A levered DCF and an unlevered DCF must land on the same equity value. Here is the FCFE build, the reconciliation to the cent, and the three ways it goes wrong.
Free cash flow to equity is net income plus depreciation and amortisation, less capital expenditure and the rise in working capital, plus net borrowing. Discount it at the cost of equity, not the WACC. In the case below a year-one FCFE of 6,479,339 at an 11.0 per cent cost of equity and 3.0 per cent growth gives an equity value of 80,991,736, exactly the enterprise value of 115,702,479 less 34,710,744 of debt that the unlevered route produces.
Worked in full in Business Valuation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Most corporate valuations run an unlevered DCF: free cash flow to the firm at the WACC, then a bridge from enterprise value to equity value. The levered route skips the bridge and values the shares directly. It is the natural method for banks and insurers, where debt is raw material rather than financing, and for any business whose debt schedule is fixed by contract, such as a buyout or a project. It is also the best audit of an unlevered DCF: if the two routes do not agree on the same facts, one of the assumptions about leverage is inconsistent, and the gap tells you how much it is worth.
An illustrative company, valued on its next-year cash flow growing at a constant rate, with debt held at 30 per cent of enterprise value. That last assumption is the one the WACC already makes, so both routes start from the same world.
| Item | Value |
|---|---|
| EBIT, year 1 | 12,000,000 |
| Depreciation and amortisation | 3,000,000 |
| Capital expenditure | 4,000,000 |
| Increase in net working capital | 1,000,000 |
| Tax rate | 25% |
| Perpetual growth | 3.0% |
| Debt as a share of enterprise value | 30% |
| Cost of debt, pre-tax | 6.0% |
| Cost of equity at that leverage | 11.0% |
NOPAT is 12,000,000 less 25 per cent tax, 9,000,000. Add back 3,000,000 of D&A, take off 4,000,000 of capex and 1,000,000 of working capital: FCFF is 7,000,000. The build is the one in how to calculate unlevered free cash flow.
WACC = 70% × 11.0% + 30% × 6.0% × (1 − 25%) = 7.70% + 1.35% = 9.05%
EV = 7,000,000 / (9.05% − 3.0%) = 115,702,479
Debt = 30% × 115,702,479 = 34,710,744. Equity = 80,991,736
Two adjustments turn the firm's cash into the shareholders' cash. First, interest: 6.0 per cent on 34,710,744 is 2,082,645, or 1,561,983 after the 520,661 tax shield. Second, net borrowing: if debt is to stay at 30 per cent of a value that grows 3.0 per cent a year, the company borrows 3.0 per cent of its debt each year, 1,041,322, and that cash goes to the shareholders.
Net income = (12,000,000 − 2,082,645) × (1 − 25%) = 7,438,017
FCFE = 7,438,017 + 3,000,000 − 4,000,000 − 1,000,000 + 1,041,322 = 6,479,339
Check from the top: 7,000,000 − 1,561,983 + 1,041,322 = 6,479,339
Excel: =NetIncome+DA-Capex-dNWC+(DebtEnd-DebtStart)
Equity value = 6,479,339 / (11.0% − 3.0%) = 80,991,736
Excel: =FCFE1/(Ke-g)
The difference from the unlevered route is zero. On 10,000,000 shares it is 8.10 a share by either method. That is not a coincidence of the numbers chosen: when debt is a constant share of value and the cost of equity is the one consistent with that leverage, the two methods are the same algebra arranged differently.
The cost of equity of 11.0 per cent belongs to a debt-to-equity ratio of 42.86 per cent. If you change the leverage you must relever the beta and recompute it, as in the step-by-step WACC; otherwise FCFE will pick up the cheap debt and none of the extra risk it puts on the shares.
Because debt is tied to value, a change in growth changes the debt, the interest and the net borrowing, and the two routes stay reconciled at every rate.
| Growth | EV | Debt | FCFE year 1 | Equity value | Per share |
|---|---|---|---|---|---|
| 2.0% | 99,290,780 | 29,787,234 | 6,255,319 | 69,503,546 | 6.95 |
| 2.5% | 106,870,229 | 32,061,069 | 6,358,779 | 74,809,160 | 7.48 |
| 3.0% | 115,702,479 | 34,710,744 | 6,479,339 | 80,991,736 | 8.10 |
| 3.5% | 126,126,126 | 37,837,838 | 6,621,622 | 88,288,288 | 8.83 |
| 4.0% | 138,613,861 | 41,584,158 | 6,792,079 | 97,029,703 | 9.70 |
One point of growth, from 2.5 to 3.5 per cent, moves EV and equity alike by 18.0 per cent, and only because debt moves with value. Hold the debt fixed in money terms instead and leverage falls as the company grows, which the constant 11.0 per cent no longer describes: the two routes then diverge, and the right fix is a cost of equity that changes year by year, or an adjusted present value.
| Error | Equity value | Error | Per share |
|---|---|---|---|
| FCFE discounted at the WACC | 107,096,510 | +32.2% | 10.71 |
| FCFF discounted at the cost of equity, read as equity | 87,500,000 | +8.0% | 8.75 |
| FCFE without the net borrowing | 67,975,207 | −16.1% | 6.80 |
| FCFF at the cost of equity, less debt | 52,789,256 | −34.8% | 5.28 |
The first is the most common in practice: a model is converted from unlevered to levered, the cash flow line is changed and the discount rate is not. It counts the tax shield and the cheap cost of debt twice, once in the cash flow and once in the rate. The third is the one that looks prudent. Leaving out the 1,041,322 of new borrowing makes FCFE 5,438,017 and the value 16.1 per cent lower, but it describes a company that lets its leverage drift towards zero while its cost of equity stays priced for 30 per cent debt. Either keep borrowing in the forecast or lower the cost of equity; doing neither is an inconsistency, not conservatism.
The book values one company three ways and turns the spread between them into a single disagreement about growth; the free workbooks for the case carry the DCF, the bridge to equity and the checks behind every figure.
FCFF is the cash the operations produce for all capital providers, before any interest or debt flows. FCFE is what is left for shareholders after after-tax interest and net borrowing. In the worked case FCFF is 7,000,000; take off 1,561,983 of after-tax interest and add 1,041,322 of new borrowing and FCFE is 6,479,339.
The cost of equity, never the WACC, because FCFE belongs to shareholders alone. At 11.0 per cent and 3.0 per cent growth the case gives an equity value of 80,991,736. Discounting the same FCFE at the 9.05 per cent WACC gives 107,096,510, an overstatement of 32.2 per cent.
Usually because the debt in the FCFE forecast does not follow the leverage assumed in the WACC and cost of equity. Hold debt at the same 30 per cent of enterprise value and let it grow with the business, and the two routes agree exactly: 80,991,736 either way. Ignoring net borrowing alone cuts the FCFE value to 67,975,207.
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.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: corporate finance, valuation and markets → · All 1340 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.