FCFF vs FCFE Valuation: Why the Two Routes Disagree

Two routes lead to an equity value for Sankalp Industrial Systems Limited, invented, and they do not land on the same number. Discounting the firm's cash flow at 12.00 per cent and bridging across reaches Rs 15,88,13,79,094. Discounting the shareholders' cash flow at 14.00 per cent and stopping there reaches Rs 14,41,38,20,431. The Rs 1,46,75,58,663 between them is the borrowing schedule, not the rate.

Two things hold that answer up. The first is a pairing rule: a flow every funder has a claim on gets the rate every funder requires, and a flow only the holders of the shares can touch gets the rate those holders require. Almost nobody gets that wrong once it is stated. The second is a consistency condition, and this is the one that bites. The two routes land on the same figure only when the borrowing level that was baked into the cost of equity is the borrowing level the schedule actually produces, in every single year and in the terminal year too. On this company they are not the same, deliberately, and Rs 1,46,75,58,663 is what the mismatch costs.

Watching two correct calculations disagree teaches more than watching one of them fail ever could. Every figure below belongs to Sankalp Industrial Systems Limited and comes from a single locked set of forecast assumptions.

What are the two routes, in one line each?

Think of a small workshop that a father and a bank both put money into. At the end of the year the workshop has cash left over after paying for everything it needs to keep running and growing. One question is what that whole pile is worth, and then how much of it belongs to the father once the bank has been settled. The other asks directly what the father's share of the flow is worth, year after year. Same workshop, two questions, two arithmetics.

The firm route values the whole pile and then subtracts what is not the shareholders'; the equity route values only what is already the shareholders' and subtracts nothing afterwards. The firm's measure counts everything the operations produce, before a single funder has been settled. Apply the weighted average cost of capital to it, 12.00 per cent here, and an enterprise value drops out. A bridge still has to be crossed. The shareholders' measure starts where the lenders finish: interest has gone out, fresh borrowing has come back in, and whatever survives that traffic is theirs. Apply the cost of equityWhat holders of the shares require each year in exchange for standing last in the queue. to that at 14.00 per cent, and an equity value drops out with nothing left to do. The contents of each measure, and the three lines that turn one into the other, are covered separately. Compressed to a single line: the shareholders' measure equals the firm's measure, minus interest after tax relief, plus whatever was borrowed net during the year. No fourth adjustment exists.

Which rate belongs to which cash flow, and what breaks if they are swapped?

The rule is short enough to hold in mind for life. Match the cash flow to the people it belongs to, then use the rate those people require. Nobody has been paid yet out of the firm's measure, so lender and shareholder both still have a claim on it, and the rate standing for the two of them jointly is the weighted average cost of capital, 12.00 per cent here. The interest has already gone out of the shareholders' measure, so nobody but a holder of the shares can reach what remains, and the rate standing for that group alone is the cost of equity, 14.00 per cent here.

A swapped pair does not produce a slightly rough answer; it produces a confidently wrong one that looks entirely normal in the output. Take the shareholders' cash flow and discount it at the blended 12.00 per cent, and the lenders are paid once inside the cash flow while the rate takes credit for their cheaper money a second time. The double credit for the lenders' cheaper money raises the equity answer by 30.84 per cent against the correctly matched figure. Run the swap the other way, charging the firm's cash flow at 14.00 per cent, and the arithmetic errs in the opposite direction: the operating equity value collapses to Rs 10,85,52,19,153. A rate built for the riskiest slice of the funding has been applied to a flow that the lenders' cheaper money is helping to produce.

Why does the firm route need a bridge and the equity route not?

The bridge is the part readers skip and then trip over. The firm route discounts a flow the lenders still have a call on, so the value it produces is a claim shared between lender and shareholder. Handing that number to a shareholder as though it were theirs is like telling a household that the flat is worth Rs 80,00,000/- while saying nothing about the Rs 30,00,000/- still owed on it. The bridge is what removes the lenders' call and adds back anything the forecast never counted.

The equity route needs no bridge because the subtraction has already happened inside the cash flow itself, year by year, rather than once at the end. Every year of the equity cash flow has had the after-tax interest taken out of it and the net new borrowing put back into it. By the time the five years and the terminal figure are discounted, the lenders have been dealt with in full. Adding a bridge on top would be counting the same claim twice. The three-line construction of that cash flow, and the reason the interest is deducted after tax rather than in full, are covered separately.

Which firm route figure is the equity route actually being compared against?

