FCFF vs FCFE: The Three Lines Between the Two Numbers

Free cash flow to the firm is the cash the whole business generates before any financing claim is met. Free cash flow to equity is what is left for the shareholders once the lenders are paid and any new borrowing is drawn. At Sankalp Industrial Systems Limited, an invented maker of industrial valves, the first runs Rs 98,00,00,000 to Rs 1,70,00,00,000 and the second Rs 87,00,00,000 to Rs 1,53,00,00,000. Three lines separate them, and there is no fourth.

The awkward part of this idea is much easier to feel in a small shop than inside a five year forecast. Start behind a counter.

A couple run a tailoring unit in a market lane. Eight machines, four people working them, and a steady stream of orders from two garment traders who pay at the end of every month. In a good year the unit throws off about Rs 11,00,000 of spare cash after everything the work itself needs: the cloth, the wages, the electricity, the two machines they had to buy to replace the two that finally died, and the extra stock of thread and lining they had to carry because the order book got bigger.

Rs 11,00,000. Now ask a question that sounds pedantic and is not. Whose Rs 11,00,000 is it?

Because the couple also have a machinery loan. The interest on it this year is Rs 2,40,000. And their bank, seeing the order book, has just raised the limit and put another Rs 1,50,000 into the account. So there are at least three defensible answers to what the unit generated this year, they are all different numbers, they are all correct, and each one answers a different question.

The Rs 11,00,000 is what the unit produced before anybody with a loan or an ownership stake took anything out of it. Counting the cash at that point is one measurement, and it answers what the tailoring unit itself is worth as a going concern, independent of how the couple happened to fund it. The figure after the interest goes out and the new bank money comes in is a second measurement, and it is the one that answers what the couple themselves are collecting.

Free cash flow to the firm and free cash flow to equity are exactly these two measurements, taken at two different points in the same stream of cash, and almost every mistake made with them comes from taking one and calling it the other. Both definitions are stated below, both are computed on five forecast years of one invented company, and the bridge that joins them is walked line by line. The bridge is short. Three lines, and that is the whole of it.

What exactly is free cash flow to the firm?

Free cash flow to the firmOperating profit after tax less net reinvestment: the cash the business generates before any financing claim. is the cash a business generates in a year, after it has paid for everything the business itself needs, and before it has paid anybody who financed it.

Two halves to that, and both matter. The first half is what the business needs. A company that wants to be operating next year has to replace worn out machinery, and a company that wants to be bigger next year has to buy capacity it does not yet have and carry more stock and more unpaid customer bills than it carries today. All of that is real cash leaving. None of it is optional if the forecast is to happen. So it comes out before anybody calls the remainder free.

The second half is the more interesting one. Nothing has been paid to a lender. Nothing has been paid to a shareholder. No borrowing has been drawn. The figure is deliberately blind to how the company arranged its funding. Two companies running identical operations, one carrying a large loan and one carrying none at all, produce exactly the same free cash flow to the firm. The blindness is not a flaw in the measure. The blindness is the whole purpose of the measure.

The worked company is Sankalp Industrial Systems Limited, a listed maker of industrial valves, precision castings and the aftermarket parts and service that go with them. Its five year forecast is taken as given here: operating profit after taxEarnings before interest and tax, taxed as though the company had no debt. of Rs 1,98,00,00,000 in Year 1, rising by exactly Rs 18,00,00,000 a year to Rs 2,70,00,00,000 in Year 5, and net reinvestmentCapital expenditure less depreciation plus the movement in net working capital. of exactly Rs 1,00,00,00,000 in every one of the five years. Where a profit figure is needed anywhere below, it is read from the record's rupee lines and never from a descriptive percentage attached to them.

Free cash flow to the firm is therefore operating profit after tax less net reinvestment, and because the reinvestment here never moves, it is simply each year's profit figure less Rs 1,00,00,00,000. Year 1 is Rs 1,98,00,00,000 less Rs 1,00,00,00,000. The answer is Rs 98,00,00,000. Why the reinvestment is Rs 1,00,00,00,000, and how that figure is built out of capital expenditure, depreciation and working capital, is covered separately; it is taken as settled here and restated.

