Financial Management Chapter 11 IM 10th Ed

8/2/2019 Financial Management Chapter 11 IM 10th Ed

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Prof. Rushen Chahal

CHAPTER 11

Capital Budgetingand Risk Analysis

CHAPTER ORIENTATION

The focus of this chapter will be on how to adjust for the riskiness of a given project orcombination of projects.

CHAPTER OUTLINE

I. Risk and the investment decision

A. Up to this point we have treated the expected cash flows resulting from aninvestment proposal as being known with perfect certainty. We will nowintroduce risk.

B. The riskiness of an investment project is defined as the variability of its cashflows from the expected cash flow.

II. What measure of risk is relevant in capital budgeting?

A. In capital budgeting, a project can be looked at on three levels.1. First, there is the project standing alone risk, which is a projects risk

ignoring the fact that much of this risk will be diversified away as theproject is combined with the firms other projects and assets.

2. Second, we have the projects contribution-to-firm risk, which is theamount of risk that the project contributes to the firm as a whole; thismeasure considers the fact that some of the projects risk will bediversified away as the project is combined with the firms otherprojects and assets, but ignores the effects of diversification of thefirms shareholders.

3. Finally, there is systematic risk, which is the risk of the project fromthe viewpoint of a well-diversified shareholder; this measure considersthe fact that some of a projects risk will be diversified away as theproject is combined with the firms other projects, and, in addition,some of the remaining risk will be diversified away by shareholders asthey combine this stock with other stocks in their portfolio.

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B. Because of bankruptcy costs and the practical difficulties involved inmeasuring a projects level of systematic risk, we will give consideration tothe projects contribution-to-firm risk and the projects systematic risk.

III. Methods for incorporating risk into capital budgeting

A. The certainty equivalent approach involves a direct attempt to allow thedecision maker to incorporate his or her utility function into the analysis.

1. In effect, a riskless set of cash flows is substituted for the original setof risky cash flows, between which the financial manager isindifferent.

2. To simplify calculations, certainty equivalent coefficients (t's) are

defined as the ratio of the certain outcome to the risky outcomebetween which the financial manager is indifferent.

3. Mathematically, certainty equivalent coefficients can be defined asfollows:

t =t

t

flowcashrisky

flowcashcertain

4. The appropriate certainty equivalent coefficient is multiplied by theoriginal cash flow (which is the risky cash flow) with this productbeing equal to the equivalent certain cash flow.

5. Once risk is taken out of the cash flows, those cash flows arediscounted back to present at the risk-free rate of interest and theproject's net present value or profitability index is determined.

6. If the internal rate of return is calculated, it is then compared with the

risk-free rate of interest rather than the firm's required rate of return.

7. Mathematically, the certainty equivalent approach can be summarizedas follows:

NPV = = +

n

1tt

rf

t

)k(1

FCF t

- IO

where t = the certainty equivalent coefficient for timeperiod t

FCFt = the annual expected free cash flow in time period

tIO = the initial cash outlay

n = the project's expected life

krf = the risk-free interest rate

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B. The use of the risk-adjusted discount rate is based on the concept thatinvestors demand higher returns for more risky projects.

1. If the risk associated with the investment is greater than the riskinvolved in a typical endeavor, then the discount rate is adjustedupward to compensate for this risk.

2. The expected cash flows are then discounted back to present at therisk-adjusted discount rate. Then the normal capital budgeting criteriaare applied, except in the case of the internal rate of return, in whichcase the hurdle rate to which the project's internal rate of return iscompared now becomes the risk-adjusted discount rate.

