2. 1 Lecture 2b The cost of capital and CAPM

3. 2 Overview The cost of capital Risk Risk and return Cost of equity: CAPM

4. 3 Cost of capital Terms on which privatised companies can raise funds for regulated businesses Two main types of capital: –Debt –Equity

5. 4 Debt or bond finance “Guaranteed” interest payments (before equity holders) Tax deductible Normally lower cost than equity Cost of debt = risk free rate plus risk premium Risk free rate measured by gov’t stocks Risk premium depends on rating assessed by rating agencies

6. 5 Equity finance Gives shareholders rights to residual incomes –higher risk than debt Shareholders can spread risk by holding balanced portfolio of equities But even a completely balanced equity portfolio has a risk = market risk –cannot be diversified This market risk has a risk premium = market risk premium (topic for another day)

7. 6 Calculating the cost of capital Weighted average cost of capital = cost of debt  proportion of debt in financing + cost of equity  proportion of equity in financing cost of finance =risk free rate +risk premium Equity risk premium = market risk premium  equity “beta” Beta measures the relative risk of the company’s equity with that of the market as a whole Based on Capital Asset Pricing Model

8. 7 CAPM Focus on the equilibrium relationship between the risk and expected return on risky assets Builds on Markowitz portfolio theory Each investor is assumed to diversify his or her portfolio according to the Markowitz model Only compensate investors for bearing non- diversifiable risk

9. 8 A. Market Portfolio From the Markowitz Portfolio Selection model –Separation Theorem –All investors hold the same portfolio of risky assets CAPM: extension of the Markowitz model –In equilibrium: this risky portfolio consists of all risky securities in the market –Hence, the name - market portfolio

10. 9 Characteristics of the Market Portfolio All risky assets must be in the market portfolio, so it is completely diversified –Contains only systematic risk All securities included in proportion to their market value In theory, should contain all risky assets worldwide

11. 10 B. Capital Market Line  Line from R F to L is the capital market line (CML)  x = risk premium = E(R M ) - R F  y = risk =  M  Slope = x/y = [E(R M ) - RF]/ M  y-intercept = R F E(R M ) RFRF Risk MM L M y x

12. 11 CML (cont’d) Relationship between risk and expected return for portfolio P (Equation for CML): Slope of the CML is the market price of risk for efficient portfolios, or the equilibrium price of risk in the market (Risk premium per unit of risk)

13. 12 C. Security Market Line The CML applies to markets in equilibrium and to the selection of efficient portfolios The Security Market Line depicts the tradeoff between risk and expected return for individual securities in equilibrium Under CAPM, all investors hold the market portfolio –How does an individual security contribute to the risk of the market portfolio? Focus: covariance between security and market

14. 13 SML (cont’d) Equation for the expected return for an individual stock, E(R i ), is similar to the CML equation:  All securities should lie on the SML The expected return on the security should be only that return needed to compensate for systematic risk (CAPM is a one-factor model)

15. 14 SML (cont’d)  Beta = 1.0 implies: as risky as market  Securities A and B are riskier than the market  Beta > 1.0  Security C is less risky relative to the market  Beta < 1.0 A B C E(R M ) RFRF 01.02.00.51.5 SML Beta M E(R)

16. 15 SML: Application to calculate the required rate of return on an asset (k i ): k i = R F +  i [ E(R M ) - R F ] – Risk-free rate (R F ) – Risk premium (  i [ E(R M ) - R F ]) Market risk premium adjusted for security i The greater the systematic risk, the greater the required return

17. 16 Finding Beta Return to market Return to Equity Low Beta =>low cost of equity Beta = 1 CoC = risk free rate + equity risk premium High Beta and equity cost Plot stock returns against market:

18. 17 Company “Beta” Ideally should relate to regulated company rather than plc Based on degree to which company returns vary with those of market. Estimated from regression equation: company return = alpha + beta  market return For regulated companies Beta should be <1

19. 18 Using data Returns to stock –price increase: log(p t )-log(p t-1 ) plus –dividend: added in at day goes ex-dividend Regressed on stock market return: –price change plus dividends Rough measure, data easily found: –just look at price changes - see today's lab

20. 19 Recent examples of the cost of capital Regulator Case Basis WACC Gearing OfgemElectricity distribution (2004)Gross, real 6.9% net of tax 4.8%57.5% OfwatWater (2004)Post tax, real5.1%55% (assumed) CC Mobile phone inquiry (2003) Pre-tax, real 11% a 10% (estimate of actual level) CC Manchester Airport (2002) Pre-tax, real 7.25% a 30-35% (estimate of actual) CC BAA (2002) Pre-tax, real 7.21% a 25% (estimate of actual level) Postcomm Consignia (2002) Pre-tax, real 9.4-11.6% 20% (actual) Ofgem Independent gas transporters (02) Pre-tax, real 6.4-8.5% 37.5% CAA NATS (2001) Pre-tax, real 7.0-8.8% 40-50% (optimal) Ofgem Transco (2001) Pre-tax, real 6.0-6.25% 62.5% Oftel Eff comp review:mobiles(01) Pre-tax, noml 13.01-16.95% 10-30% (optimal) MMC Mid Kent Water (2000) Pre-tax, real 7.4% b 35% ORR Railtrack (2000) Pre-tax, real 6.9-8.2% 50% (assumed) Ofgem NGC (2000) Pre-tax, real 5.5-6.25% 60-70% Source: Cepa: Report to the London Underground PPP Arbiter: Cost Of Capital Annex 3 ( July 2003), plus author's update. Notes: a including 0.5% uncertainty premium b including 1% small size premium and 0.3% embedded debt premium

21. 20 Further reading A study into certain aspects of the cost of capital for regulated utilities in the UK February 2003 Paper 08/03 from Ofgem Authors are academics and core paradigm is nondiversifiable risk.