Hima16 SM 11

CHAPTER 11
COVERAGE OF LEARNING OBJECTIVES

FUNDA- CRITICAL CASES,
MENTAL THINKING EXCEL,
ASSIGN- EXERCISES COLLAB., &
MENT AND INTERNET
LEARNING OBJECTIVE MATERIAL EXERCISES PROBLEM EXERCISES
S
LO1: Describe capital A1, A2, B1 26, 29, 30 51, 52, 53 68,69, 70, 71,
budgeting decisions and B2 31, 32, 33 54, 55, 56 73, 75
use the net present value 34, 35, 36 62, 64
(NPV) method to make 37, 38, 39
such decisions. 40, 41
LO2: Use sensitivity 40, 41 68, 71
analysis to evaluate effect
of changes in predictions.
LO3: Calculate the NPV 51, 52
difference between two
projects using both the
total project and
differential approaches.
LO4: Identify relevant 25, 27 51, 52, 53 68, 69, 70, 74
cash flows for NPV 54, 55, 56
analyses. 57, 60, 61
LO5: Compute the after- A3, A4, B3 42, 43, 44 57, 58, 59 70, 72
tax net present values of B4 45 60, 64, 65, 66
projects.
LO6: Explain the after-tax A5, B5 28 58, 59 71
effect of cash of disposing
of assets.
LO7: Use the payback 40, 46, 47, 48 61, 62 73
model and the accounting
rate-of-return model and
compare them with the
NPV model.
LO8: Reconcile conflict 63
between using NPV model
for making a decision and
using accounting income
for evaluating the related
performance.
LO9: Compute the impact 49, 50 66, 67
of inflation on a capital-
budgeting project.
Copyright ©2014 Pearson Education, Inc., Publishing as Prentice Hall. 193

CHAPTER 11
Capital Budgeting
11-A1 (15-25 min.) Answers are printed in the text at the end of the assignment material.
11-A2 (20-30 min.) This is a straightforward exercise.
1 & 2. The model indicates that the computers should be acquired because the net
present value is positive.
Sketch of Cash Flows

14% Total (in thousands)
Discount PV 0 1 2 3
Factor @ 14%
Cash effects of operations,
$110,000 2.3216 £ 255,376 110 110 110
Investment (240,000) (240)
Net present value £ 15,376
11-A3 (20-30 min.) This is a straightforward exercise.
1. The model indicates that the servers should not be acquired.

Discount PV 0 1 2 3
Factor @ 12%
$300,000(1-.40) 2.4018 $ 432,324 180 180 180
Cash effect of depreciation,
savings of income taxes:
$220,000 × .40 = $88,000 2.4018 211,358 88 88 88
Total after-tax effect on cash 643,682
Investment (660,000) (660)
Net present value $ (16,318)
2. The computers should be acquired. The net present value rises, and now it is
positive:
After-tax impact of disposal on cash: .60 × ($90,000 - 0) $ 54,000
PV is $54,000 × .7118 $ 38,437
Net present value as above (16,318)
New net present value $ 22,119
3. This requirement demonstrates that the choice of a discount rate often is critical.

Applying an 8% discount factor:
$300,000 × (1 - .40) × 2.5771 $463,878
$220,000 × .40 × 2.5771 226,785
$690,663
Investment (660,000)
NPV is positive, so acquire $ 30,663
11-A4 (25-30 min.)
1. Cash effects of operations:

Before tax annual cash inflow $ 420,000
Taxes @ 45%: 420,000 × .45 189,000
After-tax cash inflow $ 231,000
Present value @ 14%: $231,000 × 5.2161 $1,204,919
Cash effects of depreciation*:
Year Tax Savings** PV factor Present Value

1 .1429 × $2,000,000 × .45 = $ 128,610 .8772 $ 112,817
2 .2449 × 2,000,000 × .45 = 220,410 .7695 169,605
3 .1749 × 2,000,000 × .45 = 157,410 .6750 106,252
4 .1249 × 2,000,000 × .45 = 112,410 .5921 66,558
5 .0893 × 2,000,000 × .45 = 80,370 .5194 41,744
6 .0892 × 2,000,000 × .45 = 80,280 .4556 36,576
7 .0893 × 2,000,000 × .45 = 80,370 .3996 32,116
8 .0446 × 2,000,000 × .45 = 40,140 .3506 14,073
Total present value $579,741
* Short-cut using Exhibit 11-7: .6441 × .45 × $2,000,000 = $579,690, which differs from
the $579,741 computed above only because of rounding error.
**Factors .1429, .2449, etc. are from Exhibit 11-6.
Summary:
Present value of cash effects of operations $ 1,204,919
Present value of cash effects of depreciation 579,741
Total after-tax effect on cash $ 1,784,660
Investment (2,000,000)
Net present value is negative, so don't acquire $ (215,340)
2. The 7-year MACRS analysis will apply regardless of the economic life of the
equipment. The only change from requirement 1 will be the added five years of
cash effects from operations:
This change can be incorporated by re-computing the value of the $231,000 after-
tax inflow but now for 15 years, and then using that in the calculation:
Present value @ 14%: $231,000 × 6.1422 $1,418,848

Summary:
Present value of cash effects of operations $ 1,418,848
Present value of cash effects of depreciation 579,741
Total after-tax effect on cash $ 1,998,589
Investment (2,000,000)
NPV is still negative, so don't acquire $ (1,411)
Alternatively, the change can be incorporated by finding the present value of the
additional 5 years of $231,000 after tax savings, and adding it to the previous
NPV:
PV of $231,000 per year for 5 years at 14%
= 3.4331 × $231,000 = $793,046
To account for the delay of 10 years before
savings begin: $793,046 × .2697 $213,885*
NPV as above (215,340)
NPV is still negative, so don’t acquire. $(1,455)
* Or, $231,000 × (6.1422 – 5.2161) = $231,000 × .9261 = $213,929, which gives
the same NPV as the first approach, $(1,411).
The small relative difference in the answers here is attributable to rounding of the
present value factors. The two alternative approaches are conceptually identical
but because the present value factors are rounded to four decimal places, the
computations are numerically slightly different.
11-A5 (5-10 min.)
Many students forget to add the cash proceeds to the tax effect. Answers are in
dollars.
(a) Cash sale price 305,000 230,000

Book value 250,000 250,000
Gain (loss) 55,000 (20,000)
Effect on cash income taxes at 25%:

(b) Cash tax saving (inflow effect) 5,000
(c) Cash tax paid (outflow effect) (13,750)
Total after-tax effect on cash

(a) plus (b) 235,000
(a) minus (c) 291,250

11-B1 (15-20 min.)
1. Using the right table is essential. Factors for this part are from Table 1:
(a) PV = $22,000 × .7473 = $16,440.60
(b) PV = $22,000 × .6209 = $13,659.80
(c) PV = $22,000 × .5194 = $11,426.80
2. Use Table 2: (a) PV = $50,000 × 3.4651 = $173,255

(b) PV = $50,000 × 3.1699 = $158,495
(c) PV = $50,000 × 2.9137 = $145,685
3. Use Table 2: (a) PV = annual withdrawal × F

$6,000,000 = annual withdrawal × 13.5903
Annual withdrawal = $6,000,000 ÷ 13.5903 = $441,491.36
(b) PV = annual withdrawal × F

$6,000,000 = annual withdrawal × 9.8181
Annual withdrawal = $6,000,000 ÷ 9.8181 = $611,116.20
4. Contract Y has the higher present value despite the lower total dollars paid:
Present Value Present Value Present Value

Year @16% From Table 1 of Contract X of Contract Y
1 .8621 $215,525 $474,155
2 .7432 557,400 609,424
3 .6407 544,595 416,455
4 .5523 552,300 386,610
Total $1,869,820 $1,886,644
11-B2 (20-30 min.) This is a straightforward exercise.
1 & 2. The model indicates that the equipment should be acquired because the net
present value is positive.
Discount PV 0 1 2 3 4 5
Factor @ 14%
$140,000 3.4331 $ 480,634 140 140 140 140 140
Investment (420,000) (420)
Net present value $ 60,634

11-B3 (20-30 min.) This is a straightforward exercise.
1. The model indicates that the equipment should not be acquired.

Discount PV 0 1 2 3 4 5
Factor @ 14%
$130,000 × (1-.40) 3.4331 $267,782 78 78 78 78 78
Cash effect of depreciation,
savings of income taxes*: 3.4331 109,859 32 32 32 32 32
Total after-tax effect on cash $377,641
Investment (400,000) (400)
Net present value $ (22,359)
*Depreciation is $400,000 ÷ 5 = $80,000 per year; annual tax savings is $80,000 × .40 = $32,000.
2. The equipment should not be acquired. The net present value is negative.
After-tax impact of disposal on cash:

.60 × ($25,000 - 0) = $15,000
PV is $15,000 × .5194 $ 7,791
Net present value as above (22,359)
New net present value $(14,568)
3. Applying 10% discount factors:

$130,000 × (1 - .40) × 3.7908 $ 295,682
$80,000 × .40 × 3.7908 121,306
$ 416,988
NPV is positive, so acquire. $ 16,988
$120,000 × (1 - .30) × 2.6730 $ 224,532
$50,000 × .30 × 2.6730 40,095
$ 264,627
NPV is even more positive, so acquire. $ 114,627

11-B4 (25-30 min.)
1. See Exhibit 11-B4 on the following page for requirement 1.
2. The major reason for this requirement is to underscore the fact that the present
value of the depreciation tax savings is unchanged regardless of the length of the
economic life of the asset.
PV @ 10% of 6 years of $41,250 4.3553 × 41,250 $ 179,656

Present value of tax savings from depreciation 104,388
Total 284,044
Less: Initial Investment 300,000
NPV $(15,956)
Alternative calculation to just add present value of 6th year of operational inflow:
PV of the $41,250 to be received in the 6th year,
$41,250 × .5645 factor $ 23,286
NPV as above (39,241)
NPV is still negative, so don’t acquire. $(15,955)
Note that the alternative approaches are conceptually identical but differ numerically due
to rounding of the present value factors.
11-B5 (5-10 min.)
Many students forget to add the cash proceeds to the tax effect. Answers are in
dollars.
1. 2.
(a) Cash sale price 35,000 85,000

Book value 40,000 40,000
Gain (loss) (5,000) 45,000
Effect on cash income taxes at 30%:

(b) Cash tax saving (inflow effect) 1,500
(c) Cash tax paid (outflow effect) (13,500)
Total after-tax effect on cash

(a) plus (b) 36,500
(a) minus (c) 71,500

EXHIBIT 11-B4
(Dollar amounts in thousands) Total
1. 10% PV Sketch of Cash Flows (in dollars)
Discount @ 10% 0 1 2 3 4 5 6
Factor ($000)
Cash effects on operations,

$75 × (1 - .45) 3.7908 156.371 <––– 41.25 41.25 41.25 41.25 41.25
Cash effects of depreciation:
Savings
Year Tax Deduction @ 45%
1 .20 × $300 = $60.0 $27.0 .9091 24.546 <––– 27.0
2 .32 × 300 = 96 43.2 .8264 35.700 <–––––––––43.20
3 .192 × 300 = 57.6 25.92 .7513 19.474 <–––––––––––––––25.92
4 .1152 × 300 = 34.56 15.552 .6830 10.622 <––––––––––––––––––––15.552
5 .1152 × 300 = 34.56 15.552 .6209 9.656 <–––––––––––––––––––––––––––15.552
6 .0576 × 300 = 17.28 7.776 .5645 4.390 <–––––––––––––––––––––––––––––––– 7.776
PV of tax shield 104.388
Total after-tax effect on cash 260.759
Investment (300.000) (300)
NPV is negative, so don't acquire. (39.241)
Note: The cash effects of MACRS depreciation can be computed more easily using Exhibit 11-7. Present value of tax savings =
Original cost × Tax rate × Factor from 11-7 = $300.000 × .45 × .7733 = $104.396. This differs slightly from the $104.388
calculated above because of rounding.

