CHAPTER 12 SOLUTIONS

Solutions to Questions for Review and Discussion

1. An investment in inventory is different than an investment in machinery because inventory

cannot be depreciated like machinery. Also, inventory is used, replenished, and often
recovered at the end of the project. Machinery cannot be replenished like inventory; and only
salvage value, if any, is recovered at the end of the project.

2. Inflation can be incorporated into capital investment analysis in two ways: (1) Add the
expected inflation rate to the cost of capital rate. This assumes that inflation is the same for all
future time periods and that all cash flows are impacted by the same inflation rate. (2) Build
the impacts of inflation into the expected future cash flows. This allows different inflation rates
to be used for different cash flows and for different time periods.

3. The first problem with unequal lives is choosing the timeframe on which to base the lives. Do
you base the life of a project on the timeframe of the job to be done or on the physical life of
an asset? If the life is based on the time period of the project, the task is to find salvage
values or market values for assets before the end of their useful lives. If you choose the
physical lives of assets for the time period, how do you compare a 2-year asset with a 10-year
asset? One approach is to use the life of the shorter lived asset. This requires finding salvage
or market value for the longer lived asset before its useful life is over. Another approach is to
use the life of the longer lived asset by assuming the shorter lived asset can be extended by
another similar asset at the end of the first's life. For example, five 2-year assets may be
strung together to match one 10-year asset.

4. You are assuming that the inflation rate will be the same in all future time periods. You are also
assuming that all expected future cash flows will be affected by the same inflation rate.

5. Analyzing each phase independently determines the attractiveness of each on its own merits.
However, remember that the only way to achieve Phase II is the completion of Phase I.
Therefore, the combined analysis is done. Phase I by itself may not be an attractive project;
but, when it is continued into Phase II, the combined projects may become an attractive
investment alternative. It is important to remember that, when one alternative depends on the
completion of another, all possible combinations should be analyzed to determine the best
course of action for the company.

6. The investing decision is determining the attractiveness of an investment based solely on its
basic cash flows. The "go" or "no go" decision should be based on analyses like net present
value, internal rate of return, payback period, etc. These analyses assume a pool of long-term
funds is available to invest in attractive projects.

Generally, the acquisition is the fundamental investment decision. The financing decision
determines the specific source of funds. They represent two different sets of cash flows.
Combining the two cash flows allows the decision maker to evaluate many more combinations
of acquisition and financing choices. Only in unusual situations will the choice of financing
alternatives influence the basic investment decision.

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7. The annual cost of leasing differs from the annual cost of buying for many reasons. For
example, lease payments, which contain both interest and principal components, are entirely
deductible for income tax purposes. Whereas with loan repayments, the interest component is
deductible; but the principal repayment is not. Also, when leasing, the depreciation tax shield
is not permitted on that asset since it is not owned by the lessee. The interest rates on leases
and borrowed funds can also differ. Interest rates on leases may be lower than those on
borrowed funds to help compensate for losing the depreciation tax shield. The lease versus
purchase decision must be analyzed carefully to maximize a company's investing capabilities.

8. If cash flows of only the initial investment, sales, and operating expenses are considered,
relevant costs may be excluded from the analysis. First, the capital investment analysis
process may be the only time that a project's total picture is seen. It is here that all costs and
benefits relative to that project must be included and evaluated. Even difficult to evaluate
costs must be recognized through "best estimate" projections or at least be mentioned in the
supporting documents that will accompany any capital funding request. Second, the tangible
benefits (a positive NPV or high IRR) may hide significant issues that traditionally have not
been part of these analyses. These include legal responsibility for ecology problems, impacts
on employees, and other social or environmental impacts that could cause embarrassment or
financial loss.

9. The declining-balance and the straight-line depreciation methods are built into most of the
annual MACRS depreciation percentages. Also built in is the half-year rule.

10. The estimates of future cash flows should be tested for source credibility and reasonableness,
as well as on assumptions underlying the estimates. This can be accomplished through
sensitivity analysis, which performs "what-if" scenarios on the future cash flows to determine
how far they can change before an investment becomes unattractive. Also, a company can
assign the responsibility for the estimated future cash flows to a manager. If managers must
answer for their estimates, they are more likely to make accurate estimations. The final step is
to perform a post-audit on the project after it is in operation to measure actual investment costs
and annual benefits.

11.
(a) XYZ may have a higher hurdle rate than ABC because it is not able to obtain investing funds
as cheaply as ABC. Maybe XYZ is a smaller company, and banks are not as eager to lend it
funds. Also, XYZ might not have as much of its own funds available for investing, so it requires
a higher return before investing. XYZ's past earnings may have been volatile versus ABC's
smooth earnings pattern. It might have had a record of losses or low earnings, meaning it is
more risky. XYZ may also be a little more cautious and have added a higher risk factor to its
hurdle rate. XYZ could be in an industry where inflation is a bigger factor, so its adds a higher
inflation percentage to its hurdle rate than ABC does.

(b) Divisions in the same company can have different hurdle rates due to risk variations. It is
important to remember that capital investment dollars are scarce and that a company must use
the dollars in most profitable manner. Division G may be in a mature or stable industry where
new investments have highly predictable outcomes. Division I may be in a new business area
and not have proven its ability to pick winners. Payoff may be high, but many losers also exist.
12. Sensitivity analysis provides information on how far off estimates on future cash flows can be
before the investment decision changes. Variables most often analyzed are volume of units,
sales price, variable and fixed costs, and lives of projects. It is important to do sensitivity
analysis on the estimates of future cash flows because of the uncertainty associated with the
future. Sensitivity analysis can provide a sense of confidence in the estimates and can help
identify potentially unprofitable or high-risk investments.

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13. Expected value is the anticipated value of a variable given different expectations about the
value and is, therefore, not a "real" value. Often a company does not have a specific estimate
of the value of a certain variable in a capital budgeting decision. The company will use
weighted averages and probabilities to determine the expected value of certain variables. This
analysis allows for easy manipulation of the values through "what if" scenarios.

14. Intangible benefits and costs can be incorporated into capital investment decisions by
anticipating the possible outcomes of these costs and benefits on the decision. It is often very
difficult to put a dollar amount on the intangibles; often "gut feelings" from years of experience
help to "quantify" the intangibles. Watching the actions of others can also help to analyze the
intangibles. A company considering building a plant on the natural habitat of an endangered
species of animal may learn that another company which did the same thing had its products
boycotted by consumers. Managers should not be blinded by the dollars and cents of a
decision and should consider the intangibles associated with decisions. Also, after acquiring
experience in attempting to measure intangibles, managers can give better quantitative
estimates of these factors. Better measuring techniques and experience are the best
teachers.

15. In these days of heightened awareness regarding social issues, attractive investment
alternatives based on dollars and cents may be turned down due to the costs of social
pressures. Nuclear power is an efficient form of electricity and probably a profitable
investment, but few are willing to have a nuclear power plant in their backyards. Industrial
wastes, disadvantaged employment, handicap access, and tobacco and alcohol health effects
are examples of the public's interest in social issues which impact business decisions.

16. While not-for-profit organizations are not in business to make money, they still must cover their
costs to operate. A not-for-profit company should be concerned with providing the maximum
benefits to the people but should not rule out good business practices in the process. If a
shelter for the homeless has to purchase a new heater for the building, it should perform
capital investment analysis to find the heater that does the best job for the dollars to be spent.
Capital investment dollars are scarce even in not-for-profit organizations, so the organization
should not ignore the benefits that capital budgeting analysis can provide.

17. Advantages of life-cycle costing:

1. At the very beginning of a project, all cost and benefit elements are included in the
analysis.
2. It forces the project sponsor to make a conscious effort to plot the life of the product or
service.
3. Difficult assumptions are explicitly identified for all to evaluate.
4. With the staging of all planned costs and revenues, actual results can be compared and
evaluated on an ongoing basis. Additional "go" and "no go" points can be built into the
project.

Solutions to Exercises

Note: The solutions to exercises, problems, and cases will use the following abbreviations: PV
for present value, NPV for net present value, ROR for rate of return, IRR for internal rate of
return, and ARR for accounting rate of return.

12-1. Net cash outflow:

Cost of new machine ($200,000)
Sell old machine 50,000

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 Minus tax on gain [0.40 x ($50,000 – $20,000)] (12,000)
Net cash outflow for investment ($162,000)

12-2.
(1) Investment I Investment II
NPV, Table 2, Row 10 PV, Table 1, Row 10
(with annual cash flows (with one-time cash flow
Discount of $12,000 and an of $180,000 and an
Rate investment of $50,000) investment of $50,000)
4% $47,332 $71,680
5% 42,664 60,520
6% 38,320 50,440
8% 0,520 33,340
10% 23,740 19,480
12% 17,800 7,960
14% 12,592 (1,400)
15% 10,228 (5,540)
16% 7,996 (9,140)
18% 3,928 (15,620)
20% 304 (20,840)
22% (2,924) (25,340)
24% (5,816) (29,120)
25% (7,148) (30,740)

(2) Investment I is preferred over Investment II over the range of 10 percent to 20 percent due to
its higher NPV.