3. Expressed mathematically, the net present value using the risk-adjusted discount rate becomes

NPV = = +

n

1tt

t

k*)(1

FCF - IO

where FCFt = the annual expected free cash flow in time period

t

IO = the initial outlay

k* = the risk-adjusted discount rate

n = the project's expected life

IV. Methods for measuring a project's systematic risk

A. Theoretically, we know that systematic risk is the "priced" risk, and thus, therisk that affects the stock's market price and thus the appropriate risk with

which to be concerned. However, if there are bankruptcy costs (which areassumed away by the CAPM), if there are undiversified shareholders who areconcerned with more than just systematic risk, if there are factors that affect asecurity's price beyond what the CAPM suggests, or if we are unable toconfidently measure the project's systematic risk, then the project's individualrisk carries relevance. Moreover, in general, a project's individual risk ishighly correlated with the project's systematic risk, making it a reasonableproxy to use.

B. In spite of problems in confidently measuring an individual firm's level ofsystematic risk, if the project appears to be a typical one for the firm, thenusing the CAPM to determine the appropriate risk return tradeoffs and then

judging the project against them may be a warranted approach.C. If the project is not a typical project, we are without historical data and must

either estimate the beta using accounting data or use the pure-play method forestimating beta.

1. Using historical accounting data to substitute for historical price datain estimating systematic risk: To estimate a project's beta usingaccounting data we need only run a time series regression of the

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division's return on assets on the market index. The regressioncoefficient from this equation would be the project's accounting betaand serves as an approximation for the project's true beta.

2. The pure play method for estimating a project's beta: The pure playmethod attempts to find a publicly traded firm in the same industry asthe capital-budgeting project. Once the proxy or pure-play firm isidentified, its systematic risk is determined and then used as a proxyfor the project's systematic risk.

V. Additional approaches for dealing with risk in capital budgeting

A. A simulation imitates the performance of the project being evaluated byrandomly selecting observations from each of the distributions that affect theoutcome of the project, combining those observations to determine the finaloutput of the project, and continuing with this process until a representativerecord of the project's probable outcome is assembled.

1. The firm's management then examines the resultant probabilitydistribution, and if management considers enough of the distributionlies above the normal cutoff criterion, it will accept the project.

2. The use of a simulation approach to analyze investment proposalsoffers two major advantages:

a. The financial managers are able to examine and base theirdecisions on the whole range of possible outcomes rather thanjust point estimates.

b. They can undertake subsequent sensitivity analysis of theproject.

B. A probability tree is a graphical exposition of the sequence of possibleoutcomes; it presents the decision maker with a schematic representation ofthe problem in which all possible outcomes are graphically displayed.

VI. Other sources and measures of risk

A. Many times, especially with the introduction of a new product, the cash flowsexperienced in early years affect the size of the cash flows experienced inlater years. This is called time dependence of cash flows, and it has the effectof increasing the riskiness of the project over time.

ANSWERS TOEND-OF-CHAPTER QUESTIONS

11-1. The payback period method is frequently used as a rough risk screening device toeliminate projects whose returns do not materialize until later years. In this way, theearliest returns are emphasized, which in all likelihood have less uncertaintysurrounding them.

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11-2. The use of the risk-adjusted discount rate assumes that risk increases over time.When using the risk-adjusted discount rate method, we are adjusting downward thevalue of future cash flows that occur later in the future more severely than earlierones. This assumption can be justified because flows that are expected further out inthe future are more difficult to forecast and less certain than are flows that are

expected in the near future.

11-3. The primary difference between the certainty equivalent approach and the risk-adjusted discount rate approach is where the adjustment for risk is incorporated intothe calculations. The certainty equivalent approach penalizes or adjusts downwardsthe value of the expected annual free cash flows, while the risk-adjusted discount rateleaves the cash flows at their expected value and adjusts the required rate of return, k,upwards to compensate for added risk. In either case the net present value of theproject is being adjusted downwards to compensate for additional risk. An additionaldifference between these methods is that the risk-adjusted discount rate assumes thatrisk increases over time and that cash flows occurring later in the future should bemore severely penalized. The certainty equivalent method, on the other hand, allows

each cash flow to be treated individually.