11-1 The accountant has a limited role in the project identification phase. In the
selection phase, accountants provide information for predicting cash inflows and outflows
and often are in charge of summarizing the information using a capital budgeting model.
The post-audit phase uses information about the results of investment projects; this
information usually comes from the accounting system.
11-2 Discounted cash flow is a superior method for capital budgeting because it
measures profitability and takes into account the time value of money.
11-3 No. A higher required rate of return reduces the present value of future cash
inflows and outflows, and hence the difference between them. The initial investment (at
time zero) is unaffected. Therefore, the net present value is less. Higher discount rates
reduce the price a company should be willing to pay.
11-4 No. It is true that the DCF model assumes certainty and perfect capital markets.
But all practical capital budgeting models make even more limiting assumptions. The
DCF model is not perfect, but in most situations it is the best practical alternative.
11-5 Yes, double counting does occur if depreciation expense is considered separately.
The cost of an investment is represented by its cash outflow at year zero. An additional
consideration of depreciation would be double counting. Note, however, that the tax
savings from depreciation is considered separately.
11-6 No. The IRR and NPV models generally make the same decision. Suppose we
compute the NPV of a project using the cost of capital as the discount rate. If its NPV is
greater than zero, then its IRR is generally greater than the cost of capital.
11-7 The real-options model recognizes the value in allowing investment in stages –
that is, contingent investments. If managers can adjust the investment after gaining the
information from the early stages, they can make better decisions about late-stage
investments. Projects that allow this ability to make adjustments are often better than
similar investments that require the entire investment up front.
11-8 Sensitivity analysis is especially appropriate for organizations that do not have
accurate cash flow predictions. Sensitivity analysis can help a manager decide whether it
is worth gathering information to improve cash flow predictions.
11-9 The differential approach should lead to the same choice between alternatives as
the total approach because it merely disregards the factors that are constant for each
alternative: those that make no difference.
11-10 The NPV model is appropriate for all types of investments. However, with some
types of investments, such as those in advanced technology, NPV must be carefully
applied. Managers should quantify as many qualitative effects as best as possible and
include them in the model, or they should consider them as subjective factors in addition
to the NPV analysis.

11-11 The marginal tax rate is the rate paid on additional amounts of pretax income.
In contrast, the average tax rate is the total taxes paid divided by the total pretax income.
11-12 No. Two sets of books are appropriate. The objectives of tax reporting and
shareholder reporting differ; therefore, the rules for reporting to each differ. If companies
used tax rules for financial reporting, users of the statements would not receive the
information they judge to be most useful. Likewise, if tax authorities accepted financial
reporting rules, certain social goals sought by the taxation system would not be met.
11-13 Tax avoidance is the achieving of a reduction in income tax payments through
legal means; tax-evasion achieves the same end through illegal means. Tax avoidance is
considered moral; tax evasion, immoral. Tax avoidance uses the rules of the system (tax
laws) in an optimum way; tax evasion disregards the rules.
11-14 No. Companies have an obligation to shareholders to avoid taxes where it is

legal to do so. Tax evasion is clearly unethical as well as illegal.
11-15 Companies should prefer accelerated rather than straight-line depreciation for tax
purposes because it provides a bigger present value of tax savings by reducing taxable
income more during the earlier years of an asset's life. Because of the time value of
money, immediate tax savings are more valuable than tax savings in the future.
11-16 Yes. Two streams may be identified: (a) inflows from operations and (b) savings
of income tax outflows (which are often regarded in capital budgeting as additions to
inflows).
11-17 Because of the time value of money, the earlier a company takes tax deductions
and thereby saves taxes, the larger the present value of the tax savings.
11-18 Yes. MACRS treats assets as if they were purchased at midyear, so they have
depreciation effects for one tax year more than the number of years of their depreciable
lives. For example, if a company purchases a three-year MACRS asset during 2010 and
pays taxes on a calendar year basis, its depreciation begins July 1, 2010, and extends
through June 30, 2013, affecting taxes in 4 years (2010, 2011, 2012, and 2013).
11-19 No. Depreciation is never a cash outlay. The depreciation amount is used to
predict the income tax cash effect, but depreciation itself is not a cash effect.
11-20 It is useful to learn the "payback" and "accounting rate-of-return" methods of

capital budgeting because they are widely used today. In addition, the payback method
may give a rough indication of riskiness, and the accounting rate of return shows a
project's effect on an accrual accounting income statement. The comparative advantage of
discounted cash flow can also be seen by contrast. Surveys show that most companies use
more than one method to evaluate capital budgeting projects, so it is likely that you will
need to understand more than DCF models.

11-21 The basic flaw in the payback method is that it does not compare the total
profitability of alternative projects. It simply measures the rate of recoupment of the initial
investment. It also ignores the time value of money.
11-22 If a company makes capital-budgeting decisions using DCF and evaluates

performance using accrual accounting numbers, a conflict may arise. Often accrual
accounting can show low profits in the early years of a project's life because of high
depreciation, write-offs of old equipment that is being replaced, or slow growth in
revenues as the company penetrates new markets. Such low accrual accounting profits
might discourage managers from making investments that have a positive net present
value.
11-23 The three components of the market or nominal interest rate are: 1) risk-free
element, or pure rate of interest, 2) business-risk element, and 3) inflation element.
11-24 The correct analysis under inflation (a) uses a required rate that includes an
element attributable to inflation and (b) explicitly adjusts the predicted operating cash
flows for the effects of inflation.
11-25 It is difficult to predict the cash flows to be received from an investment in

research and development (R&D) because there is so much uncertainty involved. The
manager’s assertion that this is impossible is not uncommon. However, even investments
in R&D must, on average, return more than the cost of capital if they are to be desirable
investments. Therefore, it is usually worth the effort to predict, as well as possible given
the uncertainties, the possible outcomes of R&D activities and their effect on the
company’s cash flows. From that, a net present value can be computed.
11-26 The net present value of an investment project represents the increase (or
decrease) in the value of the firm from investing in the project, provided the cash flows
and cost of capital are estimated correctly. Thus, implementing a positive net present
value project will increase the company’s value, while implementing a negative net present
value project will decrease it.
11-27 The direct cash flows are the easiest to predict. These would include the
investment in the new machine (less any salvage value of the old machine), the savings in
labor and other variable operating costs because of the decreased production time per unit,
and the estimated salvage value of the new machine at the end of its economic life. Those
more difficult to measure are revenue from increased sales because of higher quality or
more timely delivery schedules, cost savings from reworking defective units because of the
more accurate standards of the new machine, and decreased storage costs because the
faster production process allows quicker adaptation to changes in demand and thus less
need for large inventories.
11-28 The first situation is reasonably clear. There is no legal or ethical reason not to
take the depreciation allowed by the tax law. The second is much more problematic.
Investing offshore is generally not illegal, although its ethics might be questionable. If the
offshore investment is really a sham to avoid (or evade) taxes while the company still takes
advantage of the business climate provided in the U. S. for most of its business, it is not

contributing to society as much as it is taking from it. But even more questionable is the
use of transfer prices to move profits into a tax haven. Again, there may be no technical
illegality (although there are laws relating to transfer prices that might be violated),
artificially transferring profits from the society in which the company really earns them to a
tax haven where the company is located only for the tax purposes is certainly of dubious
ethics.
11-29 (10-15 min.)

1. The present value is $640,000 and the annual payments are an annuity, requiring
use of Table 2:
(a)$640,000 = annual payment × 11.1184
annual payment = $640,000 ÷ 11. 1184 = $57,562
(b)$640,000 = annual payment × 8.5595
annual payment = $640,000 ÷ 8.5595 = $74,771
(c)$640,000 = annual payment × 6.8109
annual payment = $640,000 ÷ 6.8109 = $93,967
2. (a)$640,000 = annual payment × 8.1109
annual payment = $640,000 ÷ 8.1109 = $78,906
(b)$640,000 = annual payment × 6.7101
annual payment = $640,000 ÷ 6.7101 = $95,379
(c)$640,000 = annual payment × 5.6502
annual payment = $640,000 ÷ 5.6502 = $113,270
3. (a) Total payments= 15 × $74,771 = $1,121,565
Total interest paid= $1,121,565 - $640,000 = $481,565
(b) Total payments= 10 × $95,379 = $953,790
Total interest paid = $953,790 - $640,000 = $313,790
11-30 (10 min.) The initial step on solving present value problems focuses on a
basic question: Which table should I use? No computations should be made until you are
convinced that you are using the correct table.
1. Use Table 1, row 10, 4% column. Bank of America will lend $506,700,000. The
$750 million is a future amount. Its present value is:
PV = $750,000,000 × .6756 = $506,700,000
2. Use Table 2, row 10, 4% column. Bank of America will lend $608,317,500. The
$75 million is a uniform periodic payment at the end of a series of years.
Therefore, it is an annuity. Its present value is:
PV = $75,000,000 × 8.1109 = $608,317,500
A
In particular, note that Bank of America is willing to lend more than in

requirement 1 even though the interest rate is the same. Why? Because the bank

will receive the $750,000,000 more quickly if it receives 10 payments of
$75,000,000 per year rather than waiting to receive the entire $750,000,000 at
the end of 10 years.
11-31 (10-20 min.)
1. a. PV = $250,000 × .6806 = $170,150

b. PV = $250,000 × .5674 = $141,850
2. The annual rates would be halved and the periods doubled.

