Discounted Cash Flow and Multiples: Where Assumptions Sit

A discounted cash flow and a multiple are not two methods that give different answers. Both are one set of assumptions written two ways. One writes the assumptions out where they can be read. The other has already solved them into a single figure. Sarvani Coatings Limited at 42.0 times, taken apart, turns out to be six entries.

Underneath that answer sits arithmetic rather than an opinion. A ratio is a division, and a division has inputs. When somebody quotes a company at 42.0 times, the inputs have not gone anywhere. The inputs have been solved through and left inside the answer, in exactly the way that the number 12 does not stop containing 3 and 4 just because nobody wrote them down. Taking one figure apart entry by entry and then putting it back together again changes what a reader can see and nothing else.

Are these two different methods, or one set of assumptions written twice?

A room of trainees asked which approach is better will produce an argument about rigour. The argument that one approach is the more rigorous tool is built on a mistake. Set the two side by side, look at what each one actually contains, and the same inputs appear in both. A built stream needs a view on how fast earnings grow, for how long, what happens at the end, and what return the reader wants for waiting. A ratio is what those four things produce once the division is done, so a ratio needs exactly the same four.

The choice between the two is a choice about what appears in writing, not a choice about what is being assumed. Nothing gets added by writing the assumptions out and nothing gets removed by compressing them. The difference is the one between a recipe that lists flour, water, salt and time, and a photograph of the finished loaf. The loaf still contains all four. The four ingredients simply cannot be read off the photograph.

The household version is closer than it looks. A neighbour reports that a shop near the market changed hands at three times its annual rent. The phrase three times annual rent is doing an enormous amount of quiet work: it holds a view on whether the rent will rise, how long the tenant will stay, what the shop will be worth when the buyer wants out, and what return the buyer wanted for the risk. None of that appears in the phrase three times annual rent. All of it is inside the phrase.

What does writing every assumption down actually make visible?

One thing, and it is worth a great deal. Every assumption has to be written somewhere. A reader who disagrees can then find the exact line they disagree with and change it. Findability is the whole of the advantage. The thing being argued about is now on a row with a number in it, so a written list turns a private argument into a public one.

Visibility is the single genuine advantage of writing the assumptions out, and it has nothing whatever to do with accuracy. Most people get that distinction wrong. A list does not make the underlying guesses better. If a reader assumes a required returnThe annual return a reader decides they want for holding an asset. Where a required return comes from, and how one is built up, is taught in the valuation method material rather than here. of 12 per cent a year, writing 12 on a row does not make 12 more likely to be right. Writing 12 down only makes 12 arguable. Being right and being arguable are completely different properties, and confusing them is where most of the trouble on this subject begins.

Consider a bill from a mechanic. An itemised bill and a single total for the same repair cost exactly the same money. The line for the part already replaced last month can be pointed at, so the itemised bill is better anyway. Pointing is the entire value. An itemised bill does not make the mechanic more honest and it does not make the parts cheaper.

What does a long list hide, and where does it hide it?

Its length. Length is the half of the comparison that usually gets left out, and it is the half that costs people money. A working model may hold twenty assumptions laid out in a column, each with a number beside it, each looking equally important. Two of them decide the answer. The other eighteen move it by amounts a reader would not notice.

Visibility is not attention, and a list long enough to look thorough is a list long enough to bury the two entries that carry the answer. A reader who scrolls a twenty row column gives each row roughly the same glance, and the two rows that matter are not marked. Nothing in the column says that changing one entry moves the answer eight points while changing another moves it by two tenths of a point. Everything is presented as though it weighed the same. The list is honest and complete, and it is still hiding something.

What does compressing everything into one figure buy?

Speed across a set. One figure per name means four names can be read in a single glance and the comparison held in the head. Speed across a set is not a small thing and it is not a cheat. Speed is the reason the shorthand exists at all, and anybody who sneers at ratios has never had to look at forty companies before a morning meeting.

Comparability across a set in seconds is a real gain, and it is the only thing a compressed figure is actually good at. Consider the field Sarvani Coatings Limited sells into. In year three the field turned over Rs 48,300 crore against Rs 43,500 crore the year before, a rise of 11.0 per cent over that one year. Nandivarman Paints Limited took 30.0 per cent of it, Sarvani Coatings 5.00 per cent, Kesaria Surface Solutions Limited 3.0 per cent, and the remaining 62.0 per cent was spread across many smaller makers. Four figures, one line each, and the shape of the field is established. Writing out how each of those shares was arrived at would take four times the space and say the same thing.

What does a single figure hide?

