Chapter 26
Capital Investment Decisions
Review Questions
1. Explain the difference between capital assets, capital investments, and capital budgeting.
A capital asset is an operational asset used for a long period of time. A capital investment is the
2. Describe the capital budgeting process.
The capital budgeting process consists of the following:
• Step 1: Develop strategies (long-term goals).
3. What is capital rationing?
4. What are post-audits? When are they conducted?
A post-audit is the comparison of actual results of capital investments to the projected results. The
comparisons help companies determine whether the investments are going as planned and deserve
5. List some common cash inflows from capital investments.
6. List some common cash outflows from capital investments.
7. What is the payback method of analyzing capital investments?
8. How is payback calculated with equal net cash inflows?
9. How is payback calculated with unequal net cash inflows?
If net cash inflows are unequal, the payback period (in years) of an investment is calculated as
follows:
• Add the accumulated net cash inflows for full years before complete recovery, then
10. What is the decision rule for payback?
11. What are some criticisms of the payback method?
12. What is the accounting rate of return?
13. How is ARR calculated?
14. What is the decision rule for ARR?
15. Why is it preferable to receive cash sooner rather than later?
A dollar received today is worth more than a dollar to be received in the future because today’s
16. What is an annuity? How does it differ from a lump sum payment?
17. How does compound interest differ from simple interest?
Simple interest means that interest is calculated only on the principal amount. In contrast,
compound interest means that interest is calculated on the principal and on all previously earned
18. Explain the difference between the present value factor tables—Present Value of $1 and Present
Value of Ordinary Annuity of $1.
19. How is the present value of a lump sum determined?
20. How is the present value of an annuity determined?
21. Why are net present value and internal rate of return considered discounted cash flow methods?
Net present value (NPV) and internal rate of return (IRR) are considered discounted cash flow
22. What is net present value?
23. What is the decision rule for NPV?
24. What is the profitability index? When is it used?
The profitability index is the number of dollars received for every dollar invested, with all
calculations performed in present value dollars. It is calculated with the following formula: Present
25. What is the internal rate of return?
26. How is IRR calculated with equal net cash inflows?
If net cash inflows are equal, the internal rate of return (IRR) on an investment can be calculated
using present value (PV) tables as follows:
• Calculate the annuity PV factor using this equation:
Annuity PV factor
(i = ?, n = given)
=
Initial investment
/
Amount of each net cash inflow
27. How is IRR calculated with unequal net cash inflows?
If net cash inflows are unequal, the internal rate of return on an investment can be estimated using
trial-and-error. Start by calculating the net present value of the investment using the required rate of
28. What is the decision rule for IRR?
29. How can spreadsheet software, such as Excel, help with sensitivity analysis?
Using computer spreadsheet software, such as Microsoft Excel, can be beneficial because it allows
for easy manipulation of figures to perform sensitivity analysis. Sensitivity analysis is a “what if”
technique that shows how results differ when underlying assumptions change. Capital budgeting
30. Why should both quantitative and qualitative factors be considered in capital investment decisions?
Most companies have limited resources and have to make hard decisions about which projects to
pursue and which ones to delay or reject. These decisions are not just based on the quantitative
Short Exercises
S26-1 Outlining the capital budgeting process
Learning Objective 1
Review the following activities of the capital budgeting process:
a. Budget capital investments.
b. Project investments’ cash flows.
c. Perform post-audits.
d. Make investments.
e. Use feedback to reassess investments already made.
f. Identify potential capital investments.
g. Screen/analyze investments using one or more of the methods discussed.
Place the activities in sequential order as they occur in the capital budgeting process.
SOLUTION
S26-2 Using payback to make capital investment decisions
Learning Objective 2
Carter Company is considering three investment opportunities with the following payback periods:
Use the decision rule for payback to rank the projects from most desirable to least desirable, all else
being equal.
SOLUTION
S26-3 Using accounting rate of return to make capital investment decisions
Learning Objective 2
Carter Company is considering three investment opportunities with the following accounting rates of
return:
Use the decision rule for ARR to rank the projects from most desirable to least desirable. Carter
Company’s required rate of return is 8%.
SOLUTION
The ranking of the projects from most desirable to least desirable (highest accounting rate of return to
S26-4 Using the payback and accounting rate of return methods to make capital investment
decisions
Learning Objective 2
Consider how Stenback Valley Snow Park Lodge could use capital budgeting to decide whether the
$11,000,000 Snow Park Lodge expansion would be a good investment. Assume Stenback Valley’s
managers developed the following estimates concerning the expansion:
Assume that Stenback Valley uses the straight-line depreciation method and expects the lodge expansion
to have a residual value of $600,000 at the end of its eight-year life.
