Ch14sol cash flow estimation

Harcourt, Inc. items and derived items copyright © 2002 by Harcourt, Inc. Answers and Solutions: 14 - 1
Chapter 14
Cash Flow Estimation and Risk Analysis
ANSWERS TO END-OF-CHAPTER QUESTIONS
14-1 a. Cash flow, which is the relevant financial variable, represents the
actual flow of cash. Accounting income, on the other hand, reports
accounting data as defined by Generally Accepted Accounting Principles
(GAAP).
b. Incremental cash flows are those cash flows that arise solely from the
asset that is being evaluated. For example, assume an existing machine
generates revenues of $1,000 per year and expenses of $600 per year. A
machine being considered as a replacement would generate revenues of
$1,000 per year and expenses of $400 per year. On an incremental
basis, the new machine would not increase revenues at all, but would
decrease expenses by $200 per year. Thus, the annual incremental cash
flow is a before-tax savings of $200. A sunk cost is one that has
already occurred and is not affected by the capital project decision.
Sunk costs are not relevant to capital budgeting decisions. Within the
context of this chapter, an opportunity cost is a cash flow which a
firm must forgo to accept a project. For example, if the project
requires the use of a building which could otherwise be sold, the
market value of the building is an opportunity cost of the project.
c. Net operating working capital changes are the increases in current
operating assets resulting from accepting a project less the resulting
increases in current operting liabilities, or accruals and accounts
payable. A net operating working capital change must be financed just
as a firm must finance its increases in fixed assets.
d. Salvage value is the market value of an asset after its useful life.
Salvage values and their tax effects must be included in project cash
flow estimation.
e. The real rate of return (kr), or, for that matter the real cost of
capital, contains no adjustment for expected inflation. If net cash
flows from a project do not include inflation adjustments, then the
cash flows should be discounted at the real cost of capital. In a
similar manner, the IRR resulting from real net cash flows should be
compared with the real cost of capital. Conversely, the nominal rate
of return (kn) does include an inflation adjustment (premium). Thus if
nominal rates of return are used in the capital budgeting process, the
net cash flows must also be nominal.
f. Sensitivity analysis indicates exactly how much NPV will change in

Answers and Solutions: 14 - 2 Harcourt, Inc. items and derived items copyright © 2002 by Harcourt, Inc.
response to a given change in an input variable, other things held
constant. Sensitivity analysis is sometimes called “what if” analysis
because it answers this type of question.
g. A firm’s worst-case scenario is when all of the variables used in an
analysis are set at their worst reasonably forecasted values. On the
other hand, a best-case scenario sets all input variables at their best
reasonably forecasted values. The worst-and best-case scenarios are
then compared to a base-case in which input values are set at their
most likely values.
h. Scenario analysis is a shorter version of simulation analysis that uses
only a few outcomes. Often the outcomes considered are optimistic,
pessimistic and most likely.
i. Monte Carlo simulation analysis is a risk analysis technique in which a
computer is used to simulate probable future events and thus to
estimate the profitability and risk of a project.
j. The coefficient of variation is a standardized risk measure, obtained
by dividing the standard deviation of a variable by the expected value
of that variable. Since the coefficient of variation is standardized,
it can be used to compare the relative stand-alone risk of projects
which differ in NPV size. The standard deviation measures the
variability of the distribution about the expected value.
k. Corporate diversification involves acquiring assets whose returns are
not highly correlated with the firm’s other assets. The major stated
objectives of corporate diversification are to stabilize earnings and
reduce corporate risk. Stockholder diversification occurs when
stockholders hold a well-diversified portfolio of many companies.
There is some disagreement over the benefits of corporate diversifi-
cation to reduce risk when investors can accomplish the same result
more easily. Under some circumstances, however, diversification
benefits may only arise from corporate diversification.
l. A risk-adjusted discount rate incorporates the riskiness of the
project’s cash flows. The cost of capital to the firm reflects the
average risk of the firm’s existing projects. Thus, new projects that
are riskier than existing projects should have a higher risk-adjusted
discount rate. Conversely, projects with less risk should have a lower
risk-adjusted discount rate. This adjustment process also applies to a
firm’s divisions. Risk differences are difficult to quantify, thus
risk adjustments are often subjective in nature. A project’s cost of
capital is its risk-adjusted discount rate for that project.
14-2 Only cash can be spent or reinvested, and since accounting profits do not
represent cash, they are of less fundamental importance than cash flows
for investment analysis. Recall that in the stock valuation chapters we
focused on dividends and free cash flows, which represent cash flows,
rather than on earnings per share, which represent accounting profits.