11-4. A probability tree is a graphical exposition of the sequence of possible outcomes,presenting the decision maker with a schematic representation of the problem inwhich all possible outcomes are graphically displayed. Moreover, the computationsand results of the computations are shown directly on the tree, so that the informationcan be easily understood. Thus the probability tree allows the manager to quicklyvisualize the possible future events, their probabilities, and outcomes. In addition,the calculation of the expected internal rate of return and enumeration of thedistribution should aid the financial manager in his decision-making process.

11-5. The idea behind simulation is to imitate the performance of the project being

evaluated. This is done by randomly selecting observations from each of thedistributions that affect the outcome of the project, combining each of thoseobservations and determining the final outcome of the project, and continuing withthis process until a representative record of the project's probable outcome isassembled. In effect, the output from a simulation is a probability distribution of netpresent values or internal rates of return for the project. The decision maker thenbases his decision on the full range of possible outcomes.

11-6. The time dependence of cash flows refers to the fact that, many times, cash flows inlater periods are dependent upon the cash flows experienced in earlier periods. Forexample, if a new product is introduced and the initial public reaction is poor,resulting in low initial cash flows, then cash flows in future periods are likely to be

low also. Examples include the introduction of any new products, for example, theEdsel on the negative side, and hopefully this book on the positive side.

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SOLUTIONS TOEND-OF-CHAPTER PROBLEMS

Solutions to Problem Set A

11-1A. (a) = =

n

1i

Xi P(Xi)

A = $4,000 (0.15) + $5,000 (0.70) + $6,000 (0.15)

= $600 + $3,500 + $900

= $5,000

B = $2,000 (0.15) + $6,000 (0.70) + $10,000 (0.15)

= $300 + $4,200 + $1,500

= $6,000

(b) NPV = tt

n

1t k*)(1

FCF

+=

- I0

NPVA = $5,000 (3.605) - $10,000

= $18,025 - $10,000

= $8,025

NPVB = $6,000 (3.352) - $10,000

= $20,112 - $10,000

= $10,112

(c) One might also consider the potential diversification effect associated withthese projects. If the project's cash flow patterns are cyclically divergentfrom those of the company, the overall risk of the company may besignificantly reduced.

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11-2A. (a) = =

n

1i

Xi P(Xi)

A = $35,000 (0.10) + $40,000 (0.40) + $45,000 (0.40)

+ $50,000 (0.10)

= $3,500 + $16,000 + $18,000 + $5,000

= $42,500

B = $10,000 (0.10) + $30,000 (0.20) + $45,000 (0.40)

+ $60,000 (0.20) + $80,000 (0.10)

= $1,000 + $6,000 + $18,000 + $12,000 + $8,000

= $45,000

(b) NPV = tt

n

1t k*)(1

FCF

+= - IO

NPVA = $42,500 (3.605) - $100,000

= $153,212.50 - $100,000

= $53,212.50

NPVB = $45,000 (3.517) - $100,000

= $158,265 - $100,000

= $58,265


11-3A.Project A:

(A) (B) (A x B)Present Value

Expected (Expected Factor at PresentYear Cash Flow t Cash Flow ) (t) 5% Value

0 -$1,000,000 1.00 -$1,000,000 1.000 -$1,000,000

1 500,000 .95 475,000 .952 452,2002 700,000 .90 630,000 .907 571,4103 600,000 .80 480,000 .864 414,7204 500,000 .70 350,000 .823 288,050

NPVA = $ 726,380

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Project B:


Expected (Expected Factor at Present

Year Cash Flow t Cash Flow ) (t) 5% Value0 -$1,000,000 1.00 -$1,000,000 1.000 -$1,000,0001 500,000 .90 450,000 .952 428,4002 600,000 .70 420,000 .907 380,9403 700,000 .60 420,000 .864 362,8804 800,000 .50 400,000 .823 329,200

NPVB = $ 501,420

Thus, project A should be selected, as it has a higher NPV.

11-4A.



