CHAPTER 12 Capital Investment Decisions
P 12-41
1. Schedule of cash flows:
Y
ea
r
Cash Flow Cash Flow
0 Equipment……………………………
…
$(1,200,000)
Working capital………………………
…
(120,000)
1–7 Cost savings…………………………
…
$ 400,000
2. NPV:
Y
ea
r
Cash Flow Discount Facto
r
Present Value
0 $(1,320,000) 1.00000 $(1,320,000)
1–7 130,000 4.56376 593,289
5 (120,000) 0.56743 (68,092)
P 12-42
1. Schedule of cash flows:
Y
ea
r
Cash Flow
0 Equipment……………………………
…
$(1,750,000)
Working capital………………………
…
(90,000)
Total………………………………… $(1,840,000)
1–5 Revenues……………………………… $ 1,650,000
Operating expenses…………………
…
(1,320,000)
Total………………………………… $ 330,000
…
7–9 Revenues……………………………… $ 1,650,000
Operating expenses…………………
…
(1,320,000)
Total………………………………… $ 330,000
PROBLEMS
Item
Item
CHAPTER 12 Capital Investment Decisions
P 12-42 (Continued)
Revenues………………………………………………………………
…
$ 1,650,000
Operating expenses…………………………………………………
…
(1,320,000)
Salvage…………………………………………………………………
…
100,000
Recovery of working capital………………………………………
…
90,000
Total…………………………………………………………………
…
$ 520,000
2. Discount Facto
r
Present Value
$(1,840,000) 1.00000 $(1,840,000)
330,000 3.60478 1,189,577
P 12-43
=
The IRR is essentially 12%. The company should acquire the new system.
2. Since I = P for the IRR:
I=df × CF
3. For a life of 8 years:
I
CF
=
=
=df1.
=
=df
$60,000
5.65000
$339,000
$339,000
$60,000
Annual Cash Flow
Investment
5.65000
10
Cash Flow
0
1–5
Y
ea
r
CHAPTER 12 Capital Investment Decisions
P 12-43 (Concluded)
The IRR is between 8% and 9%—greater than the 8% cost of capital. The company
should still acquire the new system.
Minimum cash flow at 8% for 8 years:
I=df × CF
$339,000 = 5.74664 × CF
=CF
$58,991 = CF
4. Requirement 2 reveals that the estimates for cash savings can be off by as much as
$9,479 (over 15%) without affecting the viability of the new system. Requirement 3
P 12-44
1. First, calculate the expected cash flows:
Days of operation each year: 365 – 15 = 350
Revenue per day: $235 × 2 × 150 = $70,500
Annual revenue: $70,500 × 350 = $24,675,000
Annual Cash Flow = Revenues – Operating Costs
= $24,675,000 – $3,250,000
=
–
Y
2. Revised Cash Flow = (0.80 × $24,675,000) – $3,250,000
=
NPV = P
–
I
= (7.46944 × $16,490,000) – $120,000,000
=
Y
es, the aircraft should be purchased.
$339,000 ÷ 5.7466
4
$21,425,000
$16,490,000
$3,171,066
CHAPTER 12 Capital Investment Decisions
P 12-44 (Concluded)
3. NPV = (7.46944)CF – $120,000,000 = 0
=
Annual Revenue = $16,065,461 + $3,250,000
=
4. Round-Trip Average Price = (2 × $235) × 1.1 = $517
107
150
This seating rate is less than the most likely and above the least likely rate of
70%. There is some risk, since it is possible that the actual rate could be below
71%. However, the interval is 20% (70% to 90% ) and the 71% rounded from
71.33%) rate is only 6.7% of the way into the interval, suggesting a high
probability of a positive NPV.
71%==Seating Rate
=CF
==Seats to Be Sold
107 (rounded up)
$120,000,000
$55,187
7.46944
$16,065,461
$517
$19,315,461
CHAPTER 12 Capital Investment Decisions
P 12-45
1. 1.00 year $16,800
1.00 yea
r
24,000
1.00 yea
r
29,400
0.13 year * 3,800
3.13 years $74,000
2. Accounting rate of return:
Average Cash Expenses = $3,000 per yea
r
Average Depreciation
3.
Y
ea
r
0
1
2
3
4
NPV………………………………………………………
…
*
Includes $6,000 salvage.