14-3 Since the cost of capital includes a premium for expected inflation,
failure to adjust cash flows means that the denominator, but not the
numerator, rises with inflation, and this lowers the calculated NPV.
14-4 Capital budgeting analysis should only include those cash flows which will
be affected by the decision. Sunk costs are unrecoverable and cannot be
changed, so they have no bearing on the capital budgeting decision.
Opportunity costs represent the cash flows the firm gives up by investing
in this project rather than its next best alternative, and externalities
are the cash flows (both positive and negative) to other projects that
result from the firm taking on this project. These cash flows occur only
because the firm took on the capital budgeting project; therefore, they
must be included in the analysis.
14-5 When a firm takes on a new capital budgeting project, it typically must
increase its investment in receivables and inventories, over and above the
increase in payables and accruals, thus increasing its net operating
working capital. Since this increase must be financed, it is included as
an outflow in Year 0 of the analysis. At the end of the project’s life,
inventories are depleted and receivables are collected. Thus, there is a
decrease in NOWC, which is treated as an inflow.
14-6 Simulation analysis involves working with continuous probability
distributions, and the output of a simulation analysis is a distribution
of net present values or rates of return. Scenario analysis involves
picking several points on the various probability distributions and
determining cash flows or rates of return for these points. Sensitivity
analysis involves determining the extent to which cash flows change, given
a change in one particular input variable. Simulation analysis is
expensive. Therefore, it would more than likely be employed in the
decision for the $200 million investment in a satellite system than in the
decision for the $12,000 truck.
14-7 Beta (market) risk refers to the project’s effect on the corporate beta
coefficient. Within-firm (corporate) risk refers to the project’s effect
on the stability of the firm’s earnings. Stand-alone risk refers to the
inherent riskiness of the project’s expected returns when viewed alone.
Theoretically, beta (market) risk should be given greater weight for
publicly held firms, but from a practical standpoint, within-firm
(corporate) risk is probably considered more important.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS
14-1 Equipment $ 9,000,000
NWC Investment 3,000,000
Initial investment outlay $12,000,000
14-2 Operating Cash Flows: t = 1
Sales revenues $10,000,000
Operating costs 7,000,000
Depreciation 2,000,000
Operating income before taxes $ 1,000,000
Taxes (40%) 400,000
Operating income after taxes $ 600,000
Add back depreciation 2,000,000
Operating cash flow $ 2,600,000
14-3 Equipment's original cost $20,000,000
Depreciation (80%) 16,000,000
Book value $ 4,000,000
Gain on sale = $5,000,000 - $4,000,000 = $1,000,000.
Tax on gain = $1,000,000(0.4) = $400,000.
AT net salvage value = $5,000,000 - $400,000 = $4,600,000.
14-4 a. The net cost is $126,000:
Price ($108,000)
Modification (12,500)
Increase in NWC (5,500)
Cash outlay for new machine ($126,000)
b. The operating cash flows follow:
Year 1 Year 2 Year 3
1. After-tax savings $28,600 $28,600 $28,600
2. Depreciation tax savings 13,918 18,979 6,326
Net cash flow $42,518 $47,579 $34,926
Notes:
1. The after-tax cost savings is $44,000(1 - T) = $44,000(0.65)
= $28,600.
2. The depreciation expense in each year is the depreciable basis,
$120,500, times the MACRS allowance percentages of 0.33, 0.45, and

