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Weighted Average Cost of Capital

The weighted average cost of capital is the firm’s average cost of financing across debt and equity.

The questionWhat return must this business earn on its capital to satisfy lenders and shareholders, given the risk of what it does?

Pronounced wack. Often called the company's cost of capital.

Formula · Franco Modigliani and Merton Miller, 1958 onward

WACC Blended cost of capital
Equity part
Weight of equity E / (E + D)
×
Cost of equity Re, often from CAPM
+
Debt part
Weight of debt D / (E + D)
×
Cost of debt Rd, before tax
×
One minus tax rate 1 minus T
Simplified view of the WACC formula, with each source of capital weighted at market value.

When to use it

  • You need the discount rate for a DCF of a whole business or a large investment.
  • A client sets hurdle rates for capital projects, and nobody can say where the current rate came from.
  • The capital structure is under discussion and the board wants to see how the blended cost responds, with the caveats that come with that.
  • You need the capital charge for an economic value added calculation.

When to avoid it

  • The project has a different risk from the company's average, such as a new market or technology. Use a rate for that risk, usually built from comparable companies in the new activity.
  • The company is a bank or other financial firm, where debt is raw material and not a source of capital. A cost of equity is the usual basis there.
  • The company is private or early-stage, and there are no market values and no comparable betas. The inputs are guesses, so present a range and say that it is one.
  • The choice is how to fund a particular project. WACC describes the blended cost of the existing mix, and it does not say which source to use next.

Overview

WACC puts a number on the blended return a company has to earn on its capital to satisfy lenders and shareholders. It weights the cost of equity and the after-tax cost of debt by how much of the capital each supplies, at market value. Consultants use it as the discount rate in a DCF, the capital charge in EVA, and the hurdle rate for investments of average risk.

Debt cost is observable, but the cost of equity is an estimate, and a plausible range of betas alone can move WACC by a point or more. Show a range. Apply it only to cash flows with the company’s average risk, and use a different rate for a project that is riskier or safer.

What it is not

  • The interest rate on the company's debt. Debt is one input, weighted with equity, and the cost of equity is a required return that is estimated, not a rate in a contract.
  • A number you can simply look up. Published figures from data providers use their own betas, premiums, and weights, and two providers can differ for the same company.
  • A cost that falls as debt rises. Debt is cheaper after tax, but the cost of equity rises as leverage rises, and lenders charge more as the company borrows more.

The steps

  1. Decide which cash flows the rate is for

    State whether it is for the whole business, a division, or a project, and what risk those cash flows carry. A rate for the group average is wrong for a division with different risk.

  2. Set the capital structure weights

    Use market values of equity and debt, or the target mix the company intends to hold. Check the choice against peers in the same industry. Record which basis you used and why.

  3. Estimate the cost of equity

    Take a risk-free rate in the currency and horizon of the cash flows. Take a beta from comparable companies, adjusted for their leverage and for the target structure. Take an equity risk premium from a named source. Compute the cost of equity and the range from plausible inputs.

  4. Estimate the after-tax cost of debt

    Use the current yield on long-term borrowing at the company's likely rating, not the coupon on bonds issued years ago. Multiply by one minus the marginal tax rate.

  5. Combine, test, and document

    Compute WACC and test it against the ranges. Record each input, its source, and the date. Choose a single rate for the decision and keep the range next to it.

The formula

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

The cost of equity and the after-tax cost of debt, each weighted by its share of total capital at market value.

  • E: the market value of equity, meaning share price times shares outstanding.
  • D: the market value of debt. Book value is a common proxy when the debt is not traded and its rate is close to current rates.
  • Re: the cost of equity, commonly estimated with CAPM as the risk-free rate plus beta times the equity risk premium.
  • Rd: the pre-tax cost of debt, meaning the current yield the company would pay on long-term borrowing, not the coupon on old debt.
  • T: the marginal corporate tax rate, which sets the value of the interest deduction.

In practice

Start with a company whose equity is worth 600 and whose debt is worth 400, in millions, at market values. Capital is 1,000, so the weights are 60 percent equity and 40 percent debt. The risk-free rate is 4 percent, beta is 1.2, and the equity risk premium is 5 percent, so the cost of equity is 4 + 1.2 × 5 = 10 percent. The company would pay 6 percent on new long-term debt, and the tax rate is 25 percent, so after-tax debt cost is 6 × 0.75 = 4.5 percent. WACC = 0.60 × 10 + 0.40 × 4.5 = 6.0 + 1.8 = 7.8 percent.

The finance team quotes 7.8 percent, and the consultant asks which input it is most sensitive to. Beta is the weakest, since it comes from a regression on a few years of share prices and a peer set. At a beta of 1.0 the cost of equity is 9 percent and WACC is 0.60 × 9 + 1.8 = 7.2 percent. At 1.4 the cost of equity is 11 percent and WACC is 0.60 × 11 + 1.8 = 8.4 percent. The plausible beta range alone puts WACC between 7.2 and 8.4 percent, so the valuation uses 7.8 percent with that band shown beside it.

What you leave with

  • WACC as a single rate and as a range, with every input and its source.
  • The capital structure weights used, and the reason for them.
  • The cost of equity build-up: risk-free rate, beta, and equity risk premium.
  • A note on which projects or units the rate suits and which need an adjusted rate.

Failure points

Precision beyond the inputs

A WACC quoted as 7.83 percent when beta and the equity risk premium are each estimates with a wide band. The second decimal is invented, and it makes the number look more settled than it is.

One rate for every project

A company-wide WACC is used as the hurdle for everything. Risky projects clear a rate that is too low for them, and safe ones are rejected, so capital drifts toward the riskiest part of the business.

Book-value weights

Weights are taken from the balance sheet. When the market value of equity exceeds book, the debt weight is overstated, and since debt is cheaper after tax, WACC comes out too low.

Circularity ignored

Equity value depends on WACC, and market-value weights depend on equity value. People paper over this by fixing the weight at today's share price, which is wrong for a company whose structure or price is about to change. Use the target structure or iterate to a consistent answer.

Stale or mismatched inputs

A risk-free rate in a different currency from the cash flows, or the coupon on old bonds used as the cost of debt. Each looks reasonable on its own and moves the result by a visible amount.

The failures above are usually Commercial Acumen: the work was not tied to money, for the client and/or for you.

Origin

WACC is a textbook formula and not the invention of one person. Its theoretical footing is Franco Modigliani and Merton Miller's 1958 paper "The Cost of Capital, Corporation Finance and the Theory of Investment" in the American Economic Review. They showed that, without taxes and other frictions, how a firm is financed does not change its enterprise value. Their 1963 correction added the tax advantage of debt, which is the basis for reducing the cost of debt in the formula by the tax rate.

The cost of equity input is usually estimated with the capital asset pricing model, published by William Sharpe in 1964, with parallel work by others. In the version practitioners use, each source of capital is weighted by its market value.

Further reading

  • Weighted average cost of capital

    Wikipedia's overview of the formula, the tax effect, and the practical difficulty of defending one figure. Free.

  • Modigliani-Miller theorem

    Wikipedia's account of the capital structure theory behind the formula, with and without taxes. Read it to see why debt is not a free source of cheap capital.

  • Damodaran Online

    Aswath Damodaran's site at NYU Stern, with free data sets on betas and cost of capital by industry, and valuation course materials. Useful for a sanity check on a client's inputs.

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