(3) At a little over 20 percent, the NPV of Investment I becomes negative. Investment II becomes
negative at just under 14 percent. Therefore, at approximately 20 percent, neither investment
would be selected.

12-3. Since the life of each car is different, to analyze the decision convert all choices to the same
life span. The Supreme Deluxe has the longest life, 6 years, and that will be used to evaluate
all choices. Therefore, you would have to purchase two Premium Fairmonts and three
Economy Delights. The alternative that promises the greatest financial advantage is the one
with the lowest NPV of costs.

(a) Supreme Deluxe and trade every sixth year:

Investment Life of the Project

Year: 0 1 2 3 4 5 6
Original cost ($30,000)
Annual costs ($2,400) ($2,400) ($2,400) ($2,400) ($2,400) ($2,400)
Overhaul (2,000)
Trade-in value 8,000
Cash flows ($30,000) ($2,400) ($2,400) ($2,400) ($4,400) ($2,400) $ 5,600
PV factors x 1.000 x 0.909 x 0.826 x 0.751 x 0.683 x 0.621 x 0.564
PV ($30,000) ($2,182) ($1,982) ($1,802) ($3,005) ($1,490)
$ 3,158
Total PV (7,303)
NPV ($37,303)

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(b) Premium Fairmont and trade every third year:

Investment Life of the Project

Year: 0 1 2 3 4 5 6
Original cost ($20,000) ($20,000)
Annual costs ($2,000) ($2,000) ($2,000) ($2,000) ($2,000) ($2,000)
Overhaul (1,000) (1,000)
Trade-in value 8,000 8,000
Cash flows ($20,000) ($2,000) ($3,000) ($14,000) ($2,000) ($3,000) $ 6,000
PV factors x 1.000 x 0.909 x 0.826 x 0.751 x 0.683 x 0.621 x 0.564
PV ($20,000) ($1,818) ($2,478) ($10,514) ($1,366) ($1,863) $ 3,384
Total PV (14,655)
NPV ($34,655)

(c) Economy Delight and trade every second year:

Investment Life of the Project

Year: 0 1 2 3 4 5 6
Original cost ($15,000) ($15,000) ($15,000)
Annual costs ($1,500) ($1,500) ($1,500) ($1,500) ($1,500) ($1,500)
Trade-in value 8,000 8,000 8,000
Cash flows ($15,000) ($1,500) ($8,500) ($1,500) ($8,500) ($1,500) $ 6,500
PV factors x 1.000 x 0.909 x 0.826 x 0.751 x 0.683 x 0.621 x 0.564
PV ($15,000) ($1,364) ($7,021) ($1,127) ($5,806) ($932) $ 3,666
Total PV (12,584)
NPV ($27,584)

The best choice is to purchase the Economy Delight and trade every two years. This involves
purchasing three cars, but the cost is the lowest of the three alternatives.

12-4. Net investment:

Cost of new machine ($80,000)
Minus:
Trade-in allowance $ 6,000
Repairs on old machine $20,000
Minus tax benefit of repairs deduction
($20,000 x 0.40) (8,000) 12,000 18,000
Net investment ($62,000)

12-5.
NPV: Investment Life of the Project
Year: 0 1 5 6
Additional inventory (£100,000)
Increased earnings £40,000 . . . £40,000 £ 40,000
Recouped inventory 100,000
Total cash flows £40,000 £40,000 £140,000
PV – Years 1 to 5 £130,960

(16%, 5 years): £40,000 x 3.274 x 0.410

PV – Year 6 57,400
Total PV £188,360
NPV £88,360

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 This appears to be a very attractive investment. Her NPV is greater than the initial investment.
This is true even after earning 16 percent ROR. Looking at another measure, the profitability
index is 1.884 (£188,360  £100,000) – a very high value.

12-6.
(1) Alternative 1:
Investment Life of the Project
Year: 0 1 2 3 4 5
Cash flows (¥1,300,000) ¥ 400,000 ¥ 400,000 ¥ 400,000 ¥ 400,000
400,000
PV – Years 1 to 5 1,309,600
(16%, 5 years): ¥400,000 x 3.274
NPV ¥9,600

Alternative 2:
Investment Life of the Project
Year: 0 1 2 3 4 5
Cash flows. (¥1,800,000) ¥ 550,000 ¥ 550,000 ¥ 550,000 ¥ 550,000
550,000
PV – Years 1 to 5 1,800,700
(16%, 5 years): ¥550,000 x 3.274
NPV ¥700

The company should purchase the machine in Alternative 1 since it provides ¥8,900 (¥9,600 –
¥700) more than Alternative 2. It also has a slightly higher profitability index of 1.007 versus
1.0004.

(2) PV factor (IRR) = Investment  Annual cash flow

Alternative 1: = ¥1,300,000  ¥400,000 = 3.250

Alternative 2: = ¥1,800,000  ¥550,000 = 3.273

The PV factor for Alternative 1 is between 16 and 18 percent on the 5-period row (16.32
percent on a business calculator). The PV factor for Alternative 2 is very close to 16 percent
(16.021 percent on a business calculator).

(3) PV factor (IRR) = Incremental investment  Incremental cash flow

= (¥1,800,000 – ¥1,300,000)  (¥550,000 – ¥400,000)
= ¥500,000  ¥150,000 = 3.333

The PV factor 3.333 is between 15 and 16 percent (15.24 percent on a business calculator).
This is below the 16 percent minimum acceptable rate of return.

(4) Part (1) shows that both projects are acceptable using 16 percent as the minimum acceptable
ROR. The higher ROR on Alternative 1 for a lower investment implies that the marginal
investment may yield a ROR below the acceptable level. Part (3) confirms this suspicion.
Perhaps the marginal ¥500,000 can be invested elsewhere at a rate above 16 percent.
Answers to all three parts give consistent information.
12-7.
NPV: Investment Life of the Project
Year: 0 1 2 3 4 5

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-6
 Equipment cost ($800,000)
Saved operating costs $300,000 $300,000 $300,000 $300,000
$300,000
Minus depre. (MACRS):
Year 1 – 33.0% (264,000)
Year 2 – 45.0% (360,000)
Year 3 – 15.0% (120,000)
Year 4 – 7.0% (56,000)
Year 5 – 0.0% 0
Taxable income $ 36,000 ($60,000) $180,000 $244,000
$300,000
Minus taxes (40%) (14,400) 24,000 (72,000) (97,600)
(120,000)
Income after tax $ 21,600 ($36,000) $108,000 $146,400
$180,000
Plus depreciation 264,000 360,000 120,000 56,000 0
Net cash flow ($800,000) $285,600 $324,000 $228,000 $202,400
$180,000
PV factors (16%) x 1.000 x 0.862 x 0.743 x 0.641 x 0.552 x 0.476
PVs ($800,000) $246,187 $240,732 $146,148 $111,725
85,680
PV – Years 1 to 5 830,472
NPV $30,472

ARR: To find the ARR you must have smooth cash flows after depreciation over the
investment's life. Since the MACRS depreciation causes uneven cash flows, average the
taxable income amounts to smooth the cash flows. This results in an average cash flow
per year of $140,000. The average investment is $400,000 ($800,000  2).

ARR = $140,000  $400,000 = 35 %

Payback period:

Year Cash Flows Unrecovered Investment

0 ($800,000) $800,000
1 285,600 514,400
2 324,000 190,400
3 228,000 0

Payback period = 2 + ($190,400  $228,000) = 2.835 years

Approximate IRR:

Due to the uneven cash flows, approximating the IRR requires trial and error and interpolation.
The IRR solved on a business calculator is 20.4 percent.

12-8.
NPV: Investment Life of the Project
Year: 0 1 2 3 4 5, 6, & 7 8 9 10

Purchase cost ($120,000)

Operating savings $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000 $25,000
Minus MACRS depre:
Year 1 – 14.3% (17,160)

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 Year 2 – 24.5% (29,400)
Year 3 – 17.5% (21,000)
Year 4 – 12.5% (15,000)
Year 5-7 – 8.9% (10,680)
Year 8 – 4.5% ( 5,400)
Year 9 – 0.0% 0
Year 10 – 0.0% 0
Taxable income $ 7,840 ($4,400) $ 4,000 $10,000 $14,320 $19,600 $25,000 $25,000
Minus taxes (40%) 3,136 1,760 1,600 4,000 5,728 7,840 10,000 10,000
Income after tax $ 4,704 ($2,640) $ 2,400 $ 6,000 $ 8,592 $11,760 $15,000 $15,000
Plus depreciation 17,160 29,400 21,000 15,000 10,680 5,400 0 0
Net cash flow ($120,000) $21,864 $26,760 $23,400 $21,000 $19,272 $17,160 $15,000 $15,000
PV factors (14%) x 1.000 x 0.877 x 0.769 x 0.675 x 0.592 x 1.3751 x 0.351 x 0.308 x 0.270
PVs – Yrs 1 to 10 ($120,000) $19,175 $20,578 $15,795 $12,432 $26,499 $ 6,023 $ 4,620 $ 4,050
Total PV of inflows 109,172
NPV ($10,828)
1
0.519 + 0.456 + 0.400

Payback period:

Year Cash Flows Unrecovered Investment

0 ($120,000) $120,000
1 21,864 98,136
2 26,760 71,376
3 23,400 47,976
4 21,000 26,976
5 19,272 7,704
6 19,272 0

Payback period = 5 + ($7,704  $19,272) = 5.40 years

Approximate IRR:

Due to the uneven cash flows, approximating the IRR requires trial and error and
interpolation. The IRR solved on a business calculator is 11.43 percent.

