Solution manual cost accounting by lauderbach CAPITAL BUDGETING PART i

CHAPTER 7

CAPITAL BUDGETING−PART I
7-1 Risk and Capital Investments
Colgate faces lower risk than J&J because it is expanding production of
an existing, and successful, product. The major risk is that the product
will become less popular and sales will not materialize. The new plant could
also be too costly, but that seems unlikely as the technology to make
consumer products is well-established.
J&J faces risks that the drug will not prove efficacious, that the Food
and Drug Administration will not approve it, or that another company will
develop a better drug. One reason we use this example is to make the point
that R&D is just like any other investment, except that no depreciation is
involved.
7-2

Payback and Risk

Either voyage is acceptable, but most students will probably select the
shorter, safer one.
A lot can happen to a ship on a long voyage−storms, piracy, or collisions
with icebergs or rocks. Considering the hazards, who wouldn't feel a lot
safer tying up his or her money for one year rather than five despite the
advantage of the longer voyage as determined under the normal techniques of
analysis? Whether you would choose to invest in the one-year or the fiveyear opportunity depends on your attitude about risk and return. Because of
its emphasis on the rapidity of return of investment, the payback method of
evaluation gives higher priority to the one-year voyage.
7-3 Government Actions and Capital Investment
1.
Investment will increase because net cash flows will increase and more
projects will meet DCF criteria. Some students might ask about the value of

depreciation deductions, which will fall, but after-tax cash flows from
savings or higher sales will more than offset lower tax shields.
2. Investment will increase because cost of capital will decrease.
investments will meet companies’ capital budgeting criteria.

More

3. Investments will increase because cash savings from depreciation will be
immediate rather than spread out over the life of an asset. You might wish
to discuss ACRS and MACRS at this point, perhaps pointing out that lives for
tax purposes are significantly shorter than economic lives for most assets.
4. Investment should increase as it becomes profitable to substitute capital
for labor.
5. Investments will increase because as labor becomes costlier, companies
will substitute capital, just as in item 3. We tried to be very explicit
about the effects in this question because we have used it as an exam
question and gotten disappointing results. Most students say that
investments will decrease because the company will have less cash to invest,
which ignores external financing.

7-1


7-4

Capital Budgeting−Effects of Events

1. An increase in labor rates makes labor-cost-saving projects more
attractive, but makes increasing output less attractive. Increasing output
might still be attractive, but not as much as it would have been with lower

labor costs.
2. First, we have to assume that we will either reduce prices to meet the
competition, or lose volume. If we expect to hold prices and lose volume,
cost-saving investments become less desirable because they affect fewer units
(assuming that the savings are in variable costs). Certainly, decisions to
increase output will be much less desirable because the volume will not be as
high as originally forecast.
If we meet the price reductions, decisions to increase output will be
less desirable because the contribution margin from the additional sales will
be lower than otherwise. Cost-reduction investments will probably be
unaffected.
3. Investments that reduce costs become more attractive, because cost
reduction is critical in mature industries. Investments that increase output
become less attractive because the volume increases will be less than
anticipated.
7-5

Qualitative Concerns

General Note to the Instructor: The purposes of this and the following
question are (a) to encourage students to think about both the quantitative
and qualitative aspects of making decisions, and (b) to reduce students'
concentration on the mechanics of specific analytical techniques. The two
questions should probably be considered together, since one deals with
rejecting a project that is economically acceptable while the other deals
with accepting a project deemed economically unacceptable.
We introduce capital rationing, sensitivity analysis, and mutually
exclusive alternatives in Chapter 8. We leave to courses in managerial
finance the task of discussing the significance and calculation of cost of
capital and the use of risk-adjusted discount rates. Nevertheless, we have

found that, if pushed, most groups of students will come up with ideas
encompassing most of the problematic aspects of capital budgeting decisions
not covered in the current chapter. The list of reasons we offer below is
not all-inclusive but generalizes the points made by past students.
1.
a. Top-level managers might object, in principle, to owning a tobacco farm.
(Chapter 5 noted that convictions of managers could affect their decisions.)
b. Estimates about the success of the farm might vary widely and include a
significant probability of a large loss. (At this point, students might
express a lack of confidence in the estimates producing the positive NPV.)
The furor over tobacco in recent years lends an air of uncertainty as to the
future of the industry.
c. The company might have many other projects with higher returns and not be
able to fund all projects that are acceptable. (Students are usually quick
to raise the issue of limited funds, or capital rationing.)
d. The company might use other screens for its projects, such as a minimum
IRR or a maximum payback period, and this project might not meet those
cutoffs. (Chapter 8 suggests that a company might establish such cutoffs.)

7-2


2. The general note at the beginning also applies here, but this introduces
some additional ideas.
a. The project involves a product the company's top managers believe is
needed to round out its product line. (This reason relates to an overall
issue and could prevail even if analysis of the project gives full
consideration to complementary effects.)
b. The project could involve a change in the manufacturing process to meet
mandated pollution or hazardous-waste disposal guidelines. (This answer

assumes that reasonable alternatives for meeting the guidelines produce lower
IRRs, and that management has consciously decided the company should not
abandon the area of its business affected by the mandated guidelines.)
c. The project could involve improving employee relations (e.g., a
cafeteria, a recreation facility) or some other issue on which the company
might have already committed itself to making changes with the expectation of
selecting projects with the "lowest cost." (A project showing a 20% IRR is
clearly better than one showing an 8% return.)
d. The project might advance an important strategy. If the company's
reputation for high-quality products includes a role as an innovator, the
project might be accepted to retain the company's competitive edge, despite
the company's inability to quantify the advantages of maintaining that role.
If reducing cycle time, or improving logistics, is critically important, the
company might well accept a project that advances such a strategy, even
without favorable numbers.
e. Managers might believe that the combination of an attractive payback
period, relatively low risk, and their gross assessments of positive and
negative nonquantifiable factors offsets its lower IRR. (Most students are
likely to come up with this technique-related answer.)
7-6
1.

Discounting
(a)

(15 minutes)

About 12%
Investment
Divided by cash flow

Present value factor annuity of 8 years
Factor for 12%

(b)

About 12%
Investment
Divided by cash flow
Present value factor, 2 years
Factor for 12%

2.

7-7

$60,000
$12,000
5.000
4.968

(a)

$9,500 [($30,000 x 5.650) - $160,000]

(b)

Negative $3,436

Discounting

$120,000
$150,000
.800
.797

[($8,000 x 3.037) + ($4,000 x .567) - $30,000]

(10 minutes)

1.
$34,050, the present value of $50,000 five years hence at 8% ($50,000
x .681).
2.