0.15 for Years 1, 2, and 3, respectively. Depreciation expense in
Years 1, 2, and 3 is $39,765, $54,225, and $18,075. The
depreciation tax savings is calculated as the tax rate (35%) times
the depreciation expense in each year.
c. The terminal year cash flow is $50,702:
Salvage value $65,000
Tax on SV* (19,798)
Return of NWC 5,500
$50,702
BV in Year 4 = $120,500(0.07) = $8,435.
*Tax on SV = ($65,000 - $8,435)(0.35) = $19,798.
d. The project has an NPV of $10,841; thus, it should be accepted.
Year Net Cash Flow PV @ 12%
0 ($126,000) ($126,000)
1 42,518 37,963
2 47,579 37,930
3 85,628 60,948
NPV = $ 10,841
Alternatively, place the cash flows on a time line:
0 1 2 3
| | | |
-126,000 42,518 47,579 34,926
50,702
85,628
With a financial calculator, input the appropriate cash flows into the
cash flow register, input I = 12, and then solve for NPV = $10,841.
14-5 Year MACRS S-L Dep ∆Dep T(∆Dep)
0 0 0 0 0
1 $5,000,000 $5,000,000 0 0
2 9,000,000 5,000,000 $4,000,000 $1,360,000
3 7,000,000 5,000,000 2,000,000 680,000
4 6,000,000 5,000,000 1,000,000 340,000
5 4,500,000 5,000,000 ( 500,000) ( 170,000)
6 3,500,000 5,000,000 (1,500,000) ( 510,000)
7 3,500,000 5,000,000 (1,500,000) ( 510,000)
8 3,500,000 5,000,000 (1,500,000) ( 510,000)
9 3,500,000 5,000,000 (1,500,000) ( 510,000)
10 3,000,000 5,000,000 (2,000,000) ( 680,000)
11 1,500,000 0 1,500,000 510,000
PV @ 10% = $674,311
12%

With a financial calculator, input the following: CF0 = 0, CF1 = 0,
CF2 = 1360000, CF3 = 680000, CF4 = 340000, CF5 = -170000, CF6 = -510000, Nj
= 4, CF10 = -680000, CF11 = 510000, and I = 10 to solve for NPV =
$674,310.51.
Therefore, the value of the firm would increase by $674,311, each year,
if it elected to use standard MACRS depreciation rates.
14-6 a. The net cost is $89,000:
Price ($70,000)
Change in NWC (4,000)
($89,000)
After-tax savings $15,000 $15,000 $15,000
Depreciation shield 11,220 15,300 5,100
Net cash flow $26,220 $30,300 $20,100
Notes:
1. The after-tax cost savings is $25,000(1 – T) = $25,000(0.6)
= $15,000.
$85,000, times the MACRS allowance percentage of 0.33, 0.45, and
0.15 for Years 1, 2 and 3, respectively. Depreciation expense in
depreciation shield is calculated as the tax rate (40%) times the
depreciation expense in each year.
c. The additional end-of-project cash flow is $24,380:
Tax on SV* (9,620)
Return of NWC 4,000
$24,380
*Tax on SV = ($30,000 - $5,950)(0.4) = $9,620.
Note that the remaining BV in Year 4 = $85,000(0.07) = $5,950.
d. The project has an NPV of -$6,705. Thus, it should not be accepted.
0 ($89,000) ($89,000)
1 26,220 23,836
2 30,300 25,041
3 44,480 33,418

NPV = ($ 6,705)
Alternatively, with a financial calculator, input the following: CF0 =
-89000, CF1 = 26220, CF2 = 30300, CF3 = 44480, and I = 10 to solve for
NPV = -$6,703.83.
14-7 a. Sales = 1,000($138) $138,000
Cost = 1,000($105) 105,000
Net before tax $ 33,000
Taxes (34%) 11,220
Net after tax $ 21,780
Not considering inflation, NPV is -$4,800. This value is calculated as
-$150,000 +
15.0
780,21$
= -$4,800.
Considering inflation, the real cost of capital is calculated as
follows:
(1 + kr)(1 + i) = 1.15
(1 + kr)(1.06) = 1.15
kr = 0.0849.
Thus, the NPV considering inflation is calculated as
-$150,000 +
0849.0
780,21$
= $106,537.
After adjusting for expected inflation, we see that the project has a
positive NPV and should be accepted. This demonstrates the bias that
inflation can induce into the capital budgeting process: Inflation is
already reflected in the denominator (the cost of capital), so it must
also be reflected in the numerator.
b. If part of the costs were fixed, and hence did not rise with inflation,
then sales revenues would rise faster than total costs. However, when
the plant wears out and must be replaced, inflation will cause the
replacement cost to jump, necessitating a sharp output price increase
to cover the now higher depreciation charges.
14-8 E(NPV) = 0.05(-$70) + 0.20(-$25) + 0.50($12) + 0.20($20) + 0.05($30)
= -$3.5 + -$5.0 + $6.0 + $4.0 + $1.5
= $3.0 million.
σNPV = [0.05(-$70 - $3)2
+ 0.20(-$25 - $3)2
+ 0.50($12 - $3)2
+ 0.20($20 - $3)2
+ 0.05($30 - $3)2
]
= $23.622 million.
CV =
$3.0
$23.622
= 7.874.

