Corporate Finance Week 2 — Cost of Capital (WACC)

High-priority exam takeaways (slides + lecture emphasis).

1) Core idea: WACC is project-specific

Key message: The intuition “a project is good if it returns more than the firm’s WACC” is often wrong.

Discount rates (and therefore WACC) must match project risk.
Treat the project as a stand-alone firm and build inputs for that risk.
Do not let discount rates become investor-specific (e.g., “Elon vs Paulina buys Twitter” story).

Exam implication: If given “the firm’s WACC” or “how the project is financed,” do not plug it in automatically. You must justify that project risk and target capital structure match the firm; otherwise rebuild WACC using comparables.

2) WACC: formula + what must be done correctly

WACC formula

rWACC = rE * (E/(D+E)) + rD * (D/(D+E)) * (1 - t)

Mechanics you will be penalised for getting wrong

Use market value weights, not book weights.
Equity MV = price × shares; debt MV = bond price × number of bonds.
If debt isn’t traded, book value is only a reasonable proxy in specific cases (recently issued/refinanced, stable rates, unchanged credit risk).

Target leverage is not “how you finance the project”

Two classic mistakes:

Using the project’s actual financing (e.g., “100% debt funded → D/(D+E)=100%”).
Using the firm’s current leverage automatically (only valid if project risk and structure match the firm).

Correct approach: estimate a target D/(D+E) using “pure play” comparables for the project’s business.

3) Cost of equity (rE): three methods and when to use them

Week 2 covers three methods: DDM, ECM, CAPM.

(A) Dividend Discount Model (DDM) — Gordon growth

Intuition: price equals PV of expected future dividends.

Pt = E[DIVt+1] / (rE - g) ⇒ rE = (E[DIVt+1] / Pt) + g

Best for mature firms with stable dividend growth.
Weak for early-stage/high-growth/no-dividend firms.

(B) Earnings Capitalization Model (ECM)

rE = EPS1 / P0

Mainly for no-growth situations.
Not suitable for growing firms.

(C) CAPM (default workhorse)

rE = rf + βE * (Rm - Rf)

Assume CAPM is the default unless the question explicitly steers you to DDM/ECM.
CAPM returns later in capital budgeting, valuation, and M&A contexts.

4) Beta and leverage: pure play beta workflow (unlever → average → relever)

Logic

Same underlying cash-flow risk ⇒ similar asset beta (business risk).
Equity beta differs across firms mainly due to leverage (financing risk).
Example intuition: airlines’ levered betas vary widely; unlevered betas converge.

Steps you must execute

Select comparable (“pure play”) firms.
Estimate each comparable’s βE (regression of stock returns on market returns).
Unlever to βA:
βA = βD * (D/(D+E)) + βE * (E/(D+E))
Often assume βD ≈ 0 if debt is not too risky; be more careful with high leverage.
Average the comparables’ βA and treat it as the project’s βA.
Relever to the project’s βE using the project’s target D/E:
βE = βA * (1 + D/E) (if βD ≈ 0)
Plug βE into CAPM to get rE.

5) Risk-free rate and market risk premium: what to emphasise in answers

Market proxy

Use broad indices (e.g., S&P 500; FTSE All-Share / local indices are mentioned).
Use value-weighted portfolios (do not use equally-weighted).

Market risk premium (MRP)

Common practice: use historical market excess returns.
Define the period, compute averages, take the difference.
Know limitations: assumes stable risk aversion and portfolio riskiness over time.

“Two risk-free rates” point (practitioner input logic)

CAPM shows rf twice, but inputs mix forward- and backward-looking components.
Use today’s rf from current yields / the yield curve (government bond yields).
Maturity matching: choose rf maturity to match project life (short project → short bills; long-lived asset → long government bonds).

6) Cost of debt (rD): estimation methods and traps

Definition: current cost of borrowing consistent with the project’s chosen capital structure.

Core relationships

Borrowing costs depend on rates/yield curve + default risk.
rD = rf + default spread.
After-tax cost of debt: rD × (1 − marginal tax rate).

Methods (and when feasible)

If rated: use agency rating (Moody’s/S&P/Fitch etc.) + default premium.
If not traded and not rated: synthetic rating (comparables or infer from ratios like interest coverage), or use recent issue borrowing cost only if risk is similar.
Extensions: yield-to-maturity on outstanding bonds; debt beta approach.

Traps / caveats:

Do not just use the quoted interest rate if debt is very risky (default probabilities matter).
If the firm has multiple layers of debt, you may need a weighted average.

7) Is WACC constant over time?

Formally: no.
It changes if internal equity is used up, firm risk/beta changes, rates change, rating changes, or the debt/equity mix changes.
Practitioners often assume stability for simplicity.

8) What to expect on the final exam (Week 2)

Valuation problems include cost of capital (alongside capital budgeting and M&A).
You must show intermediate steps and justify assumptions.
Likely workflow:
- Target leverage from comps,
- Unlever/relever beta,
- CAPM for rE,
- Rating/default spread for rD,
- Then WACC and interpretation.
Marks are not just arithmetic: you must explain why your inputs match the project (project-specific WACC logic).

Exam checklist for any WACC/CAPM question

State: discount rate must match project risk → choose project-specific WACC.
Choose comps / pure plays and compute target D/(D+E).
Unlever comp betas → average βA → relever to project βE.
CAPM: choose rf with maturity matching; MRP consistent with market proxy.
Cost of debt: rD = rf + default spread; apply tax.
Compute WACC using MV weights and interpret economically.