12-9.
(1) While the technique will not prevent missing other important issues, the life-cycle costing
approach will require proposers of investment projects to consider the entire set of issues
concerning a proposed investment. The issues that Mark has identified should certainly be
part of the total view of all three proposals. The hospital should have in place guidelines that
will instruct managers who request capital investment money to think carefully about the
possible ramifications of their proposals. This would include hidden and indirect cost impacts,
environmental implications (both from legal and ethical perspectives), and basic social impacts.
These are particularly important because this organization is at the center of many social and
community issues.

(2) Policy statement:

I. Life-cycle costing of all investment proposals:

All projects must identify all incremental cash flows caused by the proposal. A complete
costing of the initial investment outlay includes all costs of preparing and installing any new
assets. Training costs must be estimated. Costs of disposal of old assets are relevant to
the new project.

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 Future cash flows must include all costs and revenues associated with the proposal. This
would include any estimated costs to safeguard the environmental. Disposal and
restoration costs may be significant costs.

II. All investment proposals must be accompanied by statements regarding the following
issues:

A. Environmental costs: This includes any direct or indirect site preparation costs and any
possible costs arising from adverse environmental impacts. Of particular note is the
safety of our employees and possible long-term adverse health impacts.

B. Social and community costs: This includes any direct or indirect costs from impacts on
the surrounding community, our employees, the reputation of the hospital, and our role
as a corporate citizen within this city.

Please note that proposals can also include the avoidance of these costs as part of the
justification for the proposal. For example, elimination of an environmental problem may
be the sole justification of a proposal.

12-10.
(1) Net investment:
Cost of new machine ($200,000)
Sell old machine 20,000
Tax on gain (0.40 x $20,000) (8,000)
Net cash outflow for investment ($188,000)

(2) NPV: Investment Life of the Project

Year: 0 1 2 3 4 5

Net investment ($188,000)

Yearly cash flows:
Annual returns $80,000 $80,000 $80,000 $80,000
$80,000
Minus MACRS depre 66,660 88,900 29,620 14,820 0
Taxable income $13,340 ($ 8,900) $50,380 $65,180
$80,000
Minus taxes (40%) 5,336 (3,560) 20,152 26,072
32,000
Income after tax $ 8,004 ($ 5,340) $30,228 $39,108
$48,000
Plus depreciation 66,660 88,900 29,620 14,820 0
Net cash flow ($188,000) $74,664 $83,560 $59,848 $53,928
$48,000
PV - Years 1 to 5 217,424
NPV $29,424

Since the NPV at the 16 percent minimum ROR is positive, the investment is acceptable.

12-11. Note: The calculations in this problem require a financial calculator. Also, students will
likely make numerous different assumptions. This answer assumes that all monthly
payments on loans or leases are at the end of all periods. Insurance and fees are
assumed to be paid in advance.

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Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-10
 Sam's Rent-to-Own versus Jane's credit union financing:

Per iods: 0 Months 1 to 48

Sam's options:
Option 1: Pay cash ($2,000)
Option 2: Pay monthly $75
PV – Months 1 to 48 (using 9%) ($3,014)

(Use 9 percent as the annual interest rate to discount the monthly payments.)

Jane's options, including credit union financing:

Option 1: Pay cash ($1,500)
Option 2: Go credit union
Downpayment ($150) ($33.59)
PV – Months 1 to 48 (using 9%) (1,350)
Total PV ($1,500)

Assuming that a person can find the down payment, the credit union option is the best
alternative. Notice that a typical low-income person buying at Sam's will be paying over twice
the cost of better furniture, even on a discounted basis.

Joe's Deal and Drive versus Mike's Autos and Jane's credit union financing:

Periods: PV at 9% 0 Mo 1 to 48 Annual
Joe's Deal and Drive:
Insurance (prepaid) ($6,356) ($1,800)
Credit life fee (prepaid) (202) ($5)
Car payment (11,184) (278)
($10,000 base)
Total PV ($17,742)

Periods: PV at 9% 0 Mo 1 to 24 Mo 1 to 48 Residual
Mike's Autos:
Up-front contract fee ($500) ($500)
Residual lease payment (2,507) ($3,000)
Lease payment (6,182) ($282)
($6,000 base)
Insurance (prepaid) (4,049) ($100)
Total PV ($13,238)

Periods: PV at 9% 0 Mo 1 to 48
Jane's credit union:
Downpayment ($900) ($900)
Monthly payments (8,100) ($202)
Insurance (prepaid) (4,049) ($100)
Total PV ($13,049)

The least costly alternative is Jane's credit union. However, Mike's Autos lease has a 12
percent interest rate built in. Many current leases have promotional rates well below most
lending rates (2.5 percent and 1.4 percent in advertisements in 1995). Clearly, Joe's is the
most expensive alternative with insurance being a significantly higher cost.

12-12.
Incremental depreciation:

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 Investment Life of the Project
Year: 0 1 2 3 4 5 6
New MACRS depreciation:
Year 1 – 20.0% $36,000
Year 2 – 32.0% $57,600
Year 3 – 19.2% $34,560
Year 4 – 11.5% $20,700
Year 5 – 11.5% $20,700
Year 6 – 5.8%
$10,440
Old depreciation (S-L) (5,000) (5,000) (5,000) (5,000) (5,000)
(5,000)
Incremental depreciation $31,000 $52,600 $29,560 $15,700 $15,700
5,440

NPV: Investment Life of the Project

Year: 0 1 2 3 4 5 6
Purchase cost ($180,000)
Sell old 50,000
Tax on gain (8,000)
Net investment ($138,000)
Saved operating cost $50,000 $ 50,000 $50,000 $50,000 $50,000 $50,000
Minus new operating cost (8,000) (8,000) (8,000) (8,000) (8,000) (8,000)
Total cash savings. $42,000 $ 42,000 $42,000 $42,000 $42,000 $42,000
Minus incremental depre (31,000) (52,600) (29,560) (15,700) (15,700) (5,440)
Taxable income $11,000 ($10,600) $12,440 $26,300 $26,300 $36,560
Minus taxes (40%) (4,400) 4,240 (4,976) (10,520) (10,520) (14,624)
Income after tax $ 6,600 ($6,360) $ 7,464 $15,780 $15,780 $21,936
Plus incremental depre 31,000 52,600 29,560 15,700 15,700 5,440
Net cash flow ($138,000) $37,600 $ 46,240 $37,024 $31,480 $31,480 $27,376
PV factors (16%) x 1.000 x 0.862 x 0.743 x 0.641 x 0.552 x 0.476 x 0.410
PVs ($138,000) $32,411 $ 34,356 $23,732 $17,377 $14,984 $11,224
Total PV of inflows 134,084
NPV ($3,916)

Since the NPV of replacing the existing machine is negative, the existing machine should not
be replaced.

12-13. Since the lease payments are monthly, the yearly interest rate of 12 percent must be
converted to a monthly rate by dividing by 12 (12%  12 months = 1%).

Cash purchase price €45,000

PV of lease payments €2,000 x 21.243) 42,486
Net lease advantage €2,514

If the lease is a merely a financing alternative provided by the equipment seller, the lease
advantage comes from a lower interest rate imbedded in the lease payments. Since taxes are
ignored, the deductibility of the lease payment, depreciation, and interest can be ignored.

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-12
12-14.
NPV: Investment Life of the Project
Year: 0 1 2 3 4 5 6
Purchase cost ($60,000)
Revenues:
(Inflation rate, 5%) $50,000 $52,500 $55,125 $57,881 $60,775 $63,814
Cash costs:
(Inflation rate, 5%) (25,000) (26,250) (27,563) (28,941) (30,388) (31,907)
Rental payments (10,000) (10,000) (10,000) (10,000) (10,000) (10,000)
Minus depreciation
($60,000  6) (10,000) (10,000) (10,000) (10,000) (10,000) (10,000)
Taxable income $ 5,000 $ 6,250 $ 7,562 $ 8,940 $10,387 $11,907
Minus taxes (40%) (2,000) (2,500) (3,025) (3,576) (4,155) (4,763)
Income after tax $ 3,000 $ 3,750 $ 4,537 $ 5,364 $ 6,232 $ 7,144
Plus depreciation 10,000 10,000 10,000 10,000 10,000 10,000
Net cash flow ($60,000) $13,000 $13,750 $14,537 $15,364 $16,232 $17,144
PV factors (14%) x 1.000 x 0.877 x 0.769 x 0.675 x 0.592 x 0.519 x
0.456
PV ($60,000) $11,401 $10,574 $ 9,813 $ 9,096 $ 8,424
$ 7,818
Total PV 57,126
NPV ($2,874)

Since the NPV of the project is negative, it should not be adopted.

