193
CHAPTER 12
CAPITAL BUDGETING AND
THE INVESTMENT DECISION
INTRODUCTION
Most of the matters discussed in the preceding eleven chapters concerned techniques, tools, and
methods available to management for short-run (generally defined as less than one year) decision
making. This chapter is concerned with long-run decision making for capital assets or fixed
assets. For this reason, the chapter may be studied relatively independently of others in the book,
as long as the student has a good basic knowledge of accounting and terminolgy.
TRUE OR FALSE QUESTIONS
(Correct answers indicated by T for True and F for False answers)
1. Decisions concerning investment in long-life assets are no more complex than
decisions concerning day-to-day matters.
F
2. The ARR formula is: net annual savings divided by average investment.
T
3. With the ARR method, if there is a trade-in value of the asset, that value is deducted
from initial investment (before dividing by two) to arrive at average investment.
F
4. The payback period method formula is: initial investment divided by net annual cash
savings.
T
5. Net annual cash saving in the payback period method is calculated by deducting
depreciation from net annual savings.
F
6. The payback period method measures the speed of recovering the cash put into an
investment.
T
7. Under the payback period method, the possible trade-in value of the asset at the end
of its useful life is ignored.
T
8. Both the payback period and the ARR methods ignore the time value of cash flows.
T
9. $1,000 today at 10% interest is worth more than $1,090 a year from now.
T
10. Discounted cash flow expresses future cash flows in terms of today’s value.
T
11. Discounted cash flow factors cannot be used if future cash flows are negative.
F
12. The discount rate used with the NPV investment method will be the same as the
current bank savings account interest rate.
F
13. The IRR investment method determines the interest (discount) rate that will equate
total discounted cash inflows with the initial investment.
T
194
14. A mutually exclusive alternative means that, if only one of a number of proposals is
to be accepted, the others will be rejected.
T
15. Capital rationing means that there is sufficient money to handle only a limited number
of investments in any budget period.
T
16. If both NPV and IRR are used to evaluate various alternative investments, their
ranking of these investments will always be identical.
F
17. In investment decision-making, one should ignore non-quantifiable factors.
F
18. Renting an asset, from a cash flow point of view, may be more profitable than
purchasing.
T
19. If a company leases an asset, it will have a cash flow advantage because depreciation
can be deducted and produces savings on income tax.
F
20. If, for a particular company, a purchase versus rental decision shows that the asset
should be purchased, then all future similar decisions should dictate purchase.
F
21. In deciding to purchase or lease an asset, any asset trade-in value under the ownership
option can be ignored.
F
22. In considering the leasing of an asset using discounted cash flow, the depreciation
method selected will affect the calculations.
F
MULTIPLE CHOICE QUESTIONS
(Correct answer indicated by asterisk)
1. Decisions about investing in fixed assets differ from day-to-day expense decisions because:
(a) The investment decision is affected by the future
(b) Only the general manager can be involved in the decision
(c) The relationship between increased net income from the investment and the actual
investment
(d) Year by year the additional cash flows from the investment
3. If an equipment investment was $10,000 with a 5-year life using straight-line depreciation
and provided additional annual sales revenue of $3,500 and expenses (excluding
depreciation) of $300, and the company is in a 50% tax bracket, the payback period is:
(c) 1.67 years
(d) 16.7 years
195
4. Given the facts in the preceding question, the ARR is:
(c) 6.0%
(d) 2.6%
5. A Company is trading in a fully depreciated old asset for a new one. Cost of the new asset is
$5,000 with a 5-year life and straight-line depreciation will be used. The company receives a
$500 allowance for the asset traded in. Additional sales revenue from the investment will be
$2,100 and expenses of $400 (excluding depreciation). The company is in a 25% tax
bracket. The payback period is:
(a) 7.50 years
(b) 8.33 years
6. Given the facts in the preceding question, the ARR is:
(c) 8.9%
(d) 8.0%
7. One of the criticisms of the ARR method is that it:
(c) Gives results that are not as satisfactory as the payback period method
(d) Does not allow two comparable investments to be considered at the same time
8. Average investment for the ARR method is calculated by:
(c) Dividing opening investment by 2 and adding trade-in value
(d) Dividing trade-in value by 2 and adding opening investment
9. The NPV method has an advantage over the payback period and ARR methods because:
(a) The forecasts of sales revenue and expenses are more accurate
(b) It uses discounted cash flow factors compiled by computer
10. Two alternative $15,000 investments are being considered. A 10% discount rate is used
because the company never invests at a lower rate than this. The NPV of Alternative A
shows a total present value of $12,400 and Alternative B a total present value of $12,800.
