How to Audit a DCF Model: Four Defects and Where to Find Them

Auditing a model means finding what it assumes, not checking that it adds up. Six arithmetic checks on the model below all pass. The model still carries four findings. The terminal value is 77.99 per cent of the answer. The terminal convention is worth Rs 3,75,00,00,000. The circularity in the weights is worth Rs 21,17,00,000. And terminal growth is zero in real terms.

A sheet arrives with a request to check it. Almost everybody, faced with that, does the same thing. The reviewer starts at the top left, follows each formula back to the cell it came from, and ticks along the way. Formula tracing feels like the responsible thing to do, and on a competently built model it is close to a wasted afternoon.

The everyday version of why lands harder than the finance one. A cousin is getting married and an uncle has drawn up the budget. Six hundred guests, a hall, a caterer at a rate per plate, a decorator, a tent, transport, printing, a contingency at the bottom. He adds it up in front of the family and reaches a number. The addition holds. Every line in it is correct. Nobody in that room asked the one thing the whole sheet rests on. Are six hundred people actually coming? If eight hundred arrive, every correct line is understated by a third. Addition was never the question, so no amount of re-adding will ever say so.

A company model is that budget with more rows and a longer horizon. A model almost never goes wrong on a sum; it goes wrong on a figure somebody typed and nobody argued with. Spreadsheets add correctly. Adding correctly is the one thing spreadsheets are for, and the one thing a reviewer can be certain of before opening the file. So a review that spends its hours on the arithmetic has spent them confirming the part that was never in doubt, and has left the part that decides the answer completely untouched.

The object under audit is a single finished model of Sankalp Industrial Systems Limited, an invented manufacturer of industrial valves, precision castings and the aftermarket parts and service that go with them. The model forecasts five years of free cash flow to the firmThe cash an operating business throws off for everybody who funded it, lenders and shareholders together, after tax and after paying for its own growth., discounts them at 12.00 per cent, this company's own assumed cost of capital. The model then adds a terminal value built on 5.00 per cent growth and produces an enterprise valueWhat the operating business is worth to everybody who funded it, before the borrowings are repaid and before cash and non-operating items are handled. of Rs 21,28,13,79,094 and Rs 84.41 a share. Discounting is at year end rather than mid year, and the model says so.

Building that model is a separate matter. How the base year is cleaned, how each forecast line is put together, how long the explicit period should run and how the terminal value is chosen between its two methods are each covered separately, and the walk through the build is a subject of its own. Here the model already exists, finished, with somebody's name on it. The only question is what the next two hours are spent on.

What is an audit of a model actually looking for?

A model auditA review that asks what a model assumes, not only whether it adds up. runs in two stages, and almost every review that goes wrong goes wrong by finishing the first stage and calling it a day.

Stage one asks whether the sheet does what it says it does. Does the cash flow line reconcile when it is built a second way? Does the rate come out at the figure printed beside it? Does the bridge from the business down to a single share land where the model says it lands? Those three questions have yes or no answers, they can be settled without knowing anything at all about industrial valves, and a model built by somebody competent passes every one of them. Passing them is not a compliment to the model. Passing them is a fact about spreadsheets.

Stage two asks a completely different kind of question. For every figure a person typed rather than calculated, what would have to be true about the world for that figure to be reasonable, and how much of the answer is riding on it? Stage one tests the sheet against itself; stage two tests the sheet against the world, and only stage two can find anything that matters. The difficulty is that stage two has no ticks in it. There is no cell to trace, no total to agree, nothing that turns green. The reviewer has to hold a view, and forming one takes longer than tracing a formula.

Stage two has a consequence for the model under audit. The terminal growth rate of 5.00 per cent was typed. The 12.00 per cent discount rate was assembled from inputs that were themselves typed. The 18.00 per cent return on new invested capital was typed. The rupee increase in revenue each year was typed. All the arithmetic sits downstream of those four figures, so nothing in the arithmetic of the sheet can be wrong about any of them. A perfect formula trace passes a model whose largest single assumption was never examined, and that is not a hypothetical. Exactly that happens on this model, as the four findings below show.

