How to Build a DCF Valuation: The Seven Choices That Decide It

A discounted cash flow (DCF) is built by making seven choices and then doing arithmetic, and the seven choices decide the answer before any arithmetic starts. Which cash flow, which rate goes with it, how many years get a line of their own, what takes over at the end, when cash is assumed to arrive, how inflation is handled, and what becomes of the things the business holds but does not use.

Start with a shop that is easy to picture. A cousin runs a hardware store in a market street, two shutters wide, and after eleven years he wants out. His sister might buy it. Brother and sister agree, sensibly enough, to work out what the shop earns and pay a fair price for that. So they sit down with a notebook on a Sunday afternoon and start adding.

Watch what happens in the next twenty minutes. It is exactly what happens in a spreadsheet. He writes down last year's takings and pencils in a growth number for next year. She asks whether that growth is in today's rupees or tomorrow's. He has not thought about it. He writes down what the shop clears after the boy's wages, and she asks whether her own salary, if she runs it herself, comes out of that number or not. He has not thought about that either. He assumes the shop keeps going forever. She asks how much he has to spend on new stock and new shelving each year to keep it going forever, and whether that is inside his number or outside it. The spending on stock and shelving is not inside. Then he mentions, almost in passing, that the shop includes a small godown behind it that has been shut for four years and holds nothing.

Not one of those questions is arithmetic. Every one of them changes the price. And every one of them has an exact counterpart in a professional valuation model, where it is easier to miss. A spreadsheet answers only the questions somebody typed into it.

What order is a discounted cash flow actually built in?

Not the order in which it is usually taught. Most people meet this method as a walk from left to right: forecast the revenue, work down to a cash flow, discount it, add up the column, add something for the end, done. The left-to-right walk describes the arithmetic. The walk does not describe the build, and treating it as one is how models get made whose central decisions were never actually decided.

The build runs the other way round: everything that is a judgement goes on paper first, and only then does anything get computed. There are seven steps and the first two of them do not produce a single number.

Step one, decide the object and the perimeterWhich entity and which claims a valuation is drawn around.. Which entity is being valued, which claims are inside the answer, and is the number being aimed at the value of a whole business or the value of what shareholders hold in it? The object and the perimeter are not details to be settled later. The two of them decide which cash flow is built in step three and which rate is used in step six, and a model that has not settled them will settle them by accident.

Step two, write the input sheetOne sheet holding every assumption a valuation uses, with its source and its date.. One sheet, every assumption on it, each with where it came from and when. Nothing is computed yet. Writing the input sheet is the step almost everybody skips, and the step the whole method rests on, for a reason set out below.

Step three, forecast the numerator. Revenue, margin, depreciation, capital expenditure and the movement in working capital, built so that the five agree with each other rather than being five independent guesses. How that forecast is constructed is covered separately; here it enters only as a requirement that it be internally consistent. Everything downstream inherits whatever inconsistency the forecast contains.

Step four, choose the horizon. How many years get a line of their own in the explicit forecastThe years for which each line is projected individually before a terminal method takes over. before something simpler takes over.

Step five, choose the method that produces the terminal valueThe value attributed to everything after the explicit forecast stops., and make it consistent with the forecast sitting in front of it. On a model of this shape that single step carries roughly three quarters of the answer, a fact worth knowing before the step is taken rather than after.

Step six, pair the rate with the cash flow, and fix the discounting convention. Note the verb. The rate is paired, not picked. The rate follows from step one and step three rather than being chosen alongside them.

Step seven, handle everything the forecast does not produce cash for, and then bridge from a business value to a value for a share. The cash sitting in the bank, the plot of land nobody uses, the quarter of a subsidiary somebody else holds: none of those produced a rupee of the earnings just forecast, and each has to be dealt with once and exactly once.

What goes on the input sheet before any arithmetic is done?

Every assumption, its source, and its date. The sheet is the whole of it, and the dullness of the idea is exactly why the sheet gets left out.

Here is the sheet for Sankalp Industrial Systems Limited, an invented maker of industrial valves and precision castings that also sells the replacement parts and the servicing going with them. The company is listed, holds three quarters of one subsidiary, Sankalp Coatings Private Limited, and holds 26.0 per cent of an associate, Aruna Tooling Private Limited.

Twenty-one lines. A person could read that in ninety seconds and argue with any single line of it. Being arguable line by line is the entire point.

