Cost of Capital
Financing Decisions
Cost of Capital
Syllabus tag: KASNEB CPA | Intermediate Level | CA22 Financial Management | Topic 3 Cost of Capital
Lesson objectives
By the end of this topic, you will be able to:
- Compute the cost of equity by the dividend growth model and by CAPM
- Compute the cost of preference shares
- Compute the cost of debt, irredeemable and redeemable, after tax
- Combine them into a weighted average cost of capital (WACC)
- Explain when WACC is the right discount rate and when it is not
Why this matters
Investment Appraisal discounted at "10%" without saying where 10% came from. This topic supplies that number. Get it wrong and every NPV in the paper is wrong with it.
Words to know
- Cost of equity (Ke) — the return shareholders require.
- Cost of debt (Kd) — the return lenders require, after tax relief.
- Cost of preference (Kp) — the return preference shareholders require.
- WACC — the average of these, weighted by how much of each is used.
- Beta — how much a share moves relative to the market as a whole.
- Market premium — the extra return investors demand for holding shares rather than risk-free assets.
Cost of equity: dividend growth model
Ke = (D1 / P0) + g
D1 is next year's dividend, P0 today's share price, g the growth rate.
A company just paid a dividend of KES 3.00, growth is 8%, the share trades at KES 45:
D1 = 3.00 × 1.08 = 3.24
Ke = (3.24 / 45) + 0.08 = 7.2% + 8% = 15.2%
Watch the D0 / D1 distinction. Using the 3.00 already paid gives 14.67% and is the single commonest error on this calculation.
Where growth is not given, estimate it from retention:
g = b × ROE
Retaining 60% of earnings at a 15% return on equity gives g = 0.6 × 15 = 9%.
Cost of equity: CAPM
Ke = Rf + β(Rm − Rf)
Risk-free rate 9%, beta 1.4, market return 15%:
Ke = 9 + 1.4 × (15 − 9) = 9 + 8.4 = 17.4%
The bracket is the market premium, not the market return. Using 15 instead of 6 gives 30% and should look obviously wrong.
A beta above 1.0 means the share is more volatile than the market, so shareholders demand more.
:::checkpoint The dividend growth model gave 15.2% and CAPM gave 17.4% for the same company. Both are correct calculations. Suggest two reasons the answers differ, and say which you would use to appraise a new project. :::
Cost of preference shares
Kp = D / P0
A 10% preference share of KES 100 par, trading at KES 80:
Kp = 10 / 80 = 12.5%
No tax adjustment. Preference dividends are an appropriation of profit, not an expense, so they attract no tax relief.
Cost of debt
Interest is tax deductible, so the company's cost is the after-tax figure.
Irredeemable debt: Kd = i(1 − t) / P0
12% debentures trading at KES 96, tax rate 30%:
Kd = 12 × 0.7 / 96 = 8.4 / 96 = 8.75%
Redeemable debt repays par at maturity, so the gain or loss on redemption counts. The approximation an examiner accepts:
Kd ≈ [i(1 − t) + (Redemption − Price) / n] / [(Redemption + Price) / 2]
10% debentures at KES 92, redeemable at par in 5 years, tax 30%:
Kd ≈ [7 + (100 − 92) / 5] / [(100 + 92) / 2] = 8.6 / 96 = 8.96%
Slightly higher than the irredeemable case, because the holder also collects the 8 discount at redemption.
Weighted average cost of capital
WACC = (E / (E + D)) × Ke + (D / (E + D)) × Kd
Equity 600m at Ke 17.4%, debt 400m at Kd 8.75%:
WACC = 0.6 × 17.4 + 0.4 × 8.75 = 10.44 + 3.50 = 13.94%
Use market values for the weights, not book values. Book equity is a historic figure and can be wildly out of date; the market value is what shareholders have actually committed today.
When WACC is the wrong rate
WACC is the right discount rate only when the new project carries the same business risk as the company's existing operations and is financed in roughly the same proportions. A manufacturer opening a bank should not discount that project at its manufacturing WACC — the risk is different, so the required return is different.
:::checkpoint A company's WACC is 14%. It is considering a project in a much riskier industry. If it uses 14% anyway, is it more likely to accept projects it should reject, or reject projects it should accept? Explain. :::