$66,096, PV of a 4-year annuity of $20,400 at 9% ($10,200 x 3.240).

7-3


3. He should take the $700,000 lump sum because the present value of the
annuity is only $671,000 ($100,000 x 6.710). Of course, if he lives longer,
he has a serious problem.
4.
7-8

$2,298,755

($167,000 x 13.765, the factor for 30 periods at 6%)

Time Value of Money Relationships

(10-15 minutes)

1.

Just about $8,000

$12,880 x .621, the factor for 10% and 5 years

2.

6 years

$20,000/$54,000

3.

$45,640

$10,000 x 4.564, the factor for 12% and 7 years

= .370, the factor for 18% and 6 years

4. 4 years $100,000/$34,300 = 2.915.
factor for 14% and four years, 2.914.
5.
7-9
1.

This factor is nearly equal to the

About $35,398, $200,000/5.65, the factor for 10 years at 12%
NPV and IRR Methods

(10 minutes)

$2,220
Annual cash return
Times present value factor for 4-year annuity at 10%
Present value of flows
Less required investment
Net present value

2.

A bit over 18%
Required investment
Divided by annual cash flow
Equals relevant PV factor for 4-year annuity
PV factor for 4-year annuity at 18%

7-10
1.

Basic Capital Budgeting Without Taxes

$18,800
$ 7,000
2.686
2.690

(15 minutes)

$39,550

Cash savings
Present value factor, 5 years, 10%
Present value of future flows
Investment
Net present value
2. About 20%.
$150,000/$50,000 = 3.0 = factor for five years.
closest factor is 2.991, the factor for 20%.
3.

$ 7,000
3.170
$22,190
18,800
$ 3,390

Cash Flow
$ 50,000
3.791
$189,550
150,000
$ 39,550
The

3.0 years, as calculated in requirement 2.

4. 27%, income of $20,000 ($50,000 - $30,000 depreciation) divided by
$75,000 average investment
Note to the Instructor: We stated that Ms. Pawl wanted a 10% return
from the business because an entrepreneur such as she would probably not
speak of cost of capital or cutoff rates. You might want to delve into how a
small business operator might make such judgments.

7-4


7-11
1.

Basic Capital Budgeting--Taxes (Extension of 7-10)

(15 minutes)

$16,804
Tax
$50,000
30,000
20,000
$ 6,000

Pretax cash flow
Depreciation
($150,000/5)
Increase in pretax income
Income tax at 30%

Net cash flow
Present value factor, 4 years, 10%
Present value of future flows
Investment
Net present value

Cash Flow
$ 50,000
6,000
$ 44,000
3.791
166,804
150,000
$ 16,804

2. About 14%.
$150,000/$44,000 = 3.409 = the factor for five years.
closest factor is 3.433, for 14%. The IRR is therefore a bit over 14%.
3.

3.41

The

years, as calculated in requirement 2.

4. 18.7%, income of $14,000 ($20,000 - $6,000) divided by the $75,000
average investment.
7-12
1.

Basic Cost Savings

(10-15 minutes)

$107,400
Tax

Cash savings (200,000 x $2.25)
Cash fixed costs
Pretax cash flow
Depreciation ($500,000/4)
Increase in pretax income
Income tax at 40%
Net cash flow
Present value factor, 12%, 4 years
Present value of future flows
Investment
Net present value

$450,000
200,000
250,000
125,000
125,000
$ 50,000

Cash Flow
$450,000
200,000

250,000
50,000
$200,000
3.037
$607,400
500,000
$107,400

2. NPV increases $9,540, the present value of the after-tax cash from the
$25,000 residual value to be received 4 years hence ($25,000 x 60% x .636),
since the company can ignore salvage value for depreciation.
Note to the Instructor: This is a good time to remind the class that
the sooner flows come in, the better. The total tax savings from the asset
are the same whether or not salvage value is included in the depreciation
calculations. But leaving salvage value out accelerates the savings, which
are partly repaid when the gain is realized and taxed.
7-13
1.

Basic Capital Budgeting −Services

(10-15 minutes)

$86,600
Cash operating savings
Present value factor, 5 years, 14%
Present value of future flows
Investment

7-5

Cash Flow
$200,000
3.433
$686,600
600,000


Net present value
$ 86,600
2. Nearly 20%. The factor is 3.0 ($600,000/$200,000), which is closest to
2.991, the factor for 20%. Because the 3.0 is greater than the 20% factor,
the IRR is less than 20%.
3.

3 years, as calculated in requirement 2.

4. About 27%, income of $80,000 ($200,000 - $120,000 depreciation) divided
by
$300,000 average investment.
7-14
1.

Basic Capital Budgeting With Taxes (Extension of 7-13)

(10 minutes)

Negative $23,260
Tax
$200,000

120,000
80,000
$ 32,000

Cash savings
Depreciation ($600,000/5)
Increase in pretax income
Income tax at 40%
Net cash flow
Present value factor, 14%, five years
Present value of future flows, rounded
Investment
Net present value

Cash Flow
$200,000
32,000
168,000
3.433
$ 576,740
600,000
($ 23,260)

2. The IRR is a bit over 12%. The factor is 3.571 ($600,000/$168,000),
which
is closest to 3.605, the 12% factor.
3.

3.571 years, as calculated in requirement 2.

4. 16%, income of $48,000 ($80,000 - taxes of $32,000) divided by $300,000
average investment.
7-15
1. (a)

(b)

Comparison of Methods

(20 minutes)

A 2.0 years
B 2.6 years
C 3.5 years
C, B, A

Average income
Divided by average investment
$70,000/2
Equals book rate of return
(c)

B, C, A.