Given this information one should select:
(a) Neither, until one has used the ARR method to obtain the true rate of return
(b) B because it has a higher total present value
196
11. If the total present value of a 5-year investment using NPV and a 15% rate is $82,300, and
the initial investment is $100,000, one should:
(c) Determine the IRR and decide if one would be satisfied with that rate under the
circumstances
(d) Use the payback period and ARR methods to help make the decision
12. Purchasing is always preferable to leasing an asset because:
(a) The asset will have a trade-in value at the end of its useful life
(b) By purchasing and owning the asset, one can claim depreciation expense in excess of
rental expense and thus reduce income tax
EXERCISE SOLUTIONS
E12.1 Calculate an Accounting Rate of Return (ARR):
Net Annual Saving / Average Investment = $1,400 / $5,620 = 24.9%
E12.3 Calculate the payback period.
Net annual saving: $2,900
E12.4 Calculate the Net Present Value of a specific amount of cash flow.
Year 1: $4,285 × 0.9009 = $3,860
Year 2: $4,285 × 0.8166 = $3,499
E12.5 Repayment schedule with an item cost of $22,800 requiring a principle payment of
$4,560 per year plus interest at 12%:
Yr.
Interest
Principle
Balance
0
$22,800
1
$2,736
$4,560
18,240
2
2,189
4,560
13,680
3
1,642
4,560
9,120
4
1,094
4,560
4,560
5
547
4,560
-0-
197
E12.6 Determine payback periods for two alternatives.
Alternative 1
Alternative 2
Cost of investment
$33,000
$33,000
Cash recovery:
Years 1, 2, & 3
(25,400)
Years 1, 2, 3, & 4
( 30,000)
Balance
$ 7,600
$ 3,000
Alternative 1’s payback: $7,600 / $8,200 = 0.93 + 3 = 3.93 years
Alternative 2’s payback: $3,000 / $12,100 = 0.25 + 4 = 4.25 years
E12.7 Using the information in E12.6, determine the net present values
Alternative 1
Alternative 2
Year
Factor 12%
Total PV
Total PV
1
0.8929
$ 7,143
$ 3,750
2
0.7972
6,856
4,624
3
0.7118
6,264
6,050
4
0.6355
5,211
7,308
5
0.5674
2,326
6,866
Total 5 year PV
$27,800
$28,598
Initial Investment
( 33,000)
( 33,000)
NPV
($ 5,200)
($ 4,402)
Neither alternative is a good investment because NPV is negative in both cases.
PROBLEM SOLUTIONS
P12.1 a. Determine the best purchase between three different registers using ARR.
Register A
Register B
Register C
Annual saving
$2,000
$2,000
$2,000
Annual operating costs
$ 400
$ 300
$ 300
Depreciation expense
1,160
1,200
1,280
Total cost
(1,560)
(1,500)
(1,580)
$ 440
$ 500
$ 420
Income tax
(132)
( 150)
( 126)
Net saving
$ 308
$ 350
$ 294
Register A: [$308 / ($6,300 + $500 / 2)] = $308 / $3,400 = 9.1%
Register B: [$350 / ($6,000 / 2)] = $350 / $3,000 = 11.7%
Register C: [$294 / ($6,700 + $300 / 2)] = $294 / $3,500 = 8.4%
*Register B has the highest ARR.
b. Register B should be purchased because it exceeds the 10% limit.
198
P12.2 Using information from P12.1, determine the best investment using the payback period.
A
B
C
Net annual saving
$ 308
$ 350
$ 294
Depreciation
1,160
1,200
1,280
Annual cash savings
$1,468
$1,550
$1,574
Register A: $6,300 / $1,468 = 4.3 years
P12.3 Calculate net cash flow.
Year
Cash Flow
Factor 13%
Total PV
1
$37,500
0.8850
$ 33,188
2
43,800
0.7831
34,300
3
46,300
0.6931
32,091
4
50,000
0.6133
30,665
5
60,000
0.5428
32,568
6
18,500
0.5428
10,042
Total PV
$172,854
If a 13% return is wanted, it is not achieved since the total PV is considerably less than
the initial investment of $205,000. By trial and error an IRR of 7% gives a total present
value of $205,213.
