Discounted Cash Flow: How the Model Is Built, Step by Step

A discounted cash flow values a business as the present value of the cash it will generate. For Sankalp Industrial Systems Limited, invented, five forecast years of free cash flow to the firm discounted at 12.00 per cent are worth Rs 4,68,41,43,564. The terminal value adds Rs 16,59,72,35,530. Enterprise value Rs 21,28,13,79,094 to the rupee, and Rs 84.41 a share after the bridge.

A tea shop holds the whole method already, and it shows itself faster on a footpath than in a spreadsheet. A woman who has run a small tea shop outside a bus depot for nine years offers to sell it. She takes out a notebook. Last year the shop cleared about Rs 3,00,000 after paying for milk, sugar, gas, rent and the boy who washes the glasses. A new office block is going up across the road, so she thinks it will clear a little more each year. And she wants Rs 15,00,000 for it.

A buyer now has to decide something, and the only honest way to decide it is to ask what the shop will hand over, year by year, for as long as it is kept. Rs 3,00,000 next year. Perhaps Rs 3,30,000 the year after. But the Rs 3,30,000 arriving two years from now is not worth Rs 3,30,000 today. The money could have been doing something else in the meantime, and the office block might never open. So each future year is shrunk by some amount before the years are added up, and shrunk further the further out it sits. The shop does not politely stop trading after five years. So some value has to be put on everything that happens once the counting stops.

The sequence just described is a discounted cash flow, complete, with nothing left out. The cash is forecast. Each year is shrunk for time and risk. The years are added up. A value is put on everything after the years run out, and that is added in too. Then an adjustment is made for what the business already has in the bank and what it already owes, and the total is divided by the number of shares. Every model ever opened, on any company of any size, is that sequence carried out with more columns and better vocabulary. Sankalp Industrial Systems Limited carries the whole sequence out below, with every intermediate figure printed rather than asserted.

What is a discounted cash flow actually measuring?

A discounted cash flow measures one thing, and being precise about that one thing rules out several questions people put to it. A discounted cash flowValuing a business as the present value of the cash it is forecast to generate. measures what a business is worth to whoever funded it, on the strength of the cash that business itself is expected to produce, discounted for the time and the risk between now and the day each rupee arrives. The measurement is a statement about a company. The measurement is not a statement about a share price, about what somebody else might pay, or about what the business would be worth to a buyer with plans of their own for it.

Hold on to the phrase to whoever funded it. The phrase is the source of most of the confusion in this subject. A business is funded by lenders and by shareholders together. The machines were bought with a mixture of borrowed money and shareholders' money, and the cash those machines produce belongs, in the first instance, to both. So the natural object to value is the whole operating business rather than the shareholders' slice of it. The whole operating business is the enterprise valueWhat the operating business is worth to everybody who funded it, lenders and shareholders together.. The shareholders' slice, the equity valueWhat is left for shareholders once every other claim on the business has been settled., comes afterwards by subtraction, across a five line bridge set out in full below.

A reader who has never opened a model pictures a wall of numbers. A model is not that, and what a model is physically made of is worth naming early. A model has a small number of cells somebody typed and a very large number of cells that are arithmetic. On this one the typed cells are the rupee increase in revenue each year, the margin, the depreciation rule, the capital expenditure schedule, the working capital ratio, the tax rate, the discount rate, the terminal growth rate and the return on new capital. Nine typed cells. Everything else on the sheet, the answer included, is those nine cells with arithmetic applied to them. So when a model is handed over for an opinion, the useful question is never about the arithmetic. The useful question is about which nine cells were typed, and on what basis.

Which cash flow goes into the model, and which rate goes with it?

Every discounted cash flow has exactly two halves. The numerator is cash and the denominator is a rate. The single rule governing the pair is easy to state and is broken constantly: the cash and the rate must belong to the same people. If the numerator is the cash available to lenders and shareholders together, the rate has to be the blended cost of lenders' and shareholders' money together. If the numerator is only what is left for shareholders after the lenders have been paid, the rate has to be the cost of shareholders' money alone. Mixing the two produces an answer that means nothing whatever, and the arithmetic gives no warning at all.