0 -$90,000 1.00 -$90,000 1.000 -$90,0001 25,000 0.95 23,750 .935 22,2062 30,000 0.90 27,000 .873 23,5713 30,000 0.83 24,900 .816 20,3184 25,000 0.75 18,750 .763 14,3065 20,000 0.65 13,000 .713 9,269

NPV = $ -330

Thus, this project should not be accepted because it has a negative NPV.

11-5A.

NPVA = tt

n

1t k*)(1

FCF

+=

- I0

= $30,000 (.893) + $40,000(.797) + $50,000(.712)

+ $90,000(.636) + $130,000(.567) - $250,000

= $26,790 + $31,880 + $35,600 + $57,240 + $73,710 - $250,000

= - $24,780

NPVB = t

n

1t k*)(1

FCF

+=

- I0

= $135,000(3.127) - $400,000

= $422,145 - $400,000

= $22,145

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11-6A.Project A:



0 -$ 50,000 1.00 -$ 50,000 1.000 -$ 50,000.001 15,000 .95 14,250 .943 13,437.752 15,000 .85 12,750 .890 11,347.503 15,000 .80 12,000 .840 10,080.004 45,000 .70 31,500 .792 24,948.00

NPVA = $ 9,813.25

Project B:

(A) (B) (A x B) Present ValueExpected (Expected Factor at Present

Year Cash Flow t Cash Flow ) (t) 6% Value

0 -$ 50,000 1.00 -$ 50,000 1.000 -$ 50,000.001 20,000 .90 18,000 .943 16,974.002 25,000 .85 21,250 .890 18,912.503 25,000 .80 20,000 .840 16,800.004 30,000 .75 22,500 .792 17,820.00

NPVB = $ 20,506.50

Thus project B should be selected, as it has a higher NPV

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Internal Rateof Return for Joint

0 Year 1 Year 2 Years each Branch Probability (A)(B)

$300,000 -12.95% 0.18 -2.33%

$700,000 10.92% 0.36 3.93%

$1,100,000 29.25% 0.06 1.76%

$400,000 3.15% 0.06 0.19%

$700,000 19.60% 0.15 2.94%

$1,000,000 33.33% 0.06 2.00%

$1,300,000 45.36% 0.03 1.36%

$600,000 23.74% 0.01 0.24%

$900,000 37.77% 0.05 1.89%

$1,100,000 46.08% 0 .04 1 .84%

1.00

11-7A.

(a

c)

- $1,200,000

p = 0.6

$850,000

p = 0.3

p = 0.6

p = 0.3

p = 0.2

P = 0.1

p = 0.5

p = 0.2

p = 0.1

p = 0.5

$1,000,000

p = 0.1

p = 0.4

p = 0.1

$700,000


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Expected internal rate of return = 13 .82%

d. The range of possible IRRs from 12.95% to 46.08%

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Internal Rateof Return for Joint0 Year 1 Year 2 Years 3 Years each Branch Probability (A)(B)

$230,000 130.25% 0.09 11.72%

$180,000 124.68% 0.09 11.22%

$205,000 121.09% 0.15 18.16%

$155,000 114.96% 0.15 17.24%

$180,000 111.30% 0.06 6.68%

$130,000 104.46% 0.06 6.27%]

$10,000 -42.44% 0.24 -10.19%

$0 -90.00% 0 .16 -14 .40%

1.00Expected internal rate of return = 46 .70%

d. The range of possible IRRs from 90.00% to 130.25%.

11-8A.

