Chapter 9
Capital Budgeting Decisions
QUESTIONS
1. A capital expenditure decision is a decision involving the acquisition of a long-lived asset.
2. Time value of money must be considered because the value of money received in the future
from an investment is not equivalent to the value of money expended to acquire the
investment in the current period.
3. Two approaches that consider the time value of money are the net present value (NPV)
approach and the internal rate of return (IRR) approach.
4. With the net present value approach, investments are accepted if the net present value is
equal to or greater than zero. With the internal rate of return approach, investments are
accepted if the internal rate of return is equal to or greater than the required rate of return.
5. The cost of equity is the return demanded by shareholders for the risk they bear in
supplying capital to the firm.
6. Because depreciation reduces taxable income, it results in a tax savings equal to the tax rate
times the amount of depreciation.
7. The payback method does not consider the total stream of cash flows and it does not
consider the time value of money. The accounting rate of return method does not consider
the time value of money.
8. Managers may concentrate on short-run profitability rather than net present value if their
performance is evaluated and compensated based on current period profit.
9. With uneven cash flows, the internal rate of return is calculated using a trial and error
approach. Managers “guess” at the IRR and calculate the present value. If the present
value is greater than zero, the guess is increased. If the present value is negative, the guess
is decreased.
10. In many cases, the benefits of an investment are difficult to quantify (i.e., they are soft
benefits). However, ignoring them is equivalent to ignoring cash inflows and tends to
discourage investment.
9-2
Jiambalvo Managerial Accounting
EXERCISES
E1.
Interest expense is not treated as a cash outflow because the “charge” for
interest is included in the cost of capital (i.e., the hurdle or discount rate).
E2. The NPV is positive and Pauline should make the investment.
Time
0
1
2
3
4
5
6
7
8
Cash Flow
(25,000,000)
5,500,000
5,500,000
5,500,000
5,500,000
5,500,000
5,500,000
5,500,000
5,500,000
PV Factors
1.0000
0.8929
0.7972
0.7118
0.6355
0.5674
0.5066
0.4523
0.4039
NPV
1
2
3
4
5
6
7
8
Effect on
Income
2,375,000
2,375,000
2,375,000
2,375,000
2,375,000
2,375,000
2,375,000
2,375,000
End of Year
Investment
21,875,000
18,750,000
15,625,000
12,500,000
9,375,000
6,250,000
3,125,000
0
$(25,000,000)
4,910,950
4,384,600
3,914,900
3,495,250
3,120,700
2,786,300
2,487,650
2,221,450
$
2,321,800
ROI
0.109
0.127
0.152
0.190
0.253
0.380
0.760
division by zero
not defined
Although the project has a positive NPV, if Pauline is overly focused on
short-term performance, she may hesitate to make the investment, which
has a relatively low ROI in the first year. Note that ROI increases
dramatically as the book value of the investment decreases due to
depreciation.
Chapter 9 Capital Budgeting Decisions
9-3
E3. According to Mignogna,
“You can often determine the cash benefit of increases in capacity,
production efficiency, and quality, as well as reductions in operating and
maintenance costs attributable to an investment in new technology.
However, seldom accounted for are the strategic benefits which result from
such investments. With the assistance of the accompanying decisionmaking flow chart, let’s look at a few.
First of all, is the investment required just to stay in game (for example,
required for regulatory compliance)? If so, and assuming the game is worth
being in, then you may not have any choice but to “just do it!”
Next, have you considered the importance of the investment to remain
competitive in your industry? Here, I am speaking of your ability to
acquire, or at least defend, market share. While discounted cash flow
analyses may include the benefits of reduced operating costs and so on,
they seldom consider the opportunity cost of the lost business which
results from your competitors’ ability to offer a higher quality at a reduced
cost. In other words, there may be a very real cost attached to not pursuing
an innovation.