A
$ 1,250

B
$10,000

C
$12,500

$35,000
3.6%

$35,000
28.6%

$35,000
35.7%

Investment B is the only one with a positive NPV.
A

Present
Year
Cash Flow Value
1
$35,000 $30,170
2
35,000
26,005
3
0
0
4
5,000
2,760
Total

$58,935
Investment
70,000
NPV
($11,065)

B
Cash Flow
$35,000
10,000
45,000
20,000

7-6

C
Present
Value*
$30,170
7,430
28,845
11,040
$77,485
70,000
$ 7,485

Cash Flow
$ 4,000
8,000
10,000

98,000

Present
Value
$ 3,448
5,944
6,410
54,096
$69,898
70,000
($
102)


* Present value factors are .862, .743, .641, and .552.
2. The results show that payback and book-rate-of-return rankings do not
necessarily indicate relative profitability. B is the only desirable
investment, using discounted cash flow analysis.
Investment A illustrates that payback ignores profitability; the project
has the quickest payback but little cash flow after the payback period.
Investment C has high income, but much of it comes in the last year, when the
cash flow is worth less than it would have been earlier. Investment C
returns more in total than does A, but the wait is too long to be worthwhile
at 16%.
7-16

NPV

(15-20 minutes)

Sites should acquire the machine because its NPV is $28,848.
Cost savings:
Current cost (40,000 x $0.80)
Expected cash cost [$8,400 + (40,000 x $0.10)]
Annual savings
Depreciation ($20,000/5)
Pretax income
Tax at 30%
Net cash flow
Present value factor, 5 years, 16%
Present value of future flows
Less investment
Net present value

Tax

Cash Flow

$32,000
12,400
$19,600
4,000
15,600
$ 4,680

$32,000
12,400
19,600
4,680
$14,920

3.274
$48,848
20,000
$28,848

At least two nonquantitative factors might influence the decision. The
owner might view employing high school students as a contribution to the
community and so be inclined not to purchase the new equipment. However,
with such a high NPV, it is unlikely that he would forego the purchase. He
would tend to favor the purchase even if it appeared marginally profitable,
if he had experienced problems finding reliable students.
Note to the Instructor: This exercise has several purposes. First, it
requires students to determine the cost savings, information that is provided
in most other assignments. Second, it forces consideration of qualitative
issues in a setting students are likely to understand.
7-17
a.

Capital Budgeting for a Not-for-Profit

(20 minutes)

$138,880

Annual cash flow ($300,000 - $120,000)
Present value factor, 10 years, 14%
Present value of future flows
Investment
Net present value

$180,000
5.216
$938,880
800,000
$138,880

b.

4.44 years

($800,000/$180,000)

c.

About 18%, the factor for 18% is 4.494 for students using tables.

7-18 Understanding IRR

(15-20 minutes)

General Note to the Instructor:

7-7

The purpose of this exercise is to


trace the flows so that the student can see why the IRR is the interest rate
that brings the NPV to zero.
1. $49,740, which is $20,000 x 2.487 (the factor for 10%, 3 years)

2.
Beginning Balance + Interest at 10% - Withdrawal = Ending Balance
$49,740
$4,974
$20,000
$34,714
34,714
3,471
20,000
18,185
18,185
1,819
20,000
4
The $4 difference results from rounding.
7-19
1.

NPV and IRR

(10-15 minutes)

($9,240)

Cash savings (200,000 x $2)
Depreciation ($1,000,000/4)
Increase in pretax income
Income tax at 40%
Net cash flow
Present value factor, 14%, 4 years

Present value of future flows
Investment
Net present value

Tax
$400,000
250,000
150,000
$ 60,000

$

Cash Flow
400,000

60,000
340,000
2.914
990,760
1,000,000
($
9,240)
$

2. About 13.5% from Lotus 1-2-3. The factor is 2.941 ($1,000,000/$340,000),
which is close to the 2.914 factor for 14%.
7-20
1.

Relationships

(d)

(e)

2.

(b)

(20-25 minutes)

20%, the factor for 20%, 10 years is 4.192
Cost
Divided by annual cash flow
Present value factor for 10 years

$188,640
$ 45,000
4.192

$46,080
Annual cash flow
Times the present value factor for 14%, 10 years
Present value of future cash flows
Less cost
Net present value

$ 45,000
5.216
$234,720
188,640

$ 46,080

$337,050
Annual cash flow
Times present value factor for 18%, 10 years
Cost

(e)

3.

(a)

$ 75,000
4.494
$337,050

$86,700
Annual cash flow
Times present value factor for 12%, 10 years
Present value of future cash flows
Less cost
Net present value

$ 75,000
5.650
$423,750
337,050
$ 86,700

$62,073
Cost

$300,000

7-8


Divided by the present value factor, 16%, 10 years
Equals annual cash flow
(c)

4.833
$ 62,073

10%, the factor for 10%, 10 years is 6.145.
Cost
Plus net present value
Total present value of future cash flows
Divided by annual cash flow
Equals present value factor for 10 years

4.

(a)

$300,000
81,440
$381,440
$ 62,073

6.145

$100,000
Cost
Plus net present value
Total present value
Divided by present value factor for 12%, 10
Equals annual cash flow

(d)

$450,000
115,000
$565,000
5.650
$100,000

years

About 18%, the factor for 18%, 10 years is 4.494
Cost
Divided by annual cash flow
Equals present value factor for 10 years

7-21

Comparison of Book Return and NPV

$450,000
$100,000

4.500

(15-20 minutes)

1. The hand-fed machine has the higher book rate of return on average
investment.
Revenue (200,000 x $10)
Variable costs at $4, $2
Cash fixed costs
Depreciation ($800,000/4; $1,400,000/4)
Total costs
Pretax profit
Income tax at 40%
Net income
Average investment
$800,000/2
$1,400,000/2
Book rate of return
2.

Hand-Fed
$2,000,000
800,000
725,000
200,000
1,725,000
275,000
110,000
$ 165,000
$

Semiautomatic
$2,000,000
400,000
850,000
350,000
1,600,000
400,000
160,000
$ 240,000

400,000
$
41.25%

700,000
34.3%

The semiautomatic machine has the higher NPV.
Hand-Fed

Net cash flows:
Net income
Depreciation
Net cash flow
Present value factor, 4 years, 14%
Present value
Investment
Net present value

$

165,000
200,000
$ 365,000
2.914
$1,063,610
800,000
$ 263,610

Semiautomatic
$

240,000
350,000
$ 590,000
2.914
$1,719,260
1,400,000
$ 319,260

3. The hand-fed machine has an IRR in excess of 25%; the semiautomatic
machine's IRR is between 24% and 25%.

7-9


Investment
Divided by annual cash flows (part 2)
Equals present value factor for 4 years

Closest factors:
25%
24%

$
$

Hand-Fed
800,000
365,000
2.192

Semiautomatic
$1,400,000
$ 590,000
2.373

2.362

2.362
2.404

Note to the Instructor: The above answer assumes students will limit
their search for an answer to the tables available in the text. IRR on the
hand-fed machine is between 29% and 30%.
7-22 Increasing Volume
1.