The two stages get confused for a second reason, and it is a matter of temperament rather than of technique. Stage one feels safe. The reviewer can be certain of having done it, can show what was done, and nobody can argue with a tick. Stage two feels like an opinion, and a reviewer who says the terminal growth rate assumes the company never grows again in real terms is exposed in a way that a reviewer who says one row ties to another is not. Stage two becomes respectable rather than opinionated when every finding is sized in rupees before it is spoken. An objection with no number attached is a mood. An objection with Rs 1,53,13,01,504 attached is a finding, and the person who set the assumption now has to answer it.

Which checks confirm the arithmetic, and why are they the easy half?

The arithmetic checks are worth running anyway. Stage one is quick, it is the only part of the work that produces certainty, and skipping it means every finding reported afterwards can be waved away with the suggestion that the sheet was misread. Six checks are enough on a model this size, and the shape of every one of them is identical: an arithmetic checkA test that two independent routes to the same figure land on the same figure. is two independent routes to the same figure, and it is only a check if the two routes do not share the cell under test. Recalculating a total by adding the same column again is not a check. It is the same journey twice.

Here are the six, run on this model, in the order they take least time.

Check one, the cash flow, built the long way and the short way. The long way is the definition: operating profit after tax, add back depreciation because it never left the building, deduct what was actually spent on plant, deduct what the year tied up in receivables and inventory. For Year 1 that is Rs 1,98,00,00,000 plus Rs 52,80,00,000 less Rs 1,34,80,00,000 less Rs 18,00,00,000. The total is Rs 98,00,00,000. The short way notices that capital expenditure less depreciation plus the working capital movement is simply the net new capital the business absorbed, Rs 1,00,00,00,000 here, and takes that straight off operating profit after tax: Rs 1,98,00,00,000 less Rs 1,00,00,00,000 is Rs 98,00,00,000. Two routes, no shared cell, same figure. Agrees.

Check two, the reinvestment identity, and it holds four separate times. A company grows by putting money back in, so its growth rate should equal the share of profit it reinvests multiplied by the return that new money earns. The model reinvests 50.51 per cent of Year 1 profit at an assumed 18.00 per cent return. Reinvesting at that rate predicts growth of 9.09 per cent, and profit after tax does grow 9.09 per cent from Year 1 to Year 2. Doing it again for the next three transitions gives 8.33, 7.69 and 7.14 per cent predicted against 8.33, 7.69 and 7.14 actual. Four predictions, four agreements. Putting growth, return on invested capital and value into one expression is what makes this check available at all. Koller, Goedhart and Wessels are the names attached to doing so. Agrees.

Check three, the cost of borrowing, weighted rather than averaged. The company borrows in three tranches: Rs 3,00,00,00,000 on a secured rupee term loan at 7.80 per cent, Rs 2,00,00,00,000 of listed unsecured debentures at 8.50 per cent, and Rs 1,00,00,00,000 drawn on a working capital facility at 7.60 per cent. All three rates are this company's own contracted rates and none of them is a statement about what anybody borrows at. Weight each by its size and the blend is exactly 8.00 per cent, the figure the model prints. The trap this check catches is the plain average of 7.80, 8.50 and 7.60, an unweighted 7.97 per cent. A plain average would be right only if the three tranches were the same size. Agrees.

Check four, the rate itself. The model applies 12.00 per cent. Rebuilt from the weights and the two component costs, 0.75 times 14.00 per cent plus 0.25 times 6.00 per cent is 10.50 plus 1.50. The total is 12.00 per cent exactly. Building that 14.00 per cent cost of equity, and arguing about the beta behind it, belongs to the assembly of a cost of capital. The assembly is covered separately. The audit only asks whether the printed rate is the rate the printed inputs produce. It is. Agrees, with a finding attached to the weights that arrives later.

Check five, the bridge, where a value becomes a share. Take the enterprise value of Rs 21,28,13,79,094, add cash of Rs 1,20,00,00,000, add non-operating assets of Rs 1,00,00,00,000 being a surplus land parcel and a minority holding in an associate, deduct gross borrowings of Rs 6,00,00,00,000, deduct the Rs 60,00,00,000 minority interest in the consolidated subsidiary, and the result is Rs 16,88,13,79,094. Across 20,00,00,000 shares that is Rs 84.41. Running it backwards from Rs 84.41 lands in the same place. Agrees.