(a

c)

$-100,000

p = 0.6 $100,000

$175,000

$150,000

p = 0.5

p = 0.5

p = 0.3

$200,000

p = 0.5

p = 0.5

p = 0.5

p = 0.5

p = 0.5

p = 1.0p = 0.6

$10,000

p = 1.0

p = 0.4

$0

$10,000

p = 0.4

300

p = 0.2


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SOLUTIONS TO INTEGRATIVE PROBLEM

1. First there is theproject standing alone risk, which is a project's risk ignoring the factthat much of this risk will be diversified away as the project is combined with thefirm's other projects and assets. Second, we have the project's contribution-to-firm

risk, which is the amount of risk that the project contributes to the firm as a whole;this measure considers the fact that some of the project's risk will be diversified awayas the project is combined with the firm's other projects and assets, but ignores theeffects of diversification of the firm's shareholders. Finally, there issystematic risk,which is the risk of the project from the viewpoint of a well diversified shareholder;this measure considers the fact that some of a project's risk will be diversified awayas the project is combined with the firm's other projects, and, in addition, some of theremaining risk will be diversified away by the shareholders as they combine thisstock with other stocks in their portfolio.

2. According to the CAPM, systematic risk is the only relevant risk for capitalbudgeting purposes; however, reality complicates this somewhat. In many instances

a firm will have undiversified shareholders; for them the relevant measure of risk isthe project's contribution to firm risk. The possibility of bankruptcy also affects ourview of what measure of risk is relevant. Because the project's contribution to firmrisk can affect the possibility of bankruptcy, this may be an appropriate measure ofrisk since there are costs associated with bankruptcy.

3. The primary difference between the certainty equivalent approach and the risk-adjusted discount rate approach is where the adjustment for risk is incorporated intothe calculations. The certainty equivalent approach penalizes or adjusts downwardsthe value of the expected annual free cash flows, while the risk-adjusted discount rateleaves the cash flows at their expected value and adjusts the required rate of return, k,upwards to compensate for added risk. In either case the net present value of the

project is being adjusted downwards to compensate for additional risk. An additionaldifference between these methods is that the risk-adjusted discount rate assumes thatrisk increases over time and that cash flows occurring later in the future should bemore severely penalized. The certainty equivalent method, on the other hand, allowseach cash flow to be treated individually.

4. A probability tree is a graphical exposition of the sequence of possible outcomes,presenting the decision maker with a schematic representation of the problem inwhich all possible outcomes are graphically displayed. Moreover, the computationsand results of the computations are shown directly on the tree, so that the informationcan be easily understood. Thus the probability tree allows the manager to quicklyvisualize the possible future events, their probabilities, and outcomes. In addition,

the calculation of the expected internal rate of return and enumeration of thedistribution should aid the financial manager in his decision-making process.

5. The idea behind simulation is to imitate the performance of the project beingevaluated. This is done by randomly selecting observations from each of thedistributions that affect the outcome of the project, combining each of those

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observations and determining the final outcome of the project, and continuing withthis process until a representative record of the project's probable outcome isassembled. In effect, the output from a simulation is a probability distribution of netpresent values or internal rates of return for the project. The decision maker thenbases his decision on the full range of possible outcomes.

6. Sensitivity analysis involves determining how the distribution of possible net presentvalues or internal rates of return for a particular project is affected by a change in oneparticular input variable. This is done by changing the value of one input variablewhile holding all other input variables constant.

7. The time dependence of cash flows refers to the fact that, many times, cash flows inlater periods are dependent upon the cash flows experienced in earlier periods. Forexample, if a new product is introduced and the initial public reaction is poor,resulting in low initial cash flows, then cash flows in future periods are likely to below also. Examples include the introduction of any new products, for example, theEdsel on the negative side, and hopefully this book on the positive side.

8. Project A:



0 -$150,000 1.00 -$150,000 1.000 -$150,0001 40,000 .90 36,000 .935 33,6602 40,000 .85 34,000 .873 29,6823 40,000 .80 32,000 .816 26,1124 100,000 .70 70,000 .763 53,410

NPVA = - $ 7,136

Project B:


Expected (Expected Factor at PresentYearCash Flow t Cash Flow ) (t) 7% Value

0 -$200,000 1.00 -$200,000 1.000 -$200,0001 50,000 .95 47,500 .935 44,4132 60,000 .85 51,000 .873 44,5233 60,000 .80 48,000 .816 39,1684 50,000 .75 37,500 .763 28,613

NPVB = - $ 43,283

Thus, neither project should be selected, as they both have negative NPVs.

