Terminal Value: Perpetuity Growth and Exit Multiple Compared

Terminal value is the value of everything after the explicit forecast stops. For Sankalp Industrial Systems Limited, invented, the perpetuity growth route, built so that reinvestment matches the growth it buys, gives Rs 29,25,00,00,000. The naive version of the same route gives Rs 25,50,00,00,000. An exit at the peer median of 7.8 times gives Rs 33,69,60,00,000. Neither route ranks above the other.

The whole argument is already sitting inside a decision most households in this country have had at a dining table at some point. Suppose a couple let out a two bedroom flat. The tenant has signed, so next year's rent is known. The building and the road outside are already familiar, so a reasonable guess at the year after, and at the year after that, is still worth making. Pushed to year eleven, the guessing stops being useful. Nobody knows.

So they do what every valuer does. The couple forecast the years they can picture, and then they make exactly one of two moves about all the years they cannot. The first move is to say the flat keeps being let, the rent keeps drifting up a little every year, and to price that drift going on and on. The second move is to say the flat is sold in year six, and to price it at whatever flats in that building fetch when the time comes.

The two moves are the only two terminal value methods there are, and they are not two routes to the same number. One is a claim about the asset: it keeps working, and here is how well. The other is a claim about a market: somebody turns up with a chequebook, and here is what they pay. A household that picks the first move and a household that picks the second are not disagreeing about arithmetic. The two households are disagreeing about which of two futures they are willing to put their name against.

Everything below is that dining table conversation, done on a company, with the rupees worked out to the last one so that every step can be checked. The company is Sankalp Industrial Systems Limited.

What is a terminal value, and why does a model need one at all?

Because a business does not stop, and a forecast does. The gap between a business that does not stop and a forecast that does is the whole reason the idea exists. A terminal valueThe value of everything the business produces after the explicit forecast stops. is one figure standing in for every year beyond the last year anybody was prepared to argue about, discounted to that last year.

Sankalp Industrial Systems Limited has a five year forecast built elsewhere in this sequence and restated here. Year 5 revenue is Rs 18,00,00,00,000, earnings before interest, tax, depreciation and amortisation (EBITDA) is Rs 4,32,00,00,000, profit after tax on operations is Rs 2,70,00,00,000, and free cash flow to the firm is Rs 1,70,00,00,000. The discount rate throughout is the company's own assumed weighted average cost of capital of 12.00 per cent, built elsewhere and used here as a given. Year 5 arrives and the model runs out of argued years. The valves do not stop being made on that day. Somebody has to put a number on the rest.

There is a temptation, on first meeting this, to think the answer is simply to forecast more years. Attempting it shows why nobody does. Forecasting Year 6 individually requires an argument about Year 6 revenue, Year 6 margin, Year 6 capital expenditure and Year 6 working capital. By Year 12 those arguments have stopped being research and started being decoration: they look like work, they carry the same number of decimal places as Year 1, and there is nothing behind them. A terminal value is the honest admission that from some year onward one assumption is being made rather than four, and it is better to make that one assumption visibly than to bury it in seven years of invented detail.

So the model splits into two objects with completely different characters. The explicit period is argued year by year. The terminal period is asserted in a single line. And the second object is almost always the larger of the two.

How is a terminal value built from a perpetuity growth rate?

With one line of arithmetic that has been in print since 1959. A growing perpetuityA stream of cash rising at a constant rate with no end date. is a stream of cash that rises at a constant rate and never ends, and its present value is next year's cash flow divided by the discount rate less the growth rate. The expression is Myron J. Gordon's, from Dividends, Earnings and Stock Prices in the Review of Economics and Statistics, and it is the whole of the machinery.

Three symbols, and each needs a sentence rather than a nod.

Two things about that formula catch people out, and both are worth naming before any numbers go in. The first is that the denominator is a subtraction of two small numbers, so it is violently sensitive. Twelve less five is seven. Twelve less six is six. A single point of assumed growth changed the divisor by a seventh, and that sensitivity is why the terminal line is argued over more than any other row in a model. The second is the word forever. Not thirty years. Not until the promoter retires. Every rupee put through this formula is a rupee the business is claimed to earn for the rest of time. The growth rate that goes into it is therefore not a forecast at all but a constraint.

