DCF vs Relative Valuation: What Separates the Two Answers

The two methods ask different questions. A discounted cash flow asks what a stream of cash is worth on assumptions stated out loud; a peer multiple asks what somebody is paying today for a similar stream. On Sankalp Industrial Systems Limited the first answers Rs 21,28,13,79,094 and the second Rs 22,46,40,00,000. The two answers are Rs 1,18,26,20,906 apart. Neither checks the other unless their inputs genuinely differ.

Underneath that sits a fact people find uncomfortable when they first meet it: both methods contain the same variables. Three things decide what a business is worth. How fast it grows. The return it earns on money it puts back in. How risky both of those are. A discounted cash flow gives each of the three a labelled row of its own, and a peer multiple carries all three as well, folded into a single figure that names none of them. So the difference between the two methods is not what they assume. The difference is where the assumptions are visible, and that single distinction explains why one answer can always be turned back into the other.

What is a discounted cash flow actually asking of the analyst?

A discounted cash flow asks the analyst to say, in numbers, what the business will do. How much cash it throws off in each of the next several years. How the cash behaves after that, forever. Which rate compensates for waiting and for being wrong. Once those three things have been supplied, the arithmetic is mechanical and has no opinion of its own.

The same shape appears in a fruit stall being taken over from a relative. The prospective owner could ask what the stall earns in a month, guess how that changes as the neighbourhood fills in, decide how much to take back each year for the trouble and the risk, and work out what the whole thing is worth. The whole exercise is a discounted cash flow. Every number in it belongs to the person doing the sums. Nobody handed any of them over.

For Sankalp Industrial Systems Limited, an invented listed maker of industrial valves and precision castings, the method runs on five forecast years and then a perpetuityA stream with no last payment in it. Amounts far enough out shrink to almost nothing, so the arithmetic still lands on a finite answer.. The five explicit years contribute a present valueSqueezing a future rupee back to what it would be worth in hand today, at a rate that has to be stated out loud. of Rs 4,68,41,43,564. The rate doing that discounting is 12.00 per cent, invented for this case rather than read off anything. Everything after Year 5 contributes Rs 16,59,72,35,530. The two add to an enterprise value of Rs 21,28,13,79,094. Stated in crore to two decimals, that comes to Rs 2,128.14 crore. The value that comes out is the value of Sankalp Industrial Systems Limited standaloneAs the business already runs, under nobody's plan but its own, with no buyer's savings folded into the numbers., on its own plan, at its own cost of capital, with nobody else's intentions inside it. The build of that model, year by year, is settled elsewhere and is quoted here as a finished output.

What is a peer multiple actually asking of the market?

A peer multiple asks a completely different question, and it is worth saying the question in full before comparing anything. The question is this: for businesses that look like this one, what is somebody paying right now per rupee of profit? Then it applies that answer to this company's own profit. No forecast, no rate and no view about the future is supplied. The analyst supplies a peer set and a denominator, and the market supplies the rest.

Back at the fruit stall: instead of forecasting anything, the prospective owner asks around three other stalls that changed hands last month and finds that each went for about eight months of takings. The stall in question does the same takings, so it costs about eight months of takings. No view about the neighbourhood has been formed at all. Everybody else's view has been borrowed.

For Sankalp Industrial Systems Limited the comparison set is six invented listed companies in the same industrial segment, and the median of what they trade at is 7.8 times earnings before interest, tax, depreciation and amortisation (EBITDA). Applied to the company's own Year 0 EBITDA of Rs 2,88,00,00,000, that gives an enterprise value of Rs 22,46,40,00,000, being Rs 2,246.40 crore. The absence is the point. The peer multiple never required a statement of what will happen, and that absence is exactly why the method is fast and exactly why it is hard to argue with. What those six companies trade at, and how the peer set is assembled in the first place, is settled elsewhere. The 7.8 times is taken here as a given.

One more thing sits inside that 7.8 times and it is easy to walk past. The six comparison companies trade in a market where anybody can buy a few shares. The buyer is therefore paying the price of a minority stakeOwnership on a scale that decides nothing. The profits come with it; the steering wheel does not. in a business, not the price of the business. The limit on what the number means is real, and the arithmetic will never announce it.

