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 this project is combined with firm’s other projects and assets

Three Measures of a Project’s Risk Project Standing Alone Risk Risk diversified away within firm as this project is combined with firm’s other projects and assets Project’s contribution- to-firm risk

Three Measures of a Project’s Risk Project Standing Alone Risk Risk diversified away within firm as this project is combined with firm’s other projects and assets Risk diversified away by shareholders as securities are combined to form diversified portfolio Project’s contribution- to-firm risk

Three Measures of a Project’s Risk Project Standing Alone Risk Risk diversified away within firm as this project is combined with firm’s other projects and assets Risk diversified away by shareholders as securities are combined to form diversified portfolio Project’s contribution- 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 ACF t (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 ACF t (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” $ $700

Certainty Equivalent Approach Risky Certainty Certain Cash X Equivalent = Cash Flow Factor (a) Flow Risky “safe” $ $950

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

Certainty Equivalent Method t NPV = - IO t ACF t (1 + k rf ) 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 ACF t ACF t (1 + k) t nt=1 

How can we adjust this model to take risk into account? Adjust the discount rate (k). NPV = - IO ACF t ACF t (1 + k) t nt=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 ACF t (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.