(15-20 minutes)

$2,780 thousand
Tax
$ 7,500
4,200
3,300
2,000
1,300
$
520

Contribution margin [(300 x ($90 - $65)]
Fixed cash operating costs
Pretax cash flow
Depreciation ($8,000,000/4)
Increase in taxable income
Increased taxes (40%)
Increase in net cash flow
2.

Cash Flow
$ 7,500
4,200
3,300
520
$2,780

$443 thousand

Increase in annual cash flow (requirement 1)
Present value factor, 4 years, 12%

Present value of future cash flows
Investment
Net present value

$ 2,780
3.037
$ 8,443
8,000
$
443

3. 14.6% from Lotus 1-2-3. For students using tables, the factor is 2.878
($8,000/$2,780), which falls between the values for 14% and 16%.
4.

NPV increases by $229 thousand.
Salvage value
Less tax at 40%
Net cash flow
Times factor for 4 years at 12%
Equals present value of salvage value

7-23

Investing in JIT

$600
240
360
.636

$229

(15 minutes)

$1,390 thousand
Annual savings
Less tax, at 40%
Net flow
Present value factor, 30 years, 10%
Present value of flow
Tax shield ($4.5 million/5)
Tax rate
Tax saving
Present value factor, 5 years, 10%
Present value of tax savings
Total present value of future flows
Less investment
Net present value

7-10

$

800
320
$ 480
9.427
$4,525
$

900
40%
$ 360
3.791
1,365
5,890
4,500
$1,390


Note to the Instructor: This assignment doesn't get into the details of
benefits that JIT provides, but it can serve as a basis for discussing JIT
operations and how to measure some of their benefits. The $800 thousand
stated savings can come from any number of areas including lower material and
labor costs, and lower costs for such support activities as inspection,
materials-handling, maintenance, and production scheduling. Some of these
costs are relatively easy to estimate and some are not. Among the costs of
quality that should drop are the costs of warranties, field engineering, and
other elements that result from having less than superb quality.
Other qualitative factors that managers should consider include higher
productivity as workers become more involved and more satisfied, and higher
sales because of increased quality. The importance of any such factor
depends on how well the company was doing before. In some cases the
incremental benefit could be quite high, in others relatively low.
7-24 Safety Equipment
1.

(15 minutes)

The NPV is a negative $8,051.

Savings in premiums ($93,000 - $45,000)
Depreciation ($200,000/10)
Increase in taxable income
Increased taxes at 40%
Increase in net cash flow
Present value factor, 10 years, 14%
Present value of future cash flows
Investment required
Net present value

Tax
$48,000
20,000
28,000
$11,200

Cash Flow
$ 48,000
11,200
36,800
5.216
191,949
200,000
($ 8,051)

2. The items covered in students' memos will differ, but the most likely
recommendation is to install the equipment despite its negative NPV. Memos
should include some of the following items.
(a) The analysis understates the cost savings because it does not consider

the potential for liability claims if employees are injured (or worse). The
analysis should include some estimate of the potential savings from not
increasing the potential losses in lawsuits brought by injured employees.
(b) The increased potential for injury to employees should be, in itself, a
consideration in the decision. Moreover, the cost to the company is
relatively small. (The cost of the new system is $200,000, suggesting a much
larger value for the building and its contents, and this factory is only one
of several owned by the company.)
(c) Another factor to consider in connection with the increased potential
for injury to employees is the potential for damage to the company's public
image and reputation if the public became aware that the company refused to
install new equipment.
(d) The cost savings are likely to be understated by assuming that the
premium differential this year applies to all future years. If installation
of a new system is delayed, premiums might increase even further, and, at
some point, coverage might not be available at virtually any price.
Note to the Instructor: In this slight revision of a problem used in
previous editions, we tried to make obvious the issue of risk of harm to
employees by describing the insurance coverage and asking specifically about
"other" factors. It's likely that a few students still will not recognize
that issue. Some who do see it will point out that $8,051 is a small price

7-11


to pay for a serious injury, let alone the life of even one employee. Such
an assertion presents the opportunity for class discussion of the many
situations when efforts are made to place a value on a human life (e.g.,
court cases and allocations of funds available for medical services).
Students should be encouraged to avoid making quick personal judgments

about the relative size of some known expenditure (or receipt). Such
judgments are especially to be avoided when, as indicated in the
parenthetical material in item (b), facts are available to support at least a
preliminary assessment of relative magnitude. In this case, a preliminary
assessment reduces the need to address the more general--and more difficult-task of placing a specific value on human suffering. Absent analytical
evidence that the cost is "relatively small" for the entity in question, a
student's assertion to that effect is a personal matter. For example, had
the negative NPV been, say, $200 million, individual judgments would surely
have differed.
Professor Don Lucy shared with us a suggestion by one of his students
that the company tell employees it is spending $200,000 to make them safer.
7-25
1.

Employment Options

Bob prefers the $2,000,000 for 10 years at his 10% discount rate.

Pretax flow
Less tax at 30%
After-tax flow
Present value factors
Present value
Advantage to 10-year term
2.

(15-20 minutes)

30 years
$1,200,000

360,000
$ 840,000
9.427
$7,918,680
=

10 years
$2,000,000
600,000
$1,400,000
6.145
$8,603,000

$684,320

The team prefers $1,200,000 for 30 years at its 14% discount rate.

Pretax flow
Less tax at 40%
After-tax flow
Present value factors
Present value
Advantage to 30-year term = $1,217,040

30 years
$1,200,000
480,000
720,000
7.003
$5,042,160

10 years
$2,000,000
800,000
1,200,000
5.216
$6,259,200

3. Bob wants a higher present value and the team wants a lower present
value. It's not surprising that their interests are opposed. The team's
higher discount rate leads it to prefer lower flows over a longer period, and
its higher tax rate works in the same direction. Even if they used the same
discount rate, their responses could differ because of the tax differences.
Note to the Instructor: You might extend this assignment by asking
whether the team might benefit by raising the 30-year payment so that Bob
would prefer it to the 10-year term. The 30-year payment that would make Bob
indifferent between the choices is $325,926.
Present value of 10-year payments (above)
Divided by Bob's present value factor for 30 years
Annual after-tax payment required
Divided by (1 - 30% tax rate)
Equals required payment
Present value of payment to team ($1,303,702 x .60 x 7.003)

7-12

$8,603,000
9.427
$ 912,592
70%

$1,303,702
$5,477,898


The $5,477,898 present value is less than the $6,259,200 of the $2,000,000
for 10 years, so the team could pay more than $1,303,702 over the 30 years
and be better off. The maximum that the team could pay over 30 years is
$372,411.
Present
Divided
Maximum
Divided
7-26
1.

value of 10-year payments
by factor for 30 years
after-tax payment
by 60% = maximum pretax payment

Importance of Depreciation Period

$6,259,200
7.003
$ 893,788
$1,489,647
(15-20 minutes)

Negative $1,434
Tax

$30,000
20,000
10,000
$ 4,000

Savings in cash operating costs
Less depreciation, $100,000/5
Increased taxable income
Income tax at 40%
Net cash flow
Present value factor, 5 years, 10%
Present value of future cash flows
Investment
Net present value
2.