The first pairing, used almost everywhere, is the one built here. The numerator is free cash flow to the firmCash left over after tax and after reinvestment, before any lender or shareholder has been paid anything.: the cash the operating business throws off after it has paid its tax and put back the capital it needs to keep growing, and before a single rupee has gone to a lender or a shareholder. The denominator is the weighted average cost of capitalOne blended rate for all the money in the business, debt and equity together, weighted by how much of each there is.. For Sankalp Industrial Systems Limited, invented, that rate is 12.00 per cent. How that rate is built is covered under the weighted average cost of capital, where eleven inputs go into it: a risk-free rate, an equity risk premium, a beta and the blended cost of the company's three debt tranches among them. The rate enters this walk as one settled number.

A discounted cash flow is far more a fixed sequence than it is a technique, so the shape of the whole exercise is worth seeing before any of the arithmetic. There are thirteen steps between the last completed year and a value for one share, and with the sequence in hand, every later argument about a model is an argument about one specific step in it.

Operating Cash Flow vs Free Cash Flow: Two Different Objects

Here is a mistake that costs a beginner a whole afternoon, and it is worth heading off before the arithmetic starts. A company's cash flow statement already reports a figure called cash generated from operations. The figure is right there, audited, and it looks exactly like what the model wants. Cash generated from operations is not what the model wants, and taking it is one of the more common ways a first model goes quietly wrong.

The two objects differ in three specific places. First, reported operating cash flow has usually already been reduced by interest paid, depending on the presentation, so it is a figure after the lenders have taken their share. The model values the whole business for lenders and shareholders together and subtracts the lenders' claim later, in the bridge. So the numerator has to sit before any interest. Second, reported operating cash flow has not yet paid for the machines. Capital expenditure sits in the investing section of the statement. A figure that stops at the operating section therefore describes a business that grows for free, and no business grows for free. Third, the reported figure carries whatever actually happened last year: one-off receipts, disputed refunds and timing accidents. The model wants a forward number built on stated rules.

Free cash flow is what is left after the business has paid its tax and bought the capacity it needs, and before anybody who funded it has been paid; reported operating cash flow is neither of those things. They are related, they are both cash, and they are not interchangeable. The model builds its numerator from operating profit downward rather than lifting it off a statement.

Where do the five forecast years come from?

The explicit forecastThe years a model works out one at a time, before a single formula takes over for everything afterwards. is the stretch of years an analyst is willing to argue about individually. Sankalp Industrial Systems Limited has five of them. The rule the forecast follows is a simple one, and it produces one of the more useful facts about growth. Revenue adds exactly Rs 1,20,00,00,000 every single year. Not ten per cent a year. The same rupee amount, every year.

Watch what that does. Year 0 revenue is Rs 12,00,00,00,000, so the first year's addition is a 10.00 per cent increase. The second year adds the same rupees onto a bigger base and so is only 9.09 per cent. Then 8.33, then 7.69, then 7.14. The rupees of growth never move and the growth rate falls every year anyway. Almost every maturing business looks exactly like that from the inside. A tea shop that adds two new regular customers a month is growing more slowly every month by any percentage measure, and nothing about the shop has changed.

The margin is held flat at 24.0 per cent of revenue throughout. The flat margin matters more than it looks. Nothing in this valuation rests on the company becoming more profitable. Depreciation runs at 4.0 per cent of revenue, so operating profit lands at 20.0 per cent of revenue in every year. Tax is charged at 25.0 per cent. The rate is this invented company's own assumed effective rate rather than any country's statutory rate, and it is an assumption of the worked example every time it appears. Out of that comes net operating profit after tax, or NOPATNet operating profit after tax: operating profit less tax, with no interest deducted anywhere., and it rises by exactly Rs 18,00,00,000 a year for five years running.