The third column does real work. The 25.0 per cent tax rate is written as this company's own assumed effective rate rather than as anybody's statutory rate. Presenting an assumed figure for an invented company as a rule would be a different and much worse kind of statement. The 18.00 per cent return on new capital is an assumption and is written as one. The 15.00 per cent return on capital already in the ground falls out of the reported lines rather than being chosen, and is written as computed. Two numbers that look identical in a spreadsheet cell are doing completely different jobs, and only the source column tells them apart.

A model is a machine for hiding its own assumptions, and the input sheet is what undoes that. Once a number is inside a cell it looks like a fact. The number is formatted like the numbers around it, it foots into totals, and after a week nobody remembers whether it was pulled from a filing, agreed in a meeting or typed in to make something else work. Six weeks later a reviewer who asks where the 18.00 per cent came from is asking a question nobody in the room can answer, and the honest reply, that somebody chose it in March, is not available because nobody wrote March down.

There is a second reason, and it is about time rather than about argument. Assumptions age at completely different speeds. The share count changes rarely. A market-derived rate can be stale within a quarter. A tax assumption survives until the day it does not. When a valuation is dusted off eight months later, the question is never whether the whole thing needs rebuilding; it is which four lines need refreshing. A sheet with dates answers that in a minute. A model without one has to be rebuilt from scratch or, far more commonly, is quietly reused with figures nobody has checked.

Which cash flow is used, and what does that choice commit the model to?

There are two, they measure the cash left over for different people, and the choice between them decides most of what follows.

Free cash flow to the firm is the cash the operating business throws off after it has paid its taxes and funded the investment it needs, and before anything is paid to anybody who financed it. The firm's cash flow belongs to lenders and shareholders together. Free cash flow to equity takes that same figure, subtracts the interest the lenders were paid after the tax relief on it, and adds back whatever new borrowing came in during the year. The remainder belongs to shareholders alone.

Go back to the hardware store for a second. The distinction is not abstract at all. The shop clears a certain amount each year after stock and wages and the money spent keeping the shutters and shelves in order. The amount the shop clears is the firm's cash flow: it exists whether or not there is a loan against the shop. Now suppose there is a loan, and the instalments come out of that amount, and the bank also lends a little more each year against rising stock. The amount left in the cousin's hands after all that is the shareholder's cash flow. Same shop, two different numbers, and each one is the right answer to a different question.

The chosen route here is the firm's cash flow, and it commits the model to two things. First, the answer it produces is the value of the whole operating business, so it has to be bridged afterwards: debt comes off, cash and the unused assets go on, the outside quarter of the subsidiary comes off. Walking that bridge is real work, and it is covered separately. Second, and this is the reason the route is chosen, it buys robustness to a funding mix that does not hold still. The mix affects the rate rather than the cash flow, so the firm route does not require the ratio of debt to equity to stay put through the forecast. The equity route does require it, quietly, and when the borrowing schedule drifts away from the mix the rate was built on, the two routes stop agreeing. Choosing the firm's cash flow is choosing to do a bridge at the end in exchange for not having to keep the debt ratio still in the middle.

Which rate pairs with which cash flow?

The blended one with the firm's cash flow, the shareholders' one with the shareholders' cash flow, and there is no third arrangement.

Here is the rule underneath it, and it is almost embarrassingly simple once said plainly. A discount rate is the return required by whoever the cash belongs to. So the cash and the rate have to belong to the same people. Free cash flow to the firm belongs to lenders and shareholders together, so it is discounted at the rate that blends what both of them require, weighted by how much of the money each has put in. The blended rate for this company is the 12.00 per cent weighted average cost of capital. Free cash flow to equity belongs to shareholders alone, so it is discounted at the 14.00 per cent that shareholders alone require. Where those two figures come from, and how they are estimated when a company has no share price to look at, is covered separately; here they are inputs on a sheet.

Choices one and two are not two choices at all, but one choice, made once, and then read off twice. The moment whose cash flow is being forecast has been decided, the rate is decided too. Treating the rate as a separate decision, made later, by a different person, in a different cell, is how the most consequential error available in this whole method gets made.

The mismatched version does something specific, and it is worth spelling out. Pairing the firm's cash flow with the 14.00 per cent cost of equity charges the entire business the rate that only the most expensive money in its capital structure requires. The lenders in this company are supplying a quarter of the capital at 6.00 per cent after tax. Discounting their share of the cash at 14.00 per cent prices their money as if it cost more than twice what it actually costs, and the value that comes out is too low. The mirror error, discounting shareholders' cash at the blended 12.00 per cent, does the reverse: it credits shareholders with the cheapness of borrowed money that has already been paid away as interest, and the value comes out too high.