Everything. Not most of it, not the fiddly parts. Every one of the six entries that produced 42.0 times is inside that number and none of them is legible from outside it. Ask what growth the writer assumed and the ratio will not answer. Ask what they thought the shares would be rated at when they sold, and the ratio will not answer that either.

Two writers quoting the same ratio usually disagree about exactly one entry, and neither number carries enough information for either of them to find out which. Watch it happen on the case figures. One reader wants 12 per cent a year, holds for five years and assumes an exit ratingThe multiple somebody assumes will apply to the earnings at the end of their holding period. An exit rating is an expectation about a future market rather than anything that has been measured. of 25 times: that reader is holding a view of about 24.2 per cent annual earnings growth. The second reader wants the same 12 per cent over the same five years but assumes 35 times at the end: that reader is holding about 16.1 per cent. A company growing at 24.2 per cent a year and one growing at 16.1 per cent are two entirely different companies in the reader's head. Both write down 42.0 times, and 42.0 times is the truth in both cases.

Which of the two can somebody else check without redoing the work?

The list, and it is not close. Almost nothing written stays on one screen, and that is the practical reason the whole comparison matters. Written work goes to a colleague, a committee, a client or the writer six months later. Whether the person receiving it can disagree with it cheaply decides whether it is any use.

The ability to be checked by somebody who was not in the room is what decides which of the two survives being handed over. A written list can be read line by line by a person with no knowledge of how it was made. The reader runs an eye down the entries, stops at the one they do not accept, and says so. A ratio cannot be checked that way. Disagreeing with 42.0 times in any specific manner means reconstructing all six entries first. Rebuilding all six is the original work performed a second time, and at that point nobody's work is being checked. Two answers have been produced and compared, which is fresh work.

An auditChecking somebody else's work without repeating it from scratch. In the formal sense it is a profession with its own standards; in the ordinary sense used here it just means being able to disagree with a specific line. in the ordinary sense of the word means exactly this: finding the disagreement without rebuilding the thing. Finding the disagreement without rebuilding is why an itemised list beats a total in a court, in a committee and at a kitchen table. The advantage has nothing to do with which one is more likely to be right.

Does either presentation produce more precision than the other?

Neither, and both look as though they do. The usual telling runs this comparison one way only, so run it in both.

A written build produces false precision through decimals. On the case figures the ratio is 41.9689 times when Rs 486/- is divided by the published Rs 11.58/-, and 41.9568 times when it is divided by the unrounded Rs 11.5833/- the ladder actually produces. Four decimal places look measured. The four places belong to a number whose inputs include a rating somebody guessed. A compressed figure produces false precision the opposite way, through roundness. Repeated often enough, 42.0 times starts to sound like a property of the company rather than a division somebody performed.

Both presentations rest on exactly the same assumptions, and precision is a property of the inputs rather than of the layout, so neither one is more precise than the other. The band of false precisionA figure presented in a way that suggests more accuracy than its inputs can support. Two decimal places on a number built from a guess is the standard example. is the same width in both, and the reader is looking at the same uncertainty either way.

Where does the assumption about the end sit in each one?

In both, and under two different names. A built stream carries a terminal assumptionWhat a projected stream, or the earnings at the end of it, is taken to be worth once the projection stops. Every forward-looking build has one somewhere, whatever it is called.: a row near the bottom that says what everything after the last projected year is worth. A ratio carries an exit rating: what the earnings will be priced at when the reader is finished. The terminal assumption and the exit rating are the same assumption. Not similar, not related. The same one, differently labelled, doing the same job in the same place.

One of the two presentations can look as though it avoids the assumption about the end. A reader who believes that has simply not found where it is written. There is no version of forward-looking work that escapes it, because the alternative is to assume the shares are worth nothing at the end, which is itself an assumption and a very aggressive one. Only the visibility varies. Written into a ratio it is invisible. Written into a long build it sits on a row twenty lines down. The row above it may be a working capital ratio worth two tenths of a point, and it attracts about as much attention.

What does 42.0 times look like when it is written out entry by entry?

A reader normally starts from the compressed side, so start there. Sarvani Coatings Limited is quoted at Rs 486/- on the stated date, an invented and illustrative price. The published year three profit after tax is Rs 278 crore. Spread over 24.00 crore shares that is Rs 11.5833/- a share, and it prints as Rs 11.58/-. Divide the price by the earnings baseThe earnings figure a ratio is divided by. Which figure gets used is a choice, and the same price divided by two defensible bases gives two different ratios. and the result is 41.9568 times on the unrounded figure and 41.9689 times on the printed one. Both round to 42.0 times, and 42.0 times is what gets said out loud. One number, no visible inputs.

Now write the same thing as a list, and count the rows.