Read the last three rows again. The identity the whole model turns on is in them. Net new invested capitalCapital expenditure less depreciation, plus the movement in net working capital. What growth costs in cash. is what the company puts into the ground that it did not already have: the capital spending over and above simply replacing what wore out, plus the extra receivables and inventory a bigger business has to carry. On this forecast it comes to exactly Rs 1,00,00,00,000 in every one of the five years. Check Year 1: Rs 1,34,80,00,000 of capital expenditure, less Rs 52,80,00,000 of depreciation, plus Rs 18,00,00,000 of working capital, is Rs 1,00,00,00,000.

Free cash flow to the firm is therefore just NOPAT less Rs 1,00,00,00,000, in every year, and the deduction is what growth costs in cash. Rs 1,98,00,00,000 less Rs 1,00,00,00,000 is Rs 98,00,00,000 in Year 1, and so on down to Rs 1,70,00,00,000 in Year 5. The same figure arrives the long way, the way a statement would present it: Rs 1,98,00,00,000 of NOPAT plus Rs 52,80,00,000 of depreciation less Rs 1,34,80,00,000 of capital expenditure less Rs 18,00,00,000 of working capital movement, which is Rs 98,00,00,000. Same figure, two routes, and the short route is the one that shows what is actually happening.

One more thing about the numerator, and it is the question every reader asks at exactly this point. Where is the interest? Sankalp Industrial Systems Limited pays Rs 48,00,00,000 of interest in Year 1 on Rs 6,00,00,00,000 of borrowings, and that interest appears nowhere in the table above. The absence is not an omission. Interest is a payment to one of the two groups the model is valuing the business for, so deducting it in the numerator and then deducting the whole of the debt again in the bridge would count the lenders twice.

The lenders are dealt with in exactly one place: the denominator carries their cost of money inside the blended 12.00 per cent, and the bridge later removes the principal they are owed. Nothing else in the model touches the lenders. Run the other way, valuing only the shareholders' claim, interest would be deducted in the numerator, new borrowing would be added, and the rate would have to be the cost of shareholders' money alone rather than 12.00 per cent. The equity route exists, it is a genuine method, and it does not agree with this one by construction. It is covered under free cash flow to equity.

Forward Numbers and Historical Financials: Where One Stops and the Other Starts

Notice that not one figure in the forecast table was read off a completed year. Every one of them was produced by a rule applied to Year 0. So what were the accounts for, and where exactly did they stop being used?

Historical Financials do two jobs in a discounted cash flow and only two. The first is to establish the base year: Year 0 revenue of Rs 12,00,00,00,000, EBITDA of Rs 2,88,00,00,000 at a 24.0 per cent margin, depreciation of Rs 48,00,00,000 and operating profit of Rs 2,40,00,00,000. Every forecast rule is anchored to those. The second is to supply the balance sheet items that the bridge needs at the end: Rs 1,20,00,00,000 of cash, Rs 6,00,00,00,000 of gross debt, Rs 60,00,00,000 of minority interest and Rs 1,00,00,00,000 of assets that produce none of the forecast cash. The closing balances are observed, not forecast.

Everything between the base year and the bridge is forward, and the past enters the model only as a starting point and a set of closing balances. This is worth being blunt about because it disposes of a comfortable illusion. A model resting on five audited years still contains no audited number after the first column. The accounts state where the company stood. The accounts do not state what the company will do, and a valuation is entirely a statement about what it will do. Cleaning the base year first, so that the anchor is not itself distorted by something that happened once, is a real and separate discipline, covered under normalising a base year.

How does the model turn five future years into today's money?

By multiplying each year's cash by a discount factorThe multiplier that turns a rupee arriving in a future year into its worth today.. The factor is one divided by one plus the rate, raised to the number of years of waiting. At 12.00 per cent, a rupee arriving in one year is worth 1 divided by 1.12 today, or 0.892857143 of a rupee. A rupee arriving in five years is worth 1 divided by 1.12 multiplied by itself five times, or 0.567426856. The multiplication is the entire mechanic, and the arithmetic is the same whether the subject is a tea shop or a manufacturer of industrial valves.

The five factors below carry nine decimal places on purpose. Somebody rebuilding the model who derives them slightly differently can spend an afternoon hunting a discrepancy that was never there.

