Solution manual financial management 10e by keown chapter 11

First, there is the project standing alone risk, which is a project’s risk ignoring the fact that much of this risk will be diversified away asthe project is combined with the firm’s oth

CHAPTER 11 Capital Budgeting and Risk Analysis

I Risk and the investment decision

A Up to this point we have treated the expected cash flows resulting from an

investment 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 cash

flows 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 project’s risk

ignoring the fact that much of this risk will be diversified away asthe project is combined with the firm’s other projects and assets

2 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 bediversified away as the project is combined with the firm’s otherprojects and assets, but ignores the effects of diversification of thefirm’s shareholders

3 Finally, there is systematic risk, which is the risk of the project from

the viewpoint of a well-diversified shareholder; this measureconsiders the fact that some of a project’s risk will be diversifiedaway as the project is combined with the firm’s other projects, and,

in addition, some of the remaining risk will be diversified away byshareholders as they combine this stock with other stocks in their

B Because of bankruptcy costs and the practical difficulties involved in

measuring a project’s level of systematic risk, we will give consideration tothe project’s contribution-to-firm risk and the project’s systematic risk.III Methods for incorporating risk into capital budgeting

A The certainty equivalent approach involves a direct attempt to allow the

decision 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 set

of 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 as

flowcash certain

4 The appropriate certainty equivalent coefficient is multiplied by the

original 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 are

discounted 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 ofreturn

7 Mathematically, the certainty equivalent approach can be

summarized as follows:

NPV = ∑

n 1

t rf t

t

)k(1

period t

IO = the initial cash outlay

n = the project's expected lifekrf = the risk-free interest rate

B The use of the risk-adjusted discount rate is based on the concept that

investors demand higher returns for more risky projects

1 If the risk associated with the investment is greater than the risk

involved 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 the

risk-adjusted discount rate Then the normal capital budgetingcriteria are applied, except in the case of the internal rate of return, inwhich case the hurdle rate to which the project's internal rate ofreturn is compared now becomes the risk-adjusted discount rate

3 Expressed mathematically, the net present value using the

risk-adjusted discount rate becomes

NPV = ∑

n 1

t t

t

k*)(1

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,

the risk that affects the stock's market price and thus the appropriate riskwith which to be concerned However, if there are bankruptcy costs (whichare assumed away by the CAPM), if there are undiversified shareholderswho are concerned with more than just systematic risk, if there are factorsthat affect a security's price beyond what the CAPM suggests, or if we areunable to confidently measure the project's systematic risk, then the project'sindividual risk carries relevance Moreover, in general, a project's individualrisk is highly correlated with the project's systematic risk, making it areasonable proxy to use

B In spite of problems in confidently measuring an individual firm's level of

systematic risk, if the project appears to be a typical one for the firm, thenusing the CAPM to determine the appropriate risk return tradeoffs and thenjudging 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-playmethod for estimating beta

1 Using historical accounting data to substitute for historical price

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 play

method attempts to find a publicly traded firm in the same industry

as the 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 by

randomly selecting observations from each of the distributions that affectthe outcome of the project, combining those observations to determine thefinal output of the project, and continuing with this process until arepresentative record of the project's probable outcome is assembled

1 The firm's management then examines the resultant probability

distribution, 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 proposals

offers two major advantages:

a The financial managers are able to examine and base their

decisions on the whole range of possible outcomes ratherthan just point estimates

b They can undertake subsequent sensitivity analysis of the

project

B A probability tree is a graphical exposition of the sequence of possible

outcomes; 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

flows experienced in early years affect the size of the cash flowsexperienced in later years This is called time dependence of cash flows, and

it has the effect of increasing the riskiness of the project over time

ANSWERS TO END-OF-CHAPTER QUESTIONS

11-1 The payback period method is frequently used as a rough risk screening device to

eliminate projects whose returns do not materialize until later years In this way,the earliest returns are emphasized, which in all likelihood have less uncertaintysurrounding them