The short identity can look like a trick, so Year 1 is worth running the long way once. Operating profit after tax of Rs 1,98,00,00,000, plus depreciation of Rs 52,80,00,000 because that charge took no cash, less capital expenditure of Rs 1,34,80,00,000, less the Rs 18,00,00,000 the business had to put into working capital, gives Rs 98,00,00,000. The same answer, reached the long way.

What exactly is free cash flow to equity?

Free cash flow to equityWhat is left for the shareholders after the lenders are paid and any new borrowing is drawn. is what is left of that cash once the people who lent the company money have been settled for the year, and once whatever new money they put in has arrived.

Notice the two directions. Money goes out to lenders, as interest. Money also comes in from lenders, as fresh borrowing. Both are financing events, both happen in the same year, and a measure of what the shareholders can claim has to carry both of them or it is not measuring anything coherent.

The couple in the tailoring unit understood this without any vocabulary at all. The Rs 2,40,000 of interest went out of the account. The Rs 1,50,000 of new bank money came into it. When they sat down at the end of the year to work out what it had actually left them, they netted both. Both had already happened to the same bank balance. Nobody counts only the outflow and calls the result what they have.

So free cash flow to equity is free cash flow to the firm, less the after-tax interest, plus the net new borrowing, and those two adjustments across three lines are the entire difference between the two figures. Everything else in this guide is either an explanation of one of those two lines or a demonstration of what happens when somebody gets one of them wrong.

Whose money is each one, and why must that be settled first?

A cash flow figure on its own is not a fact about a business. A cash flow figure is a fact about a business and a claimA right to be paid out of the cash a business generates, held by a lender or a shareholder., and unless the claim being stood behind is named, the number does not mean anything yet.

Think about a housing society collecting maintenance. The total collected in a month is one number. The amount left after the lift contractor and the security agency are paid is a second number. The amount left for the repair fund after everything else is a third. Nobody argues about which of the three is the real number. Everybody understands that each one answers a different question and that the question comes first.

Companies work the same way and people forget it constantly. Sankalp Industrial Systems Limited has two sorts of financier standing in a queue. Lenders are in front. Their claim is contractual, it is fixed in amount, it is dated, and it does not depend on the company having a good year. Shareholders are behind them. Their claim is whatever is left. A claim on what is left is called a residual claim, and it is the volatile one.

Free cash flow to the firm is measured before the queue starts moving, and free cash flow to equity is measured after the first people in the queue have been served. The measurement point is the entire conceptual difference between them. Every other difference between them is arithmetic that follows from that one sentence.

The queue also explains the confusion that most often catches a reader meeting both figures for the first time. The firm figure is larger, larger sounds better, and it is tempting to treat it as the serious number and the equity figure as a footnote. The ranking is backwards. The firm figure and the equity figure are not competing estimates of one quantity. Each of them measures a different quantity. Asking which is right is like asking whether a household's total earnings or its earnings after the home loan instalment is the correct figure. Both are correct. The two figures answer different questions, and using one where the other belongs produces an answer that is wrong by exactly the amount of the queue that was skipped.

How is the firm figure computed across the five years?

Straight down the record. Operating profit after tax rises by exactly Rs 18,00,00,000 each year, net reinvestment sits at Rs 1,00,00,00,000 and does not move, and the subtraction is done five times.

The series rises by exactly Rs 18,00,00,000 a year, and it does so for one reason worth holding onto: the profit rises by that amount and the reinvestment does not rise at all. Hold the cost of growth still and every rupee the profit gains arrives intact at the bottom of that little table. The equity series does not behave the same way, and the gap between the two behaviours is the sharpest fact in the subject.

Note what is not in the table. No interest. No borrowing. No dividend. Nothing about the loans Sankalp Industrial Systems Limited actually carries. The firm figure is built entirely out of operations and the capital those operations consume, and it would be identical if the company had never borrowed a rupee.