12-15. Each of these projects has benefit to Jensen Groceries. But the problem is defining the greatest
benefit to both the community and to Jensen. One could view most or all of these activities as
normal responsibilities of a local business to its community. But even from this perspective, Jensen
should evaluate the benefits received by the community. One way to evaluate these projects is to
identify the quantifiable costs and benefits, make estimates of certain intangible benefits, and at
least note other issues.

Out-of- Community Jensen's

Pocket Tangible Intangible Intangible
Costs Benefits Benefits Benefits Other issues
10K Run for Food $5,000 $10,000 Feed hungry Sales estimate Legal liability
United Way 15,000 Benefit poor $ estimate Citizenship
Gourmet Cooking 6,000 Unknown Sales estimate Reputation
Helpers 8,000 Benefit poor Employee morale Reputation

Assuming community activities expenses must be limited, someone must judge the worthiness of
these activities. Measuring intangibles must be done, even if the estimates are rough. Certain
biases may influence the decision – Jon may be a runner, or Jon's brother may be an attorney and
warn him about other race sponsors that have had personal injury lawsuits brought against them.

12-16.
(1) Operating decision: The alternative with the lowest PV of operating costs is the better investment.

Alternative A:
Investment Life of the Project
Year: 0 1 2 3 4 5 6
Operating costs (B$125,000) (B$100,000) (B$80,000) (B$80,000) (B$60,000) (B$40,000)
PV factors x 0.877 x 0.769 x 0.675 x 0.592 x 0.519 x 0.456

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-13
 PV at 14% (B$109,625) (B$76,900) (B$54,000) (B$47,360) (B$31,140) (B$18,240)
PV (B$337,265)

Alternative B:
Investment Life of the Project
Year: 0 1 2 3 4 5 6
Operating costs (B$80,000) (B$80,000) (B$120,000) (B$100,000) (B$100,000) (B$100,000)
PV factors x 0.877 x 0.769 x 0.675 x 0.592 x 0.519 x 0.456
PV at 14% (B$70,160) (B$61,520) (B$81,000) (B$59,200) (B$51,900) (B$45,600)
PV (B$369,380)

Alternative A is the better operating choice because the PV of the operating costs is B$32,115
(B$369,380 – B$337,265) less than Alternative B.

(2) Financing decision:

Alternatives A and B: The purchase price and lease payments are identical for both
alternatives.

Cash purchase price B$200,000

PV of lease payments (B$50,000 x 3.889) 194,450
Net lease advantage B$5,550

(3) The best decision is to lease Alternative A since it has the lower operating costs (Part 1) and
because leasing is better than purchasing for cash (Part 2).

12-17.
(1) Embedded interest rates:

PV factor = (Cash price - Initial cash payment)  Annual cash payment

Vehicle A: = ($54,400 – $16,000)  $16,000

= $38,400  $16,000 = 2.400 (corresponds to 12 percent)

Vehicle B: = ($74,900 – $15,000)  $15,000

= $59,900  $15,000 = 3.993 (corresponds to 8 percent)

(2) Lease or purchase:

Vehicle A: Cash purchase price $ 54,400

PV of lease payments:
Years 1 to 3 ($16,000 x 2.487) ($39,792)
Lease payment due today (16,000)
Total lease payments ($55,792)
Net purchase advantage $1,392
Vehicle B: Cash purchase price $ 74,900
PV of lease payments:
Years 1 to 5 ($15,000 x 3.791) ($56,865)
Lease payment due today (15,000)
Total lease payments ($71,865)
Net lease advantage $3,035

If we want the use of both vehicles, we should purchase Vehicle A and lease Vehicle B.
12-18. To calculate the NPV of each investment, first determine the weighted-average annual
revenue:

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-14
 $130,000 Investment:

Probability x Annual Revenue = Weighted Revenue

10% $10,000 $ 1,000
10% 20,000 2,000
15% 30,000 4,500
20% 40,000 8,000
25% 50,000 12,500
10% 60,000 6,000
10% 90,000 9,000
Weighted-average annual revenue $43,000

Investment Life of the Project

Year: 0 1 2 3 4 5
Cash flows ($130,000) $ 43,000 $ 43,000 $ 43,000 $ 43,000 $ 43,000
PV 147,619
(14%, 5 years): $43,000 x 3.433
NPV $ 17,619

$160,000 Investment:

Probability x Annual Revenue = Weighted Revenue

10% $ 20,000 $ 2,000
20% 40,000 8,000
40% 60,000 24,000
20% 80,000 16,000
10% 100,000 10,000
Weighted-average annual revenue $60,000

Investment Life of the Project

Year: 0 1 2 3 4 5
Cash flows ($160,000) $60,000 $60,000 $60,000 $60,000 $60,000
PV 205,980
(14%, 5 years): $60,000 x 3.433
NPV $ 45,980

The $160,000 investment is the more desirable alternative by $28,361 ($45,980 – $17,619).

12-19. To analyze the impacts of the mistakes in estimation, first solve for the initial NPV:

Investment Life of the Project

Year: 0 1-5 6 7 8 9 10
Investment in machinery ($800,000)
Additional inventory (100,000)
Annual revenue $200,000 $200,000 $200,000 $200,000 $200,000
$200,000
Equipment overhaul (120,000)
Released inventory
100,000
Machinery salvage
80,000
Total cash flows ($900,000) $200,000 $80,000 $200,000 $200,000 $200,000

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-15
 $380,000
PV factors (14%) x 1.000 x 3.433 x 0.456 x 0.400 x 0.351 x 0.308 x 0.270
PVs ($900,000) $686,600 $ 36,480 $ 80,000 $70,200 $ 61,600
$102,600
PV – Years 1 to 10 $1,037,480
NPV $137,480

(a) Original NPV $137,480

PV of machinery understatement (20,000) ($20,000 x 1.000)
New NPV $117,480 decrease of 14.55%

(b) Original NPV $137,480

PV of inventory needed (20,000) ($20,000 x 1.000)
PV of inventory recovery (Yr 10) 5,400 ($20,000 x 0.270)
New NPV $122,880 decrease of 10.62%

(c) Original NPV $137,480

PV of overhaul understatement (13,680) ($30,000 x 0.456)
New NPV $123,800 decrease of 9.95%

(d) Original NPV $137,480

PV of salvage overstatement (13,500) ($50,000 x 0.270)
New NPV $123,980 decrease of 9.82%

(e) Original NPV $137,480

Revenue overstatement (20,864) ($4,000 x 5.216)
New NPV $116,616 decrease of 15.18%

12-20.
(1) Straight-line depreciation:
Investment Cash Flows
Year: 0 Years 1 to 10
Equipment cost ($120,000)
Incremental cash inflow $32,000
Incremental cash outflow (6,000)
Net incremental cash flow $26,000
Minus depreciation (12,000) ($120,000  10 ys)
Taxable income $14,000
Minus taxes (40%) (5,600)
Income after tax $ 8,400
Plus depreciation 12,000
Net cash inflow $20,400
PV factor (12%) x 5.650
PV of cash inflow $115,260
NPV ($4,740)

(2) MACRS depreciation:

Investment Life of the Project

Year: 0 1 2 3 4 5 6 7-10
Purchase cost ($120,000)
Annual cash flow $26,000 $26,000 $26,000 $26,000 $26,000 $26,000 $26,000
Minus MACRS depre:

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-16
 Year 1 – 20.0% (24,000)
Year 2 – 32.0% (38,400)
Year 3 – 19.2% (23,040)
Year 4 – 11.5% (13,800)
Year 5 – 11.5% ( 13,800)
Year 6 – 5.8% ( 6,960)
Year 7-10 – 0.0% 0
Taxable income $2,000 ($12,400) $2,960 $12,200 $12,200 $19,040 $26,000
Minus taxes (40%) 800 (4,960) 1,184 4,880 4,880 7,616 10,400
Income after tax $1,200 ($7,440) $1,776 $7,320 $7,320 $11,424 $15,600
Plus depreciation 24,000 38,400 23,040 13,800 13,800 6,960 0
Net cash flow ($120,000) $25,200 $30,960 $24,816 $21,120 $21,120 $18,384 $15,600
PV factors (12%) x 1.000 x 0.893 x 0.797 x 0.712 x 0.636 x 0.567 x 0.507 x 1.5391
PVs ($120,000) $22,504 $ 24,675 $17,669 $13,432 $11,975 $ 9,321 $24,008
PV – Yrs 1 to 10 123,584
NPV $ 3,584
1
0.452 + 0.404 + 0.361 + 0.322

By accelerating the depreciation through MACRS, the NPV becomes positive. Whereas, when
using straight-line depreciation in Part 1, the NPV is negative. This shows how accelerating
depreciation can make an otherwise unattractive project acceptable. This was part of the
government's intent when the MACRS legislation was passed.