If the questions differ, why do both methods carry the same three variables?

Readers usually expect the two methods to be opposites, and they are not. Taking any multiple apart reveals three things: how fast the business grows, what it earns on the money it puts back in, and how risky both of those are. Taking a discounted cash flow apart produces the same three. Koller, Goedhart and Wessels make exactly this point in Valuation, by writing what a business is worth as one expression built from nothing else.

The difference is presentational, and presentation is not a small thing here. In a model those three sit on separate lines with separate figures, and each of them can be disagreed with separately. In a multiple they have been multiplied together and collapsed into one number that arrives with no breakdown. Both methods are carrying the same three passengers; only one of them prints a passenger list.

Where does a discounted cash flow keep the things it assumes?

In the model itself, in rows, in the analyst's own handwriting. The rows are the whole of the answer, and they carry two consequences that pull in opposite directions.

The good consequence is that anybody can attack any line. If a colleague thinks Year 3 revenue is optimistic, they can say so and point at the cell. If a lender thinks 12.00 per cent is too kind a rate, they can propose 13.00 and both sides can watch what happens. Nothing is hiding.

The uncomfortable consequence is that visibility is not the same as importance, and readers routinely spend their attention in the wrong place. In this model the five explicit forecast years carry Rs 4,68,41,43,564 of the Rs 21,28,13,79,094 answer. Everything after Year 5 carries the other Rs 16,59,72,35,530, or 77.99 per cent of the total. Four fifths of the answer sits in the two assumptions a reader spends the least time on, and one fifth sits in the five years of rows that get argued about for a week. Where a model keeps its assumptions and where it keeps its value are not the same place.

Where does a peer multiple keep the same things?

Inside one number, with no way in. Writing 7.8 times against Sankalp Industrial Systems Limited imports a complete set of views about growth, returns and risk held by whoever set the prices of those six companies. The analyst did not choose those views, cannot list them, and very likely does not know what they are.

None of that is a criticism of the method. The honest position is more interesting than a complaint. A market price is a real thing that real people committed real money to. A market price is evidence, and it is simply evidence whose reasoning has been thrown away. A multiple hands back a conclusion with the working torn off, and the only way to recover the working is to solve the conclusion backwards. The reverse arithmetic below does exactly that.

What is each method genuinely good at, and is it a tie?

The contest is not a tie, and pretending otherwise is how people end up choosing by habit. Each method is strong under conditions that can actually be named, and the conditions are properties of the company and its segment rather than preferences of the analyst.

A discounted cash flow is the stronger method when the cash stream is forecastable and the rate is arguable. A business with a long order book, stable margins and a capital plan that can be read is one where writing five years of rows is honest work rather than invention. Sankalp Industrial Systems Limited is built to be that kind of business: revenue adds exactly Rs 1,20,00,00,000 a year, the EBITDA margin does not move off 24.0 per cent, and net new capital of Rs 1,00,00,00,000 goes in every year.

A peer multiple is the stronger method when the segment is crowded with genuinely similar businesses that disclose enough for a comparable denominator to be built. Six listed companies making broadly the same products, all filing accounts that can be read, is a real information advantage and no model produces it. Where a stream can be forecast the model is the stronger evidence, where a crowd of true comparables exists the market is, and where neither condition holds the honest output is a range with both assumption sets named rather than a single figure with a false air of precision.

How does each method fail, and are the two failures the same shape?

The two failures are not the same shape at all, and the difference is why holding both methods is worth the trouble.

An intrinsic model fails by compounding. A perpetuity applies its assumption to every year that will ever exist. So one wrong assumption in the terminal block does not make the answer slightly wrong; it makes the answer wrong forever. Shave a fraction of a percentage point off the denominator and what comes out the far end is not a fraction of a percentage point of value; it is a great deal more. Nothing in the model flags any of that. The model did exactly what it was told to do.

A peer multiple fails the opposite way. The method imports a complete set of assumptions that nobody in the room has read. If the six companies in the comparison set are currently priced on an expectation about the segment that the analyst would reject if somebody stated it out loud, that expectation has been adopted anyway, silently, by using their multiple. The model's failure is that every assumption is visible and one of them can still be badly wrong; the multiple's failure is that the assumptions were never seen at all.