Requirements
1. Compute the average annual net cash inflow from the expansion.
2. Compute the average annual operating income from the expansion.
SOLUTION
Requirement 1
Average annual
cash inflow
=
Average cash spent
by each skier per day
×
Additional
skiers per day
×
Average days
of skiing per year
=
×
×
=
Average annual
cash outflow
=
Average variable cost of
serving each skier per day
×
Additional
skiers per day
×
Average days of
skiing per year
=
×
×
=
Average annual
net cash inflow
=
Average annual
cash inflow
−
Average annual
cash outflow
=
=
Requirement 2
Total net cash inflows during
operating life of expansion
=
Average annual
net cash inflow
×
Operating life
of expansion
=
×
=
$21,498,048
Total depreciation during
operating life of expansion
=
Cost
−
Residual value
=
$11,000,000
=
$10,400,000
Total net cash inflows during operating life of expansion
$ 21,498,048
Less: Total depreciation during operating life of expansion
10,400,000
Total operating income during operating life
11,098,048
Average annual operating income from expansion
Note: Short Exercise S26-4 must be completed before attempting Short Exercise S26-5.
S26-5 Using the payback method to make capital investment decisions
Learning Objective 2
Refer to the Stenback Valley Snow Park Lodge expansion project in Short Exercise S26-4. Compute the
payback for the expansion project. Round to one decimal place.
SOLUTION
Payback
=
Amount invested
Expected annual net cash inflow
=
$11,000,000
Calculated in S26-4, Requirement 1
Note: Short Exercise S26-4 must be completed before attempting Short Exercise S26-6.
S26-6 Using the ARR method to make capital investment decisions
Learning Objective 2
Refer to the Stenback Valley Snow Park Lodge expansion project in Short Exercise S26-4. Calculate the
ARR. Round to two decimal places.
SOLUTION
Average amount invested
=
Amount invested + Residual value
2
2
=
ARR
=
Average annual operating income
Average amount invested
=
Note: Short Exercises S26-4, S26-5, and S26-6 must be completed before attempting Short Exercise
S26-7.
S26-7 Using the payback and ARR methods to make capital investment decisions
Learning Objective 2
Refer to the Stenback Valley Snow Park Lodge expansion project in Short Exercise S26-4 and your
calculations in Short Exercises S26-5 and S26-6. Assume the expansion has zero residual value.
Requirements
1. Will the payback change? Explain your answer. Recalculate the payback if it changes. Round to one
decimal place.
2. Will the project’s ARR change? Explain your answer. Recalculate ARR if it changes. Round to two
decimal places.
3. Assume Stenback Valley screens its potential capital investments using the following decision
criteria:
Will Stenback Valley consider this project further or reject it?
SOLUTION
Requirement 1
If the expansion has a residual value of zero, rather than $600,000, the payback period will not change
because the payback method considers only those cash flows that occur during the payback period and
Requirement 2
If the expansion has a residual value of zero, rather than $600,000, the accounting rate of return (ARR)
will change because expected residual value is considered in the calculation of average annual operating
Total depreciation during
operating life of expansion
=
Cost
−
Residual value
=
$11,000,000
=
$11,000,000
Average amount invested
=
Amount invested + Residual value
2
=
2
=
Total net cash inflows during
operating life of expansion
=
Average annual
net cash inflow
×
Operating life
of expansion
=
×
=
$21,498,048
Calculated in S26-4, Requirement 1.
S26-7, cont.
Requirement 2, cont.
Total net cash inflows during operating life of expansion
$21,498,048
Less: Total depreciation during operating life of expansion
11,000,000
Total operating income during operating life
10,498,048
Divide by: Expansion’s operating life in years
Average annual operating income from expansion
$ 1,312,256
ARR
=
Average annual operating income
Average amount invested
=
If residual value is zero, rather than $600,000, the revised ARR for the expansion is 23.86% (rounded).
Note that this is a decrease from the 23.92% ARR calculated in Short Exercise S26-6. Although the
Requirement 3
S26-8 Using the payback and ARR methods to make capital investment decisions
Learning Objective 2
Suppose Stenback Valley is deciding whether to purchase new accounting software. The payback for the
$30,050 software package is five years, and the software’s expected life is seven years. Stenback
Valley’s required rate of return for this type of project is 9.0%. Assuming equal yearly cash flows, what
are the expected annual net cash savings from the new software?
SOLUTION
Payback
=
Amount invested
Expected annual net cash savings
Thus:
Expected annual net cash savings
=
Amount invested
=
S26-9 Using the time value of money
Learning Objective 3
Use the Present Value of $1 table (Appendix B, Table B-1) to determine the present value of $1 received
one year from now. Assume a 12% interest rate. Use the same table to find the present value of $1
received two years from now. Continue this process for a total of five years. Round to three decimal
places.