P12.4 a. Alternative 1 payback will be in Year 5, and Alternative 2 in Year 4.
Alternative 1
Alternative 2
Cost of investment
$70,000
$70,000
Cash recovery:
Years 1, 2, 3 & 4
( 60,000)
Years 1, 2, & 3
(61,200)
Balance
$ 10,000
$ 8,800
Alternative 1: $10,000 / $24,000 = 0.42 + 4 = 4.42 years.
Alternative 2: $8,800 / $10,800 = 0.81 + 3 = 3.81 years.
b. Determine net present values.
Alternative 1
Alternative 2
Year
Factor 10%
Total PV
Total PV
1
0.9091
$ 7,636
$22,000
2
0.8264
9,586
16,362
3
0.7513
12,772
12,922
4
0.6830
15,709
7,376
5
0.6209
14,902
4,967
Total 5 year PV
$60,605
$63,627
Initial Investment
( 70,000)
( 70,000)
Alternatives NPV
($ 9,395)
($ 6,373)
Neither alternative is a good investment because NPV is negative in both cases.
199
P 12.5 Determine net cash flow for Machine A and Machine B alternatives.
Year 1
Year 2
Year 3
Year 4
Year 5
Machine A
Wage saving
$9,600
$9,600
$9,600
$9,600
$9,600
Operating costs
$1,950
$1,150
$1,700
$1,150
$1,150
Depreciation
1,500
1,500
1,500
1,500
1,500
Total expenses
$3,450
$2,650
$3,200
$2,650
$2,650
Income (before tax)
$6,150
$6,950
$6,400
$6,950
$6,950
Income tax [30%]
(1,845)
(2,085)
(1,920)
(2,085)
(2,085)
Net income
4,305
4,865
4,480
4,865
4,865
Add: depreciation
1,500
1,500
1,500
1,500
1,500
Trade-in
1,500
Net cash flow
$5,805
$6,365
$5,980
$6,365
$7,865
Year 1
Year 2
Year 3
Year 4
Year 5
Machine B
Wage saving
$9600
$9600
$9600
$9600
$9600
Operating costs
$1,950
$1,250
$1,650
$1,250
$1,250
Depreciation
1,560
1,560
1,560
1,560
1,560
Total expenses
$3,510
$2,810
$3,210
$2,810
$2,810
Income (before tax)
$6,090
$6,790
$6,390
$6,790
$6,790
Income tax [30%]
(1,827)
(2,037)
(1,917)
(2,037)
(2,037)
Net income
4,263
4,753
4,473
4,753
4,753
Add: depreciation
1,560
1,560
1,560
1,560
1,560
Trade-in
700
Net cash flow
$5,823
$6,313
$6,033
$6,313
$7,013
Net NPV
Machine A
Machine B
Factor
Machine A
Machine B
Year
Cash Flow
Cash Flow
@ 12%
Total NPV
Total NPV
1
$5,805
$5,823
0.8929
$ 5,183
$ 5,199
2
6,365
6,313
0.7972
5,074
5,033
3
5,980
6,033
0.7118
4,257
4,294
4
6,365
6,313
0.6355
4,045
4,012
5
7,865
7,013
0.5674
4,463
3,979
Total 5 year PV
$23,022
$22,517
Initial investment
( 9,000)
( 8,500)
Net Present Value
$ 14,022
$ 14,017
Machine B has a slightly higher NPV and, if all other considerations are essentially
equal, should be the unit purchased.
200
P12.6 Incremental average annual cash flow for years 1 through 4.
Sales revenue
$30,000
Variable costs [80%]
$24,000
Depreciation
3,200
Total costs
(27,200)
Operating income
$ 2,800
Income tax [35%]
( 980)
Net income
$ 1,820
Add: Depreciation
3,200
Net cash flow
$ 5,020
*In Year 5, net cash flow will be $9,020 due to the $4,000 trade in.