Why is interest deducted after tax rather than in full?

Here is the first bridge line, and it is the one most often got wrong. The line is not the interest. The line is the after-tax interestThe interest charge less the tax relief it produces..

Work out where the interest figure comes from first. Sankalp Industrial Systems Limited starts Year 1 with gross debtTotal borrowings before deducting any cash. of Rs 6,00,00,00,000. Interest is charged on that opening balanceThe figure a year starts with, which is what interest is charged on here. at a blended rateOne rate representing several borrowings of different sizes and costs. of 8.00 per cent, the company's own contracted blended cost across its borrowings. The charge for the year is Rs 48,00,00,000.

Two things about that calculation are conventions of this worked example rather than laws, and a reader who assumes otherwise will not be able to rebuild these figures. First, the charge is on the balance the year opens with, not the balance it closes with, and not an average of the two. Second, one blended rate is applied across the whole borrowing rather than each individual loan being charged at its own rate. Sankalp Industrial Systems Limited does carry several separate borrowings at several different rates, and what each one costs and when each one falls due is covered separately. Rebuilding the interest line loan by loan will not reproduce the numbers below.

Now the tax. The interest charge is deductible. The company's tax bill is therefore lower than it would otherwise have been by the tax on that Rs 48,00,00,000. The company assumes a 25.0 per cent effective rate for itself, an assumption of this forecast rather than any published rate. The relief is Rs 12,00,00,000. So the interest charge takes Rs 48,00,00,000 out of the door, and Rs 12,00,00,000 that would otherwise have gone to tax stays inside. The net cash the shareholders actually surrendered is Rs 36,00,00,000.

Deducting the gross Rs 48,00,00,000 would charge the shareholders for Rs 12,00,00,000 that never left the business. So the bridge uses the after-tax figure and not the headline one.

Where does the net new borrowing figure come from?

The second bridge line is net new borrowingDebt drawn during the year less debt repaid., and it is added rather than subtracted. Readers stumble over that sign more often than over anything else here, so it is worth being blunt about why.

New borrowing is cash arriving in the company's bank account. The cash is money the shareholders did not have to provide. If the business needs Rs 1,00,00,00,000 of new capital in the ground this year and a lender puts up Rs 25,00,00,000 of it, then the shareholders are Rs 25,00,00,000 better off in cash terms this year than if they had funded the whole thing. The borrowing has to be serviced and eventually settled, and every rupee of it shows up in a later year as a bigger opening balance and a bigger interest charge. The first bridge line captures precisely that. But this year, it is cash in.

Where does the Rs 25,00,00,000 come from? Not from an independent assumption about how much the company felt like borrowing. The borrowing is tied directly to the reinvestment. Sankalp Industrial Systems Limited puts Rs 1,00,00,00,000 of net new capital into the business in each of the five years and funds 25.0 per cent of it with debt. A quarter of Rs 1,00,00,00,000 is Rs 25,00,00,000, in every year. So the borrowing line is flat while everything around it moves.

The borrowing line is flat because the reinvestment it funds is flat, and the debt balance climbs steadily for the same reason: Rs 6,00,00,00,000 at the start of Year 1 becomes Rs 7,25,00,00,000 by the end of Year 5, in five steps of Rs 25,00,00,000.

What does the bridge look like when it is run for Year 1?

Three lines, in a fixed order. Start with the firm figure. Take out the after-tax interest. Put in the net new borrowing. Read off the equity figure.

Rs 98,00,00,000, less Rs 36,00,00,000, plus Rs 25,00,00,000, is Rs 87,00,00,000.

The entire calculation is those three lines, and it is worth pausing on how small it is. Depreciation was already dealt with inside the firm figure, so the bridge makes no adjustment for it. Working capital was dealt with there too, for the same reason. There is no dividend line either. A dividend is what the shareholders choose to take out of what is available to them, and this measure is what is available rather than what is taken. The bridge has two adjustments and three lines, and everything it might have needed has already been handled upstream.