There are several other strategic considerations that are not particularly
amenable to economic analyses. Will the investment add to or enhance
your firm’s core competencies? Will it provide the capability to penetrate
new markets with your product or service? Will expanded production
capacity provide access to increased sales and more rapid learning curve
progress which will ultimately lower costs? Are you in an industry where
the market perceives technological leadership as important? You can
probably think of others specific to your own situation. Such strategic
benefits are seldom considered in discounted cash flow analyses of new
technology. Remember, there’s a big difference between running the
numbers and letting the numbers run you.”
9-4
Jiambalvo Managerial Accounting
E4. Company
Charles Schwab
McDonalds
Wal-Mart
E5.
E6.
Investment decision
Should the company purchase additional servers and other
equipment to enhance services related to the online
business?
Should the company purchase land, building, and
equipment for a new restaurant?
Should the company remodel it’s superstore on the west
side of Chicago?
Cash
Flow
$100
Present Value
Factor
.6209
Total
$62.09
Cash
Flow
$100
Present Value
Factor
3.7908
Total
$379.08
E7. The numbers decrease from left to right in a given row because cash received
in the future is worth less the higher your required rate of return.
The numbers decrease from top to bottom in a given column because cash
received further in the future is less valuable today.
E8.
Cash
Flow
$200
500
Present Value
Factor
3.7908
.6209
Total
$ 758.16
310.45
$1,068.61
Chapter 9 Capital Budgeting Decisions
E9. Plan A
Total
$100,000.00
Plan B
Cash
Flow
$ 10,000
100,000
Present Value
Factor
6.7101
.4632
Plan C
Cash
Flow
$20,000
Present Value
Factor
6.7101
Total
$ 67,101.00
46,320.00
$113,421.00
Total
$134,202.00
Plan C should be selected as it has the highest present value.
E10.
Cash
Flow
($10,000)
4,000
Present Value
Factor
1.0000
3.0373
Total
($10,000.00)
12,149.20
$ 2,149.20
The net present value is positive so the project should be undertaken.
9-5
9-6
Jiambalvo Managerial Accounting
E11. The investment should not be undertaken because it has a negative NPV.
Cash
Flow
$6,000.00
(3,500.00)
950.00
(1,800.00)
1,650.00
Present Value
Factor
(20,000.00)
5,000.00
1.0000
.2697
5.2161
Total
$8,606.56
(20,000.00)
1,348.50
($ 10,044.94)
E12. Machine A should be purchased because it has the highest positive NPV.
Machine A
Cash
Flow
$15,000.00
(50,000.00)
Present Value
Factor
4.3553
1.0000
Machine B
Cash
Flow
$20,000.00
(75,000.00)
Present Value
Factor
4.3553
1.0000
Total
$65,329.50
(50,000.00)
$15,329.50
Total
$87,106.00
(75,000.00)
$12,106.00
Chapter 9 Capital Budgeting Decisions
9-7
E13. The investment should not be undertaken because the internal rate of return
of 12% is less than the required rate of 18%.
Initial outlay
Annuity amount
Outlay ÷ annuity amount
Internal rate of return
E14. a.
Initial outlay
Annuity amount
Outlay ÷ annuity amount
Internal rate of return
$79,100.00
14,000.00
5.6500
12%
$79,137.00
22,500.00
3.5172
13%
b. Nadine should make the investment because its return of 13% is greater
than the required return of 12%.
E15. Annual depreciation
$200,000 ÷ 5 years
$40,000.00
Annual tax savings
$40,000 × .40
$16,000.00
Present value of $16,000 per year
for 5 years at 10%
$16,000 × 3.7908
$60,652.80
9-8
E16.
Jiambalvo Managerial Accounting
Year
1
2
3
4
Income (Loss)
($100,000)
(50,000)
120,000
200,000
The $100,000 loss in year 1 will offset income in year 3 resulting in a tax
savings of $40,000 (i.e., $100,000 × 40% tax rate) in year 3.
With respect to the $50,000 loss in year 2, $20,000 of it can be used to offset
income in year 3 (resulting in a tax savings of $8,000 in year 3) and $30,000
of it can be used to offset income in year 4 (resulting in a tax savings of
$12,000 in year 4).