Present values decline:
a. PV = $250,000 × .6756 = $168,900

b. PV = $250,000 × .5584 = $139,600
3. Present values rise because the money is repaid more quickly:
a. PV = $50,000 × 3.9927 = $199,635

b. PV = $50,000 × 3.6048 = $180,240
11-32 (10-15 min.)
1. $300,000 = Future amount × .6830
Future amount = $300,000 ÷ .6830

= $439,239
2. $300,000 = Annual installments × 3.1699
Annual installments = $300,000 ÷ 3.1699

= $94,640
11-33 (10 min.)
The deferral cost Jenner $1,388,800 in present value, computed as follows:

Present value of $8,000,000 in 2 years $6,611,200
Present value of $8,000,000 today 8,000,000
Sacrifice in present value $1,388,800
A more detailed analysis follows:
Present Value Present Value Present Value
@ 10% of Original of Revised
Year from Table 1 Contract Contract
2012 1.0000 $15,000,000 $ 7,000,000
2013 .9091 17,272,900 17,272,900
2014 .8264 17,354,400 23,965,600
Total $49,627,300 $48,238,500
Difference ($49,627,300 - $48,238,500) = $1, 388,800

11-34 (5-10 min.) This simple exercise requires use of both Table B-1 and Table B-2.
PV of 3 payments of $600 each: $600 × 2.7751 $ 1,665.06

PV of $3,500 payment in 3 years: $3,500 × .8890 3,111.50
Total NPV $4,776.56
11-35 (20-25 min.) This basic exercise develops comfort with the tables and the NPV
method.
Number of years 7 18 18 28
Amount of annual cash inflow $8,000 $13,749b $ 30,000 $ 16,000
Required initial investment $37,967a $70,000 $50,000 $29,000
Required rate of return 10% 18% 8%c 20%
Net present value $ 980 ($10,009) $231,157 $50,515d
a
(4.8684 × $8,000) - $980 = $38,947 - $980 = $37,967
b
(5.2732 × CF) - $70,000 = ($10,009); CF = ($70,000 - $10,009)  5.2732 = $11,377
c
(F × $30,000) - $50,000 = 231,157; F = $281,157  $30,000 = 9.3719
On the 18 year row, the factor 9.3719 is a 8% rate
d
PV Factor for 20% on 28-year row is 4.9697; $16,000 × 4.9697 = $79,515
NPV= $79,515 - $29,000 = $50,515
11-36 (10 min.)
Buy. The net present value is positive.

Initial outlay * $(44,000)
Present value of cash operating savings, from
8-year, 14% column of Table 2, 4.6389 × $22,000 102,056
* The trade-in allowance really consists of a $1,000 adjustment of the selling
price and a bona fide $20,000 cash allowance for the old equipment. The relevant
amount is the incremental cash outlay, $44,000. The book value is irrelevant.
11-37 (10-15 min.)

1. The quickest solution is to "net" the flows for each year:
1. $200,000 - $150,000 = $ 50,000 ┐
2. 250,000 - 200,000 = 50,000 ├ an annuity of 3 payments (a)
3. 300,000 - 250,000 = 50,000 ┘
4. 450,000 - 300,000 = 150,000 ┐ an annuity of 2 payments
5. 500,000 - 350,000 = 150,000 ┘ deferred three years (b)
(a) $50,000 × 2.3216 $116,080
(b)$150,000 × 1.6467 × .6750 166,728
Total $282,808
Less initial investment 235,000

Net Present Value (NPV) $ 47,808
Various other approaches would reach the same answer, but they would involve
more computations.
2. The NPV is positive because at a 12% rate, the present value of the net inflows
will be higher than at 14%, so NPV will increase.
11-38 (10 min.)
1. NPV @ 10% = $2,300 × 6.8137 = $15,671.51 - $15,000 = $671.51. With a

required rate of 10%, the NPV is positive, so this investment is desirable.
2. NPV @ 12% = $2,300 × 6.1944 = $14,247.12 - $15,000 = $(752.88). With a
required rate of 12%, the NPV is negative so the investment is undesirable.
3. The higher the required rate of return, the lower the NPV of future cash flows.
Potential investments that have an initial cash outflow for investment followed by
cash inflows will be less desirable the higher the required rate of return. In this
case the higher required rate of return makes the investment undesirable.
11-39 (10-15 min.)
1. NPV @ 10% = 10,000 × 3.7908 = $37,908 - $36,048 = $1,860

NPV @ 12% = 10,000 × 3.6048 = $36,048 - $36,048 = $0
NPV @ 14% = 10,000 × 3.4331 = $34,331 - $36,048 = $(1,717)
2. The IRR is the interest rate at which NPV = $0; therefore, from requirement 1 we
know that IRR = 12%.
3. The NPV at the company’s cost of capital, 10%, is positive, so the project should
be accepted.
4. The IRR (12%) is greater than the company’s cost of capital (10%), so the project
should be accepted. Note that the IRR and NPV models give the same decision.
11-40 (30-45 min.)
This problem deals essentially with sensitivity analysis, which asks how the basic
forecasted results will be affected by changes in the critical factors (useful life, cash flows)
that influence rate of return.
1. $40,000 ÷ $10,000 = 4 years
2. NPV= ($10,000 × 3.4331) - $40,000 = $(5,669)
3. a) NPV = ($10,000 × 2.3216) - $40,000 = ($16,784)

b) NPV = ($10,000 × 5.2161) - $40,000 = $12,161
4. NPV = ($8,000 × 3.4331) - $40,000 = ($12,535)

5. NPV = ($9,000 × 2.9137) - $40,000 = ($13,777)
11-41 (15-20 min.)
1. NPV = ($15,000 × 3.7908) - $52,000 = $56,862 - $52,000 = $4,862
2. (a) NPV = ($15,000 × 3.1699) - $52,000 = $47,549 - $52,000 = $(4,451)

(b) NPV = ($15,000 × 4.8684) - $52,000 = $73,026 - $52,000 = $21,026
3. (a) NPV = ($12,000 × 3.7908) - $52,000 = $45,490 - $52,000 = $(6,510)

(b) NPV = ($18,000 × 3.7908) - $52,000 = $68,234 - $52,000 = $16,234
4. (a) NPV = ($18,000 × 4.8684) - $52,000 = $87,631 - $52,000 = $35,631

(b) NPV = ($12,000 × 3.1699) - $52,000 = $38,039 - $52,000 = $(13,961)
5. (Savings × 3.7908) - $52,000 = 0

Savings = $52,000  3.7908
Savings = $13,717
11-42 (5-10 min.) Amounts in thousands of dollars.
Annual Income Statement Effects:

(S) Sales 750
(E) Expenses excluding depreciation 275
(D) Depreciation 200
Total expenses 475
Income before income taxes 275
(T) Income taxes outflow at 36% 99
(I) Net income 176
Total after-tax cash inflow from operations is

either S - E - T = 750 - 275 - 99 = 376 or I + D = 176 + 200 = 376
Annual Cash Flow Effects:

Cash effect of operations:
(S - E) Pretax cash inflow from operations,750 - 275 475
Multiplied by (1 – tax rate) ×.64
After-tax cash inflow from operations 304
Cash effect of depreciation tax deduction:
(D) Depreciation 200
Multiplied by tax rate ×.36
Tax savings due to depreciation 72
Total after-tax effect on cash 376
11-43 (5-10 min.)
Cash effect of operations:

Cash inflow from operations: $1,700,000 - $350,000 $1,350,000
Multiplied by (1 –37% tax rate) ×.63
After-tax inflow from operations $850,500
Cash effects of depreciation tax deduction:

Depreciation $425,000
Income tax rate 37% ×.37
Tax Savings due to depreciation 157,250
Total after-tax effect on cash $1,007,750
Another way to find the after-tax effect on cash is:
Cash inflow from operations: $1,700,000 - $350,000 $1,350,000

Actual income taxes @ 37% (342,250)
After-tax cash inflow from operations $1,007,750
11-44 (10 min.)
The month and day on which an asset is acquired does not affect its tax
depreciation. MACRS applies the half-year convention to all assets, taking ½ year of
depreciation in the year of acquisition and ½ year of depreciation in the final year of the
recovery period.
20X8 20X9
1. 3-year property: 33.33% & 44.45% of $55,000 $18,332 $24,448
2. 5-year property: 20% and 32% of $3,500 700 1,120
3. 5-year property: 20% and 32% of $16,000 3,200 5,120
4. 7-year property: 14.29% and 24.49% of $9,500 1,358 2,327
11-45 (10 min.)

This problem could be solved by specifying appropriate schedules of tax savings
and computing the present values. However, the process would be extremely time-
consuming. The steps outlined in the chapter make the computations quite simple.
(a) $220,000 × .5798 × .33 = $ 42,093
(b) $640,000 × .6810 × .33 = $ 143,827
(c) $ 40,000 × .7059 × .29 = $ 8,188
(d) $950,000 × .7975 × .45 = $ 340,931
(e) $420,000 × .7782 × .25 = $ 81,711
11-46 (10-15 min.)

Annual addition to profit = 25% × $14,000 = $3,500.
1. Payback period is $28,000 ÷ $3,500 = 8 years. It is not a good measure of

profitability because it ignores returns beyond the payback period and it does not
account for the time value of money.
2. NPV = $5,114. Reject the proposal because NPV is negative.

Computation: NPV = ($3,500 × 6.1446) - $28,000
= $21,506 - $28,000 = $(6,494)
3. ARR = (Increase in average cash flow – Increase in depreciation) ÷ Initial
investment
= ($3,500 - $2,800) ÷ $28,000 = 2.5%
11-47 (10-15 min.)
1. Investment A payback period: $36,000 ÷ $4,000 = 9 years

Investment B payback period: $36,000 ÷ $4,500 = 8 years
Investment B has the shorter payback period, so it seems more desirable using the payback
model.
2. NPV of A: $4,000 × 9.8181 = $39,272 - $36,000 = $3,272
NPV of B: $4,500 × 5.7466 = $25,860 - $36,000 = $(10,140)
Investment A has the higher NPV, so it is more desirable. In fact, investment B has a
negative NPV, so it would reduce the value of Stallone Company.
3. The payback model does not consider the overall profitability of the two investments.
It ignores all cash flows beyond the payback period and gives all cash inflows during the
payback period the same value as dollars at time zero, regardless of when received.
Although investment B returns its investment in 8 years, it has no additional cash flows.
Investment A returns its investment more slowly, but the 12 extra years of $4,000 annual
cash flows make it more valuable than investment B.
11-48 (15 min.)
1. $28,000 ÷ $7,000 = 4 years
2. $7,000 × 6.1446 = $43,012. The company should buy because the net present
value is a positive $43,012 - $28,000 = $15,012.
3. ARR = [$7,000 – ($28,000 ÷ 10 years)] ÷ $28,000 = $4,200 ÷ $28,000 = 15%
11-49 (30 min.)
1 & 2. See Exhibit 11-49 on the following page for requirements 1 and 2.
The footnotes for the exhibit follow:

a
Be sure to use a nominal discount rate, which includes an element attributable to
inflation, and adjust the predicted cash flows for inflationary effects. Each year is
adjusted for anticipated inflation: $91,000 × 1.05, $91,000 × 1.05 2, $91,000 × 1.053,
etc.

b
The annual savings in income taxes will be unaffected by inflation. Why? Because
the income-tax deduction must be based on original cost of the asset in year 0 dollars.
Amounts are 35% of (.20 × $290,000), (.32 × $290,000), (.192 × $290,000), (.1152
× $290,000), (.1152 × $290,000), and (.0576 × $290,000).
c
Shortcut using Exhibit 11-7: .5631 × $290,000 × .35 = $57,155, which differs from
the $57,158 calculated above only because of rounding error.
d
A common error is to adjust the discount rate as above but not adjust the predicted
cash inflows.
3. The method of Requirement 1 is correct. The required rate of return includes an

inflation element, and the cash inflows are adjusted for inflation. In Requirement
2 the required rate of return includes an inflation element, but the cash inflows are
not adjusted for inflation. This understates the cash flows, so the net present
value is understated. The incorrect method can lead to underinvestment, because
desirable investments can be rejected.