Solutions to Problems

12-21.
(1) To find the IRR, first calculate the annual cash flow for each machine:

Machine X Machine Y
Revenue ($10 per unit) $2,000,000 $2,000,000
Variable costs ($4 and $2 per unit) (800,000) (400,000)
Contribution margin $1,200,000 $1,600,000
Minus fixed costs (725,000) (850,000)
Operating income $475,000 $750,000
Minus depreciation (200,000)1 (350,000)2
Taxable income $275,000 $400,000
Minus taxes (40%) (110,000) (160,000)
Income after tax $165,000 $240,000
Plus depreciation 200,000 350,000
Annual net cash flow $365,000 $590,000
1
$800,000  4 years
2
$1,400,000  4 years

PV factor (IRR) = Investment  Annual net cash inflow

Machine X = $800,000  $365,000

= 2.192 (corresponds to an IRR between 25 and 30 percent, 29.30
percent on a business calculator)
Machine Y = $1,400,000  $590,000
= 2.373 (corresponds to an IRR between 24 and 25 percent, 24.73

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-17
 percent on a business calculator)

(2) Incremental IRR:

Saved variable costs ($4 – $2 per unit) $400,000

Minus additional fixed costs ($850,000 – $725,000) (125,000)
Operating income $275,000
Minus incremental depreciation ($350,000 – $200,000) (150,000)
Taxable income $125,000
Minus taxes (40%) (50,000)
Income after tax $ 75,000
Plus depreciation 150,000
Incremental annual net cash flow $225,000

Incremental IRR = Incremental investment  Incremental cash flow

= ($1,400,000 – $800,000)  $225,000
= 2.667 (corresponds to an IRR between 18 and 20 percent, 18.48
percent on a business calculator)

12-22.
(1) Payback period:
X Y Z
Investment $34,000 $25,000 $75,000
Divided by annual cash savings  8,111  7,458 14,011
Payback period, in years 4.192 3.352 5.353
Ranking 2nd 1st 3rd

IRR: The payback period is the PV factor for the IRR. Locating the factors on the
corresponding row on Table 2 gives the following approximate rates:

X Y Z
IRR 20% 15% 18%
Ranking 1st 3rd 2nd

NPV:
X Y Z
Annual cash savings $ 8,111 $ 7,458 $ 14,011
PV factor at 12% x 5.650 x 3.605 x 7.469
PV of cash savings $45,827 $26,886 $104,648
Minus investment (34,000) (25,000) (75,000)
NPV $11,827 $1,886 $29,648
Ranking 2nd 3rd 1st

Note: The preceding NPVs are based on the useful life of each individual investment. To
compare the investments to each other accurately, they must be evaluated over equal
lives. This would require using a life of 20 years or determining salvage values at some
shorter life. If 20 years is used, the company would have to invest in X twice and in Y
four times. When this is done, the NPVs of each increase, but the rankings remain
unchanged.
Profitability index: X Y Z
PV of cash savings $ 45,827 $ 26,886 $104,648
Divided by investment  34,000  25,000  75,000
Profitability index 1.35 1.08 1.40

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-18
 Ranking 2nd 3rd 1st

(2) The useful life of each of these investments is drastically different. The investment with the
longest life, Z, is preferred in NPV and the profitability index. Using the payback period, Y is
the best (to the most risk adverse investor). The highest IRR investment is X, reducing the
value of the most distant cash flows in Z.

Z also has the largest investment cost and the largest annual cash savings. Often, larger
investments will look more attractive than smaller investments. Care must be taken when
evaluating the IRR of investments. The IRR assumes we can reinvest at this high rate.

12-23. Evaluation of accepting the offer for the piece of equipment:

Cash flow today:

Purchase offer $130,000
Tax on cash received from offer (52,000) ($130,000 x 40%)
Net cash received $ 78,000

Cash flow - Years 1 to 5:

Costs to purchase part ($15) ($150,000)
Saved variable costs of production ($10) 100,000
Rental income 12,000
Additional cost of purchasing ($38,000)
Taxes saved from additional cost 15,200
Net cash costs from purchasing ($22,800)

NPV: Investment Life of the Project

Year: 0 1 2 3 4 5
Cash flows $78,000 ($22,800) ($22,800) ($22,800) ($22,800)
($22,800)
PV - Years 1 to 5 (82,194)
(12%, 5 years): ($22,800) x 3.605
NPV ($4,194)

Since the NPV of accepting the offer is negative, the offer should be refused; and the parts
should continue to be manufactured.

12-24.
(1) To solve for the approximate ROR, first determine the net investment and the annual cash
flows:

Net investment:
Purchase cost of new machine ($60,000)
Sell old machine 14,000
Net investment ($46,000)

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-19
 Annual cash flows:
Saved operating costs, old machine $25,000
New operating costs, new machine (10,000)
Annual cash flow $15,000

PV factor (approximate ROR) = Investment  Annual cash flow

= $46,000  $15,000 = 3.067

This PV factor corresponds to an IRR of between 18 and 20 percent.

(2) The PV factor for a 12 percent ROR is 3.605. Dividing this into the net investment gives the
annual cash flow necessary to achieve a 12 percent return. Then subtract $25,000, the
operating costs of the old machine, to get the operating costs of the new machine:

Annual cash flow for 12% return = $46,000  3.605 = $12,760

(needed savings to justify investment)
Operating costs of new machine = $25,000 – $12,760 = $12,240

Allowable percentage savings change = ($15,000 – $12,240)  $15,000 = 14.93%

(needed savings relative to promised savings)

(3) Currently, the new machine is earning between 18 and 20 percent, from Part (1), with a PV
factor of 3.067. To solve for the life of the project necessary for a 12 percent return, find the
factor 3.067 in the 12 percent column of Table 2 and go across to find the time required. The
factor is found between the 3- and 4-period rows. This means the machine must produce for
at least 3 to 4 years to earn a 12 percent ROI.

12-25.
Investment Life of the Project
Year: 0 1 2 3 4 5 6 7 8
Purchase cost ($300,000)
Increased working capital (100,000)
Total investment ($400,000)
Saved operating costs $100,000 $100,000 $100,000 $100,000 $100,000 $100,000 $100,000 $100,000
Minus MACRS depreciation:
Year 1 – 14.3% (42,900)
Year 2 – 24.5% (73,500)
Year 3 – 17.5% (52,500)
Year 4 – 12.5% (37,500)
Year 5 – 8.9% (26,700)
Year 6 – 8.9% (26,700)
Year 7 – 8.9% (26,700)
Year 8 – 4.5% (13,500)
Taxable income $57,100 $26,500 $47,500 $62,500 $73,300 $73,300 $73,300 $86,500
Minus taxes (40%) (22,840) (10,600) (19,000) (25,000) (29,320) (29,320) (29,320) (34,600)
Income after tax $34,260 $15,900 $28,500 $37,500 $43,980 $43,980 $43,980 $51,900
Plus depreciation 42,900 73,500 52,500 37,500 26,700 26,700 26,700 13,500
Net operating cash flow $77,160 $89,400 $81,000 $75,000 $70,680 $70,680 $70,680 $65,400
Released working capital 100,000
Net cash flow ($400,000) $77,160 $89,400 $81,000 $75,000 $70,680 $70,680 $70,680 $165,400
PV factors (14%) x 1.000 x 0.877 x 0.769 x 0.675 x 0.592 x 0.519 x 0.456 x 0.400 x 0.351
PVs ($400,000) $67,669 $68,749 $54,675 $44,400 $36,683 $32,230 $28,272 $58,055
Total PV of inflows 390,733
NPV ($9,267)

Since the project has a negative NPV, it fails to meet the rate-of-return objective of 14 percent.
12-26.
(1) a. Change in operating cash flow:

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-20
 Lost cafeteria revenue ($240,000)
Saved cafeteria expenses 265,000
Vending machine percentage
receipts ($180,000 x 10%) 18,000
Increased operating income $43,000
Minus incremental depreciation
[($120,000  6) – $10,000] (10,000)
Taxable income $33,000
Minus taxes (40%) (13,200)
Income after tax $19,800
Plus depreciation 10,000
Incremental operating cash flow $29,800

Note: The cash flow in Year 6 will be $41,800 due to the $12,000 of aftertax salvage value
($20,000 x 60%) received in that year on the vending machines.

(1) b. Net investment:

Purchase vending machines ($120,000)
Dispose of cafeteria equipment 10,000
Saved taxes on loss:
Disposal value $10,000
Book value (60,000)
Net loss ($50,000)
Tax rate x 0.40 20,000
Net investment ($90,000)

Payback period = $90,000  $29,800 = 3.02 years

(1) c. Approximate IRR:

The payback period is the PV factor for the IRR. The factor 3.020 corresponds to 24
percent on the 6 period row.