Cash Flow
$ 30,000
4,000
$ 26,000
3.791
$ 98,566
100,000
($ 1,434)

$2,920, an increase of $4,354 ($2,920 + $1,434)
1

2

Year
3

4

5

Operating savings
$30,000
$30,000
$30,000
$30,000
$30,000
Depreciation
50,000
50,000
Change in income
(20,000)
(20,000)
30,000
30,000
30,000
Tax at 40%
( 8,000)
( 8,000)
12,000
12,000
12,000
Net cash flow*
$38,000

$38,000
$18,000
$18,000
$18,000
PV factors
.909
.826
.751
.683
.621
Present values
$34,542
$31,388
$13,518
$12,294
$11,178
NPV = $2,920, total present value of $102,920 less investment of $100,000
* Net cash flow equals operating savings less tax expense (plus tax saving)
Note to the Instructor: Instructors who, like the authors, prefer that
students not spend time on the computational details associated with MACRS or
other accelerated depreciation methods can assign this problem to illustrate
the principle of increased NPV.
7-27 Introducing a New Product
1.

(20-25 minutes)

$286,000

Increase

Increase
Increase
Increase
Increase
Increase
Increase

in
in
in
in
in
in
in

contribution margin (10,000 x $52)
cash fixed costs
taxable income before depreciation
depreciation ($800,000/5)
taxable income
income taxes at 30%
after-tax cash flow

Tax
$520,000
180,000
340,000
160,000
180,000
$ 54,000

Cash Flow
$520,000
180,000
340,000
54,000
$286,000

2. 2.797 years ($800,000/$286,000)
3. About 23.1% using Lotus 1-2-3. Students using tables will see that the
rate is between 22% and 24%.

7-13


4.

$181,838

Increase in annual after-tax cash flow (requirement 1)
Times present value factor for 5 years at 14%
Equals total present value of future cash flows
Less investment
NPV

$286,000
3.433
$981,838
800,000
$181,838

5. (a) BDR should not use the 11% interest rate to determine the present
value. A return sufficient only to cover the cost of a specific debt-funding
source provides no return to the stockholders, and the company must earn a
satisfactory return for all its investors, both creditors and stockholders.
Note also that the source of debt capital for a specific project seldom will
provide 100% of the funds needed for an investment, which means owners must
provide the rest and will expect a return on their investment. Moreover,
both creditors and stockholders monitor a company's solvency by watching such
factors as the ratio of debt to equity, and the cost of obtaining capital
from either source is likely to rise as a company takes on more debt.
(b) BDR should not include the annual interest payments in computing
annual cash flow. Discounting provides for both return of capital and a
return on capital at least equal to the discount rate. Including interest
in the cash flows would provide twice for the cost of funds.
Note to the Instructor: In covering requirement (a) we try to avoid
extended discussion of the concept of cost of capital. One idea that seems
to make sense to introductory students is that money is a fungible good.
Applying this idea, a company obtaining funds from a variety of sources has a
pool of money, no part of which is identifiable by its source.
To avoid questions that might be raised later by students studying real
estate, we usually point out, after covering (a) and (b), that the analysis
of single-project real estate investments for potential equity investors is a
special case of investment evaluation.
6. (a) If the applicable tax rate is constant, accelerating depreciation
for tax purposes does not change the total taxes paid. However, the higher
tax deductions in earlier years would shift the cash outflows for taxes to
later years, so the present value of the cash outflows would be lower and the
NPV of the project higher.
(b) The payback period would be shorter because the net cash inflows

would be higher in earlier years of the project's life.
7-28

Manufacturing Cells, JIT

(20 minutes)

$2,536.4 thousand, from calculations (in thousands) below.
Cost savings ($6,579.6 - $4,718.2)
Tax on savings, at 40%
Net savings
Present value factor, 20 years, 12%
Present value of savings
Depreciation and amortization ($7.5 million/10)
$ 750.0
Tax saving at 40%
$ 300.0
Present value factor, 10 years, 12%
5.650
Present value of tax savings
Present value of all future flows
Less investment
Net present value

7-14

$ 1,861.4
744.6
1,116.8
7.469

$ 8,341.4

1,695.0
$10,036.4
7,500.0
$ 2,536.4


Note to the Instructor: Chapter 9 specifically addresses treatment of
one of the principal features of JIT, near-zero inventories, in a capital
budgeting decision.
7-29

Retirement Options

(10-15 minutes)

Waddlum's major concern is how long he will live after retirement.
Spending $80,000 per year, he will go broke in the ninth year if he takes the
lump-sum payment. Thus, if he lived longer than nine years, he would be
better off taking the $60,000 per year and living less comfortably than he
prefers.
If he took the lump-sum payment, he would use $80,000 for expenses the
first year, leaving $420,000 to be invested at 10%. That investment allows
nine withdrawals of $80,000, determined as follows.
Investment
Divided by annual withdrawals
Equals present value factor for annuity

$420,000

$ 80,000
5.25

The number of periods in the 10% column with the factor closest to 5.25 is
eight (a factor of 5.335), which means he could make nine withdrawals of
$80,000 (including the first) plus one of about $65,000 in the last year.
The $80,000 used immediately, plus the eight future withdrawals covers nine
years of retirement.
Note to the Instructor: This problem was made relatively simple by
leaving out the many other options. For example, pension plans provide for
payments to survivors after the death of the retiree. Class discussion of
this exercise can emphasize how very difficult real-life decisions can be
where an estate or other provision for survivors is desired. Still,
determining the number of years you can live as you wish from the lump-sum
investment seems to us a sensible first step in evaluating the options.
7-30
1.

Expanding a Product Line

(30 minutes)

The desk should be introduced.

The net present value is $92,200.

Sales (5,000 x $300)
Variable costs at $120
Contribution margin at $260
Fixed cash operating costs

Cash flow, before taxes
Depreciation ($1.5 million/5)
Increase in taxable income
Increased taxes (40%)
Increase in net cash flow
Present value factor, 5 years, 10%
Present value of future cash flows
Investment
Net present value
2.

