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Valuation03

Cost of capital

13 min read

Read firstTime value and discounting. Valuation without accounting is memorization.

The is where a valuation is most often wrong and least often argued about. A gets forty rows of forecast detail and one cell for , and the WACC cell moves the answer more than half the rows above it. So build it from the parts.

Cost of equity, by CAPM

Capital asset pricing model

Re=rf+β×ERPR_e = r_f + \beta \times ERP
The return equity investors require is the risk-free rate plus beta times the equity risk premium. Beta scales the market's risk premium to this particular stock.

Three inputs, each of which is a decision.

  • . The ten-year Treasury , currently around 4.2%. Match the horizon: a business valued in perpetuity is better matched by a ten-year than by a three-month bill. Free from FRED, series DGS10.
  • . The extra return required for holding equities. Estimates run from roughly 4% to 6% for the US depending on method. This site uses 4.5%, from Damodaran's implied premium series at NYU Stern, which is free and updated monthly. Say which estimate you used, because the choice is worth more than most of your forecast.
  • .How much the stock moves relative to the market. Available from most data providers, and estimated from a regression of the stock's returns on the index over some window, which means it describes the past.

Risk-free rate and equity risk premium as of 2026-08-17. US 10-year Treasury constant maturity yield, FRED series DGS10. Aswath Damodaran, NYU Stern, implied equity risk premium for the United States.

Unlevering, because a beta is contaminated by debt

An observed beta measures two things at once: how risky the business is, and how much debt is amplifying it. A company that doubles its leverage has a higher beta with exactly the same operations. To use a peer's beta you have to strip the second part out.

Unlever

βU=βL1+(1t)DE\beta_U = \frac{\beta_L}{1 + (1 - t)\frac{D}{E}}
Unlevered beta is levered beta divided by one plus one minus the tax rate times the debt to equity ratio. What is left measures business risk with the financing removed.

Relever

βL=βU×[1+(1t)DE]\beta_L = \beta_U \times \left[1 + (1 - t)\frac{D}{E}\right]
Relevered beta puts a capital structure back on. Use the target's own debt to equity ratio, not the peer's.

ConventionThe formula above assumes debt beta is zero and that the tax shield carries the same risk as the debt. Both are simplifications. There are variants that relax them, and for a non-distressed company the difference is small enough that Hamada is what almost everyone uses. Name the assumption rather than hiding it.

Putting it together

Weighted average cost of capital

WACC=EVRe+DVRd(1t)WACC = \frac{E}{V}R_e + \frac{D}{V}R_d(1-t)
WACC is the equity weight times the cost of equity, plus the debt weight times the after-tax cost of debt. Weights are market values, and V is debt plus equity.

Build one

Market inputs

Ten-year Treasury. FRED series DGS10, updated daily and free.

Damodaran publishes an implied US premium each month at NYU Stern.

Comparable company betas

Observed betas mix business risk with the effect of each company's debt. Strip the debt out, take the median of what is left, and you have a measure of the business alone.

Walmart
Unlevered0.6980.72 / (1 + 0.75 x 0.042)
Costco
Unlevered0.8310.84 / (1 + 0.75 x 0.014)
Kroger
Unlevered0.4140.55 / (1 + 0.76 x 0.432)
Dollar General
Unlevered0.5470.62 / (1 + 0.77 x 0.173)
TJX
Unlevered0.8890.90 / (1 + 0.75 x 0.017)
Unlevered beta across the set
 Value
Median0.698
Mean0.676

Median rather than mean, because one comp with an odd capital structure should not move the answer. On a set this small the two rarely agree, and the gap is worth looking at.

Target capital structure

Market value if the bonds trade, book value if they do not.

The yield its bonds trade at today, not the coupon it happens to pay.

Output

Test yourself

01Why is debt cheaper than equity?

Two reasons, and both matter. Lenders rank ahead of shareholders in a bankruptcy and their return is contractual, so they take less risk and demand less. And interest is tax deductible, so the government funds a share of it. The follow-up is why a company does not fund itself entirely with debt, and the answer is that leverage raises the risk of the equity and the probability of distress, so both the cost of equity and eventually the cost of debt rise as you add more.

02Why unlever and relever rather than just using the target's own beta?

Because a single company's measured beta is noisy, and because the target may be private, recently listed, or about to change its capital structure. Unlevering a set of peers isolates business risk from financing, the median of that is a more stable estimate than any one observation, and relevering puts the target's own structure back on. It also makes the estimate usable in an LBO, where the capital structure is about to change completely.

03Should you use book or market values to weight WACC?

Market. WACC is the return investors require on what they hold today, and what they hold today is worth its market value. Book equity is historical cost and usually much smaller, so book weights overweight debt and produce a WACC that is too low. Book value of debt is generally an acceptable proxy for market value unless the bonds trade far from par, which happens when credit deteriorates.

A tutor that knows this lesson. It asks before it explains, and it will not tell you what to do with your own money.

Every figure in this lesson that names a company comes from Target Corporation's Form 10-K for Fiscal 2025, the year ended 2026-01-31, filed 2026-03-11. Educational material, not investment advice.