14-9 a. Expected annual cash flows:
Project A: Probable
Probability × Cash Flow = Cash Flow
0.2 $6,000 $1,200
0.6 6,750 4,050
0.2 7,500 1,500
Expected annual cash flow = $6,750
Project B: Probable
Probability × Cash Flow = Cash Flow
0.2 $ 0 $ 0
0.6 6,750 4,050
0.2 18,000 3,600
Expected annual cash flow = $7,650
Coefficient of variation:
CV =
NPVExpected
=
valueExpected
deviationStandard NPVσ
Project A:
σA = $474.34.=(0.2))($750+(0.6))($0+(0.2))(-$750 222
Project B:
σB = (0.2))($10,350+(0.6))(-$900+(0.2))(-$7,650 222
= $5,797.84.
CVA = $474.34/$6,750 = 0.0703.
CVB = $5,797.84/$7,650 = 0.7579.
b. Project B is the riskier project because it has the greater variability
in its probable cash flows, whether measured by the standard deviation
or the coefficient of variation. Hence, Project B is evaluated at the
12 percent cost of capital, while Project A requires only a 10 percent
cost of capital.
Project A: With a financial calculator, input the appropriate cash
flows into the cash flow register, input I = 10, and then solve for
NPV = $10,036.25.
Project B: With a financial calculator, input the appropriate cash
flows into the cash flow register, input I = 12, and then solve for NPV
= $11,624.01.
Project B has the higher NPV; therefore, the firm should accept
Project B.

c. The portfolio effects from Project B would tend to make it less risky
than otherwise. This would tend to reinforce the decision to accept
Project B. Again, if Project B were negatively correlated with the GDP
(Project B is profitable when the economy is down), then it is less
risky and Project B’s acceptance is reinforced.
14-10 a. First, note that with symmetric probability distributions, the middle
value of each distribution is the expected value. Therefore,
Expected Values
Sales (units) 200
Sales price $13,500
Sales in dollars $2,700,000
Costs (200 x $6,000) 1,200,000
Earnings before taxes $1,500,000
Taxes (40%) 600,000
Net income $ 900,000 = Cash flow under the
assumption used in the
problem.
0 = ∑= +
8
1t
t
)IRR1(
000,900$
- $4,000,000.
Using a financial calculator, input the following: CF0 = -4000000,
CF1 = 900000, and Nj = 8, to solve for IRR = 15.29%.
Expected IRR = 15.29% 15.3%.
Assuming complete independence between the distributions, and
normality, it would be possible to derive σIRR statistically.
Alternatively, we could employ simulation to develop a distribution of
IRRs, hence σIRR. There is no easy way to get σIRR.
b. NPV = $900,000(PVIFA15%,8) - $4,000,000.
Using a financial calculator, input the following: CF0 = -4000000,
CF1 = 900000, Nj = 8, and I = 15 to solve for NPV = $38,589.36. Again,
there is no easy way to estimate σNPV.
c. (1) a. Calculate developmental costs. The 44 random number value,
coming between 30 and 70, indicates that the costs for this run
should be taken to be $4 million.
b. Calculate the project life. The 17, being less than 20,
indicates that a 3-year life should be used.
(2) a. Estimate unit sales. The 16 indicates sales of 100 units.