IRR analysis at 12% is:
Year
Cash flow
Factor 12%
Total PV
1
$5,020
0.8929
$ 4,482
2
5,020
0.7972
4,002
3
5,020
0.7118
3,573
4
5,020
0.6355
3,190
5
9,020
0.5674
5,118
Total
$20,365
The investment will earn just over 12%, so it exceeds or achieves the 12% desired, and.
the investment could be made. However, if the estimates of costs and expenses are
inaccurate, the project would not achieve the desired return.
P12.7 a. Calculation of net cash flow:
Purchasing Alternative
Year 1
Year 2
Year 3
Year 4
Year 5
Interest expense
$2,250
$1,800
$1,350
$ 900
$ 450
Depreciation
5,200
5,200
5,200
5,200
5,200
Tax deductible
$7,450
$7,000
$6,550
$6,100
$5,650
Income tax savings [28%]
( 2,086)
( 1,960)
( 1,834)
( 1,708)
( 1,582)
Net expenses
$5,364
$5,040
$4,716
$4,392
$4,068
Add: loan principal
4,500
4,500
4,500
4,500
4,500
Deduct depreciation
( 5,200)
( 5,200)
( 5,200)
( 5,200)
( 5,200)
Net cash outflow
$4,664
$4,340
$4,016
$3,692
$3,368
Rental alternative: Net cash outflow = $5,040 [$7,000 – (28% x 7,000)] per year.
Cash flow
Cash flow
Discount
Total
Total
Year
Purchase
Rental
Factor 11%
Purchase NPV
Rental NPV
0
$7,500
$ 7,500
1
4,664
$5,040
0.9009
4,202
$ 4,541
2
4,340
5,040
0.8116
3,522
4,090
3
4,016
5,040
0.7312
2,936
3,685
4
3,962
5,040
0.6587
2,432
3,320
5
3,368
5,040
0.5935
1,999
2,991
5
(4,000)
Residual
0.5935
( 2,374 )
$20,217
$18,627
201
Under these circumstances, leasing the equipment appears to be the best alternative
because total NPV of cash outflows is $1,570 less ($20,217 – $18,627).
b. 1. Use of an accelerated depreciation method rather than straight line: An
accelerated method increases depreciation expense in the early years of the
asset’s life.
2. Arrange different payment terms, such as an initial down payment less than
$7,500, and offset the lower down payment by increased yearly loan repayments.
3. Negotiations of an interest rate lower than 11%.
4. The information does not consider the cost of repairs and maintenance of the
equipment. These costs should have been considered.
P12.8 Determine net cash flow and net present values for alternatives.
Purchase Alternative:
Year 1
Year 2
Year 3
Year 4
Year 5
Income (before depreciation)
$38,000
$47,000
$55,000
$60,000
$65,000
Depreciation
( 2,200)
( 2,200)
( 2,200)
( 2,200)
( 2,200)
Operating Income [BT]
$35,800
$44,800
$52,800
$57,800
$62,800
Income tax [30%]
(10,740)
(13,440)
(15,840)
(17,340)
(18,840)
Net income
$25,060
$31,360
$36,960
$40,460
$43,960
Add: Depreciation
2,200
2,200
2,200
2,200
2,200
Residual value
2,500
Net cash flow
$27,260
$33,560
$39,160
$42,660
$48,660
Lease Alternative:
Income (before rent)
$39,000
$49,500
$57,500
$64,000
$70,000
Rent [$0.30 per mile]
( 9,000)
(13,500)
(15,000)
(16,500)
(18,000)
Net saving before tax
$30,000
$36,000
$42,500
$47,500
$52,000
Income tax [30%]
( 9,000)
(10,800)
(12,750)
(14,250)
(15,600)
Net cash flow
$21,000
$25,200
$29,750
$33,250
$36,400
NPV evaluation:
Cash flow
Cash flow
Discount
Total
Total
Year
Purchase
Rental
Factor 11%
Purchase NPV
Rental NPV
0
($13,500)
($ 13,500)
1
27,260
$21,000
0.9009
$ 24,559
$ 18,919
2
33,560
25,200
0.8116
27,237
20,452
3
39,160
29,750
0.7312
28,634
21,753
4
42,660
33,250
0.6587
28,100
21,902
5
48,660
36,400
0.5935
28,880
21,603
$123,910
$104,629
a. The purchase alternative with the higher NPV is the most favorable.
b. No, the $1,000 leasing cost increase will decrease cash flow and decrease total NPV
under the rental option.