(2) Based on operating cash flows, purchasing the vending machines appears to be a good idea.
The annual cash flows are $29,800 greater than if the cafeteria equipment is kept. The quick
payback period of three years is also a good reason to consider the purchase. Finally, the
ROR appears quite strong at 24 percent.

Guarantee must consider many qualitative factors before purchasing the vending machines.
For example, how will its employees react to the change. It is possible that the vending
machine prices will be more expensive than the cafeteria prices and that the employees will
resent having to spend more for lunches. Also, the quality of the food from the vending
machines may not be as high as the cafeteria food. The change could lower employee morale
and productivity. The managers should talk to employees to get their reactions to the
proposed change before purchasing the vending machines. However, it would be very difficult
to put a dollar amount on the reactions of employees to the change.

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-21
12-27. Net investment:

Purchase cost of new truck ($80,000)

Sell old truck 40,000
Tax savings from loss:
Market value $40,000
Book value 55,000
Net loss ($15,000)
Tax rate x 0.40 6,000
Inventory investment 15,000
Net investment ($19,000)

NPV: Investment Life of the Project

Year: 0 1 2 3 4 5
Net investment ($19,000)
Old operating costs $18,000 $18,000 $18,000 $ 18,000
18,000
Minus new operating costs (3,000) (3,000) (3,000) (3,000)
(3,000)
Operating savings $15,000 $15,000 $15,000 $ 15,000
15,000
Minus increased depre1 (5,000) (5,000) (5,000) (5,000)
(5,000)
Taxable income $10,000 $10,000 $10,000 $10,000
10,000
Minus taxes (40%) (4,000) (4,000) (4,000)
(4,000) (4,000)
Income after tax $6,000 $6,000 $6,000 $6,000 $6,000
Plus salvage 5,000
Plus depreciation 5,000 5,000 5,000 5,000 5,000
Net cash flow ($19,000) $11,000 $11,000 $11,000 $11,000
$16,000
PV – Years 1 to 4 $ 32,054
(14%, 4 years): $11,000 x 2.914
x 0.519
PV – Year 5 8,304
Total PV $ 40,358
NPV $ 21,358
1
Incremental depreciation is $16,000 - $11,000.

Since the NPV of purchasing the new truck is positive, the old truck should be replaced.

12-28.
(1) The expenditures in 2006 and 2007 are sunk costs. They cannot be recovered. They are not
relevant to the decision to go ahead with the project or stop now. They will be shown as part of
the life-cycle cost for the entire project to complete the total project picture.

(2) Life-cycle costing:

Life of the Project
2006 2007 2008 2009 2010 2011 2012 2013
Research lab costs ($100,000) ($300,000)
Developmental costs ($500,000) ($300,000)
Production eng exp (200,000) (400,000)

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-22
Equipment costs (2,000,000)
Sales 800,000 $3,000,000 $5,000,000 $4,000,000
$3,000,000
Production costs (480,000) (1,650,000) (2,500,000) (1,600,000) (1,200,000)
Advertising exp (300,000) (300,000) (200,000) (200,000) (200,000)
International fees 40,000 150,000 250,000 200,000
Taxes (40%) 40,000 120,000 280,000 432,000 (276,000) (820,000) (820,000) (560,000)
Past cash flows ($60,000) ($180,000)
Future cash flows ($2,420,000) ($248,000) $ 814,000 $1,630,000 $1,630,000 $1,240,000

Cumulative cash ($60,000) ($240,000) ($2,660,000) ($2,908,000) ($2,094,000) ($464,000) $1,166,000 $2,406,000

Taxes:
Cash taxable inc ($100,000) ($300,000) ($700,000) ($680,000) $1,090,000 $2,450,000 $2,450,000 $1,800,000
Minus depreciation (400,000) (400,000) (400,000) (400,000) (400,000)
Taxable income ($100,000) ($300,000) ($700,000) ($1,080,000) $690,000 $2,050,000 $2,050,000 $1,400,000
Taxes (40%) $40,000 $120,000 $280,000 $432,000 ($276,000) ($820,000) ($820,000) ($560,000)

(3) NPV:
Future cash flows. ($2,420,000) ($248,000) $814,000 $1,630,000 $1,630,000 $1,240,000
PV factors (15%) x 0.870 x 0.756 x 0.658 x 0.572 x 0.497 x 0.432
PV - Years 2005 to 2010 ($2,105,400) ($187,488) $535,612 $932,360 $810,110 $535,680
NPV $520,874

The project well exceeds the 15 percent hurdle rate. This analysis ignores the past two years
of sunk costs.

(4) A higher discount rate will lessen the value of the positive cash flows in the last three years of
the project. The PV of the negative cash flows early in the project's life would overwhelm the
PV of the later cash inflows at a higher ROR.

12-29. If the marketing and production staff work together in estimating the potential demand
probabilities, the company must analyze the decision as if only one machine is purchased,
then as if two machines are purchased, and so on until a total of five machines are purchased
at one time. However, if the marketing staff only provides the production staff with estimated
demand, the decision analysis changes. Start with the first alternative, analyzing each number
of machines separately.

First, calculate the expected value of the sales units for each number of machines:

Five machines are purchased:

Units
Probability x Units of Sales = Expected Value
10% 40,000 4,000
20% 80,000 16,000
30% 120,000 36,000
20% 160,000 32,000
10% 200,000 20,000
10% 240,000 24,000
Expected value of sales units 132,000

Four machine are purchased:

Units
Probability x Units of Sales = Expected Value
10% 40,000 4,000
20% 80,000 16,000
30% 120,000 36,000
20% 160,000 32,000

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-23
 10% 200,000 20,000
10% 200,000 20,000
Expected value of sales units 128,000

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-24
Three machine are purchased:
Units
Probability x Units of Sales = Expected Value
10% 40,000 4,000
20% 80,000 16,000
30% 120,000 36,000
20% 160,000 32,000
10% 160,000 16,000
10% 160,000 16,000
Expected value of sales units 120,000

Two machine are purchased:

Units
Probability x Units of Sales = Expected Value
10% 40,000 4,000
20% 80,000 16,000
30% 120,000 36,000
20% 120,000 24,000
10% 120,000 12,000
10% 120,000 12,000
Expected value of sales units 104,000

One machine is purchased:

Units
Probability x Units of Sales = Expected Value
10% 40,000 4,000
20% 60,000 12,000
30% 60,000 18,000
20% 60,000 12,000
10% 60,000 6,000
10% 60,000 6,000
Expected value of sales units 58,000

Annual cash flows: Number of Machines Purchased

1 2 3 4 5
Sales in units 58,000 104,000 120,000 128,000 132,000
Sales ($10) $580,000 $1,040,000 $1,200,000 $1,280,000 $1,320,000
Variable cost ($6) (348,000) (624,000) (720,000) (768,000) (792,000)
Contribution margin $232,000 $416,000 $480,000 $512,000 $528,000
Minus: Fixed cost (140,000) (140,000) (140,000) (140,000) (140,000)
Depreciation 1 (50,000) (100,000) (150,000) (200,000) (250,000)
Taxable income $42,000 $176,000 $190,000 $172,000 $138,000
Minus taxes (40%) (16,800) (70,400) (76,000) (68,800) (55,200)
Income after tax $25,200 $105,600 $114,000 $103,200 $82,800
Plus depreciation 50,000 100,000 150,000 200,000 250,000
Annual cash flow $75,200 $205,600 $264,000 $303,200 $332,800
PV factors (16%) x 3.685 x 3.685 x 3.685 x 3.685 x 3.685
PVs $277,112 $757,636 $972,840 $1,117,292 $1,226,368
Minus investment 2 (300,000) (600,000) (900,000) (1,200,000) (1,500,000)
NPV ($22,888) $157,636 $72,840 ($82,708) ($273,632)
1
Depreciation = (Purchase cost per machine x Number of machines purchased)  6 years
2
Investment = Purchase cost per machine x Number of machines purchased
Therefore, if the marketing and production staffs work together in preparing the estimates of
demand, the company should purchase two machines since that decision provides the highest

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-25
 NPV.

However, if the marketing department only gives the production department its estimates of
demand, then the production department would assume it needs the ability to produce 132,000
units:

Units
Probability x Units of Sales = Expected Value
10% 40,000 4,000
20% 80,000 16,000
30% 120,000 36,000
20% 160,000 32,000
10% 200,000 20,000
10% 240,000 24,000
Expected value of sales units 132,000

The Production Department would then have to purchase three machines based on this
estimate. Three machines would give it the ability to produce 160,000 units. This is 28,000
more units than necessary to meet expected sales. Now the company must determine if the
three machines meet the 16 percent ROR objective:

Annual cash flow:

Sales (132,000 units x $10) $1,320,000

Variable costs (132,000 units x $6) (792,000)
Contribution margin $528,000
Minus: Fixed costs (140,000)
Depreciation ($900,000  6 years) (150,000)
Taxable income $238,000
Minus taxes (40%) (95,200)
Income after tax $142,800
Plus depreciation 150,000
Annual cash flow $292,800
PV factors (16%) x 3.685
PV $1,078,968
Minus investment (3 x $300,000) 900,000
NPV $178,968

Since the NPV of purchasing three machines is positive, the company should purchase three
machines.