How far apart are the two answers on this company?

Far enough to matter and close enough to be tempting. No combination is worse. Here are both, against the same Year 0 EBITDA of Rs 2,88,00,00,000, so no further adjustment is needed to compare them.

The last cell of that table carries a trap that is easy to walk into. Rs 1,18,26,20,906 over Rs 21,28,13,79,094 is 5.56 per cent. The identical gap over Rs 22,46,40,00,000 is 5.26 per cent. A spread quoted with no base is not a fact. The two available bases here differ by nearly thirty basis points, and thirty basis points is enough to change how big the disagreement sounds. The base the gap was divided by belongs in the same sentence, every time.

What terminal growth rate would close the gap?

The comparison stops being a debate here and becomes arithmetic. A multiple is a value. A model turns assumptions into a value. So a value can be pushed back through the model to find the assumption that would have produced it. The question is not whether the market is right. The question is what the market would have to believe, in the model's own language, for its number to come out.

Which value should be pushed back? The comparison set's Rs 22,46,40,00,000 came out of six other companies, so that is not the figure to push back. The figure to push back is Sankalp Industrial Systems Limited's own traded enterprise valueWhat the shares fetch at the quoted price, plus the borrowings, less the cash, is what the market is putting on the whole operating business., the price its own shares carry, restated as a price for the whole operating business. Five lines get it there, and every one of them is a figure already stated above.

The traded enterprise value lands Rs 6,40,00,000 below the comparison set's answer. The market set it on this company rather than on six others, so it is the figure pushed back through the model. Why each of those five lines has the sign it has is covered separately; here the five are restated and used.

Freeze everything but one input. The rate stays at 12.00 per cent. New capital keeps earning 18.00 per cent. The five explicit years keep contributing Rs 4,68,41,43,564. Then let only the terminal growth rateForever after the last forecast year, one single rate is assumed to describe how the cash keeps rising. The terminal growth rate is that rate. move, and ask which value of it makes the whole thing add to Rs 22,40,00,00,000.

Solved, the answer is 5.7976 per cent, or 5.80 per cent to two decimals. The reinvestment rateWhat has to be ploughed back each year to buy the growth being assumed, measured against after-tax operating profit rather than against revenue. that growth demands is sitting inside the same expression, so the rate has already paid for itself. Run the model at exactly 5.80 per cent and it gives Rs 22,40,37,86,027, or Rs 37,86,027 above the traded figure. The residual is the rounding carried by stating a rate to two decimals, runs under two hundredths of one per cent of the value being tested, and is not an error in either number. Recomputed from the locked inputs the residual is Rs 0.38 crore, which is what the arithmetic gives.

What cost of capital would close the same gap?

The same distance can be walked on a different axis, and this is the half most readers never see. Leave terminal growth at 5.00 per cent. Move the cost of capital instead, and ask which rate makes the model produce Rs 22,40,00,00,000. The answer is 11.6711 per cent, or 11.67 per cent to two decimals, against the company's own 12.00 per cent.

A mechanical difference between the two directions deserves saying, and it is the kind of thing that slides past. When only growth moves, the five explicit forecast years are untouched. The discount rate that produced them has not changed, so they keep contributing Rs 4,68,41,43,564 in every run. When the rate moves, every one of those five years is re-discounted too. At 11.67 per cent the explicit period contributes Rs 4,72,64,90,283 rather than Rs 4,68,41,43,564. Solving on the growth axis touches one block of the model; solving on the rate axis touches every line in it, and that is why the rate needs less movement to do the same work.

Why is 80 basis points of growth and 33 basis points of rate the only honest way to say this?

Because either figure quoted alone invites the wrong conclusion. Say only that the market implies 5.80 per cent growth against the model's 5.00, and a reader hears a sixteen per cent difference in a growth assumption. Sixteen per cent sounds substantial. Say only that the market implies 11.67 per cent against the model's 12.00, and a reader hears a rate that is almost identical. Both descriptions are of the same disagreement about the same company on the same day.

