3.2 Cost of Capital & WACC

Cost of Debt

The cost of debt is the yield a firm pays on its borrowing. Because interest expense is tax-deductible, the government effectively subsidizes part of it, so we use the after-tax cost of debt:

After-Tax Cost of Debt = Rd x (1 - Tax Rate)

If a firm borrows at 8% and faces a 25% tax rate, the after-tax cost is 8% x (1 - 0.25) = 6.0%. This interest tax shield is why debt is the cheapest capital source and why adding debt initially lowers WACC.

Cost of Preferred Stock

Preferred stock pays a fixed dividend with no maturity. Its cost is:

Rp = Annual Preferred Dividend / Net Issue Price

A $100 par preferred paying an 8% dividend ($8) issued at a net price of $96 costs 8 / 96 = 8.33%. There is no tax adjustment: preferred dividends are paid from after-tax income and are not deductible, unlike interest. The net issue price is the market price minus any flotation cost, so flotation raises the effective cost of preferred capital.

Yield to Maturity vs. Coupon

When estimating the cost of debt, use the current yield to maturity (YTM) on the firm's outstanding bonds, not the historical coupon rate. The coupon reflects rates when the bond was issued; the YTM reflects what the firm would pay to borrow today, which is the relevant marginal cost for new financing decisions.

Cost of Common Equity

Common equity is the most expensive source because shareholders bear the most risk and have the last claim on cash flows. Two standard methods exist.

Method 1: CAPM

Re = Rf + Beta x (Rm - Rf) (covered in Section 3.1). With Rf = 4%, beta = 1.2, and a 6% market risk premium, Re = 4% + 1.2 x 6% = 11.2%.

Method 2: Dividend Growth Model (Gordon Model)

Re = (D1 / P0) + g

where D1 is next year's expected dividend, P0 is the current stock price, and g is the constant dividend growth rate. The first term (D1/P0) is the dividend yield; g is the capital-gains (growth) component.

If a stock trades at $50, pays a $2 dividend next year, and grows dividends at 5%, then Re = (2 / 50) + 0.05 = 0.04 + 0.05 = 9.0%. Note D1 is the dividend one year out; if given the current dividend D0, gross it up: D1 = D0 x (1 + g).

Which method to use: CAPM works for any firm with an estimable beta, including non-dividend-payers. The dividend growth model requires a stable, growing dividend and is sensitive to the growth assumption. In practice, analysts often compute both and reconcile. A third shortcut, the bond-yield-plus-risk-premium approach, adds a 3-5% equity risk premium to the firm's own bond yield.

Weighted Average Cost of Capital (WACC)

WACC is the blended return required across all capital providers and the standard hurdle rate for capital budgeting:

WACC = (E/V) x Re + (D/V) x Rd x (1 - T)

where E = market value of equity, D = market value of debt, V = E + D, and the weights (E/V) and (D/V) are market-value proportions. When preferred stock exists, add a (P/V) x Rp term. Always use market values, not book values, for the weights.

Full Worked Example

A firm is financed with $60 million equity and $40 million debt (V = $100M). Its cost of equity is 12%, its pre-tax cost of debt is 7%, and its tax rate is 30%.

The firm should accept projects of similar risk returning more than 9.16% and reject those returning less. WACC is valid only for projects with risk comparable to the firm's existing operations; a riskier division requires a higher, risk-adjusted hurdle rate.

Marginal Cost of Capital

The marginal cost of capital (MCC) is the cost of the next dollar of new capital. Firms first use the cheapest sources (retained earnings, low-rate debt). As these are exhausted, new equity issues carry flotation costs and new debt may require higher rates, so the MCC schedule rises in steps. A break point occurs where a source is used up and the firm must tap a costlier tier. Projects are accepted up to where the MCC equals the return on the marginal investment opportunity.

Retained Earnings vs. New Equity

Retained earnings are not free; their cost equals the cost of common equity because shareholders forgo dividends they could reinvest elsewhere. New external equity costs more than retained earnings because of flotation costs, which is why the MCC schedule jumps upward once retained earnings are exhausted.

Common WACC Traps

• Use market values, not book values, for the weights.
• Apply the (1 - T) factor only to debt, never to equity or preferred.
• Use the firm's target capital structure weights when given, not just the current mix.
• WACC is the right hurdle rate only for projects of average firm risk; use a divisional or project-specific rate for unusually risky investments.