b. Estimate the sales price. The 58 indicates a sales price of
$13,500.
c. Estimate the cost per unit. The 1 indicates a cost of $5,000.
d. Now estimate the after-tax cash flow for Year 1. It is
[100($13,500) - 100($5,000)](1 - 0.4) = $510,000 = CF1.
(3) Repeat the process for Year 2. Sales will be 200 with a random
number of 79; the price will be $13,500 with a random number of 83;
and the cost will be $7,000 with a random number of 86:
[200($13,500) - 200($7,000)](0.6) = $780,000 = CF2.
(4) Repeat the process for Year 3. Sales will be 100 units with a
random number of 19; the price will be $13,500 with a random number
of 62; and the cost will be $5,000 with a random number of 6:
[100($13,500) - 100($5,000)](0.6) = $510,000 = CF3.
(5) a. 0 = 321
)IRR1(
000,510$
)IRR1(
000,780$
)IRR1(
000,510$
+
+
+
+
+
- $4,000,000
IRR = -31.55%.
Alternatively, with a financial calculator, input the
following: CF0 = -4000000, CF1 = 510000, CF2 = 780000, CF3 =
510000, and solve for IRR = -31.55%.
b. NPV = 321
)15.1(
000,510$
)15.1(
000,780$
)15.1(
000,510$
++ - $4,000,000.
With a financial calculator, input the following: CF0 =
-4000000, CF1 = 510000, CF2 = 780000, CF3 = 510000, and I = 15
to solve for NPV = -$2,631,396.40.
The results of this run are very bad because the project’s
life is so short. Had the life turned out (by chance) to be
13 years, the longest possible life, the IRR would have been
about 25%, and the NPV would have been about $1 million.
(6) & (7) The computer would store σNPVs and σIRRs for the different
trials, then display them as frequency distributions:

Probability
of occurrence
X
XX
XXXX
XXXXXXXX
XXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXX
0 E(NPV) NPV
Probability
of occurrence
X
XX
XXXX
XXXXXXXX
XXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXX
0 E(NPV) NPV
The distribution would be reasonably symmetrical because all
the input data were from symmetrical distributions. One
often finds, however, that the input and output
distributions are badly skewed. The frequency values would
also be used to calculate σNPV and σIRR; these values would be
printed out and available for analysis.
d. It’s not strange--the risk analysis should be used as a basis for
setting the cost of capital for use in the NPV method. What can be
done is to discount at the risk-free rate to get an NPV which simply
reflects the timing of cash flows, then to use the variability of this
NPV distribution to establish the project’s riskiness, and finally to
conduct a second simulation with a risk-adjusted cost of capital before
making the final go/no-go decision on the project.
e. Dependence among the variables listed could either decrease or increase
the dispersion of the NPV distribution, depending on the type of
correlations assumed. For example, if we assume that high unit sales
are associated with strong market prices, and that high volume brings
low unit costs because of scale economies, then the NPV would probably
widen. If we assume intertemporal dependence--for example, that strong
demand in Year 1 signifies good product acceptance, hence strong sales
in Years 2 to n, this will definitely increase NPV and IRR, because
good and bad events will not cancel one another out, but will be
reinforcing. However, if we assume that low prices will produce high
unit sales, then FNPV would probably decrease.
f. The biggest problem is getting good data on probability distributions,
and especially on correlations among the input variables such as among
unit sales, sales prices, and unit costs. The second major problem is

a conceptual one--this type of analysis does not deal at all with
market (or beta) risk. A project with a high FNPV or FIRR may not be
strongly correlated with “the market,” or may even be negatively
correlated, making FNPV and FIRR not very useful as an indicator of risk.

Harcourt, Inc. items and derived items copyright © 2002 by Harcourt, Inc. Solution to Spreadsheet Problems: 14 - 13
SOLUTION TO SPREADSHEET PROBLEMS
14-11 The detailed solution for the problem is available both on the
instructor’s resource CD-ROM (in the file Solution for Ch 14-11 Build a
Model.xls) and on the instructor’s side of the Harcourt College
Publishers’ web site, http://www.harcourtcollege.com/finance/theory10e.
14-12 a. The net cost is $212,500:
Price ($180,000)
Change in NWC (7,500)
($212,500)
1. After-tax savings $49,500 $49,500 $49,500
2. Depreciation tax savings 23,001 31,365 10,455
Net cash flow $72,501 $80,865 $59,955
Notes:
1. The after-tax cost savings is $75,000(1 - T) = $75,000(0.66)
= $49,500.
$205,000, times the MACRS allowance percentage of 0.33, 0.45, and
0.15 for Years 1, 2 and 3, respectively. Depreciation expense in
depreciation shield is calculated as the tax rate (34%) times the
depreciation expense in each year.
c. The end-of-project net cash flow is $65,179:
Tax on SV* (22,321)
Return of NWC 7,500
$65,179
*Tax on SV = ($80,000 - $14,350)(0.34) = $22,321.
BV in Year 4 = $205,000(0.07) = $14,350.
d. The project has an NPV of $14,256; thus, it should be accepted.
0 ($212,500) ($212,500)
1 72,501 65,910
2 80,865 66,831
3 125,134 94,015
NPV = $ 14,256