How to Choose a Discounting Convention, and What This Model Uses

Before the factors can be applied, one choice has to be made and stated, and a great many models never state it. When exactly does a year's cash arrive? Year-end discounting is the convention used here, and it treats every rupee of a year's cash as landing on the last day of that year. Year 1 cash is discounted one full year, Year 5 cash five full years.

Cash obviously does not arrive that way. A company that sells valves collects money in every week of the year, so on average its cash arrives around the middle of each year rather than on the final evening. The alternative convention says so: mid-year discounting discounts Year 1 by half a year, Year 2 by one and a half, and so on. Mid-year discounting is not a rounder or a looser method. The convention is a different and defensible reading of the same facts.

The choice costs a measurable amount. Applied to these five years, the mid-year convention raises the present value of the explicit period from Rs 4,68,41,43,564 to Rs 4,95,72,31,590. The increase of 5.83 per cent is exactly the square root of 1.12 as a multiplier, and the gap is a real amount of money produced by nothing except a decision about which day cash is assumed to arrive. How the terminal value should be timed under that same convention is a second choice with more than one accepted answer, and it is covered under terminal value timing.

The rule to carry away is not that one convention is correct. The rule is that a model has to say which one it used, in writing, near the answer. A reader who cannot tell whether a valuation is a year-end or a mid-year figure cannot compare it with anything.

With the convention settled, the arithmetic is a single multiplication per year. Every present value below is stated to the rupee and the five of them, each rounded on its own line, add to exactly the total shown, so the printed column foots without any adjustment.

The present value column is the most useful thing here for anybody trying to feel what a discount rate is. The cash flow column rises hard: Rs 98,00,00,000 to Rs 1,70,00,00,000 is a rise of 73.47 per cent across five years. The present value column barely moves: Rs 87,50,00,000 to Rs 96,46,25,655 is a rise of 10.24 per cent, and the column actually turns down between Year 4 and Year 5, from Rs 96,59,87,479 to Rs 96,46,25,655. Growth of 11.84 per cent in Year 5 was not enough to outrun a 12.00 per cent discount rate, so a bigger cash flow arrived worth slightly less than the smaller one before it. That crossover is the discount rate becoming visible.

Add the five present values and the explicit period is worth Rs 4,68,41,43,564. Rs 4,68,41,43,564 is the entire product of forecasting five years of a real operating business in detail. Hold that figure in mind. The single most important fact about this method is what happens to it next.

How is the terminal value worked out?

The forecast stops at Year 5. The company does not. So the model needs one number standing in for every year from Year 6 onward, forever, and that number is the terminal valueThe value of everything that happens after the explicit forecast stops, collapsed into one figure.. There are two accepted ways to build it. The first is built here and the second stated alongside it. Neither is the right one. The two are answering genuinely different questions.

The first route treats everything after Year 5 as a stream growing at a steady rate forever. The formula for the value of such a stream is old and settled: next year's cash divided by the rate less the growth rate. Gordon set it out in Dividends, Earnings and Stock Prices in the Review of Economics and Statistics in 1959, and it is his expression that every model in this shape is using. Here the terminal growth rateThe rate the business is assumed to grow at forever after the explicit forecast ends. is 5.00 per cent a year in nominal rupees, and the rate is 12.00 per cent, so the divisor is 0.07.

Now the part that most first models get wrong, and it matters more than anything else in this section. Which figure is next year's cash? The tempting answer is to take Year 5 free cash flow of Rs 1,70,00,00,000, grow it by 5.00 per cent to Rs 1,78,50,00,000, and divide by 0.07, for Rs 25,50,00,00,000. The tempting answer is a real, common and published way to do it. The short route also carries a hidden assumption that nobody typed. Year 5 is still growing at over 7 per cent, so Year 5 reinvests 37.04 per cent of its NOPAT. Carrying that Year 5 cash flow into perpetuity carries the Year 5 reinvestment rate into perpetuity too, and a company growing at only 5.00 per cent forever does not need to reinvest at the rate of a company growing at 7 per cent.