EXHIBIT 11-49 At 25 Percent Sketch of Relevant Cash Flows
(See footnotes on previous page.) P.V. Present (in dollars)
Factor Value ––––––––––––––––––––––––––––––––––––
0 1 2 3 4 5 6
1. Correct Analysis
Cash operating inflows:a
Pretax inflow in year-0 dollars $140,000
Tax effect at 35% 49,000
After-tax effect $ 91,000
.8000 $ 76,440 < ––––––—95,550
.6400 64,210 <––––––––––––— 100,328
.5120 53,936 <––––––––––––––––––— 105,344
.4096 45,306 < ––––––––––––––––––––––––— 110,611
.3277 38,060 < ––––––––––––––––––––––––––––—— 116,142
Subtotal $ 277,952
Cash effect of depreciation:b
Savings in income taxesc .8000 16,240 <–––––— 20,300
.6400 20,787 <––––––––––— 32,480
.5120 9,978 <–––––––––––––––– 19,488
.4096 4,789 <––––––––––––––––––––––— 11,693
.3277 3,832 <––––––––––––––––––––––––––– 11,693
.2621 1,532 <–––––––––––––––––––––––––––––— 5,846
57,158
Investment in equipment 1.0000 (290,000) (290,000)
2. Incorrect Analysis
Cash operating inflows
after taxesd 2.6893 $ 244,726 <––––––—91,000 91,000 91,000 91,000 91,000
Tax effect of depreciation
(same as above) 57,158
Investment in equipment 1.0000 (290,000) (290,000)

11-50 (30-40 min.) Answers are in Mexican pesos.
1. After-tax cash operating savings,
.6 × 150,000 = 90,000
PV of cash operating savings, 90,000 × 3.1272 281,448
Income tax savings from depreciation
.4 × (420,000 ÷ 5) = .4 × 84,000 = 33,600
PV = 33,600 × 3.1272 105,074
PV of total savings 386,522
Required outlay at time zero (420,000)
Net present value (33,478)
Note how income taxes have a two-edged effect. They chop the present value of
the cash operating savings by 40%, but the depreciation deduction provides
income tax savings.
2. See Exhibit 11-50 on the following page for requirement 2.
3. The analysis in Requirement 2 is correct. The cash flows and the required rate of
return incorporate the 10% rate of inflation. In Requirement 1, the 18% required
rate of return includes an inflation element, but the predicted cash flows ignore
inflationary effects.
11-51 (30-35 min.)

1. Annual Operating Cash Flows
Xerox Brother Difference

Salaries $74,880(a) $58,240(b) $16,640
Overtime 3,888(c) -- 3,888
Repairs and maintenance 2,700 600 2,100
Toner, supplies, etc. 1,800 4,500 (2,700)
Total annual cash outflows $83,268 $63,340 $19,928
(a) ($12 × 40 hrs.) × 52 weeks × 3 employees = $480 × 52 × 3 = $74,880

(b) ($14 × 40 hrs.) × 52 weeks × 2 employees = $560 × 52 × 2 = $58,240
(c) ($18 × 6 hrs.) × 12 months × 3 machines = $108 × 12 × 3 = $ 3,888
Initial Cash Flows
Xerox Brother Difference

Purchase of Brother machines $ -- $60,000 $60,000
Sale of Xerox machines -- -5,250 -5,250
Training and remodeling -- 3,500 3,500
Total $ -- $58,250 $58,250

EXHIBIT 11-50
All numbers are expressed in Mexican pesos.
2. 18% Total Sketch of Relevant Cash Flows

PV Present
Factor Value 0 1 2 3 4 5
Cash operating savings:* .8475 83,903 99,000
.7182 78,212 108,900
.6086 72,904 119,790
.5158 67,966 131,769
.4371 63,356 144,946
Total 366,341
Income tax savings from
depreciation not changed
by inflation, see 1 3.1272 105,074 33,600 33,600 33,600 33,600 33,600
Total 471,415
Required outlay at time zero 1.0000 (420,000) (420,000)
Net present value 51,415
*Amounts are computed by multiplying (150,000 × .6) = 90,000 by 1.10, 1.10 2, 1.10 3, etc.

PV Present value
of $1.00 Present value of
Discounted Cash Flows Annual Cash Flows
at 14% 0 1 2 … 9 10
TOTAL PROJECT APPROACH:
Brother:
Init. cash outflow 1.0000 $ (58,250)
Oper. cash flows 5.2161 (330,388) (63,340) (63,340) … (63,340) (63,340)
Total $(388,638)
Xerox:
Oper. cash flows 5.2161 $(434,334) (83,268) (83,268) … (83,268) (83,268)
Difference in favor of
replacement $ 45,696
INCREMENTAL APPROACH:
Initial investment 1.0000 $(58,250)
Annual operating
cash savings 5.2161 103,946 19,928 19,928 … 19,928 19,928
Net present value
of purchase $ 45,696
2. The Xerox machines should be replaced by the Brother equipment.
Net savings = (Present value of expenditures to retain Xerox machines) less

(Present value of expenditures to convert to Brother machines)
= $434,334 - $388,638 = $45,696
3. a. How flexible is the new machinery? Will it be useful only for the presently
intended functions, or can it be easily adapted for other tasks that may arise over
the next 5 years?
b. What psychological effects will it have on various interested parties?
11-52 (40 min.)

At 14% for 8 Years
Total project Analysis PV Present Sketch of Cash Flows (in thousands)

Replace (A) Factor Value 1 2 3 4 5 6 7 8
Recurring cash
maintenance cost 4.6389 $ (4,175) (.9) (.9) (.9) (.9) (.9) (.9) (.9) (.9)
Recurring cash operating
cost savings* 4.6389 83,500 18.0 18.0 18.0 18.0 18.0 18.0 18.0 18.0
Disposal value of
old machine 1.0000 5,500
Initial investment 1.0000 (45,000)
Overhaul, end of 3rd yr. 0.6750 (3,713) (5.5)
Disposal value of
new machine 0.3506 2,279 6.5
Present value of net
cash outflows $ 38,391
* Half of the salary of the replaced laborer.
Keep (B)
Recurring cash
maintenance cost 4.6389 $ (6,958) (1.5) (1.5) (1.5) (1.5) (1.5) (1.5) (1.5) (1.5)
Overhaul at end of 2nd yr.
(Machine 7 yrs. old) 0.7695 (5,002) (6.5)
Present value of net
cash outflows $(11,960)
Difference in favor of
At 14% for 8 Years
PV Present Sketch of Cash Flows (in thousands)
Differential Analysis Factor Value 1 2 3 4 5 6 7 8
Replace (A)
Recurring cash
maintenance savings 4.6389 $ 2,783 .6 .6 .6 .6 .6 .6 .6 .6
Disposal value of
old machine 1.0000 5,500
Initial investment 1.0000 (45,000)
Overhaul, end of 3rd yr. 0.6750 (3,713) (5.5)
Disposal value of
new machine 0.3506 2,279 6.5
Recurring cash operating
savings 4.6389 83,500 18.0 18.0 18.0 18.0 18.0 18.0 18.0 18.0
Overhaul avoided at
end of 2nd year 0.7695 5,002 6.5
Net present value of

11-53 (30 min.)
The initial purchase cost of the golf course and the operating receipts and
disbursements for the first season of ownership are irrelevant to the present decision. The
relevant annual costs which Ms. Driver should take into consideration are:
Electricity, (300 × 1 KW) × (130 × 5 hrs.) × $.08 per KWH $15,600
Labor cost, 130 × $75 9,750
Light bulb cost 1,500
Repairs and maintenance of lighting system, .04 × $90,000 3,600
Property taxes, .017 × $90,000 1,530
Total additional operating expenses $31,980
Annual revenue from night operations:
Years 1 and 2: 130 × $420 $54,600
Years 3, 4, and 5: 130 × $300 $39,000
One-time cash flows:
Present value of initial investment $90,000
Salvage value, year 5 $35,000
Example of Cash Flow Analysis
PV PV of
Revenue Expenses Net Flow Factor Cash Flows
Year 1 $54,600 - $31,980 = $22,620 .9091 $20,564
Year 2 54,600 - 31,980 = 22,620 .8264 18,693
Year 3 39,000 - 31,980 = 7,020 .7513 5,274
Year 4 39,000 - 31,980 = 7,020 .6830 4,795
Year 5 74,000 - 31,980 = 42,020 .6209 26,090
Present value of cash flows $75,416
Since the present value of the annual cash flows is $14,584 less than the initial
investment of $90,000, the proposed lighting system should not be installed. If significant
increases in revenue were predictable, the plan might become attractive to Ms. Driver.

11-54 (20-25 min.)
Total
PV Present Sketch of Cash Flows ( in thousands)
Factor Value 0 1 2 3 4 5
Old machine:
Operating cash
Outflows 3.00 £(150,000) (50) (50) (50) (50) (50)
Disposal value .40 1,600 4
Present value £(148,400)
New machine:
Net cash outlay
(£57,000- £12,000) 1.00 £ (45,000) (45)
Operating cash
outflows 3.00 (120,000) (40) (40) (40) (40) (40)
Disposal value .40 800 2
Present value £(164,200)
NPV in favor of
old machine £ 15,800
The old machine minimizes the present value of future costs by £15,800.