IRR (by trial and error): Using 14% as the first guess:
Y
ea
r
0
1
2
…
Average Cash Revenue
= = $17,000
=
$74,000 – $6,000
Discount Facto
r
Present Value
15,000
0.63552
Discount Facto
r
Present Value
$(74,000)
14,737
24,000 0.76947 18,467
16,800 0.87719
$(74,000) 1.00000 $(74,000)
Cash Flow
$ 3,556
35,400
16,800
24,000
29,400 0.71178
19,133
1.00000
0.89286
Cash Flow
0.79719
$(74,000)
20,926
22,497
($19,800 + $27,000 + $32,400 + $32,400)
4=
$27,900
*
CHAPTER 12 Capital Investment Decisions
P 12-45 (Concluded)
4. Year
0
1
P 12-46
1. Annual CF (rebuild alternative) = $295.00 – $274.65)10,000 = $203,500
NPV = (CF × d
f
) – I = $203,500 × 3.79079) – $600,000 = $171,426
Annual CF (scrap alternative) = $4 × 10,000 = $40,000
NPV = (CF × d
f
) – I = $40,000 × 3.79079) – $0 = $151,633
The NPV of the rebuild alternative is greater and so the new demag machine should be
purchased.
f
f
Cash Flow
$(74,000)
11,200
Discount Factor Present Value
1.00000
0.89286
$(74,000)
10,000
CHAPTER 12 Capital Investment Decisions
P 12-47
1. Investment Allocation
(1) Substance abuse wing………
…
$1,500,000 $1,500,000
(2) Laboratory……………………
…
500,000 0
(3) Outpatient surgery wing……
…
1,000,000 0
2. With unlimited capital, the substance abuse wing and the laboratory would be chosen.
With limited capital, the laboratory and outpatient surgery wing would be chosen.
3. Answers may vary, but three qualitative considerations that should generally be
considered in capital budgeting evaluations include:
P 12-48
= 3.89 years
1.
=
=
$3,500,000
$3,900,000 – $3,000,000
Original Investment
Annual Cash Flow
Project
=Payback Period
$3,500,000
$900,000
CHAPTER 12 Capital Investment Decisions
P 12-48 (Concluded)
= I for the IRR, thus,
=
For 5 years and a discount factor of 3.88889, the IRR is about 9%.
3.
Y
ea
r
Discount Facto
r
Present Value
0 1.00000 $(3,500,000)
1 0.90909 859,090
2 0.82645 820,045
It is very important to adjust cash flows for inflationary effects. Since the required ra
t
of return for capital budgeting analysis reflects an inflationary component at the tim
e
NPV analysis is performed, a correct analysis also requires that the predicted operat
i
cash flows be adjusted to reflect inflationary effects. If the operating cash flows are
not adjusted, then an erroneous decision may be the outcome. Notice, for example,
that after adjusting for inflation, the new system is now favored—a totally different
decision.
P 12-49
1. Bond Cost = $3,000/$60,000 = 0.05
Cost of Capital = 0.05(0.60) + 0.175(0.40)
= 0.03 + 0.07
=0.10
3.88889
Investment
Annual Cash Flow
=df
=$3,500,000
$900,000
P = CF(df)
Cash Flow*
$(3,500,000)
945,000
992,250
CHAPTER 12 Capital Investment Decisions
P 12-50
1. Original savings and investment:
(14% rate):
Y
ea
r
CF d
f
Present Value
0 $(45,000,000) 1.00000 $(45,000,000)
1–20 4,000,000 6.62313 26,492,520
20 5,000,000 0.07276 363,800
NPV………………………………………………
…
$(18,143,680)
2. Total benefits: ($4,000,000 + $1,000,000 + $2,400,000)
(14% rate):
Y
ea
r
CF d
f
Present Value
0 $(45,000,000) 1.00000 $(45,000,000)
1–20 7,400,000 6.62313 49,011,162
20 5,000,000 0.07276 363,800
NPV………………………………………………
…
$ 4,374,962
Y
r
f
…
3. Analysis with increased investment:
(14% rate):
Y
ea
r
CF d
f
Present Value
0 $(48,000,000) 1.00000 $(48,000,000)
1–20 7,400,000 6.62313 49,011,162
20 5,000,000 0.07276 363,800
NPV………………………………………………
…
$ 1,374,962
Y
r
f
…
Y
r
f
…
CHAPTER 12 Capital Investment Decisions
P 12-50 (Concluded)
4. The automated plant is an attractive investment when the additional
benefits are considered—it promises to return at least the cost of capital
P 12-51
1. Year CF df Present Value
0 $(860,000) 1.00000 $(860,000)
1–8 225,000 4.34359 977,308
NPV……………………………………………
…
$ 117,308
…
3. The $60,000 per year is an annuity that produces a present value of
$260,615 (4.34359 × $60,000).This restores the project to a positive NPV
position ($260,615 – $29,564 = $231,051).
