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Plate 2 of 19 · Finance

The cost of capital

About 6 minutes to read, then three questions that count toward your mastery.

Investors lend and invest only if they expect a return. The cost of capital is that expected return, and it is the rate a DCF discounts at.

The idea

A company raises money from two kinds of investor. Lenders want interest; shareholders want a return high enough to compensate for the risk they carry. The cost of capital is the blend of the two: the return the company must earn on a project just to leave its investors as well off as before.

The cost of equity can’t be read off a contract, so it is estimated. The capital asset pricing model (CAPM) starts from the risk-free rate and adds the market’s equity risk premium, scaled by beta: how much the share tends to move with the market. Only that market risk earns a premium, because company-specific risk can be diversified away.

Debt is cheaper. Lenders are paid before shareholders, so they take less risk, and interest is tax-deductible, so each dollar of interest costs the company less than a dollar. The weighted average cost of capital (WACC) weights each cost by its share of the company’s market value.

The formula

kE = rf + β × ERP, WACC = EV × kE + DV × kD × (1 − T)

kE
cost of equity: the return shareholders expect
rf
risk-free rate, such as a government bond yield
β
beta: the share’s sensitivity to market moves (the market itself is 1)
ERP
equity risk premium: how much more the market is expected to return than rf
E, D, V
market values of equity and debt, and their total V = E + D
kD, T
pre-tax cost of debt, and the tax rate that interest is deducted at

A worked example

Plate 2

A packaging company’s shares are worth $750m and its debt $250m. The risk-free rate is 4.5%, its beta 0.9, the equity risk premium 5.5%. It borrows at 7% and pays tax at 21%. What is its WACC?

  1. Cost of equity: 4.5% + 0.9 × 5.5% = 4.5% + 4.95% = 9.45%.
  2. After-tax cost of debt: 7% × (1 − 0.21) = 5.53%.
  3. Weights from market values: equity 750 ÷ 1,000 = 75%, debt 25%.
  4. WACC = 0.75 × 9.45% + 0.25 × 5.53% = 7.09% + 1.38% = 8.47%.

Projects of the company’s usual risk must earn at least 8.47% a year to add value, and 8.47% is the rate to discount its free cash flow at in a DCF.

Try it

The risk-free rate is set at 4% and the equity risk premium at 5%.

1.10
30%
6.0%
25%

Build a WACC

8.00%WACC
Cost of equity
9.50%
After-tax cost of debt
4.50%
Weights, equity : debt
70% : 30%
Lowered by the tax saving on interest
0.45 points

Equity costs much more than debt after tax: that gap is why the debt share matters so much to the average.

The common mistake

Forgetting the tax saving on interest

Using the 7% pre-tax cost of debt gives 0.75 × 9.45% + 0.25 × 7% = 8.84%. That overstates the cost of capital by more than a third of a percentage point, and every DCF built on it comes out too low.

Remember

  • Cost of equity = risk-free rate + beta × equity risk premium. Beta scales the premium, not the risk-free rate.
  • Debt costs kD × (1 − tax rate) after tax, because interest is deductible.
  • Weight by market values, and use a rate that matches the project’s risk: a riskier project needs a higher rate than the company average.

Check yourself

Three questions from the Learn room’s bank. Your answers update your mastery of this skill, the same as in Practise.

Use it on real numbers

Open Cost of capital, in Finance › Valuation and try the idea on your own numbers.