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Work out a firm's weighted average cost of capital

CFA® Level I · Corporate Issuers · Capital Structure · CI.3.a

The idea

The weighted average cost of capital is the return a firm must earn to satisfy everyone who funded it, weighted by how much each provided. Debt enters after tax, because interest is deductible and the tax saving is real money — that deduction makes debt cheaper still. Equity has no such shield and carries the residual risk, so its required return is the higher of the two. The weights should be market values rather than book values, since the question is what capital costs to raise now, not what it cost historically. WACC is the discount rate for projects of average risk only; using one firm-wide rate for everything quietly subsidises the risky projects with the safe ones.

Formulas

Weighted average cost of capital

WACC = (D ÷ V) × rd × (1 − t) + (P ÷ V) × rp + (E ÷ V) × re

D, P, E
the market values of debt, preferred stock and common equity
V
the three of them added together
rd, rp, re
the before-tax cost of debt and the costs of preferred and common equity
t
the marginal tax rate

Market weights, not book, and target weights rather than today's if the company is moving towards one. Only the debt term is taxed, because only interest is deductible.

A practice question

From the question bank, with the reason each wrong option is wrong.

The weighted average cost of capital weights each source of finance by its:

  1. proportion of total capital — correct
  2. book valueWhy not: Book values record what was raised historically. The cost of capital concerns what investors require on today's values.
  3. ageWhy not: How long a security has been outstanding has no bearing on its share of the firm's financing.

Each provider's required return counts in proportion to how much of the firm's funding it supplied.

A harder one

A firm is 40% debt at a 5% pre-tax cost and 60% equity at 12%, with a 25% tax rate. Its WACC is closest to:

  1. 9.0%Why not: Understates the deduction. Ignoring the tax shield entirely gives 9.2% and applying it gives 8.7%; 9.0% follows from neither.
  2. 8.7% — correct
  3. 7.2%Why not: The equity leg alone, 0.6 times 12%, with the debt contribution left out.

The after-tax cost of debt is 3.75%, so 0.4 x 3.75 plus 0.6 x 12 gives 1.5 plus 7.2, or 8.7%.

The hardest tier

Debt appears cheaper than equity in a WACC calculation for two reasons: its lower required return, and:

  1. its longer maturityWhy not: Debt is typically shorter-dated than equity, which is perpetual, and maturity is not what makes it cheap.
  2. its lack of voting rightsWhy not: Lenders forgo votes in exchange for a prior claim, and that trade does not create the cost advantage.
  3. the deductibility of interest — correct

The tax shield is a genuine transfer from the tax authority, and it accounts for much of the apparent gap.

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