Cost of capital: the honest hurdle
Introduced| English | Meaning |
|---|---|
| weighted average cost of capital | weighted average cost of capital |
| tax shield | tax shield |
The hurdle is a blend of the actual money
- The raise is 200,000 of equity at 12% and 120,000 of debt at 6% pre-tax (tax 25%). The weighted average cost of capital 加权平均资本成本 (WACC) on market-value weights: 9.19% ✓.
- Get the blend wrong and every NPV the company computes is wrong the same way.
The formula and the weights
- WACC = (E/V) x 12% + (D/V) x 6% x (1 - 0.25) = 7.50% + 1.69% = 9.19% ✓. Weights 62.5 / 37.5.
- Weights are MARKET values (80,000 shares at 2.50), never the letterhead. The tax shield 税盾 makes debt 4.5% after tax - because the taxman pays part of the interest.
Equity 200,000, debt 120,000. The debt weight, in % (one decimal)?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
120,000/320,000 = 37.5% - and equity 62.5%. Market values, always.
k_e 12%, k_d 6% pre-tax, tax 25%, weights 62.5/37.5. WACC, in % (two decimals)?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
0.625(12) + 0.375(4.5) = 7.50 + 1.69 = 9.19%.
Debt 120,000 at 6%, tax 25%. The annual tax shield, in pounds?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
120,000 x 6% x 25% = 1,800 of tax saved - the reason debt's effective cost is 4.5%.
The 8% guess vs the 9.19% truth: by how much was the site NPV overstated, to the nearest pound?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
27,420 - 23,604 = 3,816 - the hurdle is not a rounding detail; it moves every NPV the company ever computes.
The beta-less private firm
- No beta, no quoted price. The proxy: a listed food company at beta 1.1, market 10%, risk-free 4% -> CAPM k_e = 4 + 1.1 x 6 = 10.6%; add 1.4 points of private-risk premium -> 12%.
- Every step is a judgement written down: the proxy, the premium, the market estimate. A WACC with no working is a number wearing a lab coat.
Which input, and where does it come from?
Source each WACC input correctly - market weights, after-tax debt, proxied equity cost - and spot the traps.
Proxy beta 1.1, market 10%, risk-free 4%. The CAPM k_e, in %?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
4 + 1.1(10-4) = 10.6%; +1.4 private premium = the 12% used. Each judgement written down.
Borrowing more lowers WACC at first. Why does it stop?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
The bottom of the U is the right amount of debt - not the most the bank will lend.
Match each input to its source.
Difficulty 2/5 · 140 coins + a small bonus on first completion today
Right source, right side of the formula - the four-line audit of any WACC.
A project financed entirely by debt should be appraised at 4.5%.
Difficulty 1/5 · 100 coins + a small bonus on first completion today
The company blend governs (adjusted for project risk). Financing 100% by debt just borrows against the equity cushion - the equity still expects 12%.
The debt illusion
- Borrow more and the blend falls - to 7.87% at D = 240,000. But each tranche raises the equity beta (toward 1.5) and eventually the 6% becomes 8%.
- The WACC curve is U-shaped: the bottom is the right amount of debt, not the most the bank will lend.
Three capital-cost slips
- Book-value weights - equity at par when the market says 2.50.
- Pre-tax cost of debt - or claiming the shield while forgetting interest is paid.
- Project-level debt, project-level WACC - the hurdle moves with the COMPANY blend, adjusted for project risk.
Recap
- WACC = (E/V)k_e + (D/V)k_d(1-t) at market weights.
- Private k_e by proxy, judgements written down.
- The U-curve finds the right debt - not the most available.