Solution to Spreadsheet Problems: 14 - 14 Harcourt, Inc. items and derived items copyright © 2002 by Harcourt, Inc.
Alternatively, using a financial calculator, input the following: CF0 =
-212500, CF1 = 72501, CF2 = 80865, CF3 = 125134, and I = 10 to solve for
NPV = $14,255.60.
e. (1) NPV = $5,766 at k = 12%; (2) NPV = $23,295 at k = 8%.
f. NPV = ($620) and $19,214. If the salvage value were as low as $50,000,
the NPV would be negative; therefore, the uncertainty about the salvage
value could cause the project to be rejected. A salvage value of
$51,251 (rounded to $51,000) would make you indifferent to the project.
g. NPV = $5,256 if the tax rate were changed to 46%.
h. When the base price of the machine is increased to $200,000, the NPV is
($52). You would be indifferent to the project at a machine cost of
$199,928 (rounded to $199,900).
14-13 a. Nominal WACC:
kn = WACC = wdkd(1 - T) + wceks = 0.5(12%)(1 - 0.4) + 0.5(16%)
= 3.6% + 8.0% = 11.6%.
Real WACC:
kr = (kn - i)/(1 + i) = (11.6% - 6%)/(1 + 0.06) = 5.6%/1.06 = 5.28%.
b. The relevant real cash flows are:
0 1 2 3
($18,800) $5,100a
$5,100 $5,100
2,482b
3,384 1,128
($18,800) $7,582 $8,484 $6,228
a
(R - VC - FC)(1 - T) = ($30,000 - $15,000 - $6,500)(0.60) = $5,100.
b
(Dep)(T) = $6,204(0.4) = $2,482.
When calculating the NPV based upon real cash flows, the firm's real
WACC should be utilized. If the nominal WACC were used, the discount
rate would include an inflation premium, while the cash flows would
not. The calculation would bias NPV downward.
c. Using a financial calculator, input the following: CF0 = -18800,
CF1 = 7582, CF2 = 8484, CF3 = 6228, and I = 5.28 to solve for NPV =
$1,393.28 $1,393. Therefore, the project should be accepted. If the
analyst had used the nominal WACC with real cash flows, an erroneous
reject decision would have been made.
NPVat 5.28% = -$18,800 + 1
)0528.1(
582,7$
+ 2
)0528.1(
484,8$
+
)0528.1(
228,6$
= $1,392.
NPVat 11.6% = -$18,800 + 1
)116.1(
582,7$
+ 2
)116.1(
484,8$
+ 3
)116.1(
228,6$
= $-713.7.

d. First, we must determine the relevant nominal cash flows:
0 1 2 3
Investment ($18,800)
Rev $31,800 $33,708 $35,730
VC 15,900 16,854 17,865
FC 6,890 7,303 7,742
Net Rev $ 9,010 $ 9,551 $10,123
Net Rev (1 - T) $ 5,406 $ 5,731 $ 6,074
Dep (T) 2,482 3,384 1,128
Net CF $ 7,888 $ 9,115 $ 7,202
Now, since these are nominal cash flows, the NPV can be found using the
nominal WACC:
NPV = -$18,800 + 1
)116.1(
888,7$
+ 2
)116.1(
115,9$
+ 3
)116.1(
202,7$
= $768.
Alternatively, with a financial calculator, input the following: CF0 =
-18800, CF1 = 7888, CF2 = 9115, CF3 = 7202, and I = 11.6 to solve for
NPV = $768.26.
The NPV is less than that found in Part c because the depreciation
savings do not increase with inflation.
e. The relevant after-tax cash flows are:
0 1 2 3
Investment ($18,800)
Rev $31,800 $33,708 $35,730
VC 16,125 17,334 18,634
FC 6,988 7,512 8,075
Net Rev $ 8,687 $ 8,862 $ 9,021
Net Rev (1 - T) $ 5,212 $ 5,317 $ 5,413
Dep (T) 2,482 3,384 1,128
Net CF $ 7,694 $ 8,701 $ 6,541
With a financial calculator, input the following: CF0 = -18800, CF1 =
7694, CF2 = 8701, CF3 = 6541, and I = 11.6 to solve for NPV = -$213.54
-$214.
The unanticipated inflation premium would have caused the project's
NPV to decrease from $768 (as calculated in part d) to -$214. This
would have caused the project to decrease the value of the firm by
$214.
f. (1) Biases would occur--projects' cash flows would not be adjusted for
inflation, but the market cost of capital would be, hence NPVs
would be downward biased.
(2) Long-term projects would have a greater downward bias because of
the compounding in the denominator of the NPV equation.
(3) Cash flows should be adjusted to reflect expected inflation.