Check six, the segments against the consolidated statement. Industrial valves at Rs 6,00,00,00,000, precision castings at Rs 4,20,00,00,000 and aftermarket parts and service at Rs 1,80,00,00,000 add to Rs 12,00,00,00,000, exactly the base year revenue the forecast starts from. Agrees.

Now a small lesson hidden inside that last check, and it is the most useful thing in stage one. The same addition on the divisions' operating profit before depreciation gives Rs 2,97,00,00,000. The consolidated figure is Rs 2,88,00,00,000. The segment check on profit does not tie. The difference is not an error either. Unallocated head office cost of Rs 9,00,00,000 belongs to no division and so appears in none of them. A check that fails is a question, not a verdict, and the first suspect is always the reviewer's own understanding of what the two routes were measuring. Only when that has been exhausted does a difference become a defect.

In what order should the checks be run, and why does the order matter?

Order matters because attention is the scarce thing in a review, not skill. A reviewer gets tired, gets interrupted, and whatever was left until last gets ten minutes instead of an hour. So the sequence is not a matter of tidiness. Run the checks in descending order of how much of the answer they can move. On almost every discounted cash flow that means opening the terminal block first and the revenue build last.

The revenue build is where the visible work is, so that instruction feels wrong to most people the first time they meet it. The build has the most cells, the most research behind it and the most opinions in it. The same build is also, on this model, responsible for 22.01 per cent of the answer. The single line at the bottom that nobody spent a morning on is responsible for the other 77.99 per cent. Spending the fresh hours on the forecast and the tired ten minutes on the terminal block is exactly backwards, and it is the commonest shape of a bad review.

A working order that respects that looks like this. First comes the terminal share. The terminal share tells the reviewer where the rest of the audit should point. Second comes the terminal block itself: which convention, what growth rate, what reinvestment behind the growth. Third, the rate is taken apart far enough to show what is inside the weights. Fourth, every long-run rate on the sheet is converted into real terms. The conversion takes about ninety seconds and is where the largest finding on this model lives. Only then does the work move backwards into the forecast years, and even there it starts with the assumptions that run all five years rather than with any single year.

One check belongs at the very front and takes almost no time: look at what is sitting in the base year. Everything in the forecast is a percentage of, or a growth on, the last completed year, so anything left in that year is not a one-off error of its own size. The stale figure is multiplied by every year that follows and then capitalised forever. Suppose Rs 10,00,00,000 of income that will not repeat was left in the base year, lifting the margin the forecaster then held flat for five years. Work it through this model and the effect on the answer is Rs 1,03,69,23,137, or 10.37 times the item itself. An uncleaned rupee in the base year is worth about ten rupees of enterprise value here. The cheapest check on the list is therefore also one of the largest. How a base year is actually cleaned is a subject covered separately; the audit's job is only to know what an uncleaned one costs.

How large is the terminal value, and when does its size become a finding?

Finding one is the size of the terminal value. Everything after it depends on the answer, so it comes first.

The model discounts five forecast years at 12.00 per cent. In today's money the five forecast years are worth Rs 4,68,41,43,564. The terminal valueOne figure standing in for every year after the last one the model forecasts individually., the single line standing in for everything after Year 5, is worth Rs 29,25,00,00,000 at Year 5 and Rs 16,59,72,35,530 once it is brought back to today. Added together, they come to the Rs 21,28,13,79,094 the model prints. The terminal value is 77.99 per cent of the answer, so five years of forecasting do 22.01 per cent of the work.

Take a second with the split. The proportions do not match what building the model felt like. Three weeks of that build went into the five years. The terminal value took one line and about ten seconds. The proportions of the effort and the proportions of the answer are almost exactly inverted.

Now the part that separates a useful reviewer from a noisy one. A terminal share of 77.99 per cent is not a defect, and reporting it as one is the commonest error in model review. The business does not stop trading in Year 5, and something has to stand in for Year 6 onwards, so any long-lived business valued over an explicit period of five years will be mostly terminal. Pushing the explicit period out to ten years lowers the terminal share. The same guesswork has only moved inside the forecast, where it is harder to see. The size is a property of the method, not a fault in this model.