What does the equity figure come to in each of the five years?

The same three lines, five times. The firm figure moves every year, the after-tax interest moves every year because the opening debt keeps climbing, and the borrowing does not move at all.

The arithmetic of each year is small enough to check by eye, and checking it is the point. Rs 98,00,00,000 less Rs 36,00,00,000 plus Rs 25,00,00,000 is Rs 87,00,00,000. Rs 1,16,00,00,000 less Rs 37,50,00,000 plus Rs 25,00,00,000 is Rs 1,03,50,00,000. Rs 1,34,00,00,000 less Rs 39,00,00,000 plus Rs 25,00,00,000 is Rs 1,20,00,00,000. Rs 1,52,00,00,000 less Rs 40,50,00,000 plus Rs 25,00,00,000 is Rs 1,36,50,00,000. Rs 1,70,00,00,000 less Rs 42,00,00,000 plus Rs 25,00,00,000 is Rs 1,53,00,00,000.

Across the five years the firm stream totals Rs 6,70,00,00,000 and the equity stream totals Rs 6,00,00,00,000, and the Rs 70,00,00,000 between them is Rs 1,95,00,00,000 of after-tax interest less Rs 1,25,00,00,000 of new borrowing. The bridge therefore doubles as an arithmetic check on the whole table. The same Rs 1,25,00,00,000 is what takes gross debt from Rs 6,00,00,00,000 to Rs 7,25,00,00,000, so two different totals have to agree with each other, and they do.

Why does one grow by Rs 18,00,00,000 and the other by Rs 16,50,00,000?

The fact that follows can be verified rather than believed. Being exact rather than approximate, it is the best one in the subject.

Start with what does not change. Net new borrowing is Rs 25,00,00,000 in Year 1 and Rs 25,00,00,000 in Year 2. A line that does not move contributes nothing at all to the change between two years. So the borrowing, despite being a large number in the bridge, is completely irrelevant to why the two slopes differ.

The interest is what is left. Rs 25,00,00,000 was borrowed during Year 1 and is sitting there when the next year starts, so Year 2 opens with Rs 6,25,00,00,000 of gross debt against Year 1's Rs 6,00,00,00,000. Rs 25,00,00,000 more debt at the blended 8.00 per cent is Rs 2,00,00,000 more interest. At the company's assumed 25.0 per cent effective rate, three quarters of that is a real cost and one quarter comes back as relief, so the after-tax interest rises by Rs 1,50,00,000.

Rs 18,00,00,000 of extra firm cash flow, less Rs 1,50,00,000 of extra after-tax interest, is Rs 16,50,00,000 of extra equity cash flow, and that subtraction holds for every one of the four year-pairs in the forecast without a rupee of rounding.

Check it yourself on any pair. Rs 1,03,50,00,000 less Rs 87,00,00,000 is Rs 16,50,00,000. Rs 1,20,00,00,000 less Rs 1,03,50,00,000 is Rs 16,50,00,000. Rs 1,36,50,00,000 less Rs 1,20,00,00,000 is Rs 16,50,00,000. Rs 1,53,00,00,000 less Rs 1,36,50,00,000 is Rs 16,50,00,000. Four pairs, one answer, every time.

The slope difference is also the single most useful diagnostic in the whole subject, and it is worth carrying away even if everything else is forgotten. The difference between two adjacent years of an equity cash flow series should equal the rise in the firm series less the rise in after-tax interest. If it comes out at exactly the rise in the firm series, a line that should be moving is either missing or frozen. If it comes out too large by exactly the tax on the rise in interest, the interest was deducted gross.

Is there a fourth line?

No, and this section exists because the commonest way this calculation goes wrong is not an arithmetic slip but an invented line.

The temptation is understandable. A bridge feels as though it ought to be longer. Somebody remembers that dividends are paid to shareholders and adds a dividend line. Somebody remembers preference shares and adds one for them. Somebody remembers leases and adds a lease line. Somebody who has just come from the enterprise value bridge, a genuinely long list, expects this one to look similar.

