You now have two cash flows, and from last week, two rates. That makes four possible pairings. Two are valuation and two are wreckage.
| Discount at WACC | Discount at cost of equity (Re) | |
|---|---|---|
| FCFF (all claimholders) | → Enterprise value (value of operating assets) | Undervalues the firm, and if you then also subtract debt, doubly wrong |
| FCFE (shareholders only) | Overvalues equity, a levered claim priced at a blended, safer rate | → Equity value directly |
Why must the discount rate match the cash flow?
The logic fits in a sentence. The discount rate must be the required return of the same investors whose cash flow you are discounting. FCFF belongs to all claimholders, so it meets the blended opportunity cost of all of them, which is WACC. FCFE belongs to shareholders alone, so it meets their required return, Re. For any levered firm Re > WACC, because equity is the riskier, residual claim. So every mismatch has a predictable direction:
- FCFE at WACC overvalues. You've priced the riskiest slice of the capital structure at the blended rate of the whole, and the more levered the firm, the bigger the gift. It flatters, so it's the common one.
- FCFF at Re undervalues the firm. The usual amateur form is worse. You discount FCFF at Re, then forget the bridge entirely and call the result equity value, so the number is wrong in two ways that offset without any control. Worked example 2 puts exact numbers on both disasters. On a fully consistent synthetic firm, the two mismatches misvalue equity by roughly −37% and +33% respectively. Errors that size destroy a thesis. Mistake #8 on last week's list warned you they turn up in real published work.
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How do you get from FCFF value to equity value per share?
An FCFF valuation gives you the value of operating assets. Call it EV for now, since the multiples module refines the vocabulary. You then reach shareholders' value with one explicit crossing, the bridge between the two altitudes:
Equity value = PV(FCFF @ WACC) … operating assets
+ cash & non-operating assets … surplus cash, investments — their
cash flows were never in FCFF
− market value of debt (incl. leases) … lenders get paid first
− minority interest … the slice of consolidated value
that isn't yours (M1.09)
÷ diluted shares outstanding … per-share valueEvery line is there because of a boundary you drew earlier. Cash was excluded from non-cash WC, so its value re-enters here. Lease liabilities were counted as debt in WACC, so they exit here. FCFF was pre-interest, so debt exits at market value. Consistency is what holds it together. Each item appears once and only once. It goes on one side or the other, never both. An FCFE valuation needs no bridge, since you're already home. Just add any surplus cash whose income you excluded, then divide by diluted shares. The DCF II module runs the full bridge with terminal value included. The builds here stop at the PV of the explicit period, and they're labeled that way.
Here's the mantra. Say it until it bores you, then say it in the exam: firm cash flows, firm rate, firm value. Equity cash flows, equity rate, equity value. Never cross the streams. Cross the bridge exactly once.