The household version makes it obvious. A person buying a flat to let out for five years and then sell is not really making a rental decision. The five years of rent, net of maintenance and tax and the months it sits empty, are a modest fraction of what they are putting in. Most of what they are buying is the price somebody will pay for the flat at the end. Calling that a flaw in the plan would be silly. Noticing that the plan therefore turns almost entirely on one number nobody has examined would not be silly at all, and the evening is better spent on that number than on the rent.

So the terminal share is a finding because of what it implies about direction. Every remaining check should be aimed at the 78 per cent. If the reviewer has four hours, three of them belong in the terminal block. The terminal share also converts every later finding into a common unit. Once the terminal value is known to carry 77.99 per cent of the answer, any change in it reads straight through without rebuilding anything: the change in terminal value multiplied by the Year 5 discount factor of 0.567426856 is the change in the enterprise value.

Which terminal value convention was used, and what is the other one worth?

Finding two. Having established that 77.99 per cent of the answer sits in one line, open that line and read what is inside it. The first question is not whether the growth rate is right, but which of the standard builds produced the number. Two builds are in common use, both are correct, and on this model they are Rs 3,75,00,00,000 apart.

The build this model used starts from the fact that growth has to be paid for. If the company is to grow at 5.00 per cent a year forever, and new money put into the business earns 18.00 per cent, then it must plough back 5 divided by 18 of its profit forever, or 27.78 per cent. The 27.78 per cent is the terminal reinvestment rateThe share of profit a business must plough back forever to sustain the growth rate assumed after the forecast ends., and it is not a free choice: it falls straight out of the growth rate and the return. Year 6 operating profit after tax is Rs 2,70,00,00,000 grown once at 5.00 per cent, or Rs 2,83,50,00,000. Keep thirteen eighteenths of it and hand over the rest to the business, and the cash left for the people who funded it is Rs 2,04,75,00,000. Divide by 12.00 per cent less 5.00 per cent and the terminal value is Rs 29,25,00,00,000. Damodaran is the name attached to the argument that a terminal value must be consistent with the reinvestment the growth it assumes would require, and the growing perpetuity expression itself is Gordon's.

The other build is quicker and is used everywhere. Take the last forecast year's cash flow of Rs 1,70,00,00,000, grow it once at 5.00 per cent to Rs 1,78,50,00,000, and divide by the same 7.00 per cent. The quicker build gives Rs 25,50,00,00,000.

The gap is Rs 3,75,00,00,000, or 14.71 per cent of the quicker figure, and it exists for exactly one reason. The quick version carries Year 5's reinvestment behaviour into perpetuity. In Year 5 this company was still growing at over 7 per cent, so it was reinvesting 37.04 per cent of its profit. A company growing at 5.00 per cent forever does not need to reinvest at the rate of one growing at 7 per cent, and the quick build never notices the difference. Brought back to today the Rs 3,75,00,00,000 is worth Rs 2,12,78,50,709, or Rs 10.64 a share on 20,00,00,000 shares.

A third convention exists as well, and an audit should price it while it is in the neighbourhood. Instead of a perpetuity, assume the business is sold at the end of Year 5 at the multiple similar companies trade on. Year 5 operating profit before depreciation is Rs 4,32,00,00,000, the median of the six invented peers is 7.8 times, and the exit multipleValuing the business at the end of the forecast at a multiple of that year's profit, instead of as a perpetuity. build gives a terminal value of Rs 33,69,60,00,000.

Line the three up as enterprise values and the size of the choice becomes visible. The quick perpetuity gives Rs 19,15,35,28,385. The reinvestment-consistent perpetuity, the build this model used, gives Rs 21,28,13,79,094. The exit multiple gives Rs 23,80,41,58,894. From end to end that is Rs 4,65,06,30,509, computed on the unrounded figures. The span of the three standard conventions is 99.28 per cent of everything the entire five-year forecast is worth in present value. The choice of convention is worth as much as the whole forecast. Three weeks of revenue work, or one decision about a formula, and they are the same size.

Per share the three land at Rs 73.77, Rs 84.41 and Rs 97.02. The limits on what an audit may do with those three figures are worth stating precisely. An audit may say that the model used the reinvestment-consistent build and that the alternatives are worth those amounts. An audit may not say which of the three is right. The perpetuity build makes an assumption about the economics of the business, the exit multiple build makes an assumption about what somebody will be willing to pay, and choosing between those is a judgement rather than a calculation.