4. A postaudit can help ensure that a firm’s resources are being used wisely.
It may reveal that additional resources ought to be invested or that
corrective action be taken so that the performance of the investment is
CHAPTER 12 Capital Investment Decisions
P 12-52
1. Standard (Rate = 18%):
Y
ea
r
CF d
f
Present Value
0 $(500,000) 1.00000 $(500,000)
1 300,000 0.84746 254,238
*d
f
for Years 1–10 minus d
f
for Years 1–2 (from Exhibit 12B.2)
CAM (Rate = 18%):
Y
ea
r
CF d
f
Present Value
0 $(2,000,000) 1.00000 $(2,000,000)
1 100,000 0.84746 84,746
2 200,000 0.71818 143,636
3 300,000 0.60863 182,589
…
2. Standard (Rate = 10%):
Y
ea
r
CF d
f
Present Value
0 $(500,000) 1.00000 $(500,000)
1 300,000 0.90909 272,727
2 200,000 0.82645 165,290
3–10 100,000 4.40903 440,903
NPV……………………………………………
…
$ 378,920
CAM (Rate = 10%):
Y
ea
r
CF d
f
Present Value
0 $(2,000,000) 1.00000 $(2,000,000)
1 100,000 0.90909 90,909
2 200,000 0.82645 165,290
3 300,000 0.75131 225,393
…
f
f
…
CHAPTER 12 Capital Investment Decisions
P 12-52 (Concluded)
3. Notice how the cash flows using a 10% rate in Years 8–10 are weighted compared
to the 18% rate. The difference in present value is significant. Using an excessive
discount rate works against those projects that promise large cash flows later in
P 12-53
1. Standard (Rate = 14%):
Y
ea
r
CF d
f
Present Value
0 $(500,000) 1.00000 $(500,000)
1 300,000 0.87719 263,157
2 200,000 0.76947 153,894
…
CAM (Rate = 14%):
Y
ea
r
CF d
f
Present Value
0 $(2,000,000) 1.00000 $(2,000,000)
1 100,000 0.87719 87,719
2 200,000 0.76947 153,894
3 300,000 0.67497 202,491
…
2. Standard (Rate = 14%):
Y
ea
r
CF d
f
Present Value
0 $(500,000) 1.00000 $(500,000)
1 300,000 0.87719 263,157
2 200,000 0.76947 153,894
3–10 50,000 3.56946 178,473
NPV…………………………………………………………
…
$ 95,524
The decision reverses—the CAM system is now preferable. This reversal is
attributable to the intangible benefit of maintaining market share. To remain
CHAPTER 12 Capital Investment Decisions
Case 12-54
The statement that Manny would normally have taken the first bid without
hesitation implies that the bid met all of the formal requirements outlined
by the company. If Manny’s friend had met the bid as requested, then
of the bid, especially since the winning bid was from out of state. If there
was some legitimate concern about the winning bid and Manny was
hopeful of eliminating this concern by dealing with a known quantity, then
it could be argued that the call to Todd was justifiable. If, on the other
hand, the only motive was friendship and Manny was confident that the
winning bid could execute (as he appears to have been), then the call was
improper. Confidentiality and integrity in carrying out the firm’s bidding
policies are essential.
II. Confidentiality
1. Keep information confidential except when disclosure is authorized or
legally required.
3. Refrain from using confidential information for unethical or illegal
advantage.
CASES
CHAPTER 12 Capital Investment Decisions
Case 12-55
1.
Sales (35,000 × $45)……………………………………
…
$1,575,000
Less: Variable expenses ($35.08 × 35,000).………
…
1,227,800
Contribution margin……………………………………
…
$ 347,200
Less fixed expenses:
Salaries………………………………………..………
…
$135,000
Net income……………………………………….………
…
$ 51,000
*
Reported depreciation erroneously included $2,000 for the land.
Karl is correct that the return on sales is significantly lower than the company
average.
**
Net income of $51,000 + depreciation of $56,200
Karl is wrong. The book value of the equipment and the furniture should not be
included in the amount of the original investment because there is no opportunity
cost associated with them. Excluding the book value reduces the investment from
$582,000 to $352,000. Karl’s payback would be correct if the equipment and
furniture could be sold for their book value because there would now be an
opportunity cost associated with them and that cost should be included in the
original investment.
3. NPV:
Y
ea
r
Shaftel Ready Mix
Income Statement
For the Proposed Plant
Present Value
Cash Flow
Discount Facto
r
$51,000
$1,575,000
Ratio of Net Income to Sales = = 3.24%
CHAPTER 12 Capital Investment Decisions
Case 12-55 (Continued)
IRR:
I
CF
=
Thus, the IRR is between 25% and 30%.
If the furniture and equipment can be sold for book value:
=
Thus, the IRR is between 12% and 14%.
4. Breakeven:
= $35.08X + $296,200
= $296,200
= 29,859 cubic yards
NPV (using break-even amount):
Y
ea
r
Discount Facto
r
Present Value
Thus, the IRR is between 9% and 10%.
The investment is not acceptable, although it came close. It is possible to
have a positive NPV at the break-even point. Breakeven is defined for
accounting income, not for cash flow. Since there are noncash expenses
=df
=
$9.92X
$45X
=IRR:
X
$107,200
Cash Flow
$352,000
$107,200
3.28358
$582,000
5.42910
Y
r
r
CHAPTER 12 Capital Investment Decisions
Case 12-55 (Concluded)
5. Cost of Capital = 10% for 10 years, so df = 6.14457
I
CF
$352,000
CF
= $352,000
CF = $57,286
Net Income = Sales – Variable Expenses – Fixed Expenses
= $45X – $35.08X – $296,200
= $9.92X – $296,200
= $9.92X
X
= 29,968 cubic yards
=df
6.14457 =
$1,086
$297,286
$1,086
6.14457 × CF