FNCE30011 · Essentials Of Corporate Valuation
Equity Valuation by DCF
A discounted-cash-flow valuation says that value today is the present value of expected future cash flows, discounted at a rate that reflects their risk — resting on three pillars: the time value of money, risk aversion (a risk premium added to the rate), and value additivity (the PV of a sum is the sum of the PVs). The whole subject then turns on a single discipline: choosing which cash flow to discount and pairing it with the matching rate. This chapter sets up the cash-flow cascade — operating FCF (left for all investors, and because tax is struck after interest it still contains the interest tax shield), then unlevered FCF (FCF−Y·T, with the shield removed), then FCFE (FCF−Y−PRINC, the residual to equity). Built on it are the two equity models — the FCFE model (discount FCFE at ke) and the dividend discount model (discount dividends at ke, collapsing to Gordon D1/(ke−g) under constant growth). They agree only after the DDM is reconciled for cash the firm retains or borrows — Miller–Modigliani dividend irrelevance underneath. The governing rule is the matching principle: FCFU pairs with ku, FCFE pairs with ke.
What this chapter covers
- 012.1 The DCF idea and its three pillars (time value, risk aversion, value additivity)
- 022.2 The cash-flow cascade: FCF → unlevered FCF → FCFE
- 032.3 Defining each measure and building FCF from the financial statements
- 042.4 The enterprise vs equity route and the EV→equity bridge
- 052.5 The FCFE model, the DDM and the Gordon growing perpetuity
- 062.6 Reconciling FCFE and the DDM — the surplus-cash / surplus-liability fix
Worked example: equity value two ways, then reconcile
- +1Identify. Constant-growth equity cash flows — use the FCFE model as the benchmark and the Gordon DDM as a cross-check; reconcile the gap with the retained cash.
- +1FCFE model. FCFE1 = 84(1.04) = $87.36m, so E0 = FCFE1/(ke−g) = 87.36/(0.10−0.04) = $1,456m.
- +1Naive DDM. D1 = 60(1.04) = $62.4m, so E0DDM = 62.4/0.06 = $1,040m — $416m too low, because it ignores the retained cash.
- +1Reconcile. Add the PV of the surplus-cash stream, a growing perpetuity of $24m: 24(1.04)/0.06 = 24.96/0.06 = $416m.
- +1Agree. 1,040 + 416 = $1,456m — identical to the FCFE model. The payout mix did not change value (MM dividend irrelevance).
Key terms
- Free cash flow (FCF)
- After-tax operating cash for all investors, assembled as EBIT + DEP − CAPEX − ΔWC − TAX with interest excluded. Because tax is struck after interest, FCF contains the interest tax shield Y·T.
- Unlevered FCF (FCFU)
- FCF with the interest tax shield removed: FCFU = FCF − Y·T — the cash the firm would generate with no debt. It pairs with the unlevered cost of capital ku (and with ks in the standard WACC).
- Free cash flow to equity (FCFE)
- The residual to equity after paying debt holders: FCFE = FCF − Y − PRINC, where PRINC is net principal repaid (negative if debt is drawn up). Discount FCFE at ke to value equity directly.
- The matching principle
- The discount rate must match the cash flow's risk, timing and basis. Every model is one consistent (cash-flow, rate) pair: FCFU ↔ ku, FCFE ↔ ke. Crossing them is the most expensive error in the subject.
- Gordon growing perpetuity
- The constant-growth DDM, E0 = D1/(ke−g), valid only when g < ke. The value sits one period before the first cash flow, a frequent timing slip.
Equity Valuation by DCF FAQ
Why does FCF contain the interest tax shield but unlevered FCF does not?
Because tax is computed after deducting interest, the tax bill in FCF is already lowered by the shield Y·T — so that benefit sits inside FCF. Unlevered FCF asks 'what if there were no debt?', so it adds the shield back to tax (subtracts Y·T from FCF), giving the operating cash a debt-free firm would produce. Keep them distinct: discounting one as if it were the other double-counts or omits the shield.
When do the FCFE model and the DDM disagree, and how do I fix it?
They disagree whenever the dividend differs from FCFE. If the dividend is below FCFE, the firm is retaining cash the DDM never sees, so the naive DDM is too low — add the PV of the retained (surplus-cash) stream. If the dividend is above FCFE, the firm is funding the excess with a loan, so the DDM is too high — subtract the PV of that liability. After the fix both land on the same equity value, which is MM dividend irrelevance in action.
Should I subtract interest when building FCF from the statements?
No. Interest is a financing flow, not an operating one. FCF = EBIT + DEP − CAPEX − ΔWC − TAX adds back non-cash depreciation, subtracts real capital spending and the rise in working capital, and stops there. The interest tax shield enters only through the tax line (TAX = (EBIT−Y)T). Subtracting interest again is a classic Class-2 slip.
Why does a rise in working capital reduce free cash flow?
Working capital is receivables + inventory − payables — cash tied up in running the business. When it rises, the firm has parked cash in stock or customer credit it has not yet collected, so that cash is unavailable to investors this period. ΔWC is therefore subtracted in the FCF build; a fall in working capital releases cash and adds to FCF.
Exam move
Put the cash-flow cascade and the four matched (cash-flow, rate) pairs on your A4 first — they decide every later model. Practise assembling FCF line-by-line from a statement (add back DEP, subtract CAPEX and ΔWC, never subtract interest), then peeling to FCFU and FCFE. For equity value, run the FCFE model as the benchmark and reach for the DDM only as a cross-check, always asking whether the dividend equals FCFE before trusting it — and remember the Gordon value sits one period before the first cash flow. The reconciliation rule (div < FCFE → add surplus cash; div > FCFE → subtract the funding loan) is a recurring short-answer; learn the three-line table cold.