The audit point on finding two is disclosure, not correctness: a terminal block silent about its convention is carrying an undisclosed Rs 3,75,00,00,000. This model does state it, and finding two therefore closes with a note rather than an exception. Write it down anyway. A reader six months from now, or a colleague building a version of the same model, has no way to know which of the two perpetuity figures they are looking at unless somebody wrote it in the sheet, and the two are far enough apart that guessing wrong changes the conversation entirely.

The weights in the rate use a value the model also produces. Does that matter?

Finding three, and it is the one a sharp reader spots without being told. Look at how the 12.00 per cent was weighted. Equity was taken at Rs 18,00,00,00,000, being 20,00,00,000 shares at the traded Rs 90.00, and borrowings at Rs 6,00,00,00,000. Total funding Rs 24,00,00,00,000, so 75.0 per cent equity and 25.0 per cent debt, and those weights produced the rate that produced the answer.

But the model's own answer, walked down the bridge without the non-operating items, values the equity in the operating business at Rs 15,88,13,79,094. The weight is an input to the calculation and also an output of the same calculation. Feeding an output back into its own input is a circularityA quantity that is fed into a calculation and also produced by it, so the two versions need not agree., and the circularity here is real rather than pedantic. With the model's own equity figure put into the weights instead, the debt share is not 25.0 per cent. The share is over 27 per cent, the borrowings are a bigger part of a smaller whole, the levered betaThe measure of a company's equity risk after the effect of its borrowings has been added in. goes up because more borrowing means more risk carried by the shareholders, the cost of equity goes up with it, and the rate changes. A changed rate changes the answer, and the changed answer moves the weight again.

The household version is exact and slightly absurd. Consider valuing a flat by a method whose inputs include the ratio of the outstanding home loan to the flat's value, when the value is the thing being worked out. The owner would have to guess a value, compute a ratio, get a value out, put that back in and go round again. Most people, faced with that, either shrug and use the price the neighbour's flat sold at, or go round the loop until it stops moving. Both are defensible. Doing it silently is not.

So go round the loop. Take the model's own equity output, recompute the debt to equity ratio, relever the beta from an unlevered 1.00, rebuild the cost of equity, reweight, rediscount the same unchanged cash flows, and read the new equity value. Then do it again. Going round the loop until the answer stops moving is convergenceRepeating a circular calculation with its own output until the answer stops moving., and the four passes below do exactly that.

Read the enterprise value column downwards and notice the shape. Most write-ups get that part wrong. Pass 1 does not creep towards the answer. Pass 1 overshoots it, landing about Rs 2,60,00,000 above where the sequence eventually settles. Pass 2 then undershoots, landing below. Pass 3 overshoots again by a much smaller amount, pass 4 undershoots by less than Rs 50,000, and by pass 5 the movement has disappeared into the paise. The sequence oscillates around its answer with the swings shrinking each time, rather than marching towards it from one side, and a picture that draws it as a smooth approach has drawn something that did not happen.

Where it settles is a rate of 11.935 per cent and an enterprise value of Rs 21,49,31,00,000, rounded to the nearest Rs 1,00,00,000, with an implied debt share of 27.16 per cent. Against the headline Rs 21,28,13,79,094 that is a move of Rs 21,17,00,000, or 1.0 per cent, and Rs 85.47 a share against Rs 84.41. Six passes and the figure has stopped moving entirely.

The ruling on the circularity, and why its small size is what makes the ruling defensible

The audit's treatment of finding three is not what a first-year reviewer expects. The audit reports the circularity, reports what resolving it would cost, and leaves the weights alone.

The reasoning is that Sankalp Industrial Systems Limited is listed. Its equity has an observed price, arrived at by people transacting, and the weights use that observed structure rather than an estimate. The model's own equity figure is a separate estimate of the same thing, produced by the very calculation whose input is in question, and feeding an estimate back into its own input is a choice rather than a correction. Reasonable houses do it both ways. A house that neither says which route it took nor sizes the difference in rupees has done the one unacceptable thing.