Requirements
1. What is the total present value of the cash flows received over the five-year period?
2. Could you characterize this stream of cash flows as an annuity? Why or why not?
3. Use the Present Value of Ordinary Annuity of $1 table (Appendix B, Table B-2) to determine the
present value of the same stream of cash flows. Compare your results to your answer to Requirement
1.
4. Explain your findings.
SOLUTION
Requirement 1
Time
Cash
Inflow
PV Factor
(i = 12%)
Present
Value
Present value of each year’s $1
1
(n = 1)
$ 1
0.893
$ 0.893
2
(n = 2)
0.797
3
(n = 3)
0.712
4
(n = 4)
0.636
5
(n = 5)
0.567
Total present value
$ 3.605
Requirement 2
Requirement 3
The total present value is $3.605, which is the same as in Requirement 1.
Present value
=
Amount of
each cash inflow
×
Annuity PV Factor for i = 12%, n = 5
=
×
=
$3.605
Requirement 4
The total present value of the stream of cash inflows ($3.605) is the same in Requirement 1 and
Requirement 3 because the annuity table of present value factors (Table B-2) is derived from the lump
S26-10 Using the time value of money
Learning Objective 3
Your grandfather would like to share some of his fortune with you. He offers to give you money under
one of the following scenarios (you get to choose):
1. $8,550 per year at the end of each of the next seven years
2. $48,350 (lump sum) now
3. $100,250 (lump sum) seven years from now
Requirements
1. Calculate the present value of each scenario using an 8% discount rate. Which scenario yields the
highest present value? Round to nearest whole dollar.
2. Would your preference change if you used a 12% discount rate?
SOLUTION
Requirement 1
Scenario #1:
Present value
=
Amount of
each cash inflow
×
Annuity PV Factor for i = 8%, n = 7
=
×
=
$44,511 (rounded)
Scenario #3:
Present value
=
Cash inflow
×
PV Factor for i = 8%, n = 7
=
×
=
$58,446 (rounded)
Scenario
Present Value
(i = 8%, n = 7)
#1
$44,511 (rounded)
#2
$48,350
#3
$58,446 (rounded)
S26-10, cont.
Requirement 2
Scenario #1:
Present value
=
Amount of
each cash inflow
×
Annuity PV Factor for i = 12%, n = 7
=
×
=
$39,022 (rounded)
Scenario #2: Present value is $48,350 (the cash inflow) because it would be
received now.
Scenario #3:
Present value
=
Cash inflow
×
PV Factor for i = 12%, n = 7
=
×
=
Scenario
$39,022 (rounded)
S26-11 Using NPV to make capital investment decisions
Learning Objective 4
Refer to the Stenback Valley Snow Park Lodge expansion project in Short Exercise S26-4. What is the
project’s NPV (round to nearest dollar)? Is the investment attractive? Why or why not?
SOLUTION
Time
Net
Cash
Inflow
Annuity
PV Factor
(i = 12%,
n = 8)
PV Factor
(i = 12%,
n = 8)
Present
Value
1 – 10 years
PV of annuity
$ 2,687,256(a)
4.968
$ 13,350,287
PV of residual value
0.404
242,400
Total PV of net cash inflows
13,592,687
Initial investment
(11,000,000)
$ 2,592,687
Calculated in S26-4, Requirement 1
Note: Short Exercise S26-4 must be completed before attempting Short Exercise S26-12.
S26-12 Using NPV to make capital investment decisions
Learning Objective 4
Refer to Short Exercise S26-4. Assume the expansion has no residual value. What is the project’s NPV
(round to nearest dollar)? Is the investment attractive? Why or why not?
SOLUTION
Time
Net
Cash
Inflow
Annuity
PV Factor
(i = 12%,n = 8)
Present
Value
1 – 10 years
PV of annuity
$ 2,687,256(a)
4.968
$ 13,350,287
Initial investment
$ 2,350,287
Calculated in S26-4, Requirement 1
Note: Short Exercise S26-4 must be completed before attempting Short Exercise S26-13.
S26-13 Using IRR to make capital investment decisions
Learning Objective 4
Refer to Short Exercise S26-4. Continue to assume that the expansion has no residual value. What is the
project’s IRR? Is the investment attractive? Why or why not?
SOLUTION
Annuity PV Factor
(i = ?%, n = 8)
=
Initial investment
/
Amount of each net cash inflow
=
/
=
(a)
Calculated in S26-4, Requirement 1
Annuity PV Factor
Because 4.093 is between 4.344 and 4.078, the IRR is between 16% and 18%.