Weighted-Average Cost of Capital

Builds onAfter-Tax Cost of Debt · Cost of Equity (Dividend Discount) · CAPM (Security Market Line) · Weighted Mean (Portfolio Return) — if this page feels steep, start there.

WACC = w_d\,r_d(1-t) + w_e\,r_e

$w_d, w_e$: the weights: the fraction of firm value financed by debt and by equity (market values; they sum to 1)
$r_d(1-t)$: the after-tax cost of debt — the coupon net of the interest tax shield
$r_e$: the cost of equity, from CAPM or the dividend discount model (never tax-shielded)
$WACC$: the blended price of a dollar of capital — the firm's hurdle rate and DCF discount rate

Why it must be true

A company's money comes from two kinds of investors — lenders and shareholders — each demanding their own return. The blended price of a dollar of capital is just the weighted average of what each source charges, with debt taken after its tax shield because the government subsidizes interest.

WACC is the company's hurdle: any project earning above it creates value for the capital providers as a group; anything below destroys it. It is also the discount rate that turns a firm's future free cash flows into a present value — arguably the single most consequential number in corporate finance, since every DCF valuation and capital-budgeting decision leans on it.

The derivation

Suppose fraction $w_d$ of the capital is debt costing $r_d(1-t)$ after tax, and $w_e = 1 - w_d$ is equity costing $r_e$ . A representative dollar of capital owes each class its share:

WACC = w_d \cdot r_d(1-t) + w_e \cdot r_e

The weights must be market values (what the claims are worth today), because the costs are market-demanded returns. With preferred stock in the structure, a third term $w_p r_p$ joins the sum — same weighted-average logic, one more class.

When to reach for it

Blending component capital costs into a single discount/hurdle rate, given a capital structure, component costs and a tax rate.

Listen for

“weighted-average cost of capital”“capital structure of … debt and … equity”“appropriate discount rate for the firm's cash flows”“hurdle rate for new projects”

Back-of-the-envelope

Estimate it in your head first — then the calculator only confirms.

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Shield the debt first (r_d × (1−t)), THEN weight — doing the two multiplications in that order keeps the classic error out.
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The answer must land between the after-tax debt cost and the equity cost — a weighted average cannot escape its ingredients. Distractors that sit outside the bracket are self-refuting.
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Equity-heavy structures live near r_e: at 80/20 equity/debt, WACC sits about four-fifths of the way up. Eyeball the weighting before computing.

Traps in applying it

✗Forgetting the tax shield on debt — or applying it to equity, whose dividends are not deductible.
✗Using book-value weights: the weights must reflect MARKET values of debt and equity.
✗Discounting a risky project at the company WACC — the rate matches the firm's average risk, not the project's.

Limits & criticisms

A single WACC assumes the capital structure and risk are frozen forever — but leverage drifts, and using the corporate average on projects riskier or safer than the firm systematically misprices them (the classic "WACC fallacy": safe divisions subsidize risky ones). Its inputs are estimates stacked on estimates — beta, equity premium, forward tax rate — so precision to two decimals is theater; sensitivity ranges are the honest presentation.

Where it came from

WACC crystallized from Modigliani and Miller's capital-structure work (1958–63) into the textbook form via the 1960s–70s corporate finance canon. It is the daily workhorse of valuation: every investment bank fairness opinion, private-equity model and corporate capital-budgeting memo discounts at a WACC, and regulators set utility revenues off one. The eternal fights — market vs book weights, which beta, whose tax rate — are fought precisely because a half-point of WACC can swing a valuation by billions.

One identity, 1 questions

The exam can hide any variable. Each face below is the same equation solved for a different unknown — drill them separately.

The blended hurdle

WACC = w_d r_d(1-t) + w_e r_e

The capital-budgeting face: what an average dollar of the firm's capital charges per year — beat it or don't invest.

Drill this face →

On the BA II Plus

Worked example: Capital structure: 45% debt at a pre-tax 4.5%, 55% equity at 12.5%; marginal tax rate 21%. Compute the weighted-average cost of capital.

1.0.045 [×] [(] 1 [−] 0.21 [)] [=]shield the debt cost first
2.[×] 0.45 [=] [STO] 1weight the debt component
3.0.125 [×] 0.55 [=]weight the equity component
4.[+] [RCL] 1 [=]sum → WACC (decimal)

→ 8.47%

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