And that is where the 1.0 per cent earns its place. If iterating moved the answer by 15 per cent, the ruling to use observed weights would be a dodge dressed as a convention, and an audit would have to press it. At 1.0 per cent on a valuation where a single terminal assumption is worth seven times as much, the ruling is a reasonable simplification, and the audit can say so with a number rather than a shrug. An auditor who names the circularity without computing what it costs has raised an objection; one who computes Rs 21,17,00,000 has produced a finding, and the difference between those two is most of what separates a useful review from an irritating one.

What is the terminal growth rate in real terms, and why is that the biggest finding?

Finding four takes about ninety seconds to run and is the largest thing in this guide.

The terminal growth rate is 5.00 per cent a year, forever, after Year 5. The 5.00 per cent is a nominalMeasured in money of the day, with inflation left in. rate: rupees of the day, inflation included. This example also assumes inflation of 5.00 per cent, an assumption of the example and not a statement about any economy. Put the two together with the relation between them and the realMeasured after inflation has been taken out, so it is growth in what the money can buy. terminal growth rate is 1.05 divided by 1.05 less one, or nothing at all.

The model assumes Sankalp Industrial Systems Limited never grows again in real terms after Year 5. Not slowly. Not cautiously. Not at all. The company sells exactly as many valves in Year 40 as in Year 5, at prices that go up with everything else, forever. And in a valuation where 77.99 per cent of the answer sits in the terminal block, that is the single largest assumption on the sheet.

The assumption is easy to miss. A cell holding 5.00 per cent does not read as an assumption about stopping; it reads as growth. A figure of 5.00 per cent in a cell reads to almost everybody as modest, prudent growth, and nobody thinks to divide it by anything. Compare it with a cell that said zero. Every reviewer in the building would have queried a zero within a minute. The two cells say precisely the same thing, and only one of them gets asked about.

The everyday version is a salary. Somebody announces that their pay went up 5 per cent this year, and it sounds like good news. Then the rent went up 5 per cent, the school fee went up 5 per cent and the vegetables went up 5 per cent. Nothing has improved. The household will buy exactly what it bought last year. A 5 per cent rise matched by 5 per cent inflation is not a raise but an adjustment, and calling it a raise is the same error as reading 5.00 per cent in a terminal cell as growth.

The Fisher arithmetic, and the shortcut that is 33 basis points wrong

Converting between nominal and real is one line, and worth doing properly. The shortcut most people use is wrong in a direction that flatters the answer. The Fisher relationOne plus the nominal rate divided by one plus inflation, less one, which gives the real rate. says the real rate is one plus the nominal rate divided by one plus inflation, less one. The real rate is not nominal less inflation, and the two differ by more than people expect.

The first row is the one that catches people out. A reader who subtracts gets a real cost of capital of 7.00 per cent and thinks the business is being discounted more harshly than it is; done properly it is 6.6667 per cent, and the basis pointOne hundredth of one per cent. Thirty three basis points is 0.33 per cent. gap of 33 runs the same way everywhere the shortcut is used. On a rate the subtraction error is a nuisance; on a terminal growth rate sitting near zero it is the whole difference between a small real growth assumption and none at all.

The third row matters for what comes next. One point of real growth is not a nominal 6.00 per cent. One point of real growth is 1.05 multiplied by 1.01, less one, or 6.0500 per cent. Five basis points sounds like nothing, but the terminal value divides by the discount rate less the growth rate, and that denominator here is only 7.00 per cent wide to begin with.

Why finding four is the biggest of the four, and the sentence an audit must not leave unwritten

Finding four is sized the way every other finding has been sized. Moving terminal growth from zero real to one point of real growth, a nominal 6.0500 per cent, takes the terminal value from Rs 29,25,00,00,000 to Rs 31,94,86,76,471. The enterprise value goes from Rs 21,28,13,79,094 to Rs 22,81,26,80,598. One point of real growth is worth Rs 1,53,13,01,504, or 7.20 per cent of the answer, Rs 7.66 a share, and 32.69 per cent of everything the entire five-year forecast is worth in present value.

