CHAPTER 12: COST OF CAPITAL
A. OVERVIEW Definition: Cost of capital refers to the rate of return • a firm must earn on its investment projects to increase the market value of its common shares • required by market suppliers of capital to attract funds to the firm Notes: • If project rate of return > cost of capital • If project rate of return < cost of capital • Goal: minimize cost of capital value of firm increases value of firm decreases
Assumptions: 1. Business risk (not able to cover operating costs) is unchanged 2. Financial risk (not able to cover financial obligations) is unchanged 3. Cost of capital is measured on an after-tax basis Basic equation:
kl = rl + b p + f p
Ways to evaluate the basic equation: 1. Time-series: historic cost of capital 2. Compare with other firms (cross-section) Example 1 (Time-series) Firm A had a cost of long-term debt 2 years ago of 8%. Risk-free cost of long-term debt is 4%. Business risk premium is 2%, and financial risk premium is 2%. What is the cost of long-term capital of the firm when the current risk-free cost of long-term debt is 6%? Example 2 (Cross-section comparison) Firm B is in the same business and with a financial premium of 4%. The cost of capital of firm B is higher than that of firm A by 2 %. Definition: Target capital structure refers to the desired optimal mix of debt and equity financing that most firms attempt to achieve and maintain. B. COST OF LONG-TERM DEBT Definitions • Net proceeds : Funds received from the sale of a security (e.g. bond) – Incur two types of costs: flotation and discount • Flotation costs : issuing and selling a security – Apply to all public offerings of securities (debt, preferred and common shares) – Underwriting – Administrative Discount : drop in price of the security required to sell the security to investors – Mostly long-term debt / new common shares
•
Formula before-tax cost of debt (approximation)
kd =
I+
I = annual interest in dollars Nd = net proceeds from the sale of debt (bond) n = number of years to the bond’s maturity (1000 par value) After-tax cost of debt T = tax rate
1000 − N d n N d + 1000 2
ki = k d * (1 − T )
Example Firm A sells at $960 its 20-year $1000-par-value bond with a 9% coupon rate (annual). Suppose corporate tax is 40%. Find the after-tax cost of debt.
C. COST OF PREFERRED EQUITY Formula:
kp =
Dp Np
Kp = cost of preferred equity Np = net proceeds from the sale of shares Dp = annual dollar dividend TAX ADJUSTMENT NOT REQUIRED! Example Firm A intends to issue a 10% (annual dividend) preferred share with an expected stated value of $100. Flotation costs amount to $5.6 per share. What is the cost of preferred equity?
D. COST OF COMMON EQUITY Two techniques can be used 1. Constant-growth dividend valuation model (DVM) 2. CAPM Constant-growth DVM Formula:
ks =
D1 +g Po
Po = value of common share D1 = per share dividend expected at the end of year 1 g = constant growth rate in dividends Ks = cost of common equity Capital Asset Pricing Model (CAPM) Formula:
k s = RF + b * (k m − RF )
b = beta of systematic risk of the firm RF = Risk-free rate of return Km = market return Example A firm has common stock valued at $50 per share in 2003. In the past, annual dividends per share increased from $1.19 in 1997 to $1.83 in 2002. This growth trend is expected to continue in the future. Suppose risk-free rate of interest is 7%, and the firm has a beta of 1.5. The market return is 11%. Find the cost of common equity using DVM and CAPM. E. COST OF REINVESTED PROFITS Formula:
kr = ks
Kr = cost of reinvested profits Ks = cost of common equity NO ADJUSTMENT FOR FLOTATION COSTS REQUIRED. F. WEIGHTED AVERAGE COST OF CAPITAL Definition: Weighted average cost of capital (WACC) reflects the expected average future cost of funds for the upcoming year Formula (WACC)
k a = wi * ki + w p * k p + ws * (k r or k n )
Wi = proportion of long-term debt in capital structure Wp = proportion of preferred equity in capital structure Ws = proportion of common equity in capital structure Notes: • The weights sum to 1.
• •
•
Keep weights in decimals; keep cost in %. Should we use kr or kn? – Kr is often less costly than Kn retained investment is often used first for long-term financing. How to find weights? – Book value weights: use accounting values to measure the proportion – Market value weights: use market values (prices) to measure the proportion (preferred) – Historic weights: book/market value weights based on actual capital structure proportion – Target weights: book/market value weights based on desired capital structure
Example A firm has on its books the amounts and specific (after-tax) costs shown in the following table. Find WACC. Source Book value Specific cost Long-term debt Preferred equity Common equity $700,000 50,000 650,000 5.3% 12.0 16.0
1. The text book uses slightly different notations: G. Final Notes 1. Relative risks and costs; not absolute 2. Changes in capital structure may affect • The weights in calculating WACC • The relative risks and, therefore, return on equity (and the cost of debt) 3. Combine with CAPM to assess changes in capital structures and the beta • Example Suppose a company’s debt ratio is 30%. The risk-free rate of interest is 6% and the market risk premium is 7%. The required return is 8% on debt and 14% on shares. If the company retires $97 billion of equity and instead borrows $97 billion from the bank, how would this change in debt ratio affects the risk of the company. (Assume that borrowing the additional $97D billion would increase the debt ratio to β equity = β asset tax for now. 45%.) We ignore corporate + ( β asset − β debt )
E
4. What if corporate tax is non-zero? • Example Suppose a company is currently 30% debt financed. Its levered equity beta is 1.1 and its debt beta is 0. What happens to the riskiness of its equity if debt financing is increased to 50% of the firm value? Use D a tax rate of 35%.
β levered = β u +
E
( β u − β debt )(1 − T )
5. The project cost of capital • Example Suppose a market leader is 30% debt financed in a similar project. A new company uses the market leader’s unlevered equity of 0.86 and relever it to its own target capital structure (40% debt). What is the project cost of capital? Assume the beta for debt is 0 and the cost of debt is 6%. The market risk premium is 7% and the risk-free rate of interest is 4%. 6. Flotation costs and discounts