Here is where a comparison quietly breaks, and it breaks in real work more often than any arithmetic slip. Sankalp Industrial Systems Limited holds Rs 1,00,00,00,000 of non-operating assetsThings a company holds that generate none of the profit being forecast, so their worth is added on separately., being a surplus land parcel worth Rs 45,00,00,000 and a 26.0 per cent stake in an associate worth Rs 55,00,00,000. Neither of them produces a rupee of the operating earnings that the forecast projects. The bridge from enterprise value to a full equity value therefore adds them in, and lands at Rs 16,88,13,79,094.

The equity route does not carry the non-operating assets at all. The firm route figure it is set against has to leave them out too, making Rs 15,88,13,79,094 the right comparison and Rs 16,88,13,79,094 the wrong one. The two differ by exactly the Rs 1,00,00,00,000 of non-operating assets and by nothing else. Comparing the wrong pair reports a difference of Rs 2,46,75,58,663, of which Rs 1,00,00,00,000 is not a difference in valuation method at all. The non-operating wedge is simply a difference in what was put in the box. A mismatched pair of totals is the single most common reason two routes appear irreconcilable when they are merely being asked different questions.

What does the firm route come to, worked through?

Take the firm's cash flow for the five forecast years, discount each year at 12.00 per cent on the year-end discountingCash is treated as landing in one lump at each year's close, not trickling in month by month. convention, and add a terminal value whose own reinvestment actually pays for the growth it claims. The reinvestment condition is the argument Aswath Damodaran is named for, and it is why the terminal figure here is not simply last year's cash flow grown by 5.00 per cent.

Notice how much of that answer comes from the terminal value: Rs 16,59,72,35,530 of the Rs 21,28,13,79,094 enterprise value, or 77.99 per cent. The five years everybody argues about do roughly a fifth of the work. That is worth sitting with before any comparison of routes, because both routes carry a terminal figure of the same weight and both inherit whatever that figure assumes. The non-operating assets of Rs 1,00,00,00,000 are deliberately left out of the total above, for the like-for-like reason set out earlier.

One honesty note about the digits before anything is compared. Every figure in these two columns is printed to the rupee because that is where the arithmetic settles, not because the last few digits mean anything. On an answer that is close to four-fifths terminal value, only the leading digits carry evidence and the trailing ones are simply what the division produced. Rounding them off in conversation about this company makes nothing said less true. Keeping them matters for a narrower reason: two routes have to be subtracted from one another, and a subtraction between figures rounded at different points invents differences that were never there.

What does the equity route come to, worked through?

Now run the same company the other way. The equity cash flow starts from the firm's cash flow, takes out the after-tax interest on the opening borrowings and adds back the Rs 25,00,00,000 of net new borrowing drawn in each year. The five figures fall out at Rs 87,00,00,000, Rs 1,03,50,00,000, Rs 1,20,00,00,000, Rs 1,36,50,00,000 and Rs 1,53,00,00,000. Then discount at 14.00 per cent, not at 12.00.

The terminal figure is built with the same discipline. In Year 6 the firm's measure reaches Rs 2,04,75,00,000. Deduct the after-tax interest of Rs 43,50,00,000 on the Rs 7,25,00,00,000 of debt outstanding at the end of Year 5, then add terminal net borrowing of Rs 19,68,75,000. Terminal borrowing takes the same one-quarter share of the terminal reinvestment that the annual figure takes of the annual reinvestment. The terminal equity cash flow therefore comes to Rs 1,80,93,75,000. As a growing perpetuityA stream assumed to continue without end while rising by a fixed percentage each period. at 14.00 per cent against 5.00 per cent growth, that stream is worth Rs 20,10,41,66,667 at the end of Year 5.

Both columns are arithmetically clean, both were built from the same locked forecast, and they disagree. Nothing has been fudged, no line has been dropped and no rate has been rounded differently. Two disciplined valuations of one invented company have produced two numbers, and the interesting work starts here rather than ending here.

How wide is the gap, and what is it a share of?

Subtract one from the other and the distance is Rs 1,46,75,58,663, with the equity route sitting lower. Two numbers could serve as the divisor, and they give different answers, so stating the distance as a percentage needs care. Against the firm route's Rs 15,88,13,79,094 it is 9.24 per cent. Against the equity route's own Rs 14,41,38,20,431 it would be 10.18 per cent. Neither is wrong; a sentence that gives the percentage without naming the base is.

Divide by the firm route figure throughout, so that 9.24 per cent always means Rs 1,46,75,58,663 as a share of Rs 15,88,13,79,094. Getting into the habit of naming the base is not pedantry. Once a valuation carries several enterprise values and several equity values, a bare percentage in a note is a figure nobody downstream can reproduce, and somebody working at speed will reproduce it wrongly.