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

in the future are more difficult to forecast and less certain than are flows that areexpected 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 adjustsdownwards the value of the expected annual free cash flows, while the risk-adjusted discount rate leaves the cash flows at their expected value and adjusts therequired rate of return, k, upwards to compensate for added risk In either case thenet present value of the project is being adjusted downwards to compensate foradditional risk An additional difference between these methods is that the risk-adjusted discount rate assumes that risk increases over time and that cash flowsoccurring later in the future should be more severely penalized The certaintyequivalent method, on the other hand, allows each cash flow to be treatedindividually

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 theinformation can be easily understood Thus the probability tree allows the manager

to quickly visualize the possible future events, their probabilities, and outcomes Inaddition, the calculation of the expected internal rate of return and enumeration ofthe distribution 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 ofnet present values or internal rates of return for the project The decision makerthen bases 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 in

later 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

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

Solutions to Problem Set A

n 1

t (1 k*)

FCF

= $20,112 - $10,000

= $10,112

(c) One might also consider the potential diversification effect associated with

these projects If the project's cash flow patterns are cyclically divergentfrom those of the company, the overall risk of the company may besignificantly reduced

n 1

= $153,212.50 - $100,000

= $53,212.50NPVB = $45,000 (3.517) - $100,000

= $158,265 - $100,000

= $58,265(c) One might also consider the potential diversification effect associated with

these projects If the project's cash flow patterns are cyclically divergentfrom those of the company, the overall risk of the company may besignificantly reduced

11-3A

Project A:

(A) (B) (A x B)

Present ValueExpected (Expected Factor at PresentYear Cash Flow αt Cash Flow ) × ( αt) 5% Value

Project B:

(A) (B) (A x B)

Present ValueExpected (Expected Factor at PresentYear Cash Flow αt Cash Flow ) × (αt) 5% Value

11-4A

(A) (B) (A x B)

Present ValueExpected (Expected Factor at PresentYear Cash Flow αt Cash Flow ) × (αt) 7% Value

= $22,145

Project A:

(A) (B) (A x B)

Present ValueExpected (Expected Factor at PresentYear Cash Flow αt Cash Flow ) × (αt) 6% Value

(A) (B) (A x B)

Present ValueExpected (Expected Factor at PresentYear Cash Flow αt Cash Flow ) × (αt) 6% Value

Internal Rate

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

Internal Rate

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

d The range of possible IRR’s from –90.00% to 130.25%

SOLUTIONS TO INTEGRATIVE PROBLEM

1 First there is the project standing alone risk, which is a project's risk ignoring the

fact that much of this risk will be diversified away as the project is combined with

the firm'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 contribution-to-firm as a

whole; this measure considers the fact that some of the project's risk will bediversified away as the project is combined with the firm's other projects and assets,but ignores the effects of diversification of the firm's shareholders Finally, there is

systematic 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 riskwill be diversified away as the project is combined with the firm's other projects,and, in addition, some of the remaining risk will be diversified away by theshareholders as they combine this stock with other stocks in their portfolio

2 According to the CAPM, systematic risk is the only relevant risk for capital

budgeting purposes; however, reality complicates this somewhat In manyinstances a firm will have undiversified shareholders; for them the relevant measure

of risk is the project's contribution to firm risk The possibility of bankruptcy alsoaffects our view of what measure of risk is relevant Because the project'scontribution to firm risk can affect the possibility of bankruptcy, this may be anappropriate measure of risk 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 adjustsdownwards the value of the expected annual free cash flows, while the risk-adjusted discount rate leaves the cash flows at their expected value and adjusts therequired rate of return, k, upwards to compensate for added risk In either case thenet present value of the project is being adjusted downwards to compensate foradditional risk An additional difference between these methods is that the risk-adjusted discount rate assumes that risk increases over time and that cash flowsoccurring later in the future should be more severely penalized The certaintyequivalent method, on the other hand, allows each cash flow to be treatedindividually

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 theinformation can be easily understood Thus the probability tree allows the manager

to quickly visualize the possible future events, their probabilities, and outcomes Inaddition, the calculation of the expected internal rate of return and enumeration ofthe distribution should aid the financial manager in his decision-making process

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 the