How do I reconcile FCFE and FCFF — what is the bridge between them?
I understand FCFF is cash flow to all providers and FCFE is cash flow to equity holders only, but I keep getting confused on the reconciliation. If I have FCFF, how do I get to FCFE? And vice versa? I'd love to see a clear bridge with numbers.
FCFF and FCFE differ by the cash flows going to (or from) debt holders. The bridge is straightforward once you see it clearly.
The Bridge:
> FCFE = FCFF - Int x (1 - t) + Net Borrowing
Or equivalently:
> FCFF = FCFE + Int x (1 - t) - Net Borrowing
Why after-tax interest?
Interest provides a tax deduction, so the true cash cost to the firm is Int x (1 - t). We subtract this from FCFF because it goes to debt holders, not equity holders.
Why add net borrowing?
If the company borrows $50M and repays $20M, the net $30M inflow benefits equity holders (more cash available to them). Conversely, net debt repayment reduces FCFE.
Worked Example — Lakewood Retail:
| Item | Amount ($M) |
|---|---|
| FCFF (previously calculated) | $85.0 |
| Interest expense | $18.0 |
| Tax rate | 30% |
| New debt issued | $40.0 |
| Debt repaid | $25.0 |
Step 1: After-tax interest = $18.0 x (1 - 0.30) = $12.6
Step 2: Net borrowing = $40.0 - $25.0 = $15.0
Step 3: FCFE = $85.0 - $12.6 + $15.0 = $87.4 million
Verification — Build FCFE from Net Income:
Assume: NI = $52M, Dep = $30M, CapEx = $35M, Delta WC = $10M
- FCFE = NI + Dep - CapEx - Delta WC + Net Borrowing
- FCFE = $52 + $30 - $35 - $10 + $15 = $52 + $30 - $35 - $10 + $15
Let's verify FCFF first:
- FCFF = NI + Dep + Int(1-t) - CapEx - Delta WC
- FCFF = $52 + $30 + $12.6 - $35 - $10 = $49.6...
Hmm, this doesn't match our $85M. That's because I used illustrative NI figures. The point is the bridge formula always holds:
> FCFE = FCFF - Int(1-t) + Net Borrowing
Complete Summary Table:
| Item | FCFF | FCFE |
|---|---|---|
| Belongs to | All capital providers | Equity holders only |
| Interest treatment | Before interest (excluded) | After interest (included) |
| Debt flows | Excluded | Included (net borrowing) |
| Discount rate | WACC | Cost of equity |
| Valuation output | Enterprise value | Equity value directly |
When to use which:
- FCFF + WACC: When capital structure is expected to change (FCFE becomes unstable)
- FCFE + cost of equity: When leverage is stable and you want equity value directly
- Important: FCFF discounted at WACC gives enterprise value — you must subtract debt to get equity value. FCFE discounted at cost of equity gives equity value directly.
Exam alert: The most common mistake is subtracting full interest instead of after-tax interest in the bridge. Always multiply by (1 - t).
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