1. Copyright ©2003 South-Western/Thomson Learning Chapter 10 Capital Budgeting and Risk

2. Introduction This chapter looks at adjusting a project’s risk level when it has more or less than the firm’s average risk level.

3. 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

4. Information on Risk The Society for Risk Analysis (SRA) –http://www.sra.org/index.htmhttp://www.sra.org/index.htm Official journal of the SRA is Risk Analysis –http://www.sra.org/journal.htmhttp://www.sra.org/journal.htm

5. All Equity Case The project’s risk-adjusted discount rate is found with the SML equation:

6. 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

7. Step 1: Calculate an Unleveraged Beta Convert the observed, leveraged beta,  l, into an unleveraged, or pure project beta,  u.

8. 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/

9. Step 2 Continued Calculating the required rate of return, k e, based on the new leveraged beta,  l : Calculate the risk-adjusted required return, k a *, on the new line of business:

10. Adjusting for Total Project Risk NPV-Payback approach Simulation approach Sensitivity analysis Scenario analysis Risk-adjusted discount rate approach Certainty equivalent approach

11. NPV-Payback Approach A project must have a positive NPV and a payback of less than a critical number of years to be acceptable.

12. Simulation Approach Estimate the probability distribution of each element which influences the CFs of a project. Elements Number of units soldMarket price Unit production costsNINV Unit selling costProject life Cost of capital Draw from the possibilities for the elements allowing only one element at a time to vary. Calculate NCF’s & then NPV using randomly chosen values for the elements. Repeat the process until a probability distribution of the NPV can be estimated.

13. Sensitivity Analysis Involves systematically changing relevant variables to identify which variables the NPV/IRR seems most sensitive to Allow only one key element to change for each experiment (calc of NCF’s and NPV) Useful to make sensitivity curves to 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

14. Scenario Analysis Considers the impact of simultaneous changes in key variables on the desirability of an investment project Make a draw from the distribution of each key element then use those values to calculate NCF’s 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

15. Summary of Steps for Simulation, Sensitivity, and Scenario Analysis 1. Make draws of the possible values of the key variables that affect NPV. 2. Calc annual NCF’s for a project using the new values drawn for key variables. (Calculate NCF’s for the life of the project.) 3. Calculate NPV using the set of NCF’s that you calculated in step 2. 4. Repeat steps 1, 2, and 3 to generate a large number of NPV estimates. 5. Find the mean and standard deviation of the group of NPV estimates. 6. Use the mean and std dev of NPV to estimate the probability of obtaining a NPV better than or worse than a specified NPV.

16. 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. k a * = r f + risk premium Calculate the NPV substituting k a * for k in the formula.

17. Certainty Equivalent Approach Involves converting expected risky CFs to their certainty equivalents and then computing the NPV The risk-free rate (r f ) is used as the discount rate not the cost of capital (k). t certain return risky return = The certainty equivalent factor is the ratio of the certainty equivalent CF to the risky CF:

18. The Certainty-Equivalent NPV The certainty-equivalent NPV:

19. Special Elements of Risk When Investing Abroad Captive funds Foreign government takes over assets Exchange rate risk –Risk of inflation Uncertain tax rates