11 Capital Budgeting and Risk ©2006 Thomson/South-Western
Dec 15, 2015
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Capital Budgeting and Risk
©2006 Thomson/South-Western
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Introduction
This chapter looks at adjusting a project’s risk level when it has more or less than the firm’s average risk level.
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Risk Project risk
The risk that a project will perform below expectations
Some of the risk can be diversified away. Beta risk
Depends on the risk of the project relative to the market-portfolio
Beta risk cannot be diversified away. Capital asset pricing model (CAPM)
Used to estimate risk-adjusted discount rates for capital budgeting
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Information on Risk
The Society for Risk Analysis (SRA) http://www.sra.org/index.htm
Official journal of the SRA is Risk Analysis http://www.sra.org/journal.htm
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Adjusting for Total Project Risk NPV-Payback approach
Simulation approach
Sensitivity analysis
Scenario analysis
Risk-adjusted discount rate approach
Certainty equivalent approach
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NPV-Payback Approach
A project must have a positive NPV and a payback of less than a critical number of years to be acceptable.
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Simulation Approach
Estimate the probability distribution of each element which influences the CFs of a project.
ElementsNumber of units sold Market price
Unit production costs NINVUnit selling cost Project life
Cost of capital
Calculate the NPV using randomly chosen numerical values for the elements.
Repeat the process until a probability distribution of the NPV can be estimated.
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Sensitivity Analysis
Systematically change relevant variables to measure influence on NPV/IRR
Sensitivity curves show the impact of changes in a variable on the project’s NPV
Electronic spreadsheets and financial modeling make sensitivity analysis easy to perform.
Examine the sensitivity of CF at this Web site:http://www.toolkit.cch.com/tools/tools.asp
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Scenario Analysis
Considers the impact of simultaneous changes in key variables on the desirability of an investment project
Estimate the expected NPV
Optimistic Pessimistic Most likely Estimate the Probability of each Compute the expected NPV Compute the standard deviation (SD) of
the NPV
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Risk-Adjusted Discount Rate Approach An individual project is discounted at a
discount rate adjusted to the riskiness of the project instead of discounting all projects at one rate.
ka* = rf + risk premium
Calculate the NPV substituting ka* for k in
the formula.
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Certainty Equivalent Approach
Involves converting expected risky CFs to their certainty equivalents and then computing the NPV
The risk-free rate (rf) is used as the discount rate not the cost of capital (k).
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Certainty Equivalent Approach• The certainty equivalent factor is the ratio
of the certainty equivalent CF to the risky CF:
t
certain return
risky return=
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The Certainty-Equivalent NPV
• The certainty-equivalent NPV:
n
trf
t
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αNCF0 t
tαNINVNPV
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All-Equity Case
The project’s risk-adjusted discount rate is found with the SML equation:
β)(*fme rrrk
f
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The Equity and Debt Case
Betas can be observed for firms in the same investment class as the proposed investment.
These betas can be used to estimate risk-adjusted discount rates.
A two-step process is used 1. Calculate an unleveraged beta
2. Calculate a new leveraged beta to reflect appropriate debt capacity
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Step 1: Calculate an Unleveraged Beta
Convert the observed, leveraged beta, l, into an unleveraged, or pure project beta, u.
)/)((11
ββ
EBTl
u
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Step 2: Calculate a New Leveraged Beta Calculate the new leveraged beta, l, for
the proposed capital structure of the new line of business
Glossary of terms http://www.contingencyanalysis.com/
EBT 11ββ ul
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Step 2: Continued
Calculating the required rate of return, ke, based on the new leveraged beta, l:
Calculate the risk-adjusted required return, ka
*, on the new line of business:
)equity( % )debt( % eιa kkk
*
β)(*fme rrrk
f
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Special Elements of Risk When Investing Abroad
Captive funds
Foreign government takes over assets
Exchange rate risk Risk of inflation
Uncertain tax rates