Is one of the two answers wrong, then?

No. Both are correct given what went into them, and that is precisely why the disagreement is worth studying rather than fixing. A valuation is a conditional statement: given this forecast, this rate and this funding plan, the value is that. Change one of the conditions and the value changes, and neither version has become an error. Two routes with two slightly different sets of conditions therefore give two answers.

The gap is a finding about the inputs, not a defect in either method, and treating it as a defect is what turns a useful signal into wasted hours. Something inside the two constructions is not the same, the arithmetic is reporting that fact honestly, and the job is to find out which assumption differs. There are only two candidates worth checking: the rates and the funding plan. The next two blocks eliminate one and convict the other.

Is it the discount rate? Here is how to rule it out

Every reader's first suspicion is the rate, and the reasoning behind that suspicion is sound. Two rates, 12.00 against 14.00, are the one thing that visibly differs between the columns, so a gap between the answers looks like it must come from there. Test it properly rather than arguing about it.

There is a defensible alternative cost of equity available. The weights that produced the 12.00 per cent blended rate use the observed market value of the shares. The model itself produces a lower equity figure. An input is therefore also an output, and the name for that loop is circularityA calculation where something supplied at the start is also something the calculation produces at the end.. Run that loop until it settles and the levered betaAn equity risk measure that has had a borrowing assumption folded into it, so changing the borrowing changes the measure. comes to rest at 1.27962. A beta of 1.27962 puts the cost of equity at 14.148 per cent rather than 14.00. A converged 14.148 per cent is the most defensible different rate on the table.

Rerun the equity route at that converged rate and the answer falls to Rs 14,16,27,83,648, so the gap widens to Rs 1,71,85,95,446, being 10.82 per cent of the firm route figure rather than 9.24 per cent. Watch what that does to the argument. If the rate were the cause, the most defensible correction to the rate ought to pull the two answers together. The correction pushes them apart. The evidence moves in the opposite direction to the hypothesis, so this is an elimination rather than a weak hint. The rate is not what is separating these two valuations.

So what is actually causing it?

The cost of equity of 14.00 per cent was not pulled out of the air. The rate was built on a beta levered up for a specific level of borrowing, namely debt standing at 25.0 per cent of the company's total capital measured at market values. The 25.0 per cent gearing is baked into the rate, and it stays baked in for every year the model runs, including the terminal year that carries three-quarters of the answer.

Now look at what the borrowing schedule actually does. Sankalp Industrial Systems Limited draws a flat Rs 25,00,00,000 of new debt in each of the five years, against Rs 1,00,00,00,000 of net new capital put into the business each year. So a quarter of each year's growth is funded with debt. A quarter of the new capital sounds like a match for the 25.0 per cent assumption, and the resemblance is the trap in the whole construction: a quarter of the new capital is not the same thing as a quarter of the total value, because the total value is far larger than the new capital being added to it each year.

Work out the borrowing path that would actually hold the two routes together and the mismatch becomes a number rather than an argument. The consistent path needs roughly Rs 49,92,48,222 of net new borrowing a year, not Rs 25,00,00,000. By the end of Year 5 the schedule leaves gross debt at Rs 7,25,00,00,000 while the consistent path would have reached Rs 8,49,62,41,110, a shortfall of Rs 1,24,62,41,110. The locked schedule funds a little under half as much of the growth with borrowing as the cost of equity was constructed to assume, and that shortfall, compounding across five years and into the terminal year, is the entire Rs 1,46,75,58,663.

How much does that one assumption actually move the answer?

More than most readers would guess. The borrowing schedule looks like a treasury detail. A borrowing schedule is not a growth rate, not a margin, not a discount rate, and in most conversations about a valuation nobody raises it at all. Yet the schedule moves the equity route's answer in steps of Rs 1,47,19,85,084 for every Rs 25,00,00,000 of annual net borrowing added. Each step is larger than the entire gap under investigation.

The firm route's Rs 15,88,13,79,094 does not move at any setting of that control, and watching one line stay flat while the other sweeps past it is the whole lesson in a single picture. Move the slider and two things redraw at once: the marker on the ladder of equity answers, and the bar showing where gross debt has reached by the end of Year 5. The firm route values the operating cash flows before anybody asks who funded them, so the firm route stays where it is throughout. Modigliani and Miller made exactly that point in 1958 about capital structure and firm value.