Take them one at a time. Free cash flow to equity is what is available to the shareholders, and a dividend is what the company chooses to hand over out of it. A dividend is therefore not an adjustment to it. The two are different questions, and what a company does with the cash is covered separately. Preference shares would belong in a bridge if the company had any; Sankalp Industrial Systems Limited has none in its record, so putting a line in for them would be inventing a liability. The same goes for a lease line: nothing in the record creates one, and a line with no number behind it is not a conservative adjustment, it is a fiction with a plausible name.

Free cash flow to the firm, less after-tax interest, plus net new borrowing: two adjustments, three lines, and any account or model that adds a fourth on this company has invented it.

There is a reason to be firm about this beyond tidiness. A bridge that needs an extra line to reconcile is nearly always a bridge with an error somewhere above it, and the extra line is a way of making the error disappear rather than finding it. When an equity figure will not come out, the productive move is to check the interest convention and the borrowing sign, not to add a plug.

How is each cash flow matched to the rate that belongs to it?

The two figures exist because two different sets of people have claims. The same split is the rule governing what may be done with them afterwards, and the rule is decided here even though the rates themselves are not.

A cash flow available to everybody with a claim on the business has to be discounted at a rate representing everybody with a claim on the business, weighted by how much of the funding each group provides. A cash flow available only to the shareholders has to be discounted at a rate representing the shareholders alone. How either of those rates is built, what goes into it and why, is covered separately, and deliberately after this subject: what is being discounted has to be settled before the rate that discounts it.

The matching rule is worth stating in plain words. Discounting the equity stream at a rate built for the whole business would charge the shareholders a blended cost that includes lenders those very shareholders were already paid ahead of. The same borrowing would then be charged for twice. Going the other way, discounting the firm stream at a rate built for shareholders alone would price the whole business as though every rupee of it were funded by the riskiest claim in the queue.

Neither mistake announces itself. Both produce a perfectly plausible looking number, so the matching rule has to be applied deliberately rather than noticed afterwards. The two streams feed two different valuation routes; what each route produces, and what happens when the two answers are set against each other, is covered separately.

Where does this bridge go wrong in practice?

Almost never through carelessness, and that is what makes it worth a section of its own. The bridge goes wrong when somebody is being careful and applies a reasonable sounding rule that happens to be the wrong one.

Which one should be used, and what does the choice commit the analyst to?

Neither is a better measure, and an account calling one of them the serious one has not understood the question. The choice is made by what is being measured, and once it is made, several other things stop being free choices.

Choosing the firm stream commits the analyst to two things. The rate has to represent everybody with a claim on the business, and the answer is a value for the whole business rather than for the shareholders, so getting from one to the other afterwards is a separate exercise with its own list of adjustments. The forecast's borrowing assumptions then do not touch the cash flows at all. Depending on the company, that is either an advantage or an evasion.

Choosing the equity stream commits the analyst to something quite different. The rate has to represent the shareholders alone. The forecast now has to carry an explicit borrowing schedule, year by year. Without one there is no interest line and no borrowing line, and the stream cannot be built at all. The equity route is more work and it is also more exposed: change the funding assumption and every year of the stream moves.

Both streams are built from the same forecast and the same borrowing schedule, and internal consistency between them says nothing at all about whether either will happen. Neither figure states what Sankalp Industrial Systems Limited is worth, whether the company should borrow more or less, or whether a larger equity cash flow is a better outcome than a smaller one. The two figures are inputs. Where they go next, and what happens when the two routes are set against each other, is covered separately.

Every identity above holds exactly, and that is genuinely useful: it means the bridge can be checked rather than trusted, and a reader can catch a broken model in seconds. Exact identities do not make the borrowing schedule realistic, do not hold the 8.00 per cent blended rate steady for five years, and do not make a company reinvesting Rs 1,00,00,00,000 a year fund exactly a quarter of it with debt. Every one of those is an assumption of an invented forecast. Internal consistency is a test that a wrong forecast can pass.