About 3.57 years

Tax
$1,500.0
600.0
900.0
400.0
500.0
300.0
200.0
$
80.0

Cash Flows
$1,500.0
600.0
900.0
400.0
500.0

80.0
420.0
3.791
$1,592.2
1,500.0
$
92.2
$

($1,500.0/$420.0)

3. About 12.4% from Lotus 1-2-3. Students using tables will see that the
rate is about 12%. The factor 3.57 lies just below 3.605, the factor for 12%.

7-15


7-31

Buying Air Pumps

(15-20 minutes)

The memo should present a recommendation to buy the pumps and the NPV of
the purchase alternative (shown below). The memo could also include a brief
comment on the implications of a change in the lease payments.
Lease pumps
Revenue
Operating expenses
Lease expense

Total expenses
Income before taxes

$2,400
$550
850
1,400
$1,000

Buy versus lease
Tax
$850
500
350
$140

Annual lease savings
Less depreciation ($1,500/3)
Increase in taxable income
Increase in income tax (40%)
Net cash flow
Present value factor, 3 years, 10%
Present value of future flows
Less investment
Net present value in favor of buying

Cash Flow
$ 850
140
710

2.487
$1,766
1,500
$ 266
$

Note to the Instructor: The chapter points out that financing and
investing decisions should be separated. This is an apparent exception,
though we do not view a year-to-year lease as a financing arrangement. Note
also that the company has already decided to acquire the air pumps.
Moreover, revenues exceed operating costs and lease payments, so acquiring
the pumps is profitable. Hence, the only question is how to acquire them.
(Some students will not see this point and will spend time trying to develop
separate NPV analyses for the two alternatives.)
7-32

Charitable Donation

(15-20 minutes)

1. $976,404 ($6,000,000/6.145, the present value factor for a 10-year
annuity at 10%)
2.

The lump sum, because her discount rate is lower than the university's.

Pay $6,000,000 now:
Outflow
Tax saving at 35%
Net cash outflow

$6,000,000
2,100,000
$3,900,000

Pay $976,404 annually:
Donation
Tax saving at 35%
Net cash outflow
Present value factor, 9%, 10 years
Present value of outflows
Difference (in favor of lump-sum payment)
7-33
1.

Increasing Capacity

$
$

976,404
341,741
634,663
6.418
4,073,267
173,267

$

(25 minutes)

A 200,000 increase in volume is not enough to justify the investment.

7-16


Tax
$600,000
200,000
400,000
240,000
160,000
$ 64,000

Contribution margin (200,000 x $3)
Cash fixed costs
Pretax cash flow
Depreciation ($1,200,000/5)
Increase in pretax income
Income tax at 40%
Net cash flow
Present value factor, 5 years, 14%
Present value of future flows
Investment
Net present value
2.

Cash Flows
$ 600,000
200,000

400,000
64,000
336,000
3.433
$1,153,488
1,200,000
($
46,512)
$

A 250,000 increase in volume is enough to justify the investment.
Tax
$750,000
200,000
550,000

Contribution margin (250,000 x $3)
Cash fixed costs
Pretax cash flow
Depreciation ($1,200,000/5)
Increase in pretax income
Income tax at 40%
Net cash flow
Present value factor, 5 years, 14%
Present value of future flows
Investment
Net present value

310,000
$124,000

Cash Flows
$ 750,000
200,000
550,000
240,000
124,000
426,000
3.433
$1,462,458
1,200,000
$ 262,458

$

Note to the Instructor: You might wish to point out that requirement 2
can be solved by looking at differences. The additional 50,000 pairs give:
Additional contribution margin (50,000 x $3)
Times (1 - 40% tax rate)
Equals after-tax cash flow
Times relevant present value factor
Equals additional NPV

$150,000
60%
$ 90,000
3.433
$308,970

The $308,970 plus the negative $46,512 add up to $262,458.

7-34

Funding a Pension Plan

(15 minutes)
Cash Flows
$ 25,000
10,000
$ 15,000
4.833
$ 72,495
60%
$120,825

Annual cash outflows
Less tax savings at 40%
Net cash outflows
Present value factor for 10 years at 16%
Present value of outflows
Divided by (1 - 40% tax rate)
Equals maximum before-tax amount
7-35 Research and Development Investment

(15-20 minutes)

The investment is desirable, NPV of $1.15 million, IRR of about 14.5%.

7-17

Year

Cash Flow

20X1
20X2
20X3
20X4
20X5
20X6
20X7
20X8
NPV

-$4.5
- 6.2
- 8.5
- 3.2
7.0
9.0
11.0
13.0

After-Tax

PV Factor

-$2.7
- 3.72
- 5.1

- 1.92
4.2
5.4
6.6
7.8

1.000
.893
.797
.712
.636
.567
.507
.452

Present Value
-$2.70
- 3.32
- 4.07
- 1.37
2.67
3.06
3.35
3.53
$1.15

This assignment differs from others in that it does not have a single
investment at time zero. Students should still see that the NPV is the
present value of all cash flows. For convenience, the chapter refers to
future flows and investment.

7-36

Capital Budgeting by a Municipality

(20 minutes)

1. The center should be built; the net present value of the project is
$3,893,400.
Rentals of space, etc.
Tax receipts*
Total receipts to city
Operating costs
Net cash flows
Present value factor for 30-year annuity at 8%
Present value of future receipts
Less investment required
NPV

$ 1,800,000
1,000,000
2,800,000
500,000
$ 2,300,000
11.258
$25,893,400
22,000,000
$ 3,893,400

* 200,000 persons spending $500 each gives $100,000,000 in spending per
year, and the city collects 1% of this sum, or $1,000,000.

2. Like all not-for-profit entities, a city is not trying to provide a
return to owners as a business entity must. Rather, its purpose is to
provide services for which the residents and others will pay and from which
they will receive benefits. Thus, the only element of cost of capital is the
interest rate.
Note to the Instructor: We ask students whether the investment should
be made even if it would not directly pay for itself (say if the cost were
$28,000,000). Some suggest that there are likely to be fringe benefits to
the city's businesses. Some suggest that having the convention center could
stimulate tax receipts by attracting other tax-paying businesses to the city.
That suggestion prompts other students to point out the likelihood of
additional costs (e.g., for added police and fire protection) if the city
grows as a result of the center. There are likely to be some students who
will argue that a convention center and possible growth are the last things a
city needs. Overcrowding, congestion, pollution, and other undesirable
features could emerge from the building of the center. Additionally the
estimates are very subjective. Hence the initial question eventually leads
students to recognize the possibility of conflict
between qualitative and quantitative factors.
7-37
1.