11-55 (30-35 min.) This is one of our favorite problems. The heart of the solution extends
through the first paragraph of the response to requirement 2. The remainder is amplification.
Analysis of Cash Flows
Present Proposed Difference
Revenue $200,000 $15,000*
Expenses:
Miscellaneous $100,000
Salaries 110,000 210,000 13,000
Net cash flow from operations $ (10,000) $ 2,000 $12,000
Required investment:
Equipment $ - $19,000**
Termination pay - 35,000
Total $ - $54,000 $54,000
* 10% × $150,000 = $15,000 commission.
** An acceptable alternative would be to show $3,000 and $22,000, respectively. The
incremental investment would still be $19,000.
1. Present value of $12,000 per year for

10 years at 10% = $12,000 × 6.000 $72,000
Required investment 54,000
Net present value $18,000
The requirements of the problem focus on the incremental approach. The total project
approach could view the problem as choosing the alternative that minimizes the net
present value of the future costs:
Present:
Operating cash outflows, $10,000 × 6.000 $(60,000)
Proposed:
Operating cash inflows, $2,000 × 6.000 $ 12,000
Termination pay (35,000)
Equipment (19,000)
Total $(42,000)
Difference in favor of proposed investment $ 18,000
2. The minimum amount of annual revenue that MTA would have to receive to justify the
investment would be that amount yielding an incremental net present value of zero. As
the initial investment is constant, any change in the incremental net present value is due
solely to a change in the amount of revenue. Therefore, the maximum drop in the
incremental net present value of $18,000 equals the maximum drop in the present value
of the revenue stream. This implies a maximum drop of $18,000 ÷ 6 = $3,000 in
annual revenue and a minimum amount of annual revenue of $15,000 - $3,000 =
$12,000.
Let X = Revenue at point of indifference, where net present value is zero
NPV= PV of (New annual cash flows - Old annual cash flows) –
Required investment
0 = 6.000[(X - 13,000) - (-10,000)] - 54,000

0 = 6.000(X - 13,000 + 10,000) - 54,000
0 = 6.000(X - 3,000) - 54,000
0 = 6.000X - 18,000 - 54,000
6.000X = 72,000
X = 12,000
Part 2 demonstrates sensitivity analysis, where the manager may see the potential impact
of the possible errors in the forecasts of revenue. Such analysis shows how much of a margin of
safety is available. In this case, his "best guess" is revenue of $15,000 (part 1). Sensitivity
analysis shows him that a decline of revenue would have to occur from $15,000 to $12,000
before the rate of return on the project would decline to the minimum acceptable level.
The following alternative approach to solving requirement 2 is longer, but it may be

clearer for many students:
If 10% is the minimum acceptable rate of return, the minimum acceptable net present
value must be zero, using the 10% rate:
NPV = PV of future cash flows - Initial investment
Let X = Annual cash inflow
Then 0 = 6.000(X) - $54,000
X = $54,000 ÷ 6.000 = $9,000
Present value of $9,000 per year for 10

years at 10% = $9,000 × 6.000 $54,000
Required investment 54,000
Net present value $ 0
Many students will stop at this point, giving an answer of $9,000. But the problem
asks for the minimum amount of revenue, as distinguished from the difference in cash
flows. The following analysis shows that revenue can fall to $12,000. Note also that
there can be negative cash flows under both alternatives; the alternative with the least
negative cash flow is preferable:
Difference in
Present Proposed Cash Flows
Revenue $200,000 $12,000
Expenses 210,000 13,000
Net cash flow from operations $ (10,000) $ (1,000) $9,000
11-56 (30-40 min.)
1.
Discount Present
Factor Value of Sketch of Cash Flows (thousands)
at 18% Cash Flows 0 1 2 3 4
End of Year
A. Continue with

common carriers:
385,000 lbs.@$.27 2.6901 $(279,636) (103.95) (103.95) (103.95) (103.95)
B. Purchase truck:
Cost of truck 1.0000 (75,000) (75)
Cash operating costs* 2.6901 (534,119) (198.55) (198.55) (198.55) (198.55)
Back-haul revenue,
55 trips @ $2,300 2.6901 340,298 126.5 126.5 126.5 126.5
Present value of
net cash flows $(268,821)
Difference in favor
of truck $ 10,815
*385,000 lbs. ÷ 7,000 lbs. = 55 trips
55 trips × 3,800 miles × $.95 per mile = $198,550
2. The PV of back-haul revenue must fall by $10,815 before the net present value equals
zero. Therefore, the total present value of back-haul revenue would need to be
$340,298 less $10,815, or $329,483.
Let X = number of trips

(2.6901) × ($2,300) × (X) = $329,483
$6,187 X = $329,483
X = 53.25 trips
Consequently 54 trips would have to be guaranteed to yield a non-negative present

value – 53 would be slightly too few. This means that Azra would need to be assured
that nearly every return trip would be fully loaded. Since Jetson anticipates need for up
to 100 loads, it is likely this break-even point will be reached.
3. The greatest difficulty is the reliability of the numbers in a world of uncertainty.

Although "the numbers" indicate the truck is a favorable alternative, the following other
factors could influence the final decision:
(a) If the back-haul agreement can be canceled by Retro at any time, the truck
becomes a more risky investment since the back-haul revenue is needed to make
the investment produce a return of 18% or more.
(b) What is the outlook for other investments over the life of the truck investment?
Does purchasing the truck preclude taking advantage of more favorable
opportunities during the 4-year life of the truck?
(c) Does the management have the required expertise to run the truck operation
efficiently?
(d) Will the truck give the company better service than common carriers?
(e) How certain are the predicted cash flows? Are shipment figures and operating
cost predictions considered to be relatively accurate?

11-57 (15 min.)
1. Straight-line depreciation:
Annual depreciation = $50,000 ÷ 5 = $10,000 per year
PV of tax savings = $10,000 × .40 × 3.6048 = $14,419
2. MACRS depreciation:
Year Tax Savings PV factor Present Value

1 .2000 × $50,000 × .4 = $4,000 .8929 $ 3,572
2 .3200 × 50,000 × .4 = 6,400 .7972 5,102
3 .1920 × 50,000 × .4 = 3,840 .7118 2,733
4 .1152 × 50,000 × .4 = 2,304 .6355 1,464
5 .1152 × 50,000 × .4 = 2,304 .5674 1,307
6 .0576 × 50,000 × .4 = 1,152 .5066 584
Total present value of tax savings $14,762
You can also use Exhibit 11-7: .7381 × $50,000 × .4 = $14,762.
3. Immediate write-off:
$50,000 × .4 = $20,000
4. Mr. Hiramatsu would prefer immediate write-off. Note that the total tax savings is
$20,000 under all three methods. However, only the immediate write-off provides the
entire savings immediately. Straight-line depreciation delays receipt of the tax savings
the longest, and therefore it has the lowest present value.
11-58 (30 min.)
1. See Exhibit 11-58 on the following page. There is a net disadvantage in purchasing
because the net present value is slightly negative. However, such a slight quantitative
disadvantage could be more than offset by positive factors not quantified here.

Exhibit 11-58
Present Value
Discount Total
Factors, Present
@ 16% Values
Recurring operating cash savings $20,000
Income taxes, @ 30% (6,000)
After-tax operating cash savings $ 14,000 2.2459 $31,443
Tax savings due to depreciation:
3-year property @ $46,000 10,398*
Residual value, all subject to tax
because book value will be zero $ 6,000
Less: 30% income tax
on disposal gain (1,800)
Net cash inflow $ 4,200 .6407 2,691
Initial required investment (46,000)
Net present value of all cash flows $ (1,468)
*The tax savings due to MACRS depreciation can be calculated as follows:

(1) (2) (3) (4) (5) (6)
Income Tax PV Present Sketch of Cash Flows
MACRS Deduction Savings, Factors, Values at End of Year
Year Percentage $46,000×(2) .30×(3) @ 16% (4)×(5) 0 1 2 3 4
1 .3333 $15,332 $4,600 .8621 $ 3,965 4,600
2 .4445 20,447 6,134 .7432 4,559 6,134
3 .1481 6,813 2,044 .6407 1,309 2,044
4 .0741 3,409 1,023 .5523 565 1,023
$10,398
The tax savings due to MACRS depreciation can also be computed using Exhibit 11-7: .7535 × $46,000 × .30 = $10,398.

11-59 (30 min.)
Investment $(35,000)
Cash operating savings
Annual savings $6,000
Income taxes @ 44% 2,640
After-tax effect on cash $ 3,360
Present value ($3,360 × 6.7101) 22,546
PV of tax savings from depreciation:
Investment × PV factor (Exhibit 11-7) ×
Tax rate = $35,000 × .8617 × .44 13,270*
Overhaul required:
Total cost $ 9,000
Less income tax savings @ 44% 3,960
Total after-tax effect $ 5,040
Present value ($5,040 × .5835) (2,941)
Residual value:
Cash received $ 8,500
Book value 0
Gain $ 8,500
Income tax @ 44% 3,740
Present value ($4,760 × .4632) 2,205
Net present value of all cash flows $ 80
The investment is desirable.
*The PV of the tax savings from depreciation can also be calculated as follows:
Year Tax Savings PV factor Present Value

1 .3333 × $35,000 × .44 = $5,133 .9259 $ 4,752
2 .4445 × 35,000 × .44 = 6,845 .8573 5,868
3 .1481 × 35,000 × .44 = 2,281 .7938 1,810

4 .0741 × 35,000 × .44 = 1,141 .7350 839
11-60 (45-60 min.)
A. Investment: $332,500 + (20 × $15,000) = $632,500
B. PV of cash inflows from operations:

Monthly rental payments = ($380 × 12) + ($440 × 8) = $8,080
Repair and maintenance = .15 × $8,080 = $1,212
Annual before-tax cash inflow = 12 × ($8,080 - $1,212) = $82,416
Annual after-tax cash inflow = .62 × $82,416 = $51,098
Present value of inflows @ 10% = $51,098 × 6.1446 = $313,977
C. PV of tax savings:
Annual depreciation = $632,500 ÷ 27.5 = $23,000
Annual tax savings = $23,000 × .38 = $8,740
PV of tax savings for 10 years = $8,740 × 6.1446 = $53,704
D. PV of cash effects of disposal:

Cash received $980,000
Book value [$632,500 - (10 × $23,000)] 402,500
Gain $577,500
Net cash at disposal ($980,000 - $219,450) $760,550
Time 0 present value ($760,550 × .3855) $293,192
E. Net present value at time 0:

A. Investment $(632,500)
B. PV of operating cash inflows 313,977
C. PV of income tax savings 53,704
D. PV of cash effect of disposal:

PV of net cash received 293,192
The net present value is positive, so the NPV model indicates that Hersch should purchase the apartment complex.