Growth has to be paid for, so the terminal reinvestment rate has to be whatever 5.00 per cent of growth actually costs. The cost is 5 divided by 18, or 27.78 per cent of NOPAT. This is the argument Aswath Damodaran has made most insistently, and it is his: a terminal value must be consistent with the growth it assumes. New capital in this business earns 18.00 per cent, an assumption of the forecast rather than a fact about anything. To grow 5.00 per cent forever on returns of 18.00 per cent, the company must put back 5 over 18 of its profit and no more.

Side by side, the two routes differ by Rs 3,75,00,00,000, or 14.71 per cent of the naive figure. The gap is worth being very clear about. The gap is not a rounding, it is not an error, and neither figure is a correction of the other. Both methods appear in real work. The difference is entirely that one of them lets the terminal period inherit a reinvestment rate that belongs to a faster growing period, and the other makes the reinvestment rate match the growth it is paying for. The reinvestment-consistent route is the one used here, and the argument for it is named above.

The second route ignores perpetual growth altogether and asks a different question: what would somebody pay for this business at the end of Year 5? Year 5 EBITDA is Rs 4,32,00,00,000. An exit multiple of 7.8 times, the median of an invented set of six comparable manufacturers, gives a terminal value of Rs 33,69,60,00,000.

Two sentences reconcile the routes, and any comparison of them owes the reader both. First: the perpetuity terminal value of Rs 29,25,00,00,000 is 6.77 times Year 5 EBITDA, so a business trading at 7.78 times today is being valued, on its own stated assumptions, at 6.77 times in five years. Second, run the other way: an exit at 7.8 times implies a terminal growth rate of 6.58 per cent rather than 5.00 per cent. The perpetuity route makes an assumption about the economics of the business and the exit multiple route makes an assumption about what somebody will pay, and a reader has to decide which of those two assumptions they are willing to carry. Neither method is the correction of the other.

How big is the terminal value against everything else?

Add the two halves. The enterprise value of Sankalp Industrial Systems Limited is Rs 4,68,41,43,564 plus Rs 16,59,72,35,530, or Rs 21,28,13,79,094. And now the number that ought to change how every valuation is read.

The terminal value is 77.99 per cent of the answer. The five years of forecast that took all the work, all the arguing about margins and all the meetings with the plant, do 22.01 per cent of it. The 77.99 per cent is not a quirk of this invented company. On a five year forecast at a 12.00 per cent rate with 5.00 per cent terminal growth, something in that neighbourhood is what always comes out, and the shorter the forecast the more extreme it gets. The terminal share is the honest headline of the whole method, and it belongs on the front of any model rather than buried in a tab.

A figure has just been printed to the rupee, and that deserves an explanation rather than a shrug. The enterprise value of Rs 21,28,13,79,094 is exact given the inputs, and it is stated to the rupee so that anybody rebuilding the model can confirm they have landed in the same place. The figure is not, however, knowledge to the rupee. On an answer of roughly Rs 21,28,00,00,000 that is 77.99 per cent terminal value, the load-bearing digits are the first three and the rest are the arithmetic carrying itself through.

A small demonstration of exactly that sits in the figures above. Rebuilt from the nine-decimal discount factors as printed, rather than from full precision, the enterprise value comes out at Rs 21,28,13,79,103, nine rupees higher. Both figures are the same number rounded at a different point, neither is wrong, and the drift is simply the printed factors carrying their own rounding into the product. Nine rupees on Rs 21,28,13,79,094 is the sort of difference that has cost people afternoons. If it matters to an answer, that answer did not have that much precision in it to begin with.

The Two-Stage Shape of This Model, and the Step at the Join

The model built here is a two-stage model, and naming the shape makes the next question obvious. Stage one is the five explicit years, in which growth falls from 10.00 per cent to 7.14 per cent and reinvestment runs at Rs 1,00,00,00,000 a year. Stage two is everything afterwards, at a flat 5.00 per cent forever. There are exactly two stages and the join is the last day of Year 5.