14-14 a. If the actual life is 5 years:
Amount Amount Year PV Factor
before tax after tax Event Occurs at 10% PV
Outflows:
Investment in
new equipment $30,000 $30,000 0 1.0 $30,000
Total PV of outflows $30,000
Inflows:
Revenues $10,000 $ 6,000 1-5 3.7908 $22,745
Depreciation 6,000 2,400 1-5 3.7908 9,098
Total PV of inflows $31,843
NPV = PV(Inflows) - PV(Outflows) $ 1,843
Alternatively, using a financial calculator:
Inputs 5 10 8400 0
Output = -31,842.61
NPV = PV(Inflows) – PV(Outflows) = $31,843 - $30,000 = $1,843.
If the actual life is 4 years:
Inflows:
Revenues $10,000 $6,000 1-4 3.1699 $19,019
Depreciation 6,000 2,400 1-4 3.1699 7,608
Tax savings on loss
at end of Year 4 6,000 2,400 4 0.6830 1,639
Total PV of inflows $28,266
NPV = $28,266 - $30,000 = ($1,734).
Alternatively, using a financial calculator, input the following:
CF0 = -30000, CF1 = 8400, Nj = 3, CF4 = 10800, and I = 10 to solve for
NPV = -$1,733.90 -$1,734.
N I FVPMTPV

If the actual life is 8 years:
Inflows:
Revenues $10,000 $6,000 1-8 5.3349 $32,009
Depreciation 6,000 2,400 1-5 3.7908 9,098
Total PV of Inflows $41,107
NPV = $41,107 - $30,000 = $11,107.
Alternatively, using a financial calculator, input the following:
CF0 = -30000, CF1 = 8400, Nj = 5, CF4 = 6000, Nj = 3, and I = 10 to solve
for NPV = $11,107.45 $11,107.
If the life is as low as 4 years (an unlikely event), the
investment will not be desirable. But, if the investment life is
longer than 4 years, the investment will be a good one. Therefore, the
decision will depend on the directors’ confidence in the life of the
tractor. Given the low probability of the tractor’s life being only 4
years, it is likely that the directors will decide to purchase the
tractor.
b. 8% cost of capital; NPV = $3,539. 12% cost of capital; NPV = $280.
NPV is still positive at a 12% cost of capital; therefore, the tractor
should be purchased. The project is not very sensitive because when
the cost of capital is increased by 4% NPV is still positive.
c. At $7,000 operating revenue, NPV = ($4,981). At $13,000 operating
revenue, NPV = $8,666.
With a project life of one year, NPV = ($13,636). With a project life
of ten years, NPV = $15,965.
4% cost of capital; NPV = $7,395. 16% cost of capital; NPV = ($2,496).

NPV
NPV
(Thousandsof$)
10
8
5
3
1
(5)
(3)
7
6
9
4
2
0
(6)
(4)
(2)
(1)
7 9
Pre-tax Revenues
(Thousands of $)
11 13
Sensitivity Diagram
Sensitivity Diagram
NPV vs. Project Life
15
10
20
5
0
(15)
(10)
(5)
97531
NPV
(Thousandsof$)
Project Life
(Years)
NPV
NPV
(Thousandsof$)
Sensitivity Diagram
NPV vs. Cost of Capital
7
5
9
3
1
(3)
(2)
(1)
6
4
8
2
0
1412 1610864
Cost of Capital
(%)
NPV

Harcourt, Inc. items and derived items copyright © 2002 by Harcourt, Inc. Solution to Cyberproblem: 14 - 19
CYBERPROBLEM
14-15 The detailed solution for the cyberproblem is available on the
instructor’s side of the Harcourt College Publishers’ web site:
http://www.harcourtcollege.com/finance/theory10e.

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