Cash
Flow
$40,000.00
8,000.00
12,000.00
Present Value
Factor
.6750
.6750
.5921
Total
$27,000.00
5,400.00
7,105.20
$39,505.20
Chapter 9 Capital Budgeting Decisions
E17. The annual cash inflow is $5,700, calculated as follows:
Revenue
$15,500
Less:
Cost other than depreciation
8,000
Depreciation
3,000
Income before taxes
4,500
Less taxes at 40%
1,800
Net income
2,700
Plus depreciation
3,000
Cash flow
$5,700
The net present value is positive, so the smoker should be purchased.
Cash
Flow
$5,700.00
(21,000.00)
Present Value
Factor
4.5638
1.0000
Total
$26,013.66
(21,000.00)
$ 5,013.66
E18. The payback period is 8.2 years as follows:
Cost
Cash inflows
Cost ÷ cash inflows
$41,000.00
5,000.00
8.2 years
E19. The accounting rate of return is 30%:
Average income
Average investment ($200,000 ÷ 2)
Accounting rate of return
$30,000.00
100,000.00
30.00%
9-9
9-10
Jiambalvo Managerial Accounting
E20. As indicated, the NPV is close to zero ($145.00) at a rate of 14%. Thus, the
IRR is approximately 14%. Given that the required rate of return is only
13%, the e-commerce business should be developed.
PV at
13%
Cash
Flow
$(1,000,000)
(500,000)
200,000
630,000
750,000
800,000
PV
Factor
1.0000
0.8850
0.7831
0.6931
0.6133
0.5428
PV at
14%
Cash
Flow
$(1,000,000)
(500,000)
200,000
630,000
750,000
800,000
PV
Factor
1.0000
0.8772
0.7695
0.6750
0.5921
0.5194
PV at
15%
Cash
Flow
$(1,000,000)
(500,000)
200,000
630,000
750,000
800,000
PV
Factor
1.0000
0.8696
0.7561
0.6575
0.5718
0.4972
Total
$(1,000,000)
(442,500)
156,620
436,653
459,975
434,240
$ 44,988
Total
$(1,000,000)
(438,600)
153,900
425,250
444,075
415,520
$
145
Total
$(1,000,000)
(434,800)
151,220
414,225
428,850
397,760
$ (42,745)
Chapter 9 Capital Budgeting Decisions
9-11
E21. As indicated below, the NPV is zero with a required rate of return of 9
percent. Thus, the IRR is 9 percent.
PV at
9%
Cash
Flow
$(2,200,100)
200,000
400,000
600,000
800,000
1,000,000
PV
Factor
1.0000
0.9174
0.8417
0.7722
0.7084
0.6499
Total
$(2,200,100)
183,480
336,680
463,320
566,720
649,900
$
0
E22. The online business may help the company manage a potentially stodgy
image associated with its mall locations. Also, the online business may
actually generate a number of large sales for the brick and mortar locations.
Some customers will shop the Web site to make price and quality
comparisons, but they will be unwilling to make, for example, a $5,000
purchase of a diamond ring over the Internet. Thus, after seeing
merchandise on the Web site, they may visit one of Sherman’s mall stores to
make a purchase. These potential benefits would be difficult to quantify.
E23. The annual value of the “soft” benefit must be at least $88,492.44 for the
project to have a zero net present value. Given there is general agreement
that the annual “soft” benefit will be at least $90,000, Pritchard should invest
in the flexible manufacturing system.
A. Present value needed to yield a zero NPV
$500,000.00
B. Present value of an annuity factor at 12%
5.6502
A ÷ B Required annual value of “soft benefit”
$88,492.44
9-12
Jiambalvo Managerial Accounting
PROBLEMS
P1. The original contract was worth $6,790,700 in present value terms while the
new offer is worth $6,960,460. When the time value of money is taken into
account, it is obvious that the new offer is not much better than the old one.