Stated in basis pointHundredths of a percentage point, used so that 0.80 per cent can be said as 80 without anybody mishearing it as 80 per cent. terms the pair is 80 on the growth axis and 33 on the rate axis. Draw them on one scale and the growth arrow is visibly the longer of the two, and the longer arrow pictures a real fact. The rate is the heavier lever here, so 33 basis points of it does the work that 80 basis points of growth does, and there is no sense in which one of those two readings beats the other.

When are the two methods independent, and when are they one method run twice?

The question has a test rather than an opinion behind it.

Two methods corroborate each other only when their inputs are genuinely different. A discounted cash flow built on the analyst's own forecast and own rate is one body of evidence. A peer multiple is a second body of evidence only if the prices behind it were set by a process that does not already contain those same assumptions. Often it is. Sometimes it is emphatically not: if the market is pricing those six companies by discounting broadly similar cash flows at broadly similar rates, then the borrowed multiple is the analyst's own model wearing a market's clothes.

The test is the reverse arithmetic set out above. Solving the multiple back into the growth rate and the cost of capital it implies, and laying those two figures beside the ones already sitting in the model, settles it; if they nearly match, that was not two methods but one method run twice, with the answer read off two different sheets of paper. On Sankalp Industrial Systems Limited the implied pair is 5.80 per cent and 11.67 per cent against a model carrying 5.00 per cent and 12.00 per cent. Whether 80 and 33 basis points counts as nearly matching is a judgement for the analyst. Making the comparison at all is the part that matters.

What is actually delivered when the two methods disagree?

Not a winner, and not an average. Averaging Rs 21,28,13,79,094 and Rs 22,46,40,00,000 gives a figure that neither method produced and that no assumption set stands behind. Choosing a winner is worse still. Picking one figure hides the disagreement instead of reporting it, and the disagreement is the most informative thing found.

The deliverable is a short two column note. The left column holds what the model assumes. The right column holds what the market's figure implies when it is solved backwards. Between them sits one line of distance, stated in basis points on both axes. A reader can argue with an assumption and cannot argue with a single number that arrived without one, so the deliverable when two methods disagree is a range with both assumption sets named and the distance measured.

How does a lender, an analyst or a committee actually use this in a week of work?

Three readers, three uses, and only one of the three is doing a valuation at all. The split is worth watching. The same pair of numbers comes through unchanged and gets put to work three different ways.

A lender is not really valuing Sankalp Industrial Systems Limited at all. A lender wants the room between the worth of the business and the Rs 6,00,00,00,000 of gross debt sitting against it. Both figures, Rs 21,28,13,79,094 and Rs 22,46,40,00,000, comfortably cover the debt, so for a lender the interesting output is not which is right but how far the lower one would have to fall before the cushion disappears. A lender reads a valuation as a floor test, and reaches for the more conservative of two answers by habit rather than by argument.

An equity analyst is doing the opposite. The analyst's product is the reasoning, not the figure, and the 80 basis points is the most publishable thing in the whole comparison. Writing that the traded price implies terminal growth of 5.80 per cent against a house assumption of 5.00 per cent is a statement a reader can check, disagree with and use. Writing that the shares look expensive or cheap is not. There are only two reasons a company can sit away from its comparison set. The first is a real difference in the company that nobody folded into the denominator. The second is nothing at all. A single multiple has no way of separating those two, so it raises the question and then leaves the room.

A committee wants the range and the reason for its width. A committee is actually deciding not a value but whether the width of the range is tolerable for the decision in front of it, and a five and a half per cent spread that reduces to 80 basis points of one assumption is a narrow disagreement wearing a wide costume. Presenting it as Rs 1,18,26,20,906 alone makes it sound like a problem. Presenting it as 80 basis points of a rate nobody can adjudicate makes it sound like what it is.

And a household reader with no stake in any of this can still take one habit away from it. When somebody says a price is justified because similar things sell for the same, the question to ask is what that comparison is quietly assuming. The same question works on a flat, a second-hand scooter and an industrial valve maker, and it is the only question a comparison cannot answer about itself.

Sankalp Industrial Systems Limited and the six comparison companies are invented.
Educational material. Not advice on any investment, tax, budget or market position.