202
P12.9 Calculate the payback period, ARR and NPV.
Income will be from:
Elimination of previous loss
$2,150
10% of soft drink sales revenue of $25,550
2,555
$4,705
Expenses will be:
Depreciation [($7,000 − $1,000) / 5 years]
$1,200
Machine maintenance
100
( 1,300)
Savings before income tax
$3,405
Income tax [30%]
( 1,022)
Net annual saving
$2,383
Add back depreciation
1,200
Net annual cash flow
$3,583
a. Payback period: $7,000 / $3,583 = 1.95 or 2 years
b. NPV:
Annual
Discount
Total
Year
Cash flows
Factor 12%
NPV
1
$3,583
0.8929
$3,199
2
3,583
0.7972
2,856
3
3,583
0.7118
2,550
4
3,583
0.6355
2,277
5
3,583
0.5674
2,033
5
1,000
0.5674
567
Total 5 year PV
$13,482
Less: Initial investment
( 7,000)
Net Present Value
$ 6,482
The investment should be made because the NPV is positive.
P12.10 Calculate NPV and determine whether to operate or lease.
Lease Option
Sales
Tax rate
Net Cash
Discount
Total
Year
Revenue
@ 25%
Flow
Factor 10%
PV
1
$24,000
$6,000
$18,000
0.9091
$16,364
2
24,000
6,000
18,000
0.8264
14,875
3
24,000
6,000
18,000
0.7513
13,523
4
30,000
7,500
22,500
0.6830
15,368
5
30,000
7,500
22,500
0.6209
13,970
Total NPV:
$74,100
203
Operate Option
Year 1
Year 2
Year 3
Year 4
Year 5
Sales revenue
$700,000
$750,000
$800,000
$850,000
$900,000
Operating Expenses
Variable costs [90% of SR]
$630,000
$675,000
$720,000
$765,000
$810,000
Other expenses
32,000
34,000
36,000
38,000
40,000
Depreciation
8,000
8,000
8,000
8,000
8,000
Total expenses
$670,000
$717,000
$764,000
$811,000
$858,000
Operating Income [BT]
$30,000
$33,000
$37,000
$39,000
$40,000
Income tax [25%]
( 7,500)
( 8,250)
( 9,000)
( 9,750)
(10,500)
Net Income
$22,500
$24,750
$27,000
$29,250
$31,500
Add: Depreciation
8,000
8,000
8,000
8,000
8,000
Net cash inflows
$30,500
$32,750
$35,000
$37,250
$39,500
Net Cash Flow
Cash
Discount
Total
Year
Flows
Factor 10%
PV
1
$30,500
0.9091
$27,728
2
32,750
0.8264
27,065
3
35,000
0.7513
26,296
4
37,250
0.6830
25,442
5
39,500
0.6209
24,526
Total 5 year PV
$131,057
Less: Initial investment:
( 35,000)
Net Present Value
$ 96,057
The motel, on the basis of NPV, should operate the restaurant since there is a projected
gain of $21,957 ($96,057 less $74,100).
204
CASE 12 SOLUTION
Assuming Year 2009:
Keep present arrangement: Pay monthly rent
Year
Rent
22% Tax
Net Amount
Factor 12%
Total PV
2009
$29,040
00
$6,389
$22,651
0.8929
$20,225
2010
31,944
7,028
24,916
0.7972
19,861
2011
35,138
7,730
27,408
0.7118
19,509
2012
38,652
8,503
30,149
0.6355
19,160
$78,757
Prepay $80,000 rent: If the rent is prepaid for the next four years and $80,000 is borrowed from
the bank, the interest expense at the end of the first year will be 12% × $80,000 = $9,600. The
interest will decrease by $2,400 per year.
Interest
Tax
Net
Principle
Total Cash
Factor
Total
Year
Expense
Savings
Expense
Payment
Outflow
12%
PV
1
$9,600
$2,112
$7,488
$20,000
$27,488
0.8929
$24,544
2
7,200
1,584
5,616
20,000
25,616
0.7972
20,421
3
4,800
1,056
3,744
20,000
23,744
0.7118
16,901
4
2,400
528
1,872
20,000
21,872
0.6355
13,900
$75,766
a. The offer should be accepted. The NPV of prepaying the rent is $2,997 less ($78,757 –
$75,760)