And there is a piece of housekeeping that decides everything that follows. The terminal growth rateThe rate the business is assumed to grow at forever after the forecast ends. here is 5.00 per cent in nominal growthGrowth measured in money of the day, inflation included. terms, meaning money of the day with inflation inside it, and the 12.00 per cent rate is nominal too. Both are assumptions of this worked example and neither is a statement about any real economy. A model that puts a real growth rate over a nominal discount rate has made an error nothing on the sheet will flag.

The build almost everybody meets first, and what it quietly assumes

Open any first model and the terminal line reads the same way. Year 5 free cash flow is Rs 1,70,00,00,000. Grow it once at 5.00 per cent to get Rs 1,78,50,00,000. Divide by 12.00 per cent less 5.00 per cent, or 0.07. The answer is Rs 25,50,00,00,000. Three keystrokes, one formula, and the model is finished.

Nothing about that line looks wrong, and that is exactly the difficulty. The formula is Gordon's and it is correctly applied. The cash flow is the model's own, taken from the row directly above. The rate is the model's own. The answer is the lower of the two figures worked here, so it feels careful rather than sloppy. A reviewer glancing at it has nothing to object to.

But look at what has been carried across that line without anybody typing it. Year 5 profit after tax on operations is Rs 2,70,00,00,000 and Year 5 free cash flow is Rs 1,70,00,00,000, so Sankalp Industrial Systems Limited put Rs 1,00,00,00,000 of net new capital into plant and working capital that year. Rs 1,00,00,00,000 against Rs 2,70,00,00,000 is a reinvestment rateThe share of after-tax operating profit put back into the business as new capital. of 37.04 per cent. Growing Year 5 cash flow forward does not just carry the cash flow forward. The formula carries the 37.04 per cent forward too, and it carries that rate into every year from Year 6 to the end of time.

Why does the reinvestment rate have to change when the growth rate changes?

Because growth is not free, and the price of it is fixed by how well new capital does. Koller, Goedhart and Wessels put growth, return on invested capital and value into a single expression to make that price visible: growth equals the reinvestment rate multiplied by the return on new capital. Rearrange it and the reinvestment rate equals growth divided by the return.

A sweet shop shows the mechanism before a company does. The mechanism is identical there and easier to feel. A man runs one counter and clears about a lakh a year. He wants to open a second counter, and a second counter costs him money he could have taken home. If every rupee he puts into a new counter reliably throws off eighteen paise a year, then to make his overall takings grow five per cent a year he has to keep putting back a very particular share of what he earns. Not whatever share he feels like. The share that arithmetic dictates: five over eighteen. Putting back less does not get him five per cent. Putting back more buys more growth than he claimed.

For Sankalp Industrial Systems Limited the return on new invested capitalThe profit earned on each rupee of new capital, 18.00 per cent here by assumption. is 18.00 per cent, an assumption of the forecast rather than an observation. So a terminal claim of 5.00 per cent growth forever requires reinvesting 5 divided by 18, or 27.78 per cent of profit, forever. Not 37.04 per cent. The company was reinvesting 37.04 per cent in Year 5 because it was still growing at 7.14 per cent. Once growth is declared to settle at 5.00 per cent, the bill for growth falls, and the cash left over rises.

The insistence that a terminal value be made consistent with the reinvestment its own growth would require is Aswath Damodaran's, and it is the reason this sequence uses Rs 29,25,00,00,000 as its answer rather than the other figure. The point is not that one number is bigger; the point is that the reinvestment rate is not a free parameter once the growth rate has been chosen.

Slowing a business down does the opposite of what almost everybody expects. Cutting the terminal growth rate to 3.00 per cent takes the reinvestment rate to 3 over 18, or 16.67 per cent, so 83.33 per cent of profit comes out as cash instead of 72.22 per cent. The stream being valued is growing more slowly and is simultaneously larger in its first year. The larger first-year stream is why the terminal value at 3.00 per cent is Rs 25,75,00,00,000 rather than something close to three fifths of the 5.00 per cent answer.

How much is riding on that one correction?

Rs 3,75,00,00,000 of terminal value, or 14.71 per cent of the naive figure. The correction accounts for the whole of the difference between Rs 29,25,00,00,000 and Rs 25,50,00,00,000, and every rupee of it comes from a single number nobody typed.

