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Work out a firm's weighted average cost of capital

CFA® Level I · Corporate Finance · 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. seniority in a liquidationWhy not: Seniority helps explain why debt has a lower required return, but the weight depends on how much of the capital each source supplies.
  3. ageWhy not: How long a security has been outstanding has no bearing on its share of the firm's financing.

The weighted average cost of capital (WACC) is the average rate a firm pays to those who fund it, such as lenders and shareholders. Each source counts in proportion to how much of the total funding it supplies. Formula: WACC = (Debt / Total capital) x Cost of debt + (Equity / Total capital) x Cost of equity. For example, with $40 of debt and $60 of equity, debt has a weight of 40% and equity 60%. Seniority and age do not affect the weights.

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. 9.2%Why not: This uses the 5% pre-tax cost of debt (0.4 x 5% + 0.6 x 12% = 9.2%), so it misses the tax deduction on interest.
  2. 8.7% - correct
  3. 7.2%Why not: The equity leg alone, 0.6 x 12%, with the debt contribution left out.

Find the after-tax cost of debt first, then average the two costs using the weights. Formula: WACC = Weight of debt x Cost of debt x (1 - Tax rate) + Weight of equity x Cost of equity. Step 1: 5% x (1 - 0.25) = 3.75%. Step 2: 0.4 x 3.75% = 1.5%, and 0.6 x 12% = 7.2%. Step 3: 1.5% + 7.2% = 8.7%. Using the pre-tax 5% gives 9.2%, and leaving debt out gives 7.2%.

The hardest tier

A diversified firm uses its company-wide WACC to evaluate a project in an unusually risky new division. What is the consequence?

  1. The project will be rejected even if it creates valueWhy not: That is the consequence for a project safer than the firm average, which faces too high a hurdle.
  2. There is no consequence, as WACC applies firm-wide by constructionWhy not: The firm-wide figure reflects the firm's average risk, which is exactly what this project does not have.
  3. The discount rate is too low, so risky projects are over-accepted - correct

A discount rate should match the risk of the cash flows being valued. The firm-wide WACC reflects the firm's average risk. A project in a riskier division needs a higher rate. Using the lower average rate makes the project look better than it really is. Idea: Too low a rate means risky projects are accepted too often. Example: if WACC is 8% but the project should use 12%, a project with positive net present value at 8% may be negative at 12%, so the firm would accept it wrongly.

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