Time
0
1
2
3
4
5
Cash
Flow
$3,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
PV
Factor
1.0000
0.9091
0.8264
0.7513
0.6830
0.6209
Time
1
2
3
4
5
5
Cash
Flow
1,000,000
1,100,000
1,200,000
1,300,000
1,400,000
4,000,000
PV
Factor
0.9091
0.8264
0.7513
0.6830
0.6209
0.6209
Total
$3,000,000
909,100
826,400
751,300
683,000
620,900
$6,790,700
Total
909,100
909,040
901,560
887,900
869,260
2,438,600
$6,960,460
Chapter 9 Capital Budgeting Decisions
9-13
P2. a. Present value of ship in Caribbean/Alaska itinerary at 10%
($68,095,769 × 7.6061)
$517,943,229
Present value of ship in Caribbean/Eastern Canada itinerary at 10%
($53,490,300 × 7.6061)
$406,852,571
Present value of ship in Caribbean/Alaska itinerary at 15%
($68,095,769 × 5.8474)
$398,183,200
Present value of ship in Caribbean/Eastern Canada itinerary at 15%
($53,490,300 × 5.8474)
$312,779,180
The cost of the ship is only $180,325,005. Therefore, the NPV will be positive
under all of the alternatives which provides strong evidence that the ship
should be purchased.
b. The NPV will be positive (suggesting that the ship should be purchased)
whether the required return is 10 percent or 15 percent.
c. The difference in present values is $111,090,658 ($517,943,229 $406,852,571). Thus, there is a high opportunity cost if the firm decides to
operate the ship in a Caribbean/Eastern Canada itinerary.
9-14
Jiambalvo Managerial Accounting
P3.
Year 1
Revenue
$12,000,000
Less amortization
12,000,000
Income before taxes
0
Less taxes
0
Net income
0
Add amortization
12,000,000
Cash flow
$12,000,000
Time
0
1
2
3
4
Cash
Flow
($16,000,000)
12,000,000
5,200,000
1,200,000
300,000
Year 2
$6,000,000
4,000,000
2,000,000
800,000
1,200,000
4,000,000
$5,200,000
PV
Factor
1.0000
.9091
.8264
.7513
.6830
Year 3
$2,000,000
0
2,000,000
800,000
1,200,000
0
$1,200,000
Year 4
$500,000
0
500,000
200,000
300,000
0
$300,000
Total
($16,000,000)
10,909,200
4,297,280
901,560
204,900
$ 312,940
Since the NPV is positive, the company should produce the film.
Chapter 9 Capital Budgeting Decisions
9-15
P4. Cash flow per year:
Revenue
Less costs other
than depreciation
Depreciation
Income before taxes
Less taxes
Net income
Add depreciation
Cash flow
$75,000
6,800
40,000
28,200
11,280
16,920
40,000
$56,920
Annuity factor equals cost divided by annual cash flow:
($200,000 ÷ $56,920)
3.5137
This implies an internal rate of return of approximately 13% (factor is 3.5172)
Given the internal rate of return exceeds the required rate of 12%, the company
should invest in the remodel.
9-16
Jiambalvo Managerial Accounting
P5. a. The net present value is positive ($43,496.60). Thus the company should
invest in the paint and body shop.
Net income
Add depreciation
Annual cash flow
Cash
Flow
$121,000
(700,000)
$ 51,000
70,000
$121,000
Present Value
Factor
6.1446
1.0000
Total
$743,496.60
(700,000.00)
$ 43,496.60
b. A present value of an annuity factor of 5.7851 implies an IRR of
approximately 12%.
Initial outlay
Annuity amount
$700,000
121,000
Cost ÷ annuity
5.7851
Note—the annuity factor for 12% is 5.6502.
c. The payback period is approximately 5.8 years:
Initial outlay
Annual cash flow
Number of years to recover
initial investment
$700,000
121,000
5.7851
d. The accounting rate of return is approximately 35%:
Average income
$51,000
Average investment
($700,000 ÷ 2)
350,000
Accounting rate of return
14.57%
Chapter 9 Capital Budgeting Decisions
9-17
P6. a. Present value of Machine A
Labor saving
Power saving
Chemical saving
Add. Main.