The reason comes to one sentence. The naive build makes the company go on paying Year 5's growth bill of 37.04 per cent forever, while booking only the 5.00 per cent of growth that 27.78 per cent would have bought. The company is paying for 6.67 per cent of growth and delivering 5.00. Nine and a bit points of reinvestment, held for the rest of time, discounted at 12.00 per cent, come to Rs 3,75,00,00,000.

So is the naive build simply wrong?

No. A reader who leaves thinking one of the two is a mistake will misread every model they open afterwards, so this is the part worth being careful about. Both builds are standard. Both appear in published work, in teaching material and in models used by people who know precisely what they are doing. The two builds differ in what they assume about the terminal business, and one of those assumptions is stated while the other is inherited.

In household terms once more: a man who has been paying school fees for two children stops writing that cheque when they finish. Forecasting his savings by taking last year's spare cash and growing it quietly assumes he keeps paying school fees for the rest of his life. The school-fee assumption is not an arithmetic error. It is a claim about his future spending that nobody made out loud. The reinvestment-consistent build is not more correct arithmetic; it is the same arithmetic with one inherited assumption dragged into the open and replaced by a stated one.

A reader will meet Rs 25,50,00,00,000 in somebody else's model, so it is worth being able to recognise it on sight rather than treating it as a blunder. The tell is quick. Take the terminal cash flow and divide it by the terminal profit figure to see what reinvestment rate has been assumed. If it is not the growth rate divided by the return on new capital, the terminal value is not consistent with the growth it claims. The rate may still be what the modeller intended. It is now at least visible.

How high is a terminal growth rate allowed to go?

Not as high as the company has been growing, and the reason has nothing to do with the company. A terminal growth rate runs forever. Anything growing forever faster than the economy around it eventually becomes that economy, and then becomes larger than it. The sentence should end the discussion on its own.

Sankalp Industrial Systems Limited grows revenue at 10.00 per cent in Year 1 and 7.14 per cent by Year 5. Neither is available as a terminal rate. The forecast itself is honest about this: it adds a flat Rs 1,20,00,00,000 of revenue every year, so the growth rate falls all the way down the column even though the rupees never move. A rate that is falling year on year inside the forecast cannot then be frozen at its highest reading and run to the end of time.

So what is the ceiling? The ceiling is long-run nominal growth for the economy the business sits in, and that makes the terminal growth rate the only input on the sheet that is not a question about the company at all. The 5.00 per cent used throughout is this worked example's own assumption, chosen for the example, and a reader working on a real business finds the current reading for the economy in question rather than borrowing this one.

There is a companion trap on the same input, and it is made by people who have just learned the reinvestment correction. Having raised the terminal value by making reinvestment consistent, they feel the answer has become generous, so they trim the growth rate to compensate. Trimming the rate afterwards is the same caution applied twice. The reinvestment correction was not an increase in optimism. The correction was a repair to an assumption. Applying a discount on top of it double counts a prudence that was never missing.

How is a terminal value built from an exit multiple instead?

By stopping the story rather than continuing it. The exit multiple methodValuing the terminal period as a sale at a multiple of that year's earnings. says that on the last day of Year 5 the business changes hands, and prices that sale the way sales are actually priced: a multiple of that year's earnings. Year 5 EBITDA for Sankalp Industrial Systems Limited is Rs 4,32,00,00,000. Applied at the peer medianThe middle multiple of a set of similar companies, 7.8 times here. of 7.8 times, the terminal value is Rs 33,69,60,00,000.

The 7.8 times median comes from a set of six invented companies, chosen and defended elsewhere in this subject area and restated here as one input. Whether those six belong together, and whether a company growing at a very different rate from the rest of them belongs in the set at all, are real questions and are covered separately.

The method has just assumed three things, and each is easy to miss under the arithmetic. The first is that a buyer exists in Year 5. The second is that the buyer pays a multiple resembling the one paid for similar businesses today. The third, never said out loud, is that whatever those companies are worth today reflects the same sort of business the seller will be handing over five years from now. The perpetuity method asks for a view about a company; the exit multiple method asks for a view about a market, five years before that market exists.

Neither of those is an unreasonable thing to hold. The transaction version is often the more natural one when the model is being built for a decision that genuinely ends in a sale. A person buying a shop with the intention of selling it in five years is not being sloppy when they price the exit rather than the eternity. A buyer with a five-year horizon is pricing the exit they actually plan to make.