Look hard at that join. There is a step in it. Growth drops from 7.14 per cent in Year 5 to 5.00 per cent in Year 6, and the reinvestment rate drops with it, from 37.04 per cent of NOPAT to 27.78 per cent. Free cash flow therefore jumps from Rs 1,70,00,00,000 in Year 5 to Rs 2,04,75,00,000 in Year 6, a rise of 20.44 per cent, in the single year in which the business is assumed to slow down. The jump is not a modelling error. It is the arithmetic of a company that stops paying for fast growth, and it is exactly what a two-stage model asserts about the world. Whether a real business would step like that on one particular evening is a fair objection, and it is the objection a third stage exists to answer.

What a Three-Stage DCF Would Add, and When It Earns Its Extra Stage

A three-stage discounted cash flow, or DCF, puts a transition between the two. Stage one is high growth, stage three is the steady perpetuity, and stage two is a fading corridor of five or ten years in which the growth rate and the reinvestment rate walk down gradually instead of stepping. Sankalp Industrial Systems Limited would fade from 7.14 per cent toward 5.00 per cent over, say, five further years, and the free cash flow jump at the join would be spread out into something a plant manager might recognise.

When does the extra stage earn its place? When the gap it is smoothing is large. A business growing at 7.14 per cent in its last explicit year and settling at 5.00 per cent has a small step, and a third stage would move the answer by an amount easily lost inside the assumption error already present. A business growing at 30 per cent in its last explicit year and settling at 5.00 per cent has an enormous step, and a two-stage model there is asserting something absurd. The rule of thumb worth carrying is that the extra stage is bought to fix an implausible join, not to make a model look thorough, and the shape of the model is chosen from the shape of the business rather than from habit. The choice of shape, and how the horizon is set in the first place, are covered under the forecast horizon.

How does an enterprise value become a value per share?

By walking a bridge of five lines, each with a sign and a reason, and no line on it is optional. The enterprise value of Rs 21,28,13,79,094 is what the operating business is worth to lenders and shareholders together. A shareholder does not have the operating business. A shareholder has whatever is left after the lenders are settled, plus a share of anything the company holds that the forecast never counted.

Line 2 deserves a sentence of its own because a sharp reader is about to object. The cash is added because nowhere in the forecast did the model count a rupee of it. The forecast started at revenue and worked down to free cash flow; the Rs 1,20,00,00,000 sitting in the company's bank accounts on the last day of Year 0 never entered that calculation and is therefore a separate thing the shareholder gets, on top of the business.

The objection is this. The record splits that balance into Rs 40,00,00,000 of operating cash the business genuinely needs to run and Rs 80,00,00,000 of surplus. Surely adding all of it double counts the operating part? Adding the whole balance does not double count, and the reason is structural rather than a matter of taste: net working capital in this forecast is receivables of Rs 2,16,00,00,000 plus inventory of Rs 1,44,00,00,000 less payables of Rs 1,80,00,00,000, and it contains no cash at all. The operating Rs 40,00,00,000 is nowhere inside the model, so nothing is counted twice by adding the whole balance. The gross cash convention is the one used throughout here. The other convention exists and is respectable: a house that treats the Rs 40,00,00,000 as part of the operating business adds only the Rs 80,00,00,000 of surplus and lands Rs 40,00,00,000 lower, or Rs 2.00 a share. Neither is wrong. A model that never says which one it used is.

Line 3, and Why a Non-Operating Asset Is Added Rather Than Forecast

A non-operating assetSomething the company holds that produces none of the cash flow the model forecast. is anything the company holds whose earnings never appeared in the EBITDA the forecast was built on. Sankalp Industrial Systems Limited has Rs 1,00,00,00,000 of them: a surplus land parcel valued at Rs 45,00,00,000, and a 26.0 per cent stake in Aruna Tooling Private Limited, invented, carried at Rs 55,00,00,000.

Neither belongs in the forecast and both belong in the bridge, and the test is a single question. Did the thing produce any of the EBITDA that was multiplied and discounted above? The land produces nothing. The land sits there. The associate is equity accounted, meaning its profits appear far below EBITDA in the accounts and were never inside the Rs 2,88,00,00,000 the whole forecast rests on. So valuing only the forecast cash and stopping there values the valves and castings business and silently throws away a plot of land and a quarter stake in a tooling company.

