Common mistake 1 with Cost of capital (WACC)

Using book values for the weights. Book equity can be far from its market value.

Common mistake 2 with Cost of capital (WACC)

Using the coupon rate as the cost of debt. The cost of debt is the yield the firm would pay on new debt today.

Common mistake 3 with Cost of capital (WACC)

Applying one company WACC to a division or project with different risk.

Common mistake 4 with Cost of capital (WACC)

Forgetting the tax shield on debt, or applying it to preferred dividends, which are not deductible.

EconStatsCraft › Cost of capital (WACC)

Cost of capital (WACC)

Builds the discount rate a firm's projects must clear: the CAPM cost of equity, the after-tax cost of debt and preferred, market-value weights, and how WACC shifts as the debt mix changes once beta is relevered.

The intuition

A firm raises money from shareholders and lenders, and each expects a return that matches the risk it bears. The firm's projects must earn enough to pay all of them, so the hurdle rate is the blend of their required returns, weighted by how much each has put in. Debt is cheaper than equity both because lenders are paid first and because interest reduces tax.

When to use it

Setting the hurdle rate for a project of average risk, discounting free cash flow to the firm in a valuation, or judging whether a change in capital structure lowers the cost of funding.

Where the estimator comes from

Investors' total required cash return is r_E E + r_D(1-t)D + r_P P on capital V=E+D+P, so the required return per unit of capital is the value-weighted average. The cost of equity comes from CAPM, r_E=r_f+\beta_E\,\text{ERP}. With risk-free debt, the levered beta satisfies \beta_E=\beta_A[1+(1-t)D/E] (Hamada), so business risk \beta_A can be unlevered from a comparable firm and relevered at a target capital structure.

The model

\text{WACC} = w_E\,r_E + w_D\,r_D(1-t) + w_P\,r_P,\qquad r_E = r_f + \beta_E\,\text{ERP},\qquad \beta_A = \frac{\beta_E}{1+(1-t)\,D/E}

What it assumes

Weights are market values, and they are the target capital structure the firm will keep.
The project being valued has the same risk as the firm as a whole. A riskier project needs a higher rate.
CAPM gives the cost of equity; beta, the risk-free rate and the equity risk premium are all estimates.
The Hamada relevering formula assumes debt is risk-free and has a beta of zero.

Statistical properties

Equity is always more expensive than after-tax debt.
Adding debt raises the cost of equity, because equity holders bear more financial risk.
In Modigliani–Miller without taxes WACC does not depend on leverage; the tax shield is what makes debt lower it.
Beyond some leverage, rising distress costs push the cost of debt and equity up, so WACC has a minimum.

How to read the output

The cost of equity is always above the after-tax cost of debt, because shareholders are paid last.
Asset beta measures business risk alone; equity beta adds financial risk from leverage on top.
The chart relevers beta at each debt mix with a fixed cost of debt, so WACC keeps falling. In practice the cost of debt rises with leverage, which produces a minimum.
Discount FCFF at WACC; discount FCFE at the cost of equity.

A worked reading

A firm with 600 of equity and 400 of debt by market value. With a 4% risk-free rate, a beta of 1.2 and a 5.5% equity risk premium, CAPM gives a 10.6% cost of equity. Debt costs 6% before tax and 4.5% after a 25% tax rate. WACC is 0.6 × 10.6% + 0.4 × 4.5% = 6.36% + 1.80% = 8.16%. Unlevering gives an asset beta of 0.80: the business risk alone, before the extra risk that 40% debt puts on shareholders.

Symptom → diagnosis → what to do

If you see this	It means	Do this
WACC below the risk-free rate	A sign or percent error	Check every input is in percent
WACC falls forever as debt rises	Cost of debt held fixed	Raise rd as leverage rises; the chart notes this
Weights look wrong	Book values used	Use market values of equity and debt
Cost of equity very high	Beta from a highly levered comparable	Unlever, then relever at your own structure

Common mistakes

Using book values for the weights. Book equity can be far from its market value.
Using the coupon rate as the cost of debt. The cost of debt is the yield the firm would pay on new debt today.
Applying one company WACC to a division or project with different risk.
Forgetting the tax shield on debt, or applying it to preferred dividends, which are not deductible.

Where to read this properly

CFA Institute, Corporate Issuers: Cost of Capital (Levels I and II).
Modigliani and Miller (1958, 1963), on capital structure and the tax shield.
Hamada (1972), The Effect of the Firm's Capital Structure on the Systematic Risk of Common Stocks.

Related Finance & risk

Black–Scholes option pricing · Bond price, duration & convexity · Merton distance to default · EMI / home loan planner · CAPM / beta estimation · Multi-factor model · Portfolio optimization · Value at Risk & Expected Shortfall · Performance & drawdown · Time value of money & NPV/IRR · Equity valuation (DDM, FCF, residual income) · Binomial option pricing · Option strategies (payoff & profit) · Forwards, futures & swaps · Credit risk & Basel capital · Extreme value theory (tail risk)

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Cost of capital (WACC)

The intuition

When to use it

Where the estimator comes from

The model

What it assumes

Statistical properties

How to read the output

A worked reading

Symptom → diagnosis → what to do

Common mistakes

Where to read this properly

See also

Related Finance & risk

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