Neither error announces itself. Both produce a clean column of numbers that add up correctly to a wrong answer.

How many years should the forecast be built out line by line?

The honest answer is that the number of years is not the question. The inconvenience of that answer is that the number of years is what everybody asks about.

Five is the common answer and ten is the common alternative, and neither is a reason. The real test is whether the business has reached a state by the last explicit year that could defensibly be carried forward forever. If it has, the forecast is long enough at whatever length it happens to be. If it has not, adding years does not help. The extra years are more assumptions somebody made up rather than more information about the business.

On this company the test is unusually concrete. Look at how the forecast is shaped. Revenue rises by exactly Rs 1,20,00,00,000 in every one of the five years, from Rs 12,00,00,00,000 in the base year to Rs 18,00,00,00,000 in Year 5. The rupees added never change. But the base they are added to keeps getting bigger, so the growth rate falls on its own: 10.00 per cent, then 9.09, then 8.33, then 7.69, then 7.14. Nobody forecast a slowdown. The slowdown is arithmetic.

Now look at where that leaves the model. The last explicit year grows at 7.14 per cent. The terminal method is then asked to take over at 5.00 per cent a year, forever. Between the two there is a step of 2.14 percentage points, and the model has said nothing at all about how the business crosses it. Does growth keep sliding, in which case five years was one or two years short and the sixth and seventh years would have got most of the way there on their own? Or does it settle abruptly, in which case the model is asserting a change of behaviour it never described?

Neither question can be answered from the arithmetic. Crossing the step is a judgement about the business, and that is exactly why the input sheet has to record the horizon as a choice, with a line beside it saying why five and not eight. A reviewer can then disagree with the reason. Nobody can disagree with a number that arrived without one.

Which method takes over when the forecast stops?

One of two, and they assume completely different kinds of thing about the world.

The first treats the business after the last forecast year as a growing perpetuityA cash flow assumed to grow at a constant rate forever, valued in one formula.: one cash flow, growing at one constant rate, forever, collapsed into a single expression. The growing perpetuity is the form Gordon set out, and its inputs are a cash flow, a growth rate and a discount rate. The second applies an exit multipleA terminal value found by applying a multiple to the last forecast year's earnings. to the last forecast year's earnings, as though the business were being sold at that point at whatever multiple similar businesses fetch.

The first is a claim about the economics of the business; the second is a claim about what somebody will pay. Neither is more rigorous than the other and neither is a safe default. Choosing between them is choosing which of two uncomfortable assumptions the analyst is willing to sign: that how this business behaves forever can be described, or that what a market nobody has seen will pay for it in five years can be described.

The route chosen here is the growing perpetuity. Both terminal figures for this company, and the reconciliation between them, are covered separately.

Growth forever has to be paid for forever

A consistency requirement sits inside the terminal choice, and it is the single most commonly broken rule in the whole method. Damodaran is named for the argument, and once the argument has been seen it cannot be unseen.

A business that grows has to buy the capacity to grow. New machines, new working capital, more stock on the shelves. Spending on that capacity is the reinvestment rateThe share of earnings put back into the business to fund growth., and it is a deduction from the cash the business hands over. So growth and cash flow pull against each other: more growth means more reinvestment means less cash this year, in exchange for more cash later.

Now watch what the careless version of a terminal value does. The careless version takes the last forecast year's cash flow, grows it by 5.00 per cent, and drops it into a perpetuity formula. In doing so it has assumed the business grows forever at 5.00 per cent while spending exactly what it was spending in the last forecast year, when it was growing at 7.14 per cent. The model has assumed growth without paying for it. The effect is not small and the effect is not a rounding.

The disciplined version asks what reinvestment the assumed growth actually requires. If new capital in this business earns 18.00 per cent, and the business is to grow at 5.00 per cent forever, then the share of earnings it must put back forever is 5 divided by 18, being 27.78 per cent. Not the 37.04 per cent that Year 5 happened to be reinvesting. The terminal cash flow is then built from that reinvestment rate rather than inherited from a year that was growing faster.

The relationship underneath is worth stating in plain words because it is the frame Koller, Goedhart and Wessels put growth, return on invested capital and value into a single expression with: growth equals the share of earnings reinvested, multiplied by the return those earnings earn. Rearranged, the share that must be reinvested equals the growth sought divided by the return earned. The 5 over 18 comes from that rearrangement, and it is why a terminal growth rate is never a free parameter.

Should each year's cash be treated as arriving on the last day, or through the year?

