0.9091
$0.8264
$0.7513
$0.6830
11%
.9009
.8116
.7312
.6587
12%
.8929
.7972
.7118
.6355
NPV NPV
Project A Project B
A.
$24,820 $93,072
B.
$(180) $93,072
C.
$(180) $13,072
D.
$24,820 $13,072
31. An entity is contemplating investing in a long-term project. A comparison of two mutually
exclusive projects reveals that Project A has an initial outlay of $10,000 with cash inflows of
$3400 for years 1–5; Project B has a cash outlay of $4500 with cash inflows of $1400 for years 1–
5. If the minimum rate of return is 20%, which of the following statements is incorrect?
A.
The internal rate of return suggests that Project A would be accepted and Project B would
not.
B.
The net present value suggests that Project A would be accepted and Project B would not.
C.
The net present value for Project B is a negative amount.
D.
If the projects were not mutually exclusive, the net present values would suggest that both
projects should be selected.
32. You have an opportunity to purchase the Kuppajo Cafe, a busy shop near your office. The owner is
asking $49,000. After satisfying yourself as to the accuracy of the firm’s past financial statements,
you note that it generated $12,000 per year in net cash flow. You believe you could operate the
business for 4 years and sell it for $30,000. What is the maximum amount you would be willing to
pay for the business if you wished to earn at least a 10% return on your investment?
N periods
Interest rate 1 2 3 4
10% $0.9091 $0.8264 $0.7513 $0.6830
11% .9009 .8116 .7312 .6587
12% .8929 .7972 .7118 .6355
A.
$33,467
B.
$58,528
C.
$68,690
D.
$95,096
33. The Bee Family Fun Centre is for sale at an asking price of $400,000. The audited financial
statements show that the business generates approximately $43,000 per year in net cash flow. You
believe you could operate the business for 3 years and sell it for $500,000. What is the maximum
amount you would be willing to pay for the business if you wished to earn at least a 10% return on
your investment?
N periods
Interest rate 1 2 3 4
10% $0.9091 $0.8264 $0.7513 $0.6830
11% .9009 .8116 .7312 .6587
12% .8929 .7972 .7118 .6355
A.
$629,000
B.
$500,000
C.
$482,582
D.
$375,655
34. A business is for sale at $100,000. Discounting the expected cash inflows and expected cash
outflows (except the purchase price) at 12% yields an amount of $94,741. Based on this
information:
A.
the minimum price you should pay for the business is $94,741.
B.
at a purchase price of $100,000, the business is projected to earn just a little more than
12%.
C.
a higher discount rate would make this business opportunity more attractive.
D.
the investment opportunity should be rejected if a 12% return is required.
35. Which of the following will increase future value relative to present value?
A.
A higher interest rate
B.
A shorter period
C.
More safety
D.
Less risk
36. Which of the following combinations of interest rate and number of periods is needed for
calculation of the present value of an investment that involves an annual interest rate of 12% for 3
years with monthly compounding?
Number of periods Interest rate
A.
3 12%
B.
6 6%
C.
12 3%
D.
36 13%
37. A series of equal amounts received or paid over a specified number of equal time periods is known
as an:
A.
allotment.
B.
apportionment.
C.
annuity.
D.
allowance.
38. An annuity is a series of:
A.
equal amounts paid or received over a specified number of unequal time periods.
B.
unequal amounts paid or received over a specified number of equal time periods.
C.
equal amounts paid or received over an unspecified number of equal time periods.
D.
equal amounts paid or received over a specified number of equal time periods.
39. Which of the following best expresses the concept of compound interest?
A.
Calculating interest on an annuity.
B.
Earning interest on interest already earned.
C.
Making complicated interest calculations.
D.
Making more than one interest payment.
40. Earning interest in one period on interest earned in an earlier period is known as:
A.
simple interest.
B.
compound interest.
C.
combined interest.
D.
composite interest.
41. If you placed $1000 in a savings account today, how much would you have one year from now if
the bank paid 8% interest?
A.
$1800
B.
$1080
C.
$1008
D.
$1000
42. Which of the following formulas would you use to correctly calculate the future amount of an
investment of $600 that was earning interest at 8% annually for three years?
A.
$600 1.08 1.08 1.08
B.
$600 1.08 3
C.
3 $600 0.08
D.
(1.08 3) $600
SHORT ANSWER
1. Describe the accounting rate of return (ARR) and payback period methods of evaluating capital
projects, including the formula and decision criterion associated with each method.
2. Describe the major disadvantages of using the accounting rate of return (ARR) and payback period
methods as bases for evaluating capital projects.
PROBLEM
1. Harglo Construction is considering purchasing a radio antenna for broadcasting to service trucks
over the airwaves, rather than using telephone lines. The antenna is expected to reduce cash
operating costs by $2000 the first year, $2500 the second year, and $3000 the third year. The
antenna will cost $6000, will last 3 years (due to technological advances), and will have no
residual value at the end of its life. Harglo’s minimum acceptable rate of return is 8%.