11-61 (15-20 min.) Amounts are in thousands of Japanese yen.
1. Depreciation expense: (¥400,000 - ¥50,000) ÷ 10 = ¥35,000
2. Net income:
Revenues ¥330,000
Less expense:
Depreciation ¥ 35,000
Other 165,000 200,000
Operating income ¥130,000
Less income tax (60%) 78,000
Net income ¥ 52,000
3. Cash flow: ¥52,000 + ¥35,000 = ¥87,000 per year

or ¥330,000 - ¥165,000 - ¥78,000 = ¥87,000
4. Payback period: ¥400,000 ÷ ¥87,000 = 4.6 years
You might note that 4.6 years is a reasonably long payback period for United States companies, and many companies would be
inclined to reject such a project. However, in Japan managers tend to take a longer-run point of view, and a 4.6-year payback
period is often acceptable.
5. Accounting rate of return: ¥52,000 ÷ ¥400,000 = 13%

or, if average investment is used:
(¥400,000 + ¥50,000) ÷ 2 = ¥225,000 average investment;
¥52,000 ÷ ¥225,000 = 23.1%
6. NPV: Annual cash flows, ¥87,000 × 5.2161 ¥453,801

Salvage value, ¥50,000 × 0.2697 13,485
Gross present value ¥467,286
Less: Investment 400,000
Net present value ¥ 67,286

11-62 (50-60 min.)
1.
Table of Cash Flows:
Net Deprec-
End Operating Operating After-Tax iation Net
Of Cash Cash Operating Tax Cash
Year Inflow Outflow Cash Flow Shield Flow
2013 $ 0 $199,500 $(199,500) $0 $(199,500)
2014 100,000 100,000 0 11,400* 11,400
2015 220,000 180,000 24,000** 11,400 35,400
2016 340,000 260,000 48,000 11,400 59,400
2017 460,000 320,000 84,000 11,400 95,400
2018 470,000 280,000 114,000 11,400 125,400
2019 410,000 200,000 126,000 11,400 137,400
2020 150,000 120,000 18,000 11,400 29,400
* ($199,500 ÷ 7) × .4 = $11,400
** ($220,000 - $180,000) × (1 - .4) = $24,000; etc.
Table of Cumulative Cash Flows:

PV Cumulative
End Cumulative
of PV of
Of Net Cash
Net Cash Net Cash
Year Flow
Flow Flow
2013 $(199,500) 1.000 $(199,500) $(199,500)
2014 (188,100) .8475 9,662 (189,838)

2015 (152,700) .7182 25,424 (164,414)
2016 (93,300) .6086 36,151 (128,263)
2017 2,100 .5158 49,207 (79,056)
2018 127,500 .4371 54,812 (24,244)
2019 264,900 .3704 50,893 26,649
2020 294,300 .3139 9,229 35,878
2. The payback time is just under four years as shown by the Cumulative Net Cash Flow column. Because the maximum allowable
payback period is 3 years, DGI would not produce the game if the company uses the payback method.
3. The NPV is $35,878. The project has an NPV greater than zero at a discount rate of 18%. Therefore, the company would produce
the game if it uses the NPV method.
4. The payback model and NPV model lead to different decisions. In general, the NPV method leads to better decisions than the
payback model because the payback model doesn’t measure profitability. Therefore, DGI should probably accept the project and
produce the game. A final recommendation would also depend on other factors such as
 Potential for proprietary position – such as an important patent that provides a market advantage,
 Potential for collaborations and outside funding,
 Need to establish competency in a technology,
 Potential for spin-off products, and
 Need to round out a profitable product line.

11-63 (20-35 min.)
1. $50,000 × 5.3349 factor $266,745

($35,000 + $7,000) × .4665 factor 19,593
Total present value $286,338
Less initial investment:
$251,000 + $7,000 258,000
Net present value (NPV) $ 28,338
2. a. Annual depreciation is ($251,000 - $35,000) ÷ 8 = $27,000

Increase in expected average annual operating income = $50,000 - $27,000
= $23,000
Initial investment is $258,000
Rate of return is $23,000 ÷ $258,000 = 8.9%
b. Note the rate of return is not twice the 8.9%. Why? Because the
investment at the end of eight years is not zero:
Investment at end of 8 years: $35,000 + $7,000 = $ 42,000
Initial investment 258,000
Total $300,000
"Average" investment: $300,000 ÷ 2 = $150,000
Rate of return is $23,000 ÷ $150,000 = 15.3%
3. The model in requirement 1 would induce a positive decision. However, the

8.9% accounting rate of return based on an initial investment might induce a
negative decision because it is less than 10%. An administrator's reluctance to
buy would be understandable if there is no reasonable consistency between the
decision model and the performance evaluation model. If decisions are supposed
to be based on DCF models, and performance is evaluated on accrual accounting
models, the latter tend to be persuasive.

11-64 (20 min.)
1. Investment = $2,200,000 + $1,480,000 = $3,680,000

Annual cash inflow = 300 skiers × 40 days × $65/skier-day = $780,000
Annual cash outflow = (200 days × $500/day)+($9/skier-day × 300 × 40) = $208,000
PV of cash flows @ 14% = ($780,000 - $208,000) × 6.6231 = $3,788,413
NPV = $3,788,413 - $3,680,000 = $108,413
The new lift will create value of $108,413, so it is a profitable investment.
2. After-tax cash flows = $572,000 × .6 = $343,200
PV of after-tax cash flows @ 8% = $343,200 × 9.8181 = $3,369,572
PV of tax savings = $3,680,000 × .4 × .7059 (from Exhibit 11-7) = $1,039,085
NPV after-tax = $3,369,572 + $1,039,085 - $3,680,000 = $728,657
The investment in the lift is more profitable on an after-tax basis than on a pretax
basis.
3. Subjective factors that might affect this decision include:

 Profits on sales of food, rental of equipment, and other items purchased by the
additional skiers.
 More satisfied customers because of less crowding on the days that the additional
lift does not result in additional skiers being attracted to Deer Valley.
 Additional skiers may not be as many as estimated if the weather is poor.

11-65 (30 min.)
Investment $(85,000)
Net cash operating inflows
Annual savings (60,000 – 42,000) $18,000
After-tax effect on cash $12,600
Present value ($12,600 × 5.2161) 65,723
PV of tax savings from depreciation:
$8,000 × .30 × 5.2161 12,519
Residual value of new machine:
Cash received $ 5,000
Book value 5,000
Loss $ 0
Income tax savings @ 30% 0
Total after-tax cash inflow effect $ 5,000
Present value ($5,000 × .2697) 1,349
Disposal of old machine:
Cash received $ 8,000 $ 8,000
Book value 30,000
Loss $22,000
Income tax savings @ 30% 6,600
Total after-tax cash inflow effect $14,600
Present value ($14,600 × 1.000) 14,600
Net present value of all cash flows $ 9,191
The investment is desirable.
11-66 (40-50 min.)
1. See Exhibit 11-66 on the following page for the solution to requirement.
2. The greatest difficulty is the reliability of the numbers in a world of uncertainty.
Although "the numbers" indicate the truck is a favorable alternative, the following
other factors could influence the final decision:
(a) If the back-haul agreement can be canceled by Retro at any time, the truck
becomes a more risky investment since the back-haul revenue is needed to make
the investment produce an after-tax return of 20% or more.
(b) What is the outlook for other investments over the life of the truck investment?
Does purchasing the truck preclude taking advantage of more favorable
opportunities during the 5-year life of the truck?
(c) Does the management have the required expertise to run the truck operation
efficiently?
(d) Will the truck give the company better service than common carriers?
(e) How certain are the predicted cash flows? Are shipment figures and operating
cost predictions considered to be relatively accurate?

EXHIBIT 11-66 Total Present
After-Tax Cash Flows (in dollars)
Value Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

Alternative 1: Continue w/ common carrier
500,000 lbs @ 26¢ $130,000
Inc. tax savings @ 40% (52,000)
After-tax (Year 0) $ 78,000
Adjust $78,000 for 10% inflation
$78,000 × 1.1; × 1.12; × 1.13; × 1.14; × 1.15 (85,800) (94,380) (103,818) (114,200) (125,620)
Present value factor @ 20% .8333 .6944 .5787 .4823 .4019
Present value $(302,679) (71,497) (65,537) (60,079) (55,079) (50,487)
Alternative 2: Purchase truck
Initial cash investment (50,000)
Depreciation deductions:
Year % Deduction Tax Savings
1 20 $ 10,000 $4,000 4,000
2 32 16,000 6,400 6,400
3 19.2 9,600 3,840 3,840
4-5 11.52 5,760 2,304 2,304 2,304
6 5.76 2,880 1,152 1,152
Back-haul revenue*
50 trips** @ $2,400 $120,000
Income tax @ 40% (48,000)
After-tax $ 72,000 72,000 72,000 72,000 72,000 72,000
Cash operating costs:
250,000 miles† @ 90¢ $225,000
Income tax savings (90,000)
$135,000
Adjust $135,000 for inflation after Year 1
$135,000 × 1.1; × 1.12; × 1.13; × 1.14 (135,000) (148,500) (163,350) (179,685) (197,654)
Total cash flow (50,000) (59,000) (70,100) (87,510) (105,381) (123,350) 1,152
Present value factors @ 20% 1.0000 .8333 .6944 .5787 .4823 .4019 .3349
Present value (298,497) (50,000) (49,165) (48,677) (50,642) (50,825) (49,574) 386
PV difference in favor of purchasing truck $ 4,182
*Not subject to inflation due to 5-year agreement. **500,000 lbs ÷ 10,000 lbs/trip = 50 trips 50 trips @ 5,000 round-trip miles = 250,000 miles
†

11-67 (20-30 min.)
1 & 2. See Exhibit 11-67 for the solution to requirements 1 and 2.
3. Correct analysis of inflation can affect decisions. Using a required rate of return
that includes an inflation element but neglecting to adjust cash inflows for
inflation will understate the present value, causing possible rejection of desirable
projects.
11-68 (25-30 min.) Amounts are in Estonian kroons (EEK).
Annual cash savings (EEK 520,000 × 5) EEK 2,600,000

Additional operating expenses (1,800,000)
Net annual savings EEK 800,000
Investment EEK 2,800,000
1. NPV = (EEK 800,000 × 4.9676*) - EEK 2,800,000

= EEK 3,974,080 - EEK 2,800,000
= EEK 1,174,080
*From Table 2, 12% column, 8-year row.
The system should be purchased because the NPV is positive.
2. Pessimistic:
Annual savings = EEK 800,000 - EEK 520,000 = EEK 280,000
Economic life = 5 years
NPV = (EEK 280,000 × 3.6048) - EEK 2,800,000
=EEK 1,009,344 - EEK 2,800,000 = EEK (1,790,656)
Optimistic:
Annual savings = EEK 800,000 + EEK 520,000 = EEK 1,320,000
Economic life = 10 years
NPV = (EEK 1,320,000 × 5.6502) - EEK 2,800,000
= EEK 7,458,264 - EEK 2,800,000 = EEK 4,658,264
Most likely: NPV = EEK 1,174,080 (from requirement 1)
This analysis shows that predictions of savings and economic life can greatly
affect the decision. Although the expected NPV is EEK 1,174,080, it is possible
that the realized NPV might be as low as a negative EEK 1,790,656. It might be
worthwhile to gather more information about the savings and economic life
before making the decision.

