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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