Put that beside the other findings honestly. The ranking is not obvious, and one of the three comparisons runs the other way. One point of real growth is about seven times the circularity finding of Rs 21,17,00,000. One point of real growth is smaller, though, than the terminal convention gap of Rs 2,12,78,50,709 in present value. So on a single point of growth, finding two is larger.

One point of growth is not what makes finding four the biggest. The range the assumption opens, and the fact that nobody looked at it, are what make it the biggest. The model's own other terminal convention, an exit at the 7.8 times peer median, implies real growth of about 1.5048 per cent rather than zero. Run this model at 1.50 per cent real and the enterprise value is Rs 23,78,76,44,027, or Rs 2,50,62,64,933 above the headline and larger than the convention gap. Run it at minus 1.00 per cent real, a business shrinking gently in what it can actually sell, and the answer is Rs 20,12,62,33,704. The reasonable range around an assumption nobody examined is wider than any of the other three findings, and the assumption itself was never written down in words anywhere on the sheet.

Which gives the single most useful sentence an audit of this model can produce, and it is the one to write down before anything else: the two terminal conventions in this model differ not only in rupees but in whether this business grows in real terms at all, one assuming zero forever and the other about one and a half per cent. Nothing in the record supports either view, and the audit says so and stops. The audit calls the assumption neither too low nor too cautious nor wrong, and reaches no conclusion about the value of the business.

What becomes of a finding once it exists?

A finding that stays in the reviewer's head is not a finding. A finding has to leave the room in a form somebody else can act on, and the form is fixed: three columns and no more.

Column one is the finding itself, in one sentence, stated as what the model assumes rather than as an accusation. Column two is its size, in rupees and as a percentage of the answer. A number is what turns an objection into something a person has to respond to. Column three is what would have to change for the model to say something different, stated as an assumption about the business rather than as an instruction to edit a cell, and it is the column almost everybody leaves out.

Leaving out column three is what makes a review adversarial. Without it, the reader hears the reviewer saying the model is wrong. With it, the reader hears the reviewer saying the model is carrying this assumption, here is what it is worth, and here is the belief somebody would need in order to change it. The second conversation is the one that actually improves a model, and it is also the only one an audit is entitled to have. Deciding what to believe about a business is not the auditor's job.

Now the other half: what physically happens next. Having found that terminal growth is zero in real terms, there are three things a reviewer can do, and the most tempting one is the worst.

Take the middle branch seriously for a moment. Editing the cell is genuinely tempting and usually done with good intentions. The reviewer has spotted something real. Fixing it takes four seconds. The answer becomes, by the reviewer's own lights, better. Nobody has to be told they were wrong. Those four seconds separate the model from the person responsible for it, and that separation is the one thing a model cannot survive. Six months later somebody asks why the terminal growth rate is 6.05, and there is no answer, because the person who typed 5.00 did not type 6.05 and the person who typed 6.05 did not sign the model. Every scenario, every sensitivity and every summary built on the old figure is now inconsistent with the sheet, and nothing on screen says so.

What does this audit deliberately leave alone?

Quite a lot, and naming it is part of doing the work honestly.

The audit leaves alone the build. Every figure audited here was produced by procedures covered separately: how a base year is cleaned before anything is forecast, how each forecast line is put together, which cash flows are genuinely incremental, how long the explicit period should run, and how a terminal value is chosen between its two methods. The audit takes all of that as given and reads the output.

The audit leaves alone the cost of capital. The audit checked that 0.75 times 14.00 plus 0.25 times 6.00 comes to 12.00 per cent, and it audited what sits inside the weights, but it did not estimate a beta, argue about an equity risk premium or defend the risk-free rate used, all of which are covered separately. The audit also never re-derives the rate for the unlisted subsidiary, a different figure for good reasons that belong to that subject.

The audit leaves alone the comparison between this valuation and the other ways of pricing the same company. Peer trading levels, prices paid in past transactions, and what a financial buyer could pay are three separate subjects, each producing a different figure for reasons of its own, and an audit of a model is not the place to reconcile them. The audit also does not reconcile the firm route against the equity route. The two differ here by construction and are treated separately.

And it leaves alone every question about whether the model's answer is correct. An audit finds what a model assumes; it never finds whether the answer is right, because the answer cannot be checked against anything. The limit is not modesty. The limit is the actual boundary of the technique.