Four inputs, one relevering step and target weights produce the discount rate, and each of the usual shortcuts moves the value by five to twenty per cent.
WACC is the cost of equity and the after-tax cost of debt, each weighted by its share of the target capital structure at market value. With an unlevered beta of 0.90 relevered to 1.14, a cost of equity of 10.50 per cent, a cost of debt of 4.88 per cent after tax and weights of 74.07 and 25.93 per cent, the WACC is 9.04 per cent. On a business with 5,000,000 of next-year free cash flow growing at 2.0 per cent, that rate gives an enterprise value of 71,010,586.
Worked in full in Business Valuation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The formula fits on one line. The value is decided by four choices inside it: which beta, which leverage, which cost of debt and which weights. Each is shown below, followed by what happens to the value when it is made carelessly.
| Input | Value | Source in practice |
|---|---|---|
| Risk-free rate | 4.25% | Long government bond yield in the cash flows' currency |
| Equity risk premium | 5.50% | House view or published survey |
| Unlevered (asset) beta | 0.90 | Median of listed peers, each unlevered |
| Target debt to equity | 35% | Peer median or the target structure, at market value |
| Tax rate | 25% | Marginal rate on which interest is deducted |
| Credit spread | 2.25% | Where the company could borrow today |
Step 1: relever the beta. Peer betas are measured on shares, so they carry each peer's own leverage. Unlever them, take the median, then relever at the target structure.
βL = βU × [1 + (1 − t) × D/E] = 0.90 × [1 + 0.75 × 0.35] = 0.90 × 1.2625 = 1.14
Step 2: cost of equity by CAPM. The relevered beta multiplies the equity risk premium: 1.14 (1.136 unrounded) times 5.50 per cent adds 6.25 points to the risk-free rate.
Ke = rf + βL × ERP = 4.25% + 6.25% = 10.50%
Step 3: after-tax cost of debt. The company borrows at the risk-free rate plus 2.25 per cent, so 6.50 per cent. Interest is deductible, so the cost to the company is 6.50 per cent times 0.75, or 4.88 per cent.
Step 4: weights. A debt-to-equity ratio of 35 per cent means debt is 0.35 of every 1.35 of capital: 25.93 per cent debt and 74.07 per cent equity.
WACC = E/V × Ke + D/V × Kd × (1 − t)
= 74.07% × 10.50% + 25.93% × 4.88% = 7.777% + 1.264% = 9.04%
In Excel, with named cells: =Bu*(1+(1-Tax)*DE) for the beta, =Rf+BetaL*ERP for the cost of equity, =(Rf+Spread)*(1-Tax) for debt, and =1/(1+DE)*Ke+DE/(1+DE)*Kd_at for WACC.
| Component | Rate | Weight | Contribution |
|---|---|---|---|
| Cost of equity (levered beta 1.14) | 10.50% | 74.07% | 7.777% |
| Cost of debt after tax (6.50% pre-tax) | 4.88% | 25.93% | 1.264% |
| WACC | 100% | 9.04% |
Equity supplies 86 per cent of the rate on 74 per cent of the capital. That is why the beta and the equity risk premium deserve more of the reviewer's time than the cost of debt: one more point of premium lifts WACC by 0.84 points and takes the illustrative value from 71,010,586 to 63,428,672.
| Unlevered beta | D/E 0% | D/E 20% | D/E 35% | D/E 50% |
|---|---|---|---|---|
| 0.80 | 8.65% | 8.57% | 8.53% | 8.49% |
| 0.90 | 9.20% | 9.10% | 9.04% | 9.00% |
| 1.00 | 9.75% | 9.62% | 9.56% | 9.50% |
Read across a row and leverage barely moves WACC: from 9.20 to 9.00 per cent between no debt and 50 per cent debt to equity, because the cheaper debt is offset by a riskier equity. What remains is the tax shield. Read down a column and the beta moves it by over half a point for each 0.10. The asset beta is the input; the leverage is mostly a rearrangement.
| WACC | Enterprise value | Change |
|---|---|---|
| 8.00% | 83,333,333 | 17.4% |
| 8.50% | 76,923,077 | 8.3% |
| 9.04% | 71,010,586 | 0.0% |
| 9.50% | 66,666,667 | −6.1% |
| 10.00% | 62,500,000 | −12.0% |
The rate is then applied to a terminal value that usually carries most of the answer, which is why a quarter-point error here is magnified; see what percentage of a DCF the terminal value should be. When the debt amortises and leverage falls over the forecast, a single constant WACC is itself an approximation, discussed in does a constant WACC overstate value.
Relever the peer asset beta at the target leverage, price equity with CAPM, take debt after tax, and weight both at the same market-value structure: here 9.04 per cent. Spend the review time on the beta and the premium, which carry 86 per cent of the rate. The free workbook for this book runs the full discounted cash flow and its cost-of-capital sensitivity grid, and the DCF terminal value template takes the rate from there.
Market values, or a target capital structure expressed in market terms, consistent with the leverage used to relever the beta. In the illustrative case, weighting by book values of 20 million of equity and 18 million of debt puts debt at 47.37 per cent, cuts WACC from 9.04 to 7.84 per cent and inflates enterprise value by 20.7 per cent, while the cost of equity still assumes the lower leverage.
Because interest is deductible, so each unit of interest costs the company only one minus the tax rate, and the free cash flow being discounted is computed with tax on unlevered profit. At 6.50 per cent pre-tax and 25 per cent tax the after-tax cost is 4.88 per cent. Using 6.50 per cent instead raises WACC to 9.46 per cent and lowers value by 5.6 per cent.
Take the peer group's unlevered (asset) beta and apply the target leverage with the Hamada formula: levered beta equals unlevered beta times one plus (one minus tax) times debt over equity. An unlevered 0.90 at 35 per cent debt to equity and 25 per cent tax becomes 0.90 times 1.2625, or 1.14, which adds 6.25 points of premium to the risk-free rate.
This article is one calculation from Business Valuation. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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