It should be noted that the first approach indicates purchasing two machines, while the second
approach indicates purchasing three machines. The difference is a result of the way in which
the expected values were handled in each approach.

NOTE: Students with a background in statistics may ask about using confidence intervals
built around one or two standard deviations from the expected value to determine
the number of machines necessary. This is an excellent way to approach to
problem but is too advanced for most undergraduate students at this level.

12-30.
(1) Acquire new tractor:

Investment Life of the Project

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-26
 Year: 0 1 2 3 4 5 6
Purchase cost ($80,000)
Gain from sale 5,000
Tax on gain (40%) (2,000)
Net investment ($77,000)
Costs savings $25,000 $25,000 $25,000 $25,000 $25,000 $25,000
Salvage in Year 6 10,000
Minus MACRS depre:
Year 1 – 20.0% (16,000)
Year 2 – 32.0% (25,600)
Year 3 – 19.2% (15,360)
Year 4 – 11.5% (9,200)
Year 5 – 11.5% (9,200)
Year 6 – 5.8% (4,640)
Taxable income $ 9,000 ($600) $ 9,640 $15,800 $15,800 $30,360
Minus taxes (40%) (3,600) 240 (3,856) (6,320) (6,320) (12,144)
Income after tax $ 5,400 ($360) $ 5,784 $ 9,480 $ 9,480 $18,216
Plus depreciation 16,000 25,600 15,360 9,200 9,200 4,640
Net cash flow ($77,000) $21,400 $25,240 $21,144 $18,680 $18,680 $22,856
PV factors (14%) x 1.000 x 0.877 x 0.769 x 0.675 x 0.592 x 0.519 x 0.456
PVs ($77,000) $18,768 $19,410 $14,272 $11,059 $ 9,695 $10,422
PV –Years 1 to 6 $83,626
NPV $6,626

Helsel Brothers should purchase the new tractor because the investment meets the 14% cutoff rate.

(2) In computing the NPV of the purchase versus lease decision, remember that the first lease
payment is due now rather than at the end of the first year. Also, the annual savings are
irrelevant since they are the same whether the tractor is purchased or leased. The purchase
results in a net cash inflow (from the depreciation tax shield), while the lease results in a net
cash outflow (from the aftertax lease payments). Therefore, the NPV computation is based on
the savings of the purchase over the lease.

Investment and depreciation tax shield cash flows:

Purchase Lease Savings

Tax Investment Payments Purchase
Annual Shield & Salvage Cash After Tax Over
Year Depreciation at 40% Value Inflow (Outflow) Lease
0 $ 0 $ 0 ($77,000) $ 0 ($14,400)1 ($62,600)
1 16,000 6,400 0 6,400 (14,400) 20,800
2 25,600 10,240 0 10,240 (14,400) 24,640
3 15,360 6,144 0 6,144 (14,400) 20,544
4 9,200 3,680 0 3,680 (14,400) 18,080
5 9,200 3,680 0 3,680 (14,400) 18,080
6 4,640 1,856 6,000 2 7,856 0 7,856
1
$24,000 x 0.60
2
$10,000 x 0.60 (Salvage value is a gain, which is taxed at 40%.)
NPV of purchase savings:

Investment Life of the Project

Year: 0 1 2 3 4 5 6
Net investment (Part 1) ($77,000)
1st net lease pay't 14,400

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-27
Total investment ($62,600)
Purchase savings $20,800 $24,640 $20,544 $18,080 $18,080 $ 7,856
PV factors (14%) x 1.000 x 0.877 x 0.769 x 0.675 x 0.592 x 0.519 x 0.456
PVs ($62,600) $18,242 $18,948 $13,867 $10,703 $ 9,384 $ 3,582
PV - Years 1 to 6 $74,726
NPV $12,126

It would be to Helsel Brothers’ advantage to purchase the tractor since the NPV of the
purchase
minus the lease cash flows is $12,126.

12-31.
(1) The financing decision should be made after the investment decision is made. The three
alternatives are evaluated as follows:

Internal funds:
Investment Life of the Project
Year: 0 1 2 3 4 5
Equipment cost ($1,000,000)
Depreciation $200,000 $200,000 $200,000 $200,000 $200,000
Tax savings (40%) 80,000 80,000 80,000 80,000 80,000
PV – Years 1 to 5 336,960
NPV ($663,040) (6%1, 5 years): $80,000 x 4.212

Bank loan:
Investment Life of the Project
Year: 0 1 2 3 4 5
Down payment ($100,000)
Loan payment ($237,418) ($237,418) ($237,418) ($237,418) ($237,418)
Interest component $ 90,000 $ 75,258 $ 59,042 $ 41,205 $ 21,583
Interest tax savings 36,000 30,103 23,617 16,482 8,633
Depreciation tax savings 80,000 80,000 80,000 80,000 80,000
Net cash flow ($121,418) ($127,315) ($133,801) ($140,936) ($148,785)
PV factors (6%)1 x 0.943 x 0.890 x 0.840 x 0.792 x 0.747
PV – Years 1 to 5 (562,964)
NPV ($662,964)

Lease:
Investment Life of the Project
Year: 0 1 2 3 4 5
Initial payment ($50,000)
Annual payments ($220,000) ($220,000) ($220,000) ($220,000) ($220,000)
Tax savings (40%) 20,000 88,000 88,000 88,000 88,000 88,000
Aftertax cash flow ($30,000) ($132,000) ($132,000) ($132,000) ($132,000) ($132,000)
PV – Years 1 to 5 (555,984)
NPV ($585,984) (6%1, 5 years): $132,000 x 4.212
1
Aftertax interest cost of borrowed funds (Borrowing cost - Tax benefit)
(a) The appropriate interest rate is the aftertax normal borrowing rate, 10 percent minus 4 percent
or a 6 percent discount rate. The cost of capital is probable not preferred because it
represents a longer term discount rate. The alternatives available would normally be
considered short-term borrowing.
(b) The least cost alternative is leasing. This is apparently due to a lower imbedded interest rate
in the lease contract.

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-28
(2) Qualitative factors to be considered:

(a) Do better alternatives exist for using the cash on hand that will yield more than the costs of the
bank loan? The answer is probably yes.
(b) Will this bank borrowing use the firm's borrowing capacity that might be needed for other
purposes?
(c) Would leasing provide greater opportunities for upgrading if technology changes quickly?
(d) Why is the lease's imbedded interest rate so low? Could we negotiate for a better cash
purchase price?
(e) If we own the machine, do we have greater control over its use?

12-32.
(1) To calculate the PVs, use the 15 percent hurdle rate, which includes the inflation factor:

Investment Life of the Project

Year: 0 1 2 3 4 5
Purchase equipment ($200,000)
Sales ($100) $200,000 $200,000 $200,000 $200,000 $200,000
Variable costs ($40) (80,000) 80,000 (80,000) (80,000) (80,000)
Contribution margin $120,000 $120,000 $120,000 $120,000 $120,000
Minus: Fixed costs (50,000) (50,000) (50,000) (50,000) (50,000)
Depreciation (40,000) (40,000) (40,000) (40,000) (40,000)
Taxable income $30,000 $30,000 $30,000 $30,000 $30,000
Minus taxes (40%) (12,000) (12,000) (12,000) (12,000) (12,000)
Income after tax $18,000 $18,000 $18,000 $18,000 $18,000
Plus depreciation 40,000 40,000 40,000 40,000 40,000
Net cash flow ($200,000) $58,000 $58,000 $58,000 $58,000 $58,000
PV of inflows 194,416
(15%, 5 years): $58,000 x 3.352
NPV ($5,584)

(2) To calculate the PVs, adjust cost and revenue elements for inflation (4 percent increase for sale;
8 percent increase for variable costs) and use 22 percent as the discount rate [(1 + 0.15) x (1 +
0.06)] – 1:

Investment Life of the Project

Year: 0 1 2 3 4 5
Purchase equipment ($200,000)
Selling price per unit1 $100.00 $104.00 $108.16 $112.49 $116.99
Variable cost per unit1 40.00 43.20 46.66 50.39 54.42
Contrib margin per unit $ 60.00 $ 60.80 $ 61.50 $ 62.10 $ 62.57
Times number of units 2,000 2,000 2,000 2,000 2,000
Contrib margin dollars. $120,000 $121,600 $123,000 $124,200 $125,140
Minus: Fixed costs 50,000 52,000 54,000 56,000 58,000
Depreciation 40,000 40,000 40,000 40,000 40,000
Taxable income $ 30,000 $ 29,600 $ 29,000 $ 28,200 $ 27,140
Minus taxes (40%). 12,000 11,840 11,600 11,280 10,856
Income after tax. $ 18,000 $ 17,760 $ 17,400 $ 16,920 $ 16,284
Plus depreciation 40,000 40,000 40,000 40,000 40,000
Net cash flow ($200,000) $ 58,000 $ 57,760 $ 57,400 $ 56,920 $ 56,284
PV factors (15%) x 1.000 x 0.820 x 0.672 x 0.551 x 0.451 x 0.370
PVs ($200,000) $ 47,560 $ 38,815 $ 31,627 $ 25,671 $ 20,825
PV – Years 1 to 5 $164,498

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-29
 NPV ($35,502)
1
Amounts compounded for all years and then rounded to nearest cent each year.