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$200,000 -12.08% 0.12 -1.45%

$300,000 0.00% 0.28 0.00%

$250,000 0.00% 0.08 0.00%

$450,000 20.55% 0.20 4.11%

$650,000 37.26% 0.12 4.47%

$300,000 17.54% 0.04 0.70%

$500,000 36.19% 0.10 3.62%

$700,000 51.84% 0.04 2.07%

$1,000,000 71.94% 0 .02 1 .44%

1.00

Part9

-$600,000

$350,000

p = 0.3

p = 0.7

p = 0.4

$300,000

p = 0.2

p = 0.5p = 0.4

p = 0.3

p = 0.2

p = 0.1

p =0.5

p = 0.2

$450,000

p = 0.2

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The range of possible IRRs from -12.08% to 71.94%.

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Solutions to Problem Set B

11-1B. (a) X = =

n

1i

Xi P(Xi)

X A = $5,000 (0.20) + $6,000 (0.60) + $7,000 (0.20)

= $1,000 + $3,600 + $1,400

= $6,000

X B = $3,000 (0.20) + $7,000 (0.60) + $11,000 (0.20)

= $600 + $4,200 + $2,200

= $7,000

(b) NPV = tt

n

1t k*)(1

FCF

+=

- I0

NPVA = $6,000 (3.517) - $10,000

= $21,102 - $10,000

= $11,102

NPVB = $7,000 (3.127) - $10,000

= $21,889 - $10,000

= $11,889


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11-2B. (a) X = =

n

1i

Xi P(Xi)

X A = $40,000 (0.10) + $45,000 (0.40)

+ $50,000 (0.40) + $55,000 (0.10)

= $4,000 + $18,000 + $20,000 + $5,500

= $47,500

X B = $20,000 (0.10) + $40,000 (0.20)

+ $55,000 (0.40) + $70,000 (0.20) + $90,000 (0.10)

= $2,000 + $8,000 + $22,000 + $14,000 + $9,000

= $55,000

(b) NPV = tt

n

1t k*)(1

FCF

+=

- I0

NPVA = $47,500 (3.696) - $125,000

= $175,560 - $125,000

= $50,560

NPVB = $55,000 (3.517) - $125,000

= $193,435 - $125,000

= $68,435


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11-3B.Project A:



0 -$100,000 1.00 -$100,000 1.000 -$100,0001 600,000 .90 540,000 .952 514,0802 750,000 .90 675,000 .907 612,2253 600,000 .75 450,000 .864 388,8004 550,000 .65 357,500 .823 294,222 .50

NPVA = $ 1,709,327 .50

Project B:

(A) (B) (A x B) Present ValueExpected (Expected Factor at Present

Year Cash Flow t Cash Flow ) (t) 5% Value

0 -$100,000 1.00 -$100,000 1.000 -$100,0001 600,000 .95 570,000 .952 542,6402 650,000 .75 487,500 .907 442,162.503 700,000 .60 420,000 .864 362,8804 750,000 .60 450,000 .823 370,350

NPVB = $1,618,032 .50

Thus, project A should be selected, as it has a higher NPV.

11-4B.(A) (B) (A x B)

Present ValueExpected (Expected Factor at Present

Year Cash Flow t Cash Flow ) .( t) 8% Value

0 -$100,000 1.00 -$100,000 1.000 -$100,0001 30,000 0.95 28,500 .926 26,3912 25,000 0.90 22,500 .857 19,2833 30,000 0.83 24,900 .794 19,771

4 20,000 0.75 15,000 .735 11,0255 25,000 0.65 16,250 .681 11,066

NPV = -$ 12,464

Thus, this project should not be accepted because it has a negative NPV.

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11-5B.

