Risk and the Cost of Capital

1. Risk and the Cost of Capital John E. Parsons March 21, 2014 Financing Energy Investments Université Paris Dauphine

2. Different Aspects of Risk Enter our Calculations in Different Places • The numerator contains the expected cash flows. • Therefore, it already includes a recognition of how risks may lower the cash flows below the “planned” or pro forma level. That is, it may already reflect one type of “discount” or “haircut”. • For bonds, the expected cash flow includes a recognition that the company may default so that the investor’s expected cash flow is below the promised cash flow or “principal”. • For most projects or corporate assets, there is no such thing as a “promised” cash flow. Nevertheless, we may find ourselves working with something comparable. There may be benchmark cash flows calculated via many different formulas which do not incorporate risk. From these, we calculate the expected cash flow via some adjustment.

3. Different Aspects of Risk Enter our Calculations in Different Places (cont.) • The denominator adjusts for: • Time • An additional adjustment for Risk. Two investments with the same expected cash flow are worth different amounts according to how “risky” they are. • The variable “r” is the risk-adjusted discount rate. • It is NOT an adjustment for downside risk – that’s already incorporated into the expected cash flow. • It is an adjustment for variability AROUND the expected cash flow, on both the up and the downside. • Where do we get that adjustment?

4. 3 Questions • How should I value risk? What discount rate should I apply? • How do others value risk? What discount rates do they apply? • How is risk valued in the capital markets? What discount rates are applied there?

5. The Equity Risk Premium:The Value of an Investment of $1 in 1900

6. The Equity Risk Premium:Real Returns

7. Volatility in Stock Market Returns

8. The Basic Risk-Return Tradeoff

9. The Basic Risk-Return Tradeoff

10. From Portfolios to Individual Stocks • Returns average, but risk doesn’t.

11. Diversification Eliminates Some Risk, While Some Risk Remains

12. Diversification Eliminates Some Risk, While Some Risk Remains Why pay for unique risk?

13. The Formula for Portfolio Risk:a special example • N stocks • Average variance, V • Average covariance, C • An equal amount invested in each stock, 1/N • What is the total risk or portfolio variance: • Gradually increase the number of stocks

14. Beta is a Stock’s Covariance with the Market

15. Measuring Beta

16. Risk and Return • Portfolio theory underlies the determination of a cost of capital. • When two or more assets are combined into a portfolio, the total risk is less than the sum of the individual risks. This is the benefit of diversification. • In analyzing a given asset’s risk, we commonly speak of diversifiable risk and non-diversifiable risk. Diversifiable risk is the portion that “disappears” when the asset is added to a large, well diversified portfolio. The non-diversifiable is the portion that doesn’t disappear. The non-diversifiable risk is the amount that a marginal investment in the specific asset adds to the total portfolio’s risk. • The same categories are also called ideosyncratic risk and market risk, respectively. • Market risk is also called Beta risk. • Expected return is proportional to Beta risk:

17. The Security Market Line

18. Measuring Beta: Results for US Electric Utilities

19. From Measured Betas to Expected Returns

20. From Equity Market Returns Back to Project Discounting • Microsoft example. • 100% equity • Equity beta is the company’s asset beta. • Capital market data tells us something about the “right” average discount rate for corporate asset cash flows. • 12.9%

21. Value Additivity V#1 + V#2 + V#3 = VA

22. Conservation of Expected Return

23. Conservation of Risk (Beta Risk)

24. Beta Accounts

25. The End