EXHIBIT 11-67
14% Total Sketch of Relevant Cash Flows
PV Present (in dollars)
Description Factor Value 20X0 20X1 20X2 20X3 20X4 20X5
1. Per Problem Instructions (But that is

an incorrect analysis, which includes an
inflation element in the discount rate
but does not adjust the predicted cash
flows for inflation.)
Cash operating savings 3.4331 $ 6,866 2,000 2,000 2,000 2,000 2,000
New machine, investment 1.0000 (7,000) (7,000)
Net present value $ (134)
2. Correct Analysis:
(Includes an inflation element in
both the discount rate and the
predicted cash flows.)
Cash operating savings: .8772 $ 1,860 2,120*

.7695 1,729 2,247
.6750 1,608 2,382
.5921 1,495 2,525
.5194 1,390 2,677
$ 8,082
New machine, investment 1.0000 (7,000) (7,000)
*2,000 × 1.06, then 2,000 × (1.06)2, then 2,000 × (1.06)3, etc.

3. Investment in new technology often has many effects that are difficult to quantify. A
special report in Business Week reported that most companies do not provide a
quantitative cost justification for the purchase of computers. However, the article
goes on to point out that analyses such as NPV are being increasingly demanded by
top management to justify investment in new technology.
The company should be concerned with the amount of investment specified. The
system can be purchased for EEK 2,800,000, but might additional costs be incurred
in implementing the system?
Will the quality of design be improved by the new system? Or might the system be
incapable of meeting current standards?
Maybe most important, the analysis is based on the implementation of CAD only. Is
there any chance that the CAM portion will be used? If so, the purchase has more
value than shown in the analysis of CAD only.
11-69 (30-40 min.) This case focuses on the appropriate baseline for NPV analysis for an
investment in a high technology production system. It highlights the possible loss of
competitive position if the company does not undertake the investment. The potential
magnitude of errors from omission of some factors in an NPV analysis is shown.
1. This is a straightforward NPV analysis:
End Present Value Differential Present Value

of @ 12% Net of Differential
Year from Table 1 Cash Flow Cash Flow
2011* 1.0000 $(6,000,000) $(6,000,000)
2012 .8929 (400,000) (357,160)
2013 .7972 1,400,000 1,116,080
2014 .7118 1,400,000 996,520
2015 .6355 1,400,000 889,700
2016 .5674 1,400,000 794,360
2017 .5066 1,400,000 709,240
Total $(1,851,260)
* Or beginning of 2012.
The investment in the CIM has a negative NPV of more than $1,850,000. It appears
that it would be a mistake to invest.

2. An additional advantage of the CIM must be recognized in this analysis. In the
absence of investment in the CIM, some of the existing contribution margin will be
lost each year. Investment avoids this loss, so the amount of the contribution margin
that would have been lost is in essence a savings from investment in the CIM.
The current market share of 40% and sales of $12 million implies that each 1% of the
market is worth sales of $12,000,000 ÷ 40 = $300,000. Current sales are
$12,000,000 and variable costs are $4,000,000 + $2,000,000 = $6,000,000, making
the contribution margin percentage 50%. Therefore, for each $1 of lost sales,
Nashville Tool loses $.50 in contribution margin. The loss of $300,000 in sales
results in a loss of $150,000 in contribution margin.
Therefore, the potential lost contribution margin each year is:
Lost Lost
Year Market Share Lost Sales Contribution Margin
2012 3% $ 900,000 $ 450,000
2013 6% 1,800,000 900,000
2014 9% 2,700,000 1,350,000
2015 12% 3,600,000 1,800,000
2016 15% 4,500,000 2,250,000
2017 18% 5,400,000 2,700,000
Combining the savings from variable costs with the savings in contribution margin,
the NPV becomes a positive $4,017,325, computed as follows:
Present Value Invest. Savings in Total Diff. PV of

@ 12% from and Cost Contribution Cash Diff. Cash
Year Table 1 Savings* Margin Flow Flow
2011 1.0000 $(6,000,000) $(6,000,000) $(6,000,000)
2012 .8929 (400,000) $ 450,000 50,000 44,645
2013 .7972 1,400,000 900,000 2,300,000 1,833,560
2014 .7118 1,400,000 1,350,000 2,750,000 1,957,450
2015 .6355 1,400,000 1,800,000 3,200,000 2,033,600
2016 .5674 1,400,000 2,250,000 3,650,000 2,071,010
2017 .5066 1,400,000 2,700,000 4,100,000 2,077,060
Total $ 4,017,325
*These cost savings are the same as those in part 1 because even though the variable cost of goods sold
declines with the decrease in sales, this only occurs if the CIM investment is not made. If the
investment is made, market share remains constant at 40% ($12,000,000 in revenues) every year, and
thus the cost savings are also a constant $1,400,000 per year.
The picture has changed radically from that in requirement 1. Avoiding the lost
contribution margin has made the CIM a very desirable investment.
3. To the Board of Directors:
I recommend that Nashville Tool invest in the new CIM system. I have made two net
present value analyses, the first one showing a negative NPV of more than

$1,850,000 and the second showing a positive NPV of over $4 million. Let me
explain why the second analysis is better.
The first analysis compares revenues and costs under the CIM to those that would be
incurred if operations continue exactly as they did in 2011. However, if we do not
invest in CIM, operations will not continue the way they are today. Many of our
competitors are investing in technologically sophisticated production systems, and if
we do not invest, they will have advantages over us in quality of products, response
to design changes desired by our customers, and flexibility of delivery schedules.
Investment in the CIM will not only save variable costs of production, it will allow us
to maintain our market share.
The second analysis uses the correct baseline for comparisons. It compares the costs
and revenues with the CIM to those we expect if we do not invest. It includes
consideration of the lost sales, and therefore lost contribution margin, that we would
experience if our competitors gain a competitive advantage by investing in CIM while
we do not. If we do not upgrade to CIM or some similar system in the next six years,
we risk losing nearly half our business. This risk is much greater than that of not
achieving all the cost savings projected for the CIM.
In addition to the items included in my analysis, there are other potential benefits to
investing in the CIM. First, it encourages our employees to think about the
production process and places where we might eliminate or reduce non-value-added
activities. It also introduces technologically sophisticated operations so that future
expansion of similar activities may be easier.
In summary, cost savings alone do not justify investment in the CIM. But cost
savings are not the only advantage of investment. When we add the extra
contribution margins from business we will maintain only if we invest in the CIM,
plus other qualitative advantages, the investment is certainly desirable.

11-70 (30-40 min.)
This problem includes a complex analysis of relevant costs in addition to its focus on
an investment decision. This solution will first identify the relevant costs in four categories:
1. Initial investment
2. Current annual quality control costs
3. Annual quality control costs with new process
4. Forgone profits if quality is not improved
Initial investment:
Worker training $950,000
X-ray machine 250,000
Total investment $1,200,000
Current annual quality control costs:
Inspection cost $ 30,000
Correction of defects (1,500 × $85) 127,500
Refunds to customers (500 × $210) 105,000
Total current quality control costs $ 262,500
Annual quality control costs with new process:

Inspection cost ($30,000 + $60,000) $ 90,000
Correction of defects (450 × $50) 22,500
Refunds to customers (50 × $315) 15,750
Total new quality control costs 128,250
Net savings in quality control costs $ 134,250
Difference in contribution margin if quality is not improved:
2014 $ 0
2015 350,000 (5,000 × $70)
2016 700,000 (10,000 × $70)
2017 1,050,000 (15,000 × $70)
Therefore, the total annual cash flows from the change in the quality control process are:
Differences
Net Savings in Total Net Cash
in Quality Contribution Flow from
Control Costs Margin Operations
2014 $134,250 $ 0 $ 134,250
2015 134,250 350,000 484,250
2016 134,250 700,000 834,250
2017 134,250 1,050,000 1,184,250
The net present value of the investment in the new quality control is positive, so invest:
Total Sketch of annual cash flows

PV of $1 Present
@ 20% Value |–––––––|–––––––|–––––––|–––––––|
0 1 2 3 4
Initial investment 1.0000 $(1,200,000)

Annual cash flows .8333 111,871 <––––134,250
.6944 336,263 <–––––––––––484,250
.5787 482,780 <–––––––––––––––––––834,250
.4823 571,164 <––––––––––––––––––––––––1,184,250

11-71 (60-90 min.)
This is a complex problem because it requires comparing three alternatives. It

reviews Chapter 6 as well as covering several of the topics of Chapter 11. The following
answer uses the total project approach. The total net future cash outflows are shown for each
alternative.
1. Alternative A: Continue to manufacture the parts with the current tools.

Annual cash outlays
Variable cost, $92 × 8,000 $(736,000)
Fixed cost, 1/3 × $45 × 8,000 × .6 (72,000)
Tax savings, .4 × ($736,000 + $72,000) 323,200
After-tax annual cost $(484,800)
Present value, 3.6048 × $484,800 $(1,747,607)
PV of remaining tax savings on MACRS:
11.52% × $2,000,000 × .4 × .8929 82,290
5.76% × $2,000,000 × .4 × .7972 36,735
Total present value of costs, Alternative A $(1,628,582)
Alternative B: Purchase from outside supplier

Annual cash outlays
Purchase cost, $110 × 8,000 $(880,000)
Tax savings, $880,000 × .4 352,000
Present value, $528,000 × 3.6048 $(1,903,334)
Sale of old equipment:
Sales price $ 400,000
Book value [(11.52% + 5.76%) × $2,000,000] 345,600
Gain $ 54,400
Taxes @ 40% (21,760)
Total after-tax effect ($400,000 - $21,760) 378,240
Total present value of costs, Alternative B $(1,525,094)

Alternative C: Purchase new tools
Investment $(1,800,000)
Annual cash outlays
Variable cost, $73 × 8,000 $(584,000)
Fixed cost (same as A) (72,000)
Tax savings, .4 × ($584,000 + $72,000) 262,400
Present value, $393,600 × 3.6048 (1,418,849)
Tax savings on new equipment* 579,217
Effect of disposal of new equipment
Sales price $ 500,000
Book value 0
Gain $500,000
Taxes @ 40% 200,000
Present value, $300,000 × .5674 170,220
Effect of disposal of old equipment (see Alternative B) 378,240
Total present value of costs, Alternative C $(2,091,172)
* Using the MACRS schedule for tax depreciation, the depreciation rate for each year of a 3-
year asset's life is shown in Exhibit 11-6:
Depreciation Tax PV Present

Year Rate Savings Factor Value
1 33.33% .3333 × $1,800,000 × .40 = $239,976 .8929 $214,275
2 44.45% .4445 × 1,800,000 × .40 = 320,040 .7972 255,136
3 14.81% .1481 × 1,800,000 × .40 = 106,632 .7118 75,901
4 7.41% .0741 × 1,800,000 × .40 = 53,352 .6355 33,905
Using Exhibit 11-7, we get .8044 × $1,800,000 × .4 = $579,168, which differs from $579,217
by a $49 rounding error.
The alternative with the lowest present value of cost is Alternative B, purchasing from
the outside supplier.
2. Among the major factors are (1) the range of expected volume (both large increases
and decreases in volume make the purchase of the parts relatively less desirable), (2)
the reliability of the outside supplier, (3) possible changes in material, labor, and
overhead prices, (4) the possibility that the outside supplier can raise prices before the
end of five years, (5) obsolescence of the products and equipment, and (6) alternate
uses of available capacity (alternative uses make Alternative B relatively more
desirable).

