BFC2140 · Corporate Finance
Cost of Capital
The cost of capital is the return a firm must earn on its investments to satisfy all its investors, and it is the discount rate for average-risk projects. This chapter covers the after-tax cost of debt (based on the bond's YTM, not its coupon), the cost of preference shares, the cost of equity via both the DDM and the CAPM, and the weighted average cost of capital (WACC) using market-value weights — plus divisional/project cost of capital, SML mispricing errors and flotation costs. It is examined as a signature Section C question: a full multi-component WACC build, with reasoning about when the firm-wide WACC is and is not the right rate.
What this chapter covers
- 01Cost of debt: pre-tax = YTM on existing bonds, after-tax = r_D(1 − T)
- 02Cost of preference shares: r_p = D_p/P_p (or per net proceeds)
- 03Cost of equity by the dividend-discount model: rₑ = D₁/P₀ + g
- 04Cost of equity by the CAPM: rₑ = R_f + β[E(R_m) − R_f]
- 05WACC = wₑ·rₑ + w_p·r_p + w_D·r_D(1 − T) with market-value weights
- 06Why market-value weights are preferred to book-value weights
- 07Divisional/project cost of capital and the SML over- and under-investment errors
- 08Flotation (issue) costs and how they reduce a project's NPV
Full multi-component WACC build
- 1 markAfter-tax cost of debt: the pre-tax cost is the bond's YTM of 9.81%, so after tax r_D(1 − T) = 9.81% × (1 − 0.30) = 6.87%.
- 1 markCost of preference shares as a perpetuity: r_p = D_p/P_p = 1.50/12 = 12.50%.
- 1 markCost of equity by the CAPM: rₑ = R_f + β[E(R_m) − R_f] = 5 + 1.1(11 − 5) = 5 + 6.6 = 11.60%.
- 2 marksCompute market values: debt = 8,000 × 960 = $7.68m; preference = 4m × 12 = $48.0m; equity = 6m × 8 = $48.0m; total V = $103.68m.
- 1 markCompute the market-value weights: w_D = 7.68/103.68 = 0.0741; w_p = 48.0/103.68 = 0.4630; wₑ = 48.0/103.68 = 0.4630.
- 1 markWeight the component costs: WACC = 0.0741(6.87) + 0.4630(12.50) + 0.4630(11.60) = 0.509 + 5.788 + 5.371.
- 1 markSum to the WACC: 0.509 + 5.788 + 5.371 = 11.67%.
Key terms
- Cost of debt
- The return debtholders require, measured by the YTM on the firm's existing bonds (not the coupon rate). Because interest is tax-deductible, the relevant figure in WACC is the after-tax cost, r_D(1 − T).
- Cost of preference shares
- The return preference shareholders require: r_p = D_p/P_p, treating the fixed preference dividend as a perpetuity. There is no tax adjustment because preference dividends are not tax-deductible.
- Cost of equity
- The return ordinary shareholders require, estimated two ways: the dividend-discount model rₑ = D₁/P₀ + g, or the CAPM rₑ = R_f + β[E(R_m) − R_f]. It is the most expensive component because equity bears the most risk.
- Weighted average cost of capital (WACC)
- The blended after-tax required return on all the firm's capital: WACC = wₑ·rₑ + w_p·r_p + w_D·r_D(1 − T), using market-value weights. It is the discount rate for average-risk projects financed in the firm's existing mix.
- Market-value weights
- The proportions of debt, preference and equity based on current market values rather than balance-sheet (book) values. Market values reflect what investors actually require today, so they are the correct weights for WACC.
- Divisional / project cost of capital
- A risk-matched discount rate used when a project or division has different systematic risk or financing from the firm overall. Using the firm-wide WACC for such projects causes SML errors — accepting too-risky projects and rejecting safe ones.
Cost of Capital FAQ
Why is the cost of debt the YTM and not the coupon rate?
The coupon rate is a historical, contractual figure fixed when the bond was issued; it does not reflect what lenders require today. The yield to maturity is the market's current required return on the firm's debt — the rate that prices the existing bonds — so it is the true cost of raising new debt of similar risk. After applying the tax shield, the WACC uses r_D(1 − T), the after-tax YTM. Plugging the coupon rate into WACC is a classic error that misstates the cost of debt.
Should I use the DDM or the CAPM for the cost of equity?
Both are valid and the question usually tells you which inputs you have. Use the CAPM (R_f + β[E(R_m) − R_f]) when you are given beta, the risk-free rate and a market-risk premium. Use the DDM (D₁/P₀ + g) when you have the current price, next dividend and a growth rate. They estimate the same quantity — the return shareholders require — so when both are available they should give similar answers; large differences signal a questionable input (often the growth rate).
Why must WACC use market-value weights?
Because WACC is the return the firm must earn for today's investors, and investors price their claims at market values, not at the historical book values recorded on the balance sheet. Market values reflect current required returns and the true relative size of each financing source. Using book weights — especially for equity, whose market value usually differs greatly from book — distorts the blend and the resulting discount rate.
When is the firm's WACC the wrong discount rate for a project?
When the project's systematic risk or financing mix differs materially from the firm's overall. The WACC is only appropriate for average-risk projects financed in the firm's existing proportions. For a riskier or safer project you should use a risk-matched rate — often a pure-play comparable's beta. Misusing the firm-wide WACC causes the SML investment errors: a firm with a low WACC over-invests in risky projects (accepting some that should be rejected) and under-invests in safe ones, because the single rate does not match each project's true required return.
How is the cost of capital examined in BFC2140?
It is the Week 10 topic and a signature Section C question on the final (Weeks 5-12 are emphasised). The full WACC build — costing debt (after-tax YTM), preference and equity, then blending with market-value weights — is explicitly listed among the high-yield recurring exam skills. Expect also conceptual parts on why market weights and the YTM are used, and Section C reasoning about divisional cost of capital and SML mispricing/flotation costs.
Exam move
Treat the WACC as the capstone that ties the unit together — it reuses bond YTM, the CAPM, the DDM and preference-share valuation in one calculation. Practise full builds end to end and set them out as a table (component, cost, market value, weight) so no step is skipped. Burn in the three rules that examiners test: pre-tax cost of debt is the YTM not the coupon, the (1 − T) tax shield applies only to debt, and weights are market values not book values. Be able to switch between the CAPM and DDM for the cost of equity depending on the inputs given. Beyond the arithmetic, prepare the conceptual Section C answers: why market weights, why a risk-matched (divisional) rate rather than the firm-wide WACC for off-risk projects, the SML over/under-investment errors, and how flotation costs reduce a project's NPV.