Comparison of NPV and Profit

(25-30 minutes)

The capital-intensive process gives the higher income.
Labor

7-18

Capital


Intensive
$5,000,000
2,000,000
3,000,000
1,400,000
1,600,000
640,000
$ 960,000

Sales (100,000 x $50)
Variable costs at $20, $10
Contribution margin
Fixed costs*
Taxable income
Income taxes (40%)
Net income

Intensive
$5,000,000
1,000,000
4,000,000
2,100,000
1,900,000
760,000
$1,140,000

* $400,000 + ($4,000,000/4); $600,000 + ($6,000,000/4)
2. The labor-intensive process gives the higher book rate of return on
average investment.
Labor
Capital
Intensive
Intensive
Net income
$ 960,000
$1,140,000
Divided by average investment
$2,000,000
$3,000,000
Equals book rate of return
48%
38%
3. The labor intensive process has the higher NPV.
Labor
Capital
Intensive
Intensive
Contribution margin from requirement 1
$3,000,000
$4,000,000
Fixed cash operating costs
400,000
600,000
Change in pretax cash flow
2,600,000
3,400,000

Depreciation ($4,000,000/4; $6,000,000/4)
1,000,000
1,500,000
Increase in taxable income
1,600,000
1,900,000
Increased taxes (40%)
640,000
760,000
Increase in net income
960,000
1,140,000
Add back depreciation (not a cash flow)
1,000,000
1,500,000
Net cash flow
$1,960,000
$2,640,000
Present value factor, 4 years, 16%
2.798
2.798
Present value of future cash flows
$5,484,080
$7,386,720
Investment required
4,000,000
6,000,000
Net present value
$1,484,080
$1,386,720

Difference in NPVs = $97,360
4. The memo should report the NPVs of the two alternatives and express a
preference for the labor-intensive process because of its higher NPV. The
memo should also note the relatively small difference between the NPVs and
urge further consideration of qualitative factors that might tip the decision
one way or the other. The memo should emphasize that the preference was
based on NPV rather than book rate of return, and it could point out that
book rates of return overstate the differences between the two alternatives.
7-38

Capital Budgeting for a Computer Service Company

Additional revenues (12 x $40,000)
Additional cash expenses (12 x $4,000)
Cash flow before taxes
Depreciation (given)
Income before taxes
Income taxes, 40%
Net cash flow after taxes
Present value factor, 4 years, 16%
Present value of future annual cash flows
Present value of salvage value ($300,000 x .552)
Total present value of investment
Investment
Net present value
7-39 Reevaluating an Investment (20 minutes)

7-19

(25 minutes)

Tax
$480,000
48,000
432,000
225,000
207,000
$ 82,800

Cash Flows
$ 480,000
48,000
432,000
82,800
349,200
2.798
$ 977,062
165,600
1,142,662
1,200,000
($
57,338)
$


An analysis using discounted cash flow techniques shows that the
investment was unwise. Both NPV and IRR suggest the same answer.
Net present value method
Annual cost savings
Depreciation
Increase in taxable income

Income tax at 40% rate
Net cash flow
Present value factor, 10 years, 16%
Present value of returns
Investment
Net present value

Tax
$69,000
25,000
44,000
$17,600

Cash Flows
$ 69,000
17,600
$ 51,400
4.833
$248,416
250,000
($ 1,584)

Note to the Instructor: It's important to point out that the wisdom of
the original investment decision has no bearing on whether the machinery
should be replaced now. Similar machinery purchased now might yield a return
greater than 16%. What can be said is that if the machinery available now
would cost $250,000, have a 10-year life with no salvage value, provide
$69,000 in savings, and be depreciated using the straight-line method, it is
unwise to buy it, though just barely.
7-40

1.

Purchase Commitment

(20-25 minutes)

The offer should be rejected because NPV is a negative $87,320.

Annual cash flows
Interest ($2,000,000 x 8%)
Savings in purchase price [($1.00 - $.80) x 1,000,000]
Total
Less additional income tax at 40%
Net after-tax cash flow
Present value factor, 5 years, 12%
Present value of annual flows
Present value of loan repayment ($2,000,000 x .567)
Total present value
Investment
NPV
2.

$

160,000
200,000
360,000
144,000
$ 216,000
3.605

$ 778,680
1,134,000
1,912,680
2,000,000
($
87,320)

$1.04037

Required investment
Present value of loan repayment (from requirement 1)
Required present value of annual cash flows
Divided by present value factor, 5 years, 12%
Equals required after-tax cash flows
Divided by (1 - the 40% tax rate)
Equals required pretax cash flows
Less interest receipts
Equals required annual savings in copper price
Divided by annual maximum purchases
Equals required savings per pound
Plus price of copper from Boa
Equals required market price

$2,000,000
1,134,000
$ 866,000
3.605
$ 240,222
60%
$ 400,370

160,000
$ 240,370
1,000,000
$
.24037
.80000
$ 1.04037

Note to the Instructor: We use the term "relevant discount rate"
because the loan is a relatively riskless investment, or at least one that is
less risky than those normally encountered by the firm. The discount rate

7-20


should probably be the cost of capital, but using a lower rate might be
desirable depending on the credit worthiness of Boa Company.
One could also argue that this type of investment is extremely risky
taken as a whole because its success depends on estimates of the prices of a
raw material the price of which is known to fluctuate greatly. The problem
provides the opportunity to discuss how managers might predict future prices
of copper and to lead into the topic of sensitivity analysis in Chapter 9.
7-41

New Product−Complementary Effects

(25 minutes)

The product should be introduced; the investment's NPV is $8,551,320.
Tax

Cash Flows
Contribution margin, new cleaner
($22 - $12) x 800,000
$8,000,000
$ 8,000,000
Lost contribution margin, lost sales of
existing product, ($15 - $9) x 300,000
1,800,000
1,800,000
Net additional contribution margin
6,200,000
6,200,000
Additional cash operating costs
1,400,000
1,400,000
Cash flow before taxes
4,800,000
4,800,000
Less depreciation, $10,000,000/10
1,000,000
Increase in taxable income
3,800,000
Income tax at 40%
$1,520,000
1,520,000
Net cash operating flows
$ 3,280,000
Present value factor 12%, 10 years
5.650
Present value of future operating flows

$18,532,000
Present value of salvage value ($100,000 x 60% x .322)
19,320
Total present value
18,551,320
Investment
10,000,000
Net present value
$ 8,551,320
7-42 Discounts and Cash Flows
1.