The test is not whether the company holds it; the test is whether the model already counted the cash it produces. Anything counted goes in the forecast. Anything not counted goes in the bridge at its own separate value. Getting this backwards in either direction is a real error: forecasting the associate's profits inside EBITDA and then adding the stake in the bridge counts it twice, and leaving it out of both simply loses it. Which assets qualify, and how each is valued when its own value is not observable, is covered under non-operating assets.

Line 5 has its own logic worth thirty seconds. Consolidation takes 100 per cent of a subsidiary's cash flow, so the forecast consolidated 100 per cent of Sankalp Coatings Private Limited. The group holds only 75.0 per cent of it. So a quarter of the coatings cash that was just valued belongs to somebody else entirely, and the Rs 60,00,00,000 carrying value of that quarter comes out on the way to the shareholders' figure.

One other figure travels with this bridge and the two must never be confused. Rs 15,88,13,79,094 is the equity value of the operating business on its own, being the enterprise value less gross debt plus cash less minority interest, with the assets outside the forecast left out. A route that values the shareholders' cash flow directly also excludes those assets, so Rs 15,88,13,79,094 is the figure used when the two routes are compared. The two figures differ by exactly the Rs 1,00,00,00,000 of line 3, and a valuation that reports one while meaning the other has lost a plot of land and a stake in a tooling company.

What does running the same model backwards establish?

Everything so far has run in one direction: assumptions in, value out. Nine typed cells produced Rs 21,28,13,79,094. There is a second exercise using the identical sheet in the opposite direction, and confusing the two is how a valuation quietly turns into an argument.

What a Reverse DCF Reads Out of a Traded Figure

A reverse discounted cash flowRunning the model backwards to read out what assumption a given value already contains. takes a value as given and solves for the assumption that would produce it. Sankalp Industrial Systems Limited's traded enterprise value is Rs 22,40,00,00,000, arrived at from the other side of the same bridge: market capitalisation of Rs 18,00,00,00,000 plus gross debt of Rs 6,00,00,00,000 plus minority interest of Rs 60,00,00,000 less cash of Rs 1,20,00,00,000 less the Rs 1,00,00,00,000 of assets outside the forecast.

Hold the rate at 12.00 per cent, hold the five forecast years exactly where they are, and ask what terminal growth rate would carry the model to Rs 22,40,00,00,000 instead of Rs 21,28,13,79,094. The answer is 5.80 per cent. Alternatively, hold terminal growth at 5.00 per cent and ask what rate would do it. The answer is 11.67 per cent.

The whole distance between this model and the traded figure is 80 basis points of assumed growth, or 33 basis points of rate, and stating it that way is the only honest way to state it. In rupees the two look Rs 1,11,86,20,906 apart, which sounds like a chasm. In assumptions they are a rounding apart. Notice which of those two framings a reader would find more useful, and notice that almost every published discussion uses the first.

DCF vs Reverse DCF: Same Sheet, Opposite Direction

The two exercises produce objects of completely different kinds, so the distinction is worth drawing out precisely. A discounted cash flow puts assumptions in and gets a value out; a view goes in and the sheet converts it into rupees. A reverse discounted cash flow puts a value in and gets assumptions out; a figure somebody else produced goes in and the sheet converts it into a sentence about what that figure contains.

The second exercise never tests anything. The absence of a test is the part readers get wrong most often. Learning that Rs 22,40,00,00,000 embeds 5.80 per cent terminal growth says nothing whatever about Sankalp Industrial Systems Limited. The reverse run states what assumption is inside a number, and it produces a question rather than an answer: is 5.80 per cent an assumption worth carrying, or is it not? A reverse run converts a value into an assumption. Judging the assumption is a separate act that the arithmetic cannot perform.

How far does the answer move when the assumptions move together?

The control above moved one assumption. Nobody who disagrees with a model disagrees about one assumption. A person who thinks the business will do better than this forecast holds one underlying view, and one view usually produces four changes at once: faster growth, a better margin, a slightly lower rate and a slightly higher terminal growth rate. Moving one input at a time is a sensitivity. Moving several together is a scenario, and only the second shows how wide an answer really is.