Add. Misc.
Total
Cost
Installation
Residual value
Cash
Flow
$21,000
1,300
2,900
(1,000)
(2,200)
22,000
(43,000)
(4,500)
3,200
PV
Factor
Total
2.9137
1.0000
1.0000
.5921
NPV
$ 64,101.40
(43,000.00)
(4,500.00)
1,894.72
$18,496.12
b. Present value of Machine B
Labor saving
Power saving
Chemical saving
Add. Main.
Add. Misc.
Total
Cost
Installation
Residual value
Cash
Flow
$29,000
1,900
3,200
(1,200)
(2,300)
30,600
(73,000)
(5,000)
5,200
PV
Factor
Total
2.9137
1.0000
1.0000
.5921
NPV
$ 89,159.22
(73,000.00)
(5,000.00)
3,078.92
$14,238.14
c. Both NPVs are greater than zero, so both are acceptable investments.
However, the company should purchase machine A since it has the highest
NPV.
9-18
Jiambalvo Managerial Accounting
P7. Crown should invest in the new limousine since the NPV is positive.
Net income
Add depreciation
Annual cash flow
Cash
Flow
$29,790.00
20,000.00
(80,000.00)
$17,790
12,000
$29,790
Present Value
Factor
3.4331
.5194
1.0000
Total
$102,272.05
10,388.00
(80,000.00)
$ 32,660.05
P8. Island Ferry should not invest in the boat because the NPV is negative.
Revenue
Less:
Labor
Fuel
Maintenance
Miscellaneous
Depreciation
Income before taxes
Taxes
Net income
Depreciation
Annual cash flow
Cash
Flow
$136,100.00
62,000.00
(828,000.00)
$293,000
84,000
15,800
26,700
3,500
95,750
67,250
26,900
40,350
95,750
$136,100
Present Value
Factor
4.9676
.4039
1.0000
Total
$676,090.36
25,041.80
(828,000.00)
($126,867.84)
Chapter 9 Capital Budgeting Decisions
P9. a. Revenue (35,000 × $35)
Less:
Component cost
Direct labor
Depreciation
Miscellaneous
Advertising
Income before taxes
Taxes
Net income
Depreciation
Annual cash flow
Cash
Flow
$153,000.00
10,000.00
(310,000.00)
$1,225,000
300,000
400,000
60,000
180,000
130,000
155,000
62,000
93,000
60,000
$ 153,000
Present Value
Factor
3.4331
.5194
1.0000
Total
$525,264.30
5,194.00
(310,000.00)
$220,458.30
b. The payback period is approximately 2 years:
Initial outlay
Annual cash flow
$310,000
153,000
Number of years to recover
initial investment
2.026 years
c. The accounting rate of return is 60%:
Average income
Average investment
($310,000 ÷ 2)
Accounting rate of return
$93,000
$155,000
60%
d. Given the positive NPV, company should invest in Autodial.
9-19
9-20
Jiambalvo Managerial Accounting
P10. Year
1
Income
$45,000
Deprec.
50,000
Cash flow $95,000
2
3
4
5
6
7
48,750 52,688 56,822 61,163 65,721 70,507
50,000 50,000 50,000 50,000 50,000 50,000
98,750 102,688 106,822 111,163 115,721 120,507
Year
1.
2.
3.
4.
5.
6.
7.
Cash flow
$95,000
98,750
102,688
106,822
111,163
115,721
120,507
Factor
.8772
.7695
.6750
.5921
.5194
.4556
.3996
Total
$ 83,334.00
75,988.13
69,314.40
63,249.31
57,738.06
52,722.49
48,154.60
7.
50,000
.3996
19,980.00
0.
- 400,000
1.0000
- 400,000.00
NPV
$ 70,480.99
Given the positive NPV, the company should invest in the new business.