Terminal Growth vs Exit Multiple: Reading One Assumption Out of the Other

Here is the move that turns two separate methods into one picture, and it runs in both directions. The two are not rival opinions. The two methods are two coordinates of the same point, and either one can be converted into the other by arithmetic alone.

First direction. Take the terminal value the perpetuity route produced, Rs 29,25,00,00,000, and divide it by Year 5 EBITDA of Rs 4,32,00,00,000. The answer is 6.77 times. 6.77 times is the implied exit multipleThe multiple a perpetuity terminal value works out to when divided by that year's earnings., and the reading is genuinely useful. The traded enterprise value of Sankalp Industrial Systems Limited today is Rs 22,40,00,00,000 against Year 0 EBITDA of Rs 2,88,00,00,000, which is 7.78 times. So a company trading at 7.78 times today is being valued, on its own assumptions, at 6.77 times in five years. The comparison describes what the model contains. Whether the drop is warranted is a separate question.

Second direction, and it is the more startling one. Ask what terminal growth rate would make the perpetuity build produce exactly 7.8 times Year 5 EBITDA. Solve it and the answer is 6.58 per cent, to two decimal places; carried further the root sits at 6.5831 per cent. 6.58 per cent is the implied terminal growthThe growth rate an exit multiple works out to when read back through the perpetuity build. hidden inside the peer median. Applying the median as an exit was never a way of avoiding a growth assumption. Applying the median was a growth assumption of 6.58 per cent, made silently, one and a half points above the 5.00 per cent the same model states out loud a few rows higher.

The pair of conversions shows the heart of the matter. There is no such thing as choosing a multiple without choosing a growth rate, and no such thing as choosing a growth rate without choosing a multiple. Whichever end of the sheet is typed into, both have been set. The only question left is whether the other one was read before moving on.

What does each terminal value do to the finished answer?

The choice of terminal value moves the answer by more than the whole forecast is worth, and that sentence is not a figure of speech. The arithmetic follows, and every line of it is a consequence of figures already established rather than a new assumption.

None of these three conventions touches a single forecast year, so the present value of the five explicit forecast years is Rs 4,68,41,43,564 and does not move. The Year 5 discount factor at 12.00 per cent with year-end discounting is 0.567426856. Each terminal value is discounted once by that factor, added to the explicit period, and then walked across the same bridge to a figure per share. The bridge deducts a net minus Rs 4,40,00,00,000, being cash and non-operating assets added and gross debt and minority interest taken off, and divides by 20,00,00,000 shares. The bridge is identical in all three columns and is built elsewhere in this sequence.

Now put the two ends of that row side by side. The spread across the three conventions is Rs 4,65,06,30,509. The entire present value of the five-year explicit forecast is Rs 4,68,41,43,564. Choosing between three ordinary terminal value conventions moves the answer by 99.28 per cent of everything five years of forecasting were worth.

Several numbers have just been printed to the rupee, so two notes on precision go with that figure. The spread is computed on the unrounded enterprise values; subtracting the two figures as they would be printed in crore, Rs 2,380.42 crore less Rs 1,915.35 crore, gives Rs 465.07 crore instead, and the difference between the two answers is rounding rather than a defect. Neither figure has been adjusted to make the subtraction come out. And on an answer where roughly four fifths rests on one typed growth rate, the last two digits of any of these rupee figures carry no information whatever; they are printed so a reader can check the arithmetic, not because the model knows the answer to the rupee.

Which of the two methods should a reader use?

Nothing in the arithmetic settles it.

The question has no arithmetic answer. The perpetuity route asks for a view about the economics of a business: that it grows at some rate forever and earns some return on the capital it puts in forever. The exit multiple route asks for a view about a market: that in Year 5 somebody turns up and pays a multiple resembling what is paid for similar businesses now. The two are different kinds of belief, and no amount of working shows one to be the safer thing to believe. The arithmetic can still show exactly what each belief costs, and exactly what the other one, the one not being looked at, is set to.

So the useful question is not which method is right. The live question is which assumption the analyst is willing to put a name against, and whether the one the method chose has been looked at. A reader who applies the peer median as an exit has chosen 6.58 per cent of growth forever whether or not they intended to. A reader who types 5.00 per cent of growth has chosen 6.77 times whether or not they intended to. Neither is exempt from the other. The discipline is to read both readings out loud before moving on.