The static readings, for anyone who would rather not drag anything. At nil net borrowing the equity route gives Rs 12,94,18,35,347. At Rs 25,00,00,000 a year, the locked schedule, it gives Rs 14,41,38,20,431. At Rs 50,00,00,000 it gives Rs 15,88,58,05,515. At Rs 75,00,00,000 it gives Rs 17,35,77,90,600. At Rs 1,00,00,00,000 it gives Rs 18,82,97,75,684. The firm route reports Rs 15,88,13,79,094 at every one of those five settings.

Under what condition do the two routes agree?

The ladder answers this exactly. Somewhere between Rs 25,00,00,000 and Rs 50,00,00,000 of annual net borrowing the equity route crosses the firm route's flat line, and the crossing point sits at about Rs 49,92,48,222 a year. Set the schedule there and the equity route returns Rs 15,88,10,95,163 against the firm route's Rs 15,88,13,79,094, a difference of Rs 2,83,931 on a figure above Rs 15,88,00,00,000. For teaching purposes the two answers have met.

Stated as a rule rather than as a number: the two routes agree only where one level of borrowing does two jobs at once, sitting inside the cost of equity and coming out of the schedule, in every year of the forecast and in the terminal year as well. That is a demanding condition. The condition is almost never met by accident, and it is not met here because the schedule was written by one hand and the beta was levered by another. Checking it in advance converts a mysterious disagreement into a predictable one, and predictable disagreements do not cost anybody a weekend.

Why does a valuation normally take the firm route?

Because of what the last three blocks showed, and for a reason that is practical rather than theoretical. Both routes are correct in principle. Only one of them survives a company whose funding mix is moving, and almost every company's funding mix moves. A business that borrows to build a plant, repays over four years, refinances at the end and draws on a working capital facility in between has a level of debt that changes every single year, and the equity route requires that path to be right before it will give a stable answer.

The firm route is used almost everywhere because it does not require the level of debt to hold still, so a changing funding plan shifts the bridge at the end without disturbing the valuation of the operating business at all. Change the borrowing and the firm route's enterprise value is untouched; only the debt line in the bridge moves, and it moves by an amount that can be read off the balance sheet rather than modelled. Robustness buys the firm route its position, at a price worth being honest about. The firm route requires a bridge with several lines in it, each of which can be wrong, and it hides the funding question rather than answering it. The gain in stability is paid for in visibility.

When is the equity route the one to reach for anyway?

There is a real case for it, and it is not a consolation prize. The equity route earns its place when the funding plan is the subject of the analysis rather than something looked past. If a company's borrowing is deliberately being wound down over the forecast, or wound up, and the effect of that on the shareholders is the question, then a method that puts the borrowing inside the cash flow shows what a method that bridges at the end will bury.

The equity route earns its place wherever the level of borrowing is genuinely stable or is itself under examination. No other route works once something outside the operating business constrains the cash flow reaching shareholders. A household deciding whether it can afford a second home does not value the house and then subtract the loan; it looks at what is left over each month after the instalment, because the instalment is the constraint. The same instinct is right wherever a repayment schedule, and not the operations, is what determines what shareholders actually receive. On this company, though, the borrowing plan is neither stable nor the subject, so the firm route's Rs 15,88,13,79,094 is the operating equity figure this analysis carries forward.

How a lender, an analyst and a household actually use this

A credit analyst at a lender runs the firm route first and then reads the bridge backwards. A lender watches the enterprise value of Rs 21,28,13,79,094 against the Rs 6,00,00,00,000 of gross debt. The ratio between those two says how much value would have to evaporate before the lending is at risk. Both equity numbers, Rs 15,88,13,79,094 and Rs 14,41,38,20,431, sit comfortably above the debt, so the lender is largely uninterested in which of them is right. The lender does care about the borrowing schedule, now shown to be a live valuation assumption rather than a treasury footnote.

An equity analyst uses the disagreement as a diagnostic. Running both routes takes half a morning once the model exists, and the size of the gap shows immediately whether the cost of equity and the funding plan in the model were built by the same set of assumptions. A gap of 9.24 per cent is not a number to publish; it is a number to explain, and the explanation belongs in the assumptions note rather than in the valuation output. An analyst who runs only one route never learns that the two halves of the model disagree with each other.

And a household meets the same idea without any of the vocabulary. A household running a shop asks two different questions in the same week: what the shop would be worth if it were sold, and how much can actually be taken out of it each month while the loan is running. The first question is the firm route and the second is the equity route. The answers differ for exactly the reason they differ here: the repayment plan sits between them. Neither question is the wrong one. Asking one and using the answer to the other is the mistake.

Sankalp Industrial Systems Limited is invented.
Educational material. Not advice on any investment, tax, budget or market position.