Capital Budgeting and Risk

1. 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.htm • Official journal of the SRA is Risk Analysis • http://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 • Calculate an unleveraged beta • 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, ke, based on the new leveraged beta, l: • Calculate the risk-adjusted required return, ka*, 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. • 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.

13. Sensitivity Analysis • Involves systematically changing relevant variables to identify which variables the NPV/IRR seems most sensitive to • 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 • 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. 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.

16. certain return = t risky return 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). • The certainty equivalent factor is the ratio of the certainty equivalent CF to the risky CF:

17. The Certainty-Equivalent NPV • The certainty-equivalent NPV:

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