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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 Certain
Cash X Equivalent = Cash
Flow Factor (a) Flow
Certainty Equivalent Approach
Risky Certainty Certain
Cash X Equivalent = Cash
Flow Factor (a) Flow
Risky “safe”
$1000 .70 $700
Certainty Equivalent Approach
Risky Certainty Certain
Cash X Equivalent = Cash
Flow 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.
