Chapter 11:Capital Budgeting and

Risk Analysis

2002, Prentice Hall, Inc.

Three Measures of a Project’s Risk

Project Standing Alone Risk

Three Measures of a Project’s Risk

Project Standing Alone Risk

Risk diversified away

within firm as thisproject is combined

with firm’s otherprojects and assets

Three Measures of a Project’s Risk

Project Standing Alone Risk

Risk diversified away

within firm as thisproject is combined

with firm’s otherprojects and assets

Project’scontribution-to-firm risk

Three Measures of a Project’s Risk

Project Standing Alone Risk

Risk diversified away

within firm as thisproject is combined

with firm’s otherprojects and assets

Risk diversified away

by shareholders as securities are combined

to form diversifiedportfolio

Project’scontribution-to-firm risk

Three Measures of a Project’s Risk

Project Standing Alone Risk

Risk diversified away

within firm as thisproject is combined

with firm’s otherprojects and assets

Risk diversified away

by shareholders as securities are combined

to form diversifiedportfolio

Project’scontribution-to-firm risk

Systematic risk

Incorporating Risk into Capital Budgeting

Two Methods:• Certainty Equivalent Approach• Risk-Adjusted Discount Rate

How can we adjust this model to take risk into account?

NPV = - IO ACFt(1 + k) t

n

t=1

How can we adjust this model to take risk into account?

• Adjust the After-tax Cash Flows (ACFs), or• Adjust the discount rate (k).

NPV = - IO ACFt(1 + k) t

n

t=1

Certainty Equivalent Approach

• Adjusts the risky after-tax cash flows to certain cash flows.• The idea:

Certainty Equivalent Approach

• Adjusts the risky after-tax cash flows to certain cash flows.• The idea:

Risky Certainty CertainCash X Equivalent = CashFlow Factor (a) Flow

Certainty Equivalent Approach

Risky Certainty CertainCash X Equivalent = CashFlow Factor (a) Flow

Risky “safe”$1000 .70 $700

Certainty Equivalent Approach

Risky Certainty CertainCash X Equivalent = CashFlow Factor (a) Flow

Risky “safe”$1000 .95 $950

• The greater the risk associated with a particular cash flow, the smaller the CE factor.

Certainty Equivalent Method

tNPV = - IO t ACFt(1 + krf)

n

t=1

Certainty Equivalent Approach

• Steps:1) Adjust all after-tax cash flows by

certainty equivalent factors to get certain cash flows.

2) Discount the certain cash flows by the risk-free rate of interest.

Incorporating Risk into Capital Budgeting

• Risk-Adjusted Discount Rate

How can we adjust this model to take risk into account?

NPV = - IO NPV = - IO ACFACFtt(1 + k)(1 + k) tt

nn

t=1t=1

How can we adjust this model to take risk into account?

• Adjust the discount rate (k).

NPV = - IO NPV = - IO ACFACFtt(1 + k)(1 + k) tt

nn

t=1t=1

Risk-Adjusted Discount Rate

• Simply adjust the discount rate (k) to reflect higher risk.• Riskier projects will use higher risk-

adjusted discount rates.• Calculate NPV using the new risk-

adjusted discount rate.

Risk-Adjusted Discount Rate

NPV = - IO ACFt(1 + k*)t

n

t=1

Risk-Adjusted Discount Rates

• How do we determine the appropriate risk-adjusted discount rate (k*) to use?• Many firms set up risk classes to

categorize different types of projects.

Risk Classes

Risk RADR Class (k*) Project Type 1 12% Replace equipment, Expand current business 2 14% Related new products 3 16% Unrelated new products 4 24% Research & Development

Summary: Risk and Capital Budgeting

You can adjust your capital budgeting methods for projects having different levels of risk by:

• Adjusting the discount rate used (risk-adjusted discount rate method),

• Measuring the project’s systematic risk,• Computer simulation methods,• Scenario analysis,• Sensitivity analysis.