How to Check Discount Rate Consistency in a Valuation

A discount rate is consistent when it matches the cash flow it discounts on four counts: nominal against real, whose claim the cash flow is, which currency it sits in, and whether terminal growth stays below it. Sankalp Industrial Systems Limited passes three of them at 12.00 per cent. Its weights use an equity value the model does not produce, and running that loop to a settled point moves the answer Rs 21.17 crore.

Here is the idea underneath all four. A discount rate does not belong to a company. The rate belongs to a pairing, and the pairing is what gets checked. The second stream belongs to a different set of people, so the same 12.00 per cent that is exactly right against one stream of cash is wrong against another stream from the same company in the same year. No step asks whether the rate was built well. Each asks whether the rate and the cash flow at hand belong together, and each has a plain answer rather than a matter of degree.

Every figure below belongs to Sankalp Industrial Systems Limited, an invented manufacturer. Its model takes free cash flow to the firmCash thrown off by the operating business before any funder is served, so lenders and shareholders both still have a claim on it. across Years 1 to 5, at Rs 98.00, 116.00, 134.00, 152.00 and 170.00 crore, using a weighted average cost of capitalBlend the return lenders want with the return shareholders want, in the proportions each has put in, and the blend is this rate. of 12.00 per cent, a terminal growth rate set at 5.00 per cent, and year-end discountingEvery year's cash is booked at that year's close, so nothing is treated as arriving month by month.. The model produces an enterprise value of Rs 2,128.14 crore: Rs 468.41 crore of it earned by Years 1 to 5, and 77.99 per cent of it by the terminal valueOne lump standing in for everything the business does after the last forecast year, rather than a year by year list.. The four checks take that build as given and test the rate against the cash flow it was used on.

What are the four checks, taken as a set?

The four checks run in order, stopping at the first one that cannot be answered. Each is a question about the pairing, and each returns a pass or a fail rather than a score. Three of the four pass on this model, one fails, and the one that fails is worth more to a reader than the three that pass.

Step one: are the cash flows and the rate both nominal, or both real?

The simplest household version comes first. A salary went up 6.00 per cent this year and the rent on the same flat went up 5.00 per cent. Is the household better off by 6.00 per cent, by 1.00 per cent, or by something else? The question only has an answer once it is settled whether the count is in rupees that include rising prices or rupees that have had rising prices taken out. Mixing the two makes the sum stop meaning anything. A valuation does exactly that when it discounts one kind of rupee at the other kind of rate.

On this model the check passes. The five cash flows are stated in nominal rupees, meaning inflation is already inside them, and the 12.00 per cent is a nominal rate built from a nominal risk-free rateBefore any extra risk gets priced on top, this is the floor return an investor starts from. of 7.75 per cent. Both sides carry inflation, so the pairing is sound and the check moves on.

On the day the relation is needed, the exact figure is what is needed and not the shortcut. So the relation is worth working anyway. Inflation is taken at 5.00 per cent, a figure this worked model assumes rather than a level anybody observed. The real cost of capital then comes from the Fisher relation, named for Irving Fisher, who set out how a quoted rate, expected inflation and the real rate underneath them fit together.

What does step one turn up that ought to stop a reader cold?

Once the distinction between nominal and real is in view, the terminal growth rate on this model repays a look. The terminal growth rate is 5.00 per cent a year forever, in nominal rupees. The inflation this worked model sets is 5.00 per cent. Set side by side, the two admit only one reading. Read in real terms, the model has Sankalp Industrial Systems Limited running level with prices and getting no further from Year 6 onward, and 77.99 per cent of the enterprise value rests on that.

Notice what step one has just done. Step one was a housekeeping check that passed in a line, and running it properly surfaced the single largest assumption in the model. The ordinary yield of these checks runs like that: they are cheap, they mostly pass, and the act of running them forces a reader back onto numbers that had stopped being read.

None of this makes the assumption wrong. A mature manufacturer keeping pace with prices and adding nothing on top of them is a perfectly defensible thing to assume. Assuming it without noticing is the indefensible part. Terminal growth gets typed in as a rounded number that looks conservative, and inflation never gets written down beside it.

Step two: does the rate belong to the same claimant as the cash flow?

Think of the cash drawer of a small hardware shop at the end of a trading day. Some of what is in there is already spoken for by the supplier who delivered on credit that morning. The rest belongs to the shopkeeper. Both piles are cash in the same drawer, but the person who has a claim on each pile is different, and so is what each pile is worth to the shopkeeper. A valuation makes exactly the same distinction, and step two is the check that the piles have not been mixed.

Every funder at once has a claim on the firm stream, so the firm stream takes the blended rate. The equity stream is struck only after the lenders have been served, so it takes the cost of equity. Swapping those two is the whole of what step two catches. On this company those two rates are 12.00 per cent for the blend and, for the cost of equityWhatever survives once everybody holding a contract has been paid is what a shareholder ends up with, and this is the return they want for carrying it., 14.00 per cent. There is no discretion in which one goes where. The claimant decides it.

What does step two look like when it fails?

Run both routes on Sankalp Industrial Systems Limited and they do not meet. The firm route gives an operating equity value of Rs 1,588.14