(a)
Compute the net present value of the investment in the antenna.
(b)
If Harglo’s cost of capital was 12%, would this proposal be acceptable?
2. The Sloopy Jeans Company is considering the purchase of a machine that would increase the
company’s cash inflows by $12,000 per year for six years. Operation of the machine would
increase the company’s cash payments by $400 in each of the first three years, $800 the fourth
year, and $1000 in the fifth and sixth years. The machine costs $50,000 and would have a residual
value of $2000 at the end of the sixth year.
(a)
Compute the payback period for this machine.
(b)
Compute the net present value of the investment in the machine, assuming a
minimum acceptable rate of return of 16%.
3. The Tearess Company can accept either Proposal A or Proposal B (but not both), or it can reject
both investment proposals. Proposal A requires an investment of $7000 and promises increased net
cash inflows of $2600 for five years. Proposal B requires an investment of $7000 and promises
increased net cash inflows of $3000 in each of the first three years, $2000 in the fourth year and
$2200 in the fifth year. The company’s minimum acceptable rate of return is 20%.
Prepare an analysis to determine which (if either) of the proposals should be selected for
investment.
4. First Time Cinema, Inc., is a small company that produces movies for artists who have little prior
experience in the film industry. Because of the high risk associated with these projects, the
company will not accept projects that have a payback period of more than three years. The
company is considering three projects and requests your assistance in evaluating their potential
given their projected cash flows.
Year
Project 1
Project 2
Project 3
0
$(150,000)
$(25,000)
$(100,000)
1
$ 50,000
$ 19,000
$ (20,000)
2
$ 100,000
$ 1000
$ 40,000
3
$ 1000
$ 10,000
$ 40,000
4
$ 1000
$ 10,000
$ 40,000
5
$ 1000
$ 10,000
$ 450,000
(a)
Calculate the payback period for each project.
(b)
Which project(s) would you accept? Why?
(c)
Discuss any reasons why you are satisfied or dissatisfied with the results of
your analysis above.
Payback period:
Year 2 =
100,000
Project 2: 2.5 years
Year 1 =
$ 19,000
Year 3 =
Project 3: 4 years
Year 1 =
$(20,000)
Year 3 =
5. Second Time Cinema, Inc., is a small company which produces movies for artists who have some
prior experience in the film industry. Because of the high risk associated with these projects, the
company will not accept projects that have an Accounting Rate of Return of less than 25%. The
company is considering three projects and requests your assistance in evaluating their potential
given their projected cash flows. All of the initial investments are assets which have an estimated
life of five years and will be depreciated on a straight-line basis.
Year
Project 1
Project 2
Project 3
0
$(150,000)
$(25,000)
$(100,000)
1
$ 170,000
$ 6000
$ (20,000)
2
$ 60,000
$ 33,000
$ 20,000
3
$ 34,000
$ 9000
$ 20,000
4
$ 34,000
$ 7000
$ 85,000
5
$ 34,000
$ 5000
$ 140,000
(a)
Calculate the ARR (on initial investment) for each project.
(b)
Which project(s) would you accept? Why?
(c)
Discuss any reasons why you are satisfied or dissatisfied with the results of your
analysis above.
measures available.
There are many reasons to be dissatisfied. First, although the ARR for Project 2 is
slightly less than Project 3, a much larger percentage of the cash flow is received in
years 1 and 2 than for Project 3 (the one selected using ARR).
investment, even though it has the smallest ARR. Even without calculating, it is
apparent that the large cash flow received in year 1 for Project 1 would be sufficient
compensation to the company to substantially lower the risk assumed.
6. A company is considering two projects with the following cash flows: (Albright, 12, p.4)
Year
Project A
Project B
0
$(526,677)
$(74,809)
1
$ 180,000
$ 30,000
2
$ 180,000
$ 30,000
3
$ 180,000
$ 30,000
4
$ 180,000
$ 30,000
5
$ 180,000
-0-
Present value of $1 to be received after N periods:
N Periods
Interest Rate
1
2
3
4
5
19%
0.8403
0.7062
0.5934
0.4987
0.4190
20%
0.8333
0.6944
0.5787
0.4823
0.4019
21%
0.8264
0.6830
0.5645
0.4665
0.3855
22%
0.8197
0.6719
0.5507
0.4514
0.3700
Present value of an annuity of $1 for N periods:
N Periods
Interest Rate
1
2
3
4
5
19%
0.8403
1.5465
2.1399
2.6386
3.0576
20%
0.8333
1.5278
2.1065
2.5887
2.9906
21%
0.8264
1.5095
2.0739
2.5404
2.9260
22%
0.8197
1.4915
2.0422
2.4936
2.8636
(a)
Assuming a discount rate of 20% and no taxes, compare these projects using Net
Present Value (NPV). Which project would you accept? Why?
(b)
Calculate the Internal Rate of Return (IRR) of each project using the partial tables
provided. Which project would you accept relying solely on the IRR to make your
decision?
(c)
Considering both IRR and NPV, which project would you accept? Why?