Both conventions are in ordinary use, neither is wrong, and the difference between them is worth more than most of the assumptions people spend a day arguing about.

Under year-end discountingTreating each year's cash as arriving on the last day of that year., Year 3's cash flow is treated as landing on the final day of Year 3, and it is therefore discounted three full years. Under mid-year discountingTreating each year's cash as arriving evenly through the year., the same cash is treated as arriving evenly across the year, so on average it lands at the midpoint and is discounted two and a half years. No business actually collects its money in one lump on the last afternoon of December, so the mid-year convention is arguably the more realistic of the two. The year-end convention is simpler and is what this example uses.

Here is the part that surprises people. Removing half a year of discounting from every flow multiplies every present value by the same factor: the square root of one plus the rate. At 12.00 per cent that factor is the square root of 1.12, or 1.0583005, so every present value rises by 5.8301 per cent. The size of the cash flows does not matter, nor which year they fall in, nor whether they are rising or falling. The mid-year effect is arithmetic on the rate alone, and so it can be stated exactly without rerunning anything.

On the five forecast years of this company the present value of the explicit period is Rs 4,68,41,43,564 under the year-end convention and Rs 4,95,72,31,590 under the mid-year one, a difference of Rs 27,30,88,026. Both figures are rounded to the rupee for display; on a figure of this size the last two digits carry no information at all, and the point being made is the 5.8301 per cent, not the rupees.

The tidy version of this story is not available. The 5.8301 per cent above is the effect on the explicit period only. The effect of a mid-year convention on the terminal value is a separate question, and the answer to it depends on how the timing of a stream that begins after the last forecast year and runs forever is treated. More than one treatment is defensible. The explicit-period effect is exact; the rest is not. Anybody claiming the whole answer moves by exactly 5.83 per cent has quietly assumed something about the terminal value that they have not said out loud.

Refusing the tidy version is itself the lesson in miniature. A convention nobody argues about moved a large sum, and the reason nobody argues about it is that it never gets written down. Which is what step two of the build order is for.

How are currency and inflation kept consistent through the model?

By choosing one basis for the cash flow and using the identical basis for the rate, and by never mixing the two.

A cash flow can be built in nominal termsIncluding inflation, both in the cash flow and in the rate., meaning in the rupees of the year it arrives, with inflation inside it. Or it can be built in real termsExcluding inflation, both in the cash flow and in the rate., meaning in today's rupees, with inflation stripped out. Both are perfectly valid. Mixing one of each is not valid: a cash flow carrying inflation, discounted at a rate that has had inflation removed, or the reverse. The model then either credits the business with price rises it never charges for, or charges it for price rises it never gets.

Sankalp's model is built in rupees of the day throughout and discounted at a rate in rupees of the day. The choice commits the model to an inflation assumption now sitting in two places at once: inside the revenue line, and inside the 12.00 per cent.

What would the alternative look like? Take the 12.00 per cent and the 5.00 per cent expected inflation this example assumes, and put them through the relation Irving Fisher set out: divide one plus the rate by one plus inflation. The division gives 1.12 over 1.05, being 1.0666667, so the real rate is exactly 6.6667 per cent. Notice what the shortcut gives. Subtracting 5.00 from 12.00 gives 7.00 per cent, a full 33 basis points too high, and a third of a percentage point on a discount rate is not a rounding on a long-lived stream. The two bases produce the same answer only when each is applied properly to its own kind of cash flow.

The uncomfortable consequence, and it has to be said out loud

Here is where this choice stops being bookkeeping. Terminal growth in this model is 5.00 per cent a year in rupees of the day. Expected inflation is 5.00 per cent. Put those two sentences next to each other and read them slowly.

The model assumes the company does not grow at all in real terms after Year 5. Not slowly. Not modestly. Not at all. Everything the terminal value credits the business with after the fifth year is the price level moving, and none of it is more valves, more castings, more service contracts or better prices.

Zero real growth may well be the right assumption. Assuming a manufacturer expands in real terms forever is a much bolder claim than assuming it does not. But it is an assumption of enormous consequence and it is completely invisible in the output, where a reader sees a growth rate of 5.00 per cent and, unless they happen to remember the inflation line on the sheet, reads it as a business that keeps getting bigger. On a model of this shape, where roughly 78 per cent of the answer sits in the terminal value, this is the single largest thing in the whole exercise, and it is hiding behind two identical numbers that were entered on different days for different reasons.

