THE COST OF CAPITAL

1. THE COST OF CAPITAL • The cost of capital for a firm is the minimum return investors require to make the purchase of all of the operating assets of a firm attractive • Cost of Capital depends on use of funds rather than source • Uses of the cost of capital • Firm valuation • Discount rate for investment decision making • Minimum rate of return investors require to shift their dollars from other alternatives to a given investment • Also referred to as “required return” or “hurdle rate

2. COST OF CAPITAL MEASUREMENT • Some preliminary issues • The cost of capital cannot be directly observed • Focus on the liability side of the balance sheet • Use returns on publicly traded financial securities • The estimated cost of capital should: • Make common sense • Investors should require higher returns on “riskier” assets • The estimate should be a “reasonable” magnitude (with a base rate taken from the long-term Treasury bond yield) • Be reasonably stable over time

3. RETURNS TO BUYING A FIRM • Balance Sheet identity: assets = liabilities • Balance sheet “reduction” Net Working Capital Want return for this Can identify return for these Short-term liabilities Short-term assets Debt   Debt Net Debt Long-term assets Long-term assets Long-term assets Equity Equity Equity

4. THE RETURN ON A PORTFOLIO • $500 invested in bonds which have a 6% return • $1500 invested in stocks which have a 10% return • Bond investment grows to $530 after 1 year [$500 * (1.06)] • Stock investment grows to $1650 after 1 year [$1500 * (1.10)] • Total $2000 investment grows to $2180 • Return on portfolio is 9% • Alternative way to determine portfolio return: weighted average of returns on parts of the portfolio • 25% (by value) invested in bonds, 75% invested in stocks • Return on portfolio = 0.25 * 6% + 0.75 * 10% = 9%

5. COST OF CAPITAL: CALCULATION • After tax cost of capital is the weighted average of required returns on different types of liabilities used to finance the assets under consideration. Formally: kc = (D/V ) * kd * (1-t) + (E/V ) * ke kd = cost of debt D=value of debt ke = cost of equity E=value of equity kc = overall cost of capital V=D+E t = firm’s marginal tax rate

6. COST OF CAPITAL (WACC) EXAMPLE • $1 million capital required (for a project) • capital structure: 40% debt ($400) @ 8% pre-tax (4% after-tax*) 1.6% 60% equity ($600) at 14% required return 8.4% weighted average (after tax): 10.0% # * tax rate (t) = 50%; # note that before tax W.A.C.C. is 10%/(1 - 0.5) = 20.0%

7. WACC EXAMPLE (CONTINUED) • EBIT = $1m x 20.0% (before tax) $200,000 • interest = $400,000 x 8% $32,000 • EBT (earnings before tax) = EBIT - interest $168,000 • tax (@ 50%) $84,000 • EAT (earnings after tax) = EBT - tax $84,000

8. WACC EXAMPLE (CONTINUED) • Earnings after tax (“residual” before equity holders $84,000 • equity holders required return = $600,000 x 14% $84,000 • “residual” after equity holders required return $0 “EVERYONE” IS SATISFIED!

9. CAPITAL STRUCTURE • Use market rather than book values of debt and equity if available • “Target” capital structure: • estimate the firm’s current capital structure • review the capital structure of comparable firms • review management’s plans for future financing

10. COST OF DEBT (kd) • Required return necessary to buy the debt of the firm • Use current as opposed to past yields, or required returns • Examine yields on newly issued bonds that are of “comparable” risk (bond rating) • Take government yields and add a “premium” based on historical experience • KEY: rates are observable • Match with term of projects • Focus on “permanent” debt (can include short term)

11. COST OF EQUITY (ke) • Problem: we cannot observe require equity returns directly (we can only observe current equity prices and past returns) • Two Basic Approaches: • estimate the expected(internal rate of) return to owning the company’s stock using a valuation model like the dividend discount model • estimate the market’s requiredreturn on the firm’s equity => need a risk pricing model (e.g. CAPM) • Note: in an efficient market required and expected returns should be the same

12. COST OF EQUITY: THE DIVIDEND DISCOUNT MODEL (DDM) With constant growth: where: P0 = current price D1 = expected dividend next year ke = cost of equity (required return) g = anticipated growth of dividends D1 P0 = Ke - g

13. THE DDM: IMPLEMENTATION • Estimating the growth rate (g) • historic dividend growth rate • analyst forecasts of earnings growth (if dividend payout rate is constant) • g = ROE x (1-payout rate) • Compute keimplicit in DDM model • Problem: growth is rarely constant D1 P ke = + g

14. THE CAPITAL ASSET PRICING MODEL (CAPM) • The CAPM relates the cost of equity for an individual asset to that asset’s beta. Formally: ke = rf + b RP where: ke = required rate of return on equity rf = risk-free rate b = beta of stock (risk relative to market) RP = expected market risk premium

15. THE CAPITAL ASSET PRICING MODEL (CAPM): ASSUMPTIONS • Investors choose investments which maximize expected returns given a certain level of portfolio standard deviation • Investors plan investments for one identical holding period • Investors pay no taxes or transactions costs • All investors have the same beliefs regarding asset characteristics and the same information • All assets can be traded • Investors can borrow or lend at a risk-free rate.