(20 minutes)

No, $50 is less than the present value of two $28 payments.
Present value of $28 in one year ($28 x .893)
Present value of $28 now
Total present value

$25.004
28.000
$53.004

The assumption of 100% renewals for the second year is critical to seeing
the question as a comparison of the present values of two cash inflow
options. Both the costs and the quantity sold (number of subscription-years)
are the same for the two subscription plans. Hence, the magazine has no
reason to offer the extended subscription at a rate that is not equivalent to
what it would receive from a one-year subscription plus renewal.
2.

$53.00, the present value of two $28 payments.

3. Yes, the NPV is $310.70 with the two-year subscription, $276.44 with the
one year. The $50 rate increases total volume enough to offset the expected
loss of subscriptions after the first year. The calculations below use a
batch of 10, as suggested in the assignment.
Receipts today from two-year subscriptions (10 x $50)
Present value of variable cost {[$10 + ($10 x .893)] x 10}
Net present value

$500.00
189.30
$310.70

Receipts today from 10 one-year subscriptions (10 x $28)

$280.00

7-21


Present value of 6 renewals ($28 x .893 x 6)
Total present value
Present value of variable costs [($10 x 10) + ($10 x 6 x .893)]
Net present value

150.02
430.02
153.58

$276.44

4. About $46.57. This part requires restating the two-year analysis above
with the NPV of the one-year subscriptions as the required NPV.
NPV of one-year subscriptions
Plus present value of variable costs, two-year (above)
Total required present value
Divided by 10 equals required two-year rate

$276.44
189.30
$465.74
$ 46.57

Note to the Instructor: The situation in this assignment is familiar to
students and to anyone else on mailing lists. You might point out that
advertising is a major source of revenue to magazines and that advertising
rates depend to a great extent on paid circulation. Therefore, the magazine
could earn more, by way of higher ad rates, if offering a bargain two-year
rate keeps subscribers for a longer time. The company in this problem might
be able to offer a two-year rate even lower than the $46.57 computed in
requirement 4 determined that the higher advertising rates commanded by the
higher circulation would offset the lower rate.
7-43
1.

Quality Improvement

(15-20 minutes)

About $3.16 million, from calculations (in millions) below.
Savings in variable costs ($58.0 x .10)
Less additional cash fixed costs
Pretax cash flow
Depreciation ($6.5/5)
Increase in taxable income
Income tax at 40%
Net cash flow
Present value factor, 5 years, 12%
Present value of future flows
Investment
Net present value

2.

Tax
$5.80
2.20
3.60
1.30
2.30
$0.92

Cash Flow
$5.80
2.20
3.60
0.92
2.68
3.605

$9.66
6.50
$3.16

About $16.1 million, from the following calculations (in millions).
Additional revenue* ($117.8 x .10)
Less additional cash fixed costs**
Pretax cash flow
Depreciation ($6.5/5)
Increase in taxable income
Income tax at 40%
Net cash flow
Present value factor, 5 years, 12%
Present value of future flows
Investment
Net present value

Tax
$11.78
2.20
9.58
1.30
8.28
$ 3.31

Cash Flow
$11.78
2.20
9.58
3.31

$ 6.27
3.605
$22.60
6.50
$16.10

* The company gains revenue by selling formerly spoiled units.
**Total variable costs remain constant because the factory works at the
same rate.
7-44

Long-Term Special Order

(35 minutes)

7-22


The memo should report that (1) accepting the order is wise even if the
company cannot increase capacity; (2) the NPV of undertaking the expansion is
a negative $10,742; and (3) the proposed limited expansion is probably unwise
because it allows the company to recover only the 10,000 units of regular
sales lost by accepting the order.
Accept the order without expanding
Contribution margin as is [200,000 x ($12 - $7)]
Contribution margin if order accepted:
190,000* x ($12 - $7)
40,000 x ($9 - $7)
Total if order accepted

$1,000,000
$

950,000
80,000
$1,030,000

* Capacity of 230,000 units - 40,000 for special order = 190,000 for sales
at regular prices.
Accept the order and expand
Increased contribution margin (10,000 x $5)
Increased fixed costs
Increased cash flow before taxes
Depreciation ($100,000/5)
Increase in taxable income
Taxes (40%)
Net change in cash flow after taxes
Present value factor, 5 years, 14%
Present value of future cash inflows
Investment required
Net present value
7-45
1.

Analyzing a New Product

Tax
$50,000
20,000
30,000

20,000
10,000
$ 4,000

Cash Flow
$ 50,000
20,000
30,000
4,000
$ 26,000
3.433
$ 89,258
100,000
($ 10,742)

(40-45 minutes)

The investment has an NPV of $1,616,712.

Tax
Revenue (30,000 x $90)
$2,700,000
Variable costs:
Materials (30,000 x $10)
300,000
Labor (30,000 x $17)
510,000
Variable overhead (30,000 x $10*)
300,000
Commissions (30,000 x $4)

120,000
Total (30,000 x $41)
1,230,000
Contribution margin (30,000 x $49)
1,470,000
Cash fixed costs
200,000
Pretax cash flow
1,270,000
Depreciation ($3,000,000/10)
300,000
Increase in pretax income
$ 970,000
Income tax at 40%
$ 388,000
Net cash flow
Present value factor, 10 years, 14%
Present value of future flows
Present value of salvage** ($100,000 x .60 x .270)
Total present value
Investment
Net present value

* Calculation of variable overhead per unit:

7-23

Cash Flows
$2,700,000
300,000

510,000
300,000
120,000
1,230,000
1,470,000
200,000
1,270,000
388,000
882,000
5.216
$4,600,512
16,200
4,616,712
3,000,000
$1,616,712
$


Total overhead per unit
Less fixed overhead per unit
Variable overhead per unit

($600,000/30,000)

$30
20
$10

**Residual value is taxable because the full cost was depreciated over the
project's useful life.

2.

Barker's analysis is deficient in the following ways.

(a) The existing fixed manufacturing costs allocated to the new product are
sunk and irrelevant. Only the $200,000 incremental amount is relevant.
(b) The allocated selling and administrative expenses are likewise
irrelevant. Only the $4 commission is relevant.
(c) The $900,000 already spent for research and development is a classic
example of a sunk cost and is irrelevant.
(d) Barker ignored the salvage value, though it should be included in the
calculation. The item is not large in this case, but it could be significant
in another.

7-24