11.72 (30 min.)
1. From Note 1, Nike uses the straight-line method for reporting to shareholders. Nike
probably uses MACRS, an accelerated depreciation method, for reporting to tax
authorities because that will maximize the present value of the tax savings from
depreciation.
2. From Note 3, the original cost of Nike’s machinery and equipment is $2,115.0 million.
If Nike invests an average of about $400 million a year, the average useful life would
be just over 5 years: $2,115.0 ÷ 400 = 5.2875 years.
3. Let CF be the minimum average annual pre-tax cash inflow:
$432,000,000 = CF × 3.4331
CF = $125,833,790
4. a) Payback period = $432,000,000 ÷ $125,833,790 = 3.43 years
b) Accounting rate of return:
Income = $125,833,790 – ($432,000,000 ÷ 5) = $39,433,790
Average investment = $432,000,000 ÷ 2 = $216,000,000
Accounting rate of return = $39,433,790 ÷ $216,000,000
= 18.3%
11-73 (20-30 min.) For the solution to this Excel Application Exercise, follow the step-by-step
instructions provided in the textbook chapter.
1. NPV = ($16,000 × 3.2743) - $60,000 = $(7,611)
2. Payback period = $60,000 ÷ 16,000 = 3.75 years
3. The NPV is negative, so do not invest in the machine.
11-74 (20 min.)

The purpose of this exercise is to see how financial analyses and behavioral and
ethical issues interact in decision making. We first present the NPV analysis that should form
the basis of Rossi’s meeting with Sharma. Then we discuss other items that are likely to
surface in the meeting.
To gain a 16% rate of return, the net present value at 16% must be positive. For
Delhi Chicken Soup, optimistic, expected, and pessimistic present values of predicted cash
inflows, assuming cash flows at the end of each year, are (in thousands of dollars):
(1) (2) (3) (4) (5) (6) (7)

Optimistic Expected Pessimistic
PV of Cash Present Cash Present Cash Present
$1 at Flow Value Flow Value Flow Value
Year 16% (1) × (2) (1) × (4) (1) × (6)
1 .8621 800 690 600 517 400 345

2 .7432 1,800 1,338 1,200 892 600 446
3 .6407 2,500 1,602 1,500 961 500 320
4 .5523 4,000 2,209 2,200 1,215 400 221
5 .4761 5,000 2,381 2,600 1,238 200 95

Total 8,220 4,823 1,427
The investment and salvage values do not depend on the optimistic and pessimistic
forecasts:
Investment (1.0000 × $6,000,000) $(6,000,000)
Salvage value of facilities (.4761 × $1,200,000) 571,320
Total $(5,428,680)
Therefore, net present values are:

Optimistic ($8,220,000 - $5,428,680) $ 2,791,320
Expected ($4,823,000 - $5,428,680) $ (605,680)
Pessimistic ($1,427,000 - $5,428,680) $(4,001,680)
If you believe the expected amounts, the product has a negative present value and
should not be launched.
Sharma might raise some of the following issues supporting the project:
 The required rate of return is less than 16%.
 The optimistic scenario is more likely than the pessimistic scenario, making the expected
cash flows more than those listed.
 The cash flow predictions for either the optimistic or pessimistic scenarios (or both) are
understated.
 The contribution margin is 58% rather than 50%.
 The investment is less than $6 million.
For example, he might maintain that the required rate of
return for a project of this risk should be 12% instead of 16%. Then
the product’s expected net present value would be $5,434,000 -
$6,000,000 + (.5674 x $1,200,000) = $114,088:
(1) (2) (3) (4) (5) (6) (7)
Optimistic Expected Pessimistic
PV of Cash Present Cash Present Cash Present
$1 at Flow Value Flow Value Flow Value
Year 12% (1) × (2) (1) × (4) (1) × (6)
1 .8929 800 714 600 536 400 357

2 .7972 1,800 1,435 1,200 957 600 478
3 .7118 2,500 1,780 1,500 1,068 500 356
4 .6355 4,000 2,542 2,200 1,398 400 254
5 .5674 5,000 2,837 2,600 1,475 200 113
Total 9,308 5,434 1,558
Or he might maintain that each expected cash flow should be $200,000 higher,
making the net present value $4,823,000 + ($200,000 × 3.2743) - $5,428,680 = $49,180. Or,

if the contribution margin were 58% rather than 50%, the net present value would be
[$4,823,000 × (58/50)] - $5,428,680 = $166,000. Finally, if the investment is less than
$6,000,000 by at least $605,680, the net present value would be positive.
Sharma could use some combination of these changes to make the net present value
of the product positive.
The ethical issues in this exercise can be revealing. If Rossi believes her information
is accurate, it would be unethical to produce biased numbers just to satisfy Sharma. Among
the ethical requirements for management accountants are to “communicate information fairly
and objectively,” “disclose fully all relevant information,” and “prepare concise and clear
reports and recommendations after appropriate analyses of relevant and reliable information.”
These standards would be violated if Rossi were to change her analysis just to satisfy Sharma.
Therefore, Rossi should report numbers that she believes are accurate. This may
upset her supervisor, Sharma, and that may create problems for Rossi. Nevertheless, using
biased information to justify a manager’s pet projects can create more serious problems.
11-75 (35-50 min.) NOTE TO INSTRUCTOR: This solution is based on the web site as it
was in late 2012. Be sure to examine the current web site before assigning this problem, as
the information there may have changed.
1. Carnival Corporation operates 100 cruise ships under the following lines: Carnival
Cruise Lines, Holland America Line, Princess Cruises and Seabourn in North
America; P&O Cruises, and Cunard Line in the United Kingdom; AIDA in Germany;
Costa Cruises in Southern Europe; Iberocruceros in Spain; and P&O Cruises in
Australia. At the time this solution was prepared, Carnival planned to add 9 new
cruise ships by March 2016, reflecting plans for significant growth in business.
2. From Carnival’s 2011 Annual Report, its capacity (defined as available berths) has
increased each of the last five years:
Passengers Carried Passenger Capacity (# of berths)
2007: 7,672,000 158,352
2008: 8,183,000 169,040
2009: 8,519,000 180,746
2010: 9,147,000 191,464
2011: 9,559,000 195,872
The passengers carried (capacity used) and capacity increased by about 24% from
2007 to 2011.
3. Carnival continues to expand its fleet, though some of the new vessels will replace
older ships. It has a total of 10 new vessels on order. Three of the ships will be
delivered in 2012 and the remaining 7 will be delivered at a rate of 2 or 3 per year.
4. In 2011, Carnival invested $2.7 billion in property and equipment, and Carnival used
about $1.1 billion of cash for financing activities, paying off short-term and long-term
debt, paying dividends, and purchasing treasury stock during the year. About $3.8
billion of cash was generated by operating activities.

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CHAPTER 11

COVERAGE OF LEARNING OBJECTIVES

Copyright ©2014 Pearson Education, Inc., Publishing as Prentice Hall. 193

11-A2 (20-30 min.) This is a straightforward exercise.

Sketch of Cash Flows

11-A3 (20-30 min.) This is a straightforward exercise.

1. The model indicates that the servers should not be acquired.

Sketch of Cash Flows

Copyright ©2014 Pearson Education, Inc., Publishing as Prentice Hall. 194

11-A4 (25-30 min.)

1. Cash effects of operations:

Cash effects of depreciation*:

Year Tax Savings** PV factor Present Value

Copyright ©2014 Pearson Education, Inc., Publishing as Prentice Hall. 195

11-A5 (5-10 min.)

(a) Cash sale price 305,000 230,000

Effect on cash income taxes at 25%:

Total after-tax effect on cash

Copyright ©2014 Pearson Education, Inc., Publishing as Prentice Hall. 196

2. Use Table 2: (a) PV = $50,000 × 3.4651 = $173,255

3. Use Table 2: (a) PV = annual withdrawal × F

(b) PV = annual withdrawal × F

Present Value Present Value Present Value

11-B2 (20-30 min.) This is a straightforward exercise.

Copyright ©2014 Pearson Education, Inc., Publishing as Prentice Hall. 197

1. The model indicates that the equipment should not be acquired.

Sketch of Cash Flows

After-tax impact of disposal on cash:

3. Applying 10% discount factors:

Copyright ©2014 Pearson Education, Inc., Publishing as Prentice Hall. 198

1. See Exhibit 11-B4 on the following page for requirement 1.

PV @ 10% of 6 years of $41,250 4.3553 × 41,250 $ 179,656

11-B5 (5-10 min.)

(a) Cash sale price 35,000 85,000

Effect on cash income taxes at 30%:

Total after-tax effect on cash

Copyright ©2014 Pearson Education, Inc., Publishing as Prentice Hall. 199

Cash effects on operations,

Copyright ©2014 Pearson Education, Inc., Publishing as Prentice Hall. 200

Copyright ©2014 Pearson Education, Inc., Publishing as Prentice Hall. 201

11-14 No. Companies have an obligation to shareholders to avoid taxes where it is

11-20 It is useful to learn the "payback" and "accounting rate-of-return" methods of

Copyright ©2014 Pearson Education, Inc., Publishing as Prentice Hall. 202

11-22 If a company makes capital-budgeting decisions using DCF and evaluates

11-25 It is difficult to predict the cash flows to be received from an investment in

Copyright ©2014 Pearson Education, Inc., Publishing as Prentice Hall. 203

11-29 (10-15 min.)

In particular, note that Bank of America is willing to lend more than in

Copyright ©2014 Pearson Education, Inc., Publishing as Prentice Hall. 204

11-31 (10-20 min.)

1. a. PV = $250,000 × .6806 = $170,150

2. The annual rates would be halved and the periods doubled.

a. PV = $250,000 × .6756 = $168,900

3. Present values rise because the money is repaid more quickly:

a. PV = $50,000 × 3.9927 = $199,635

11-32 (10-15 min.)

1. $300,000 = Future amount × .6830

Future amount = $300,000 ÷ .6830

2. $300,000 = Annual installments × 3.1699