16. INVESTMENT POSSIBILITIES Possible combinations of M and risk free investment Return Best combination of risky securities + Best risky portfolio, M Rf (return on risk- free investment Standard Deviation of Returns

17. THE CAPM: EQUILIBRIUM • Under CAPM assumptions, all investors will hold a combination of the risk-free asset and the ultimately diversified portfolio, the market portfolio. • The market portfolio is the (weighted) average of all risky assets. • Investors with average risk tolerance will hold the market portfolio • less risk tolerant investors will hold some of the market portfolio and lend at the risk free rate • more risk tolerant investors will lever the market portfolio by borrowing at the risk free rate.

18. THE RELEVANT MEASURE OF RISK FOR AN INDIVIDUAL INVESTMENT • Since investors hold the market portfolio, the relevant measure of risk for an individual asset is the contribution that asset makes to the risk of the market portfolio. • Formally, this contribution is given by an asset’s “beta”: cov (rA, rM) bA = s 2M

19. THE CAPM: GRAPHICALLY Required or Expected rate of Return, E(Ri) Slope = RP Risk Premium bi* RP Risk Free Rate, Rf bi Risk,b

20. AN EXAMPLE.... • Assume that: Rf = 8%; E(Rm) = 12% => The market risk premium = 4% • A low risk company, say b=0.5, would require a risk premium = 0.5*4% = 2%. The required return for such a company’s equity would be 2% plus the risk free rate of 8% for a total of 10%. • A medium risk company, with b=1.0, would require a total expected return = 12%. • A high risk company, with b=2.0, would require a total expected return = 16%.

21. THE CAPM: INPUTS • b - beta • Beta for an asset of similar risk to the market portfolio = 1. • Typical range of betas: 0.5 - 2.0 • rf - risk free rate • Current yield on government bonds • Match to life of assets (10-20 year) • RP - expected market risk premium • Historic average of difference between the return on the market portfolio (e.g. TSE300) and the return on long-term government bonds

22. BETA MEASUREMENT RSTOCK slope = beta Beta is the slope in a regression of the returns on an individual stock on the “market” portfolio (e.g. TSE300) • Issues: • Length of historical period for estimating beta • Return interval (daily, weekly, monthly, etc.) • Historic versus predictive betas x x x x x x RTSE x x x x

23. ALCAN BETA (1995-2000)

24. ALCAN BETA (1998-2000)

25. PORTFOLIO BETAS • The beta of a portfolio is the weighted average of the betas of individual investments (weighted by investment) • Example: • Company A: bA = 0.8 • Company B: bB = 1.4 • 25% invested in A, 75% invested in B • Portfolio beta: bP = 0.25 * 0.8 + 0.75 * 1.4 = 1.25

26. PORTFOLIO BETAS To see this, consider the CAPM Return to Company A :ke,A = rf + bA RP Return to Company B : ke,B = rf + bB RP Return to portfolio: ke, P = 0.25 * ke,A + 0.75 * ke,B ke, P = 0.25 * (rf + bA RP ) + 0.75 * (rf + bB RP ) ke, P = rf + (0.25 * bA + 0.75 *bB ) * RP Alternatively, directly from the CAPM ke, P = rf + bP RP This implies: bP = 0.25 * bA + 0.75 *bB

27. WHAT IF THERE ARE OTHER FINANCIALCLAIMS AS PART OF THE FIRM’S PERMANENT CAPITAL STRUCTURE? • WACC equals weighted average of all financial claims (be careful to adjust for taxes where appropriate) • Example: preferred stock • What is the cost of preferred stock (kP)? • similar principles as with debt • In general: kP = Dividend Current Price

28. ALCAN COST OF CAPITAL

29. ALCAN COST OF CAPITAL

30. SUMMARY • Cost of capital is computed as a weighted average of costs of debt & equity (WACC or kc) • WACC captures required return for various investors providing financing for firm • Final number should “make sense”