3. Regardless of which method is used to consider inflation, the project remains unacceptable
with negative NPVs. However, the NPV from Part (2) is not as bad as that in Part (1). The
method used in Part (2) is a little more realistic in that the company can use different inflation
rates in different years if its managers feel it is necessary. The method used in Part (1)
assumes the same inflation rate in all future years, an unrealistic occurrence in this case. It
also assumes that all cash flows are affected by the same inflation rate, whereas the method
in Part (2) can use a different rate for any forecast item.

12-33. Note: This problem requires a computer spreadsheet to do the sensitivity analysis. Although
the work can be done by hand, it is time consuming and inefficient to do so.

(1) NPV:
Investment Life of the Project
Year: 0 1 2 3 4 5
Purchase fixed assets ($125,000)
Increase in working capital (45,000)
Net investment ($170,000)
Sales ($28) $280,000 $280,000 $280,000 $280,000 $280,000
Variable costs ($15) (150,000) (150,000) (150,000) (150,000) (150,000)
Contribution margin $130,000 $130,000 $130,000 $130,000 $130,000
Minus: Fixed costs (24,000) (24,000) (24,000) (24,000) 24,000)
Depreciation (25,000) (25,000) (25,000) (25,000) 25,000)
Taxable income $81,000 $81,000 $81,000 $81,000 $81,000
Minus taxes (40%). (32,400) (32,400) (32,400) (32,400) (32,400)
Income after tax. $48,600 $48,600 $48,600 $48,600 $48,600
Plus: Depreciation 25,000 25,000 25,000 25,000 25,000
Fixed asset recovery 25,000
Working cap recovery 45,000
Net cash flow ($170,000) $73,600 $73,600 $73,600 $73,600 $143,600
PV – Years 1 to 4 $210,128
(15%, 4 years): $73,600 x 2.855 x 0.497
PV – Year 5 71,369
Total PV $281,497
NPV $111,497

(2) The basic approach is to see what changes in variable cost will reduce the $111,497 NPV to
zero. A starting point is to divide the NPV by the PV factor in Table 2 for 15 percent ($111,497
 3.352 = $33,263). This amount when divided by 10,000 units ($3.33) suggests the starting
point for looking for an increase in variable costs. But this calculation still results in a positive
NPV. So, go with a "what-if" approach until you find the right value.

The correct answer is approximately $20.54 for variable costs. Consequently, variable costs
can be underestimated by $5.54; and the project will still be acceptable.

(3) The same "what-if" approach is taken for the volume of units. The volume could fall by 4,264
units to 5,736 units.

(4) Using a "what-if" approach, the fixed costs could increase by $55,438. Fixed costs could rise
to $79,438, and the investment proposal would still be acceptable.

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-30
Solution to Cases

CASE 12A – Plastic Productions, Inc.

MEMO

From: Clyde Ringer, Controller

To: Megan Messana, President

Subject: Analysis of the acquisition of a plastic injection molding press

The following data will analyze the possible acquisition of new equipment for our injection molding
operations. Using the cash-flow forecasts already prepared, the analysis will compare purchase
and leasing alternatives. Notice that the estimated cash inflows from using the machine have not
been included since they will be identical for either forms of financing.

First, a comparison of leasing and buying is presented:

PV of leasing:
Investment Life of the Project
Year: 0 1 2 3 4 5
Lease payment ($6,000) ($6,000) ($6,000) ($6,000) ($6,000) ($6,000)
Tax shield 2,400 2,400 2,400 2,400 2,400 2,400
Aftertax cost ($3,600) ($3,600) ($3,600) ($3,600) ($3,600) ($3,600)
PV factors (14%) x 1.000 x 0.877 x 0.769 x 0.675 x 0.592 x 0.519
PVs ($3,600) ($3,157) ($2,768) ($2,430) ($2,131) ($1,868)
Net cost to lease ($15,955)

PV of buying:
Life of the Project
Year: 1 2 3 4 5 6
Depreciation (MACRS):
Year 1 – 20.0% $ 5,000
Year 2 – 32.0% $ 8,000
Year 3 – 19.2% $ 4,800
Year 4 – 11.5% $ 2,875
Year 5 – 11.5% $ 2,875
Year 6 – 5.8% $ 1,450
Tax savings (40%) $ 2,000 $ 3,200 $ 1,920 $ 1,150 $ 1,150 $ 580

Investment Life of the Project

Year: 0 1 2 3 4 5 6
Purchase cost ($25,000)
Aftertax maintenance ($540) ($540) ($540) ($540) ($540) ($540)
Depre tax savings 2,000 3,200 1,920 1,150 1,150 $580
Aftertax cash ($25,540) $1,460 $2,660 $1,380 $610 $610 $580
PV factors (14%) x 1.000 x 0.877 x 0.769 x 0.675 x 0.592 x 0.519 x 0.456
PVs ($25,540) $1,280 $2,046 $932 $361 $317 $264
PV – Years 1 to 5 $5,540
Net cost to buy ($20,340)

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-31
Without considering the financing costs of the purchase, it appears to be cheaper to lease the
machine by $4,341 ($20,296 – $15,955) than to buy it.

Ordinarily, the acquisition decision is made first, then the financing decision is made. Comparison
of leasing and buying with considering financing shows:

Loan Beginning Interest Interest + Tax Aftertax Net

Cash
Year Payment Balance Expense Principal Depre Depre Savings1 Maintenance Cost
0 $0 $0 $0 $0 $0 $0 $0 $540 $5402
1 6,428 25,000 3,500 2,928 5,000 8,500 3,400 540 3,568
2 6,428 22,072 3,090 3,338 8,000 11,090 4,436 540 2,532
3 6,428 18,734 2,623 3,805 4,800 7,423 2,969 540 3,999
4 6,428 14,929 2,090 4,338 2,875 4,965 1,986 540 4,982
5 6,428 10,591 1,483 4,945 2,875 4,358 1,743 540 5,225
6 6,428 5,646 790 5,638 1,450 2,240 896 0 5,532

1
(Interest + depreciation) x 40%
2
Loan payment - tax savings + aftertax maintenance

NPV:
Investment Life of the Project
Year: 0 1 2 3 4 5 6
Net cash costs ($540) ($3,568) ($2,532) ($3,999) ($4,982) ($5,225) ($5,532)
PV factor (14%) x 1.000 x 0.877 x 0.769 x 0.675 x 0.592 x 0.519 x 0.456
PVs ($540) ($3,129) ($1,947) ($2,699) ($2,949) ($2,712) ($2,523)
PV – Years 1 to 6 ($15,959)
Cost to buy ($16,499)

With considering financing, it is still cheaper to lease the machine by $544 ($16,499 – $15,955)
than to buy it.

Notice that the net lease advantage dropped from $4,341, when financing costs were ignored, to
$544, when financing costs were considered. This is because the interest portions of the loan
payments can be deducted for tax purposes, thereby saving tax dollars. Since it only costs $544
more to purchase the machine than to leasing it, we may decide it is better to buy since, at the end
of six years, we own the machine. However, we agree that the machine will have to be replaced at
the end of six years due to wear on the injection valve and hydraulics system. Given this fact, it is
in our best interests to lease the machine.

CASE 12B – Divisional Performance in the Lansing Corporation

(1) With no limitation on the level of capital spending, the projects should be ranked using either
the NPV or the IRR method. The NPV method could use dollars of NPV or the profitability
index. Projects A, B, D, E, and F meet the basic criteria of a positive NPV and an IRR of
greater than 12 percent. A choice must be made between Projects A and D. Project A has a
higher IRR (35 percent versus 22 percent) and profitability index (1.66 versus 1.46). But
Project D generates a higher NPV ($74,374 versus $69,683). With unlimited investment
dollars, Project D would probably get the nod to attain the largest profit level. Yet, Project A
would generate the highest ROR.

(2) With resources limited to $450,000, the following would maximize the profitability index:

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-32
 NPV Profitability Index Investment Investment Total
Project A $69,683 1.66 $106,000 $106,000
Project F 69,513 1.53 130,000 236,000
Project B 23,773 1.12 200,000 436,000

Project D was not included because Project A was. The remainder, $14,000, is not used and is
assumed to be used elsewhere or earns the hurdle rate of 12 percent.

(3) Each division's level of risk is different because each division is operating in a different
industry. Management should expect a higher ROR from capital projects in divisions that have
more risk. Management should judge the inherent risks on a specific project basis, within
specific divisions, and within the total corporate portfolio.

Managerial Accounting Solutions, Schneider/Sollenberger, 4th Edition, Chapter 12, Page 12-33