Derive FCFF and FCFE, the free cash flows to the firm and to its shareholders, using the cash flow statement
The idea
Free cash flow to the firm starts from operating cash flow, adds back after-tax interest expense because the measure is before payments to any capital provider, and subtracts capital expenditure. Free cash flow to equity starts from operating cash flow, subtracts capital expenditure and adds net borrowing. The adjustment for interest is where errors happen: under standards that classify interest paid as operating, it has already been deducted and must be added back for the firm measure; where the company classifies it as financing, it has not, and adding it back double-counts.
Formulas
Free cash flow to the firm
FCFF = CFO + interest × (1 − t) − FCInv
- CFO
- cash flow from operating activities
- interest
- interest expense already deducted in arriving at CFO
- t
- the marginal tax rate
- FCInv
- investment in fixed capital
Cash available to everyone who funded the business, lenders included, so the interest already taken out is added back — after tax, because the deduction was real. Discount it at the WACC, not the cost of equity.
Free cash flow to equity from the cash flow statement
FCFE = CFO − FCInv + net borrowing
- CFO
- cash flow from operating activities
- FCInv
- investment in fixed capital, the capital expenditure
- net borrowing
- debt raised in the period less debt repaid
Read straight off the statement of cash flows: CFO is the subtotal, capital expenditure sits in investing, and net borrowing is issuance less repayment in financing. The difference from free cash flow to the firm is who the cash is free for.
A practice question
How is free cash flow to equity calculated from operating cash flow?
- Operating cash flow less capital expenditure plus net borrowing — correct
- Operating cash flow plus capital expenditureWhy not: Capital expenditure is cash that left the business to maintain capacity. Adding it would count money that was spent as though it were available.
- Operating cash flow less dividends paidWhy not: Dividends are one of the things free cash flow to equity is available *for*. Deducting them answers what was left after the distribution, not what funded it.
Equity holders receive what is left after the business is maintained and after the lenders' net position has been settled.
A harder one
Why is after-tax interest added back when computing free cash flow to the firm?
- Because interest is not a real costWhy not: It is a real cost and a real payment. It is added back because of who receives it, not because it is notional.
- Because the measure precedes all providers — correct
- Because interest is always classified as financingWhy not: It is not always — US GAAP requires operating, and IFRS permits a choice. If it were always financing there would be nothing in the operating figure to add back.
Interest is a payment to lenders, and the measure is taken before payments to any capital provider. Free cash flow to the firm belongs to debt and equity together, so deducting one provider's return would make it belong to equity alone.
The hardest tier
A company classifies interest paid as financing. What happens if the analyst still adds it back to operating cash flow?
- Nothing, the result is the sameWhy not: The result differs by the whole after-tax interest amount, which for a levered company can be substantial.
- Free cash flow to the firm is understatedWhy not: Backwards. Adding back a deduction that never happened inflates the figure rather than depressing it.
- Free cash flow to the firm is overstated — correct
The interest was never deducted from the operating figure, so adding it back invents cash. The add-back only corrects a deduction that actually happened.
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