Contrast the terminal assumption with the last explicit year, where the same arithmetic gives a much less silent answer. Year 5 grows at 7.14 per cent in rupees of the day against 5.00 per cent inflation, so by the Fisher relation the real growth in that year is about 2.04 per cent. The model therefore has real expansion right up to the last forecast year and exactly none of it thereafter. Whether that discontinuity is deliberate or accidental is a question only the input sheet can answer, and it is one of the best questions a reviewer can ask.

What happens to the things the forecast does not produce cash for?

Assets the forecast produces no cash for come out of the forecast and go into the bridge, at their own value, and one question sorts every one of them.

Did this asset produce a rupee of the earnings being forecast? If yes, it is inside the model already and nothing more is owed to it. If no, it is not in the model at all, and its value has to be added separately or it is simply lost.

Go back to the godown behind the hardware store, shut for four years, holding nothing. The godown contributes not one rupee to what the shop clears, so no forecast of what the shop clears will ever contain it. If the cousin values the shop by what it earns and stops there, he has just given his sister a godown for free. The fix is not to invent some rent the godown does not receive. Value the earnings of the shop, then add the godown separately at what the godown is worth.

The same logic, on the same company. A non-operating assetSomething the company holds that produces none of the earnings being forecast. here means Rs 45,00,00,000 of surplus land and a Rs 55,00,00,000 holding in the associate, Aruna Tooling Private Limited. The land grows nothing and makes nothing. The associate holding is equity accounted, so its profits never enter the EBITDA the forecast was built on. Neither produced a rupee of the earnings in the model, so neither belongs in the model, and both belong in the bridge at their own value. The Rs 1,20,00,00,000 of cash is treated the same way, and so, on the other side of the ledger, are the claims: the Rs 6,00,00,00,000 of debt and the Rs 60,00,00,000 minority interest representing the quarter of Sankalp Coatings Private Limited that the group does not hold.

The sorting question is about earnings, not about importance. A large, valuable, strategically vital asset that generates none of the forecast earnings is still a bridge line. A dull piece of working capital that quietly produces them is inside the forecast. Sorting by how much something matters, rather than by whether it earned, is how assets get counted twice or not at all. The alternative treatment, forecasting the income these items produce inside the model, would be defensible only if the forecast EBITDA actually contained that income. It does not. How the bridge itself is walked, line by line, is covered separately.

Which two conventions must appear on the face of a finished valuation?

The discounting convention and the currency and inflation basis. Two short lines, and without them one answer cannot be compared with another.

The first line says whether cash is treated as arriving at year end or through the year. On this example it is year end. The second says what basis the cash flows and the rate are on. On this example it is rupees of the day at a rate in rupees of the day. That is it. Two sentences, at the top of the output, beside the answer.

Two valuations of the same business can differ by more than 5.8301 per cent for reasons that have nothing to do with the business at all, and the only defence against that is to state the conventions where the answer is. Imagine two analysts hand in numbers for this company and one is meaningfully higher. Without the convention lines, the entire discussion becomes an argument about the business: about margins, about the terminal rate, about whether the capital expenditure is realistic. With the convention lines, the first thirty seconds of the meeting reveals that one of them used mid-year discounting, and the argument about the business can begin from a level footing rather than a false one.

The two lines have something in common worth noticing. Neither is a judgement about the company. Both are choices about how the arithmetic is expressed. Being mere choices is precisely why they get left out, and precisely why leaving them out is so expensive: nobody thinks to defend a decision they do not remember making.

What do the seven choices look like together?

Laid out in one place, with the alternative named beside each one, they stop looking like technical settings and start looking like what they are: seven arguments somebody had to win before a single cell was filled in.

Reading down the chosen column gives the model's whole character in seven lines. The model values the business rather than the shareholders' slice of it. The blended rate follows from that. Five explicit years run line by line, and then the terminal method takes over. The handover goes to an assumption about economics rather than an assumption about a buyer. Cash is treated as arriving on the last day of each year. The whole thing works in rupees of the day at a rate in rupees of the day, and so assumes no real growth after Year 5. And the unused assets stay out of the forecast and are added afterwards.

Every one of those seven could have gone the other way, and every one of them moves the answer. Not one of them is visible in the number the model prints.

Which four checks catch a model built in the wrong order?

Four, and all of them are quick. Each one looks for a mismatch rather than for an arithmetic error. The arithmetic in this method is mechanical and rarely goes wrong in an interesting way.

Notice that none of the four requires opening the model. All four are read off the input sheet and the two convention lines, the strongest possible argument for writing both.