Chapter 9 Capital Budgeting Decisions
9-21
P11. a. The cost of capital includes an allowance for expected inflation. Thus, in
periods where expected inflation is high, the cost of capital is high, and
firms demand a high return on their investments.
b. Note that cash flows increase by 4% per year (except for the cash flow
related to the depreciation tax shield).
Year 1
Year 2
$575,000 $598,000
Cost savings
Taxes on
cost savings
-201,250 -209,300
Tax savings
related to depre. 140,000 140,000
Cash flow
$513,750 $528,700
Year
1
2
3
4
5
Cash flow
$513,750
528,700
544,248
560,418
577,235
Less cost of machine
Net present value
Year 3
$621,920
Year 4
$646,797
Year 5
$672,669
-217,672
-226,379
-235,434
140,000
$544,248
140,000
$560,418
140,000
$577,235
Factor
.9091
.8264
.7513
.6830
.6209
Total
$ 467,050
436,918
408,894
382,765
358,405
2,054,032
2,000,000
$ 54,032
Given the positive NPV, the company should invest in the manufacturing
equipment.
9-22
Jiambalvo Managerial Accounting
P12. Note that in problem 11, the NPV was only $54,032 using a 10% required
rate of return. This suggests that to determine the IRR, we should start with
a return larger than, but close to, 10 percent. Below, the cash flows are
brought to present value using an 11% rate of return. Since the sum of the
present values is approximately equal to the cost of the investment (a
difference of $1,620), the internal rate of return is approximately 11%.
Given that this is greater than the required return of 10%, the investment
should be undertaken.
Year
1.
2.
3.
4.
5.
Cash flow
$513,750
528,700
544,248
560,418
577,235
Less cost of machine
Net present value
Factor
.9009
.8116
.7312
.6587
.5935
Total
$ 462,837
429,093
397,954
369,147
342,589
2,001,620
2,000,000
$
1,620
Chapter 9 Capital Budgeting Decisions
9-23
P13. Most likely, a higher required rate of return should be used reflecting the
increased risk of the investment.
P14. a. Richards is evaluated and compensated based on ROI which has some
measure of income in the numerator (and a measure of investment in the
denominator). Thus, he will be highly focused on income. Some
investment opportunities facing his division may increase shareholder
wealth (as indicated by positive NPVs) but have a negative effect on
short-run accounting income. If that will cause Richards to miss a bonus
target, he may pass on these valuable investments.
b. I believe this will mitigate the problem. If Richards owns a great deal of
stock/and or options, he will have a strong incentive to work to increase
the firm’s stock price. And stock prices are likely to be positively
impacted when the firm takes on projects with positive NPVs.
9-24
Jiambalvo Managerial Accounting
P15.
Revenue
Less:
Ingred.
Salary
Misc.
Depre.
Inc. before taxes
Taxes
Net income
Depre.
Cash flow
Year 1
$63,000
Year 2
$69,300
Year 3
$76,230
Year 4
$83,853
Year 5
$92,238
25,200
25,000
2,200
8,000
60,400
2,600
1,040
1,560
8,000
$ 9,560
27,720
27,000
2,400
8,000
65,120
4,180
1,672
2,508
8,000
$10,508
30,492
29,000
2,600
8,000
70,092
6,138
2,455
3,683
8,000
$11,683
33,541
31,000
2,800
8,000
75,341
8,512
3,405
5,107
8,000
$13,107
36,895
33,000
3,000
8,000
80,895
11,343
4,537
6,806
8,000
$14,806
Year
1.
2.
3.
4.
5.
Cash flow
$ 9,560
10,508
11,683
13,107
14,806
Factor
.8850
.7831
.6931
.6133
.5428
Total
$ 8,460.60
8,228.81
8,097.49
8,038.52
8,036.70
5.
2,000
.5428
1,085.60
0.
-40,000
1.0000
- 42,000.00
NPV
($
52.28)
Using a rate of return of 13%, the NPV is approximately zero. Therefore, the
IRR is approximately 13%. Melrose should investment in the delivery
business given that the company’s required rate of return is only 10%.