NPVA = tt

n

1t k*)(1

FCF

+=

- IO

= $30,000 (.885) + $40,000(.783) + $50,000(.693)

+ $80,000(.613) + $120,000(.543) - $300,000

= $26,550 + $31,320 + $34,650 + $49,040

+ $65,160 - $300,000

= - $93,280

NPVB = t

n

1t k*)(1

FCF

+=

- IO

= $130,000(3.127) - $450,000

= $406,510 - $450,000

= -$43,490

11-6B.Project A:


Expected (Expected Factor at PresentYear Cash Flow t Cash Flow ) x (t) 7% Value

0 -$ 75,000 1.00 -$ 75,000 1.000 -$ 75,000.00

1 20,000 .95 19,000 .935 17,765.002 20,000 .85 17,000 .873 14,841.003 15,000 .80 12,000 .816 9,792.004 50,000 .70 35,000 .763 26,705 .00

NPVA = ($ 5,897 .00)

Project B:


Expected (Expected Factor at PresentYear Cash Flow t Cash Flow ) x (t) 7% Value

0 -$ 75,000 1.00 -$ 75,000 1.000 -$ 75,000.001 25,000 .95 23,750 .935 22,206.252 30,000 .85 25,500 .873 22,261.503 30,000 .80 24,000 .816 19,584.004 25,000 .75 18,750 .763 14,306 .25

NPVB = $ 3,358 .00

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Thus project B should be selected, as it has a higher NPV.

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$300,000 -15.12% 0.06 -0.9072%

$700,000 7.69% 0.30 2.3070%

$1,100,000 25.25% 0.24 6.0600%

$400,000 0.00% 0.06 0.0000%

$700,000 15.75% 0.15 2.3625%

$900,000 24.73% 0.06 1.4838%]

$1,300,000 40.44% 0.03 1.2132%

$600,000 46.82% 0.03 1.4046%

$900,000 58.94% 0.06 3.5364%

$1,100,000 66.27% 0 .01 0 .6627%1.00


11-7B.

(a

c)

-$1,300,000p = 0.2

p = 0.1

p = 0.5

p = 0.3

$750,000

p = 0.6

p = 0.2

p = 0.4

p = 0.1

p = 0.5

p = 0.6

$1,500,000p = 0.1

p = 0.3

p = 0.1

$900,000


23/25

Prof. Rushen Chahal

(d) The range of possible IRRs from -15.12% to 66.27

50


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0 Year 1 Year 2 Years 3 Years each Branch Probability (A)(B)

$255,000 115.83% .105 12.16227%

$205,000 110.76% .105 11.6298%

$210,000 101.15% .175 17.7013%

$160,000 95.18% .175 16.6565%

$170,000 86.57% .070 6.0599%

$120,000 79.42% .070 5.5594%

$10,000 -46.70% .180 -8.4060%

$0 -91.67% .120 -11 .0004%

1.00


(d) The range of possible IRRs from 91.67% to 115.83%

11-8B.

(a

c)

-$120,000

p = 0.7

$100,000

$180,000

p = 0.2

$140,000

p = 0.5

p = 0.5

p = 0.3

$225,000

p = 0.5

p = 0.5p = 0.5

p = 0.5

p = 0.5

p = 1.0

p = 0.6

$10,000

p = 1.0

p = 0.4

$0

$10,000

p = 0.3

304


25/25

Prof. Rushen Chahal

MADE IN THE U. S. A., DUMPED IN BRAZIL, AFRICA, . . .(Ethics in Capital Budgeting)

OBJECTIVE: To force the student to recognize the role ethical behavior plays in allareas of Finance.

DEGREE OF DIFFICULTY: Easy

Case Solution:

With ethics cases there are no right or wrong answers - just opinions. Try to bring out asmany opinions as possible without being judgmental. In this case the question centersaround what to do when a product is no longer salable.

Documents

Financial Management Chapter 11 IM 10th Ed