Every one of the six entries was already inside 42.0 times doing its work silently, so nothing whatever was added in that translation. The arithmetic runs like this, and it runs backwards from the price rather than forwards to a value. Compounding Rs 486/- forward across five years at a required return of 12 per cent reaches Rs 856.50/-. At 25 times, that price needs earnings per share of Rs 34.26/- in year five. On 24.00 crore shares that is a profit after tax of about Rs 822 crore. Taking Rs 11.5833/- up to Rs 34.26/- inside those five years needs about 24.2 per cent a year, and the same calculation on the printed Rs 11.58/- also gives 24.2 per cent. The 24.2 per cent is not something the reader chose. The growth path is what the price already contains once the reader states the other five.

Now run it the other way, and the point lands. Change exactly one entry: the rating at the end, from 25 times to 35 times. Every other row stays where it is. Rs 856.50/- at 35 times needs earnings per share of Rs 24.47/-, and moving Rs 11.5833/- up to Rs 24.47/- inside the same horizon needs about 16.1 per cent a year. The growth entry has fallen 8.1 points, taken from the unrounded values rather than by subtracting the two printed figures. And the compressed number has not moved at all. The price did not move and the earnings did not move, so the figure reads 42.0 times before the change and 42.0 times after it.

So which entries are actually carrying the answer? Nudge three of them by the same 40 per cent and watch. The required return goes from 12 to 16.8 per cent and the growth entry rises to 29.5 per cent, a move of 5.3 points. The horizon goes from five years to seven and the growth entry falls to 20.6 per cent, a move of 3.6 points. The rating at the end goes from 25 to 35 times and the growth entry falls to 16.1 per cent, a move of 8.1 points. The earnings base is published, so a made-up 40 per cent cannot be applied to it. Move it to its one documented alternative instead: on the underlying Rs 11.48/- the growth entry is 24.4 per cent, a move of 0.2 of a point. The earnings base row is not a like-for-like test and should not be read as one.

Then the part a reader should take away. Handed that six row table, somebody can point at the rating row and say twenty five is too generous, in under a minute, having built nothing. Handed 42.0 times, they cannot say anything specific at all until they have reconstructed all six entries. Reconstructing them is the original work performed a second time by a person who did not want to do it. The difference between the two is not about rigour. The difference is about whether the work can be argued with.

How does an analyst actually choose between the two in a working week?

By asking who is going to read it and what they will need to do with it. Who reads it and what they must do with it is the whole decision, and it is far more practical than the argument about rigour suggests.

The job on a Monday morning is to decide which four of forty names deserve a week, so an analyst screening that list uses compressed figures. Sarvani Coatings has several published on the same illustrative price of Rs 486/-: 42.0 times earnings, 26.0 times year three earnings before interest, tax, depreciation and amortisation (EBITDA) of Rs 446 crore on an enterprise value of Rs 11,592 crore against a market value of Rs 11,664 crore, 7.85 times a book value of Rs 61.92/-, and a dividend of Rs 4.00/- giving a yield of 0.82 per cent and a payout of 34.5 per cent. Six seconds of reading, and the name either survives the screen or does not.

The written list is for the moment the work stops belonging to its author and somebody else has to accept or reject it. When the same analyst takes a view to an investment committee, the compressed figure is useless, because a committee cannot approve a number it cannot interrogate. The list goes in front of them instead, with the two entries that carry the answer pulled to the top and stated in words. A lender does the same thing when a credit paper goes to a sanctioning authority, and a household does it without noticing when they justify a large purchase by saying what they are assuming about next year's income rather than quoting a total.

One last thing about the case figures, of the sort that separates a careful reader from a fast one. The earnings base entry looked harmless in the sensitivity test, moving the answer only 0.2 of a point. The earnings base is not harmless in the other direction. Move from the published Rs 11.58/- to the underlying Rs 11.48/-, which comes out of profit before tax of Rs 371 crore less a Rs 9 crore non-recurring itemAn amount inside a published year that is not expected to appear again, such as a one-off receipt or charge. Which items qualify, and how they are separated, is settled in the earnings quality material. and plus a Rs 6 crore charge, giving Rs 368 crore and about Rs 275.6 crore after tax at the published effective tax rateThe tax charge in a published year divided by that year's profit before tax. An effective tax rate is a reported outcome rather than a statutory rate, and the two differ for many reasons. of 25.1 per cent, and the ratio itself moves from 42.0 times to 42.3 times. So the same entry barely touches the list and visibly touches the compressed figure. The difference in weight is not a mechanism worth building a theory on. The two presentations do not even carry their entries with the same weight, and that is one more reason to state which base was used.

Sarvani Coatings Limited, Nandivarman Paints Limited and Kesaria Surface Solutions Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.