Both of the cases below move exactly four assumptions: the rupee increase in revenue each year, the EBITDA margin, the rate and the terminal growth rate. The return on new invested capital is held at 18.00 per cent in all three cases. Holding it still isolates what those four assumptions do on their own.

The Bull Case: Four Assumptions Moved Upward at Once

Revenue adds Rs 1,50,00,00,000 a year instead of Rs 1,20,00,00,000. The margin is 25.0 per cent instead of 24.0. The rate is 11.50 per cent instead of 12.00. Terminal growth is 5.50 per cent instead of 5.00. Every one of those four is a small, arguable, entirely reasonable change, and not one of them would raise an eyebrow in a meeting.

Together the four produce an enterprise value of Rs 26,26,89,00,000, being 23.44 per cent above the base case. Four modest changes compound into that. On its own base year EBITDA of Rs 3,00,00,00,000 it works out at 8.76 times, against the base case's 7.39 times. The two scenario cases are stated to the nearest lakh and the base case alone to the rupee.

The Bear Case, and the Thing About It That Surprises Everyone

Revenue adds Rs 80,00,00,000 a year, the margin is 22.5 per cent, the rate is 12.50 per cent and terminal growth is 4.00 per cent. Enterprise value Rs 16,54,94,00,000, being 22.24 per cent below base, and 6.13 times its own base year EBITDA of Rs 2,70,00,00,000.

Now the fact that catches almost every reader, and it is worth stopping on because it teaches something the arithmetic does not advertise. The bear case has more free cash flow in Year 1 than the base case does: Rs 1,15,93,00,000 against Rs 98,00,00,000. A company growing more slowly needs less new machinery and carries less inventory and fewer receivables, so it reinvests less, so more cash survives. Slower growth is not less cash in the near term. Slower growth is less cash later, and the whole of the difference lands in the terminal value.

The household version of this is immediate. A person who takes a job in another city earns more and also pays a deposit, a broker and a month of two rents, so their bank balance next month is lower than it would have been had they stayed put. Nobody thinks the move was therefore worse. Growth costs cash now and pays cash later, in a business exactly as in a household, and a cash flow forecast that shows the bear case ahead in Year 1 is describing that and not a mistake.

How DCF Assumptions Affect Valuation Range, Stated Plainly

The three cases run from Rs 16,54,94,00,000 to Rs 26,26,89,00,000. The spread is Rs 9,71,95,00,000, or 58.73 per cent of the bear case. Any spread stated as a percentage must say which end it was divided by. The other end gives a different and equally true figure.

So what is the output of this exercise? Not Rs 21,28,13,79,094. A single figure carries a precision the model does not have and hides the four decisions that actually decided it, so the output is the range with the assumptions that produced each end named beside it. The base case is not a most likely value and the middle of the range has no special authority; it is simply the case whose four assumptions were argued above. Averaging the three into one number would destroy the only information the exercise produced.

What does this model deliberately leave out?

Quite a lot, and naming it is part of using the method honestly rather than a disclaimer bolted on at the end. The 12.00 per cent rate was restated here, not built. Where it comes from, how a beta is estimated, what the weights should be and what to do about a business with no share price at all are each a substantial subject and are covered separately. A reader who wants to argue with this valuation has a strong line of attack there.

The method also leaves out every other way of putting a number on the same company. A discounted cash flow values Sankalp Industrial Systems Limited standing alone, at its own cost of capital, on its own forecast, with nobody's plans attached. The method does not price it against what similar businesses trade at, against what buyers have paid for whole companies in past deals, or as a target funded largely with debt. Each of those produces a different figure, each for a good reason, and each is covered separately.

And it leaves out the procedures behind its own inputs. How the base year is cleaned before anything is forecast, how each forecast line is actually built, which cash flows count as genuinely incremental, how the horizon is chosen, how the terminal value is settled and how a finished model is audited are all real disciplines with real content. Each of those procedures is covered separately, where it is taught properly, and only its result appears in this walk. The statements themselves, and what an accrual or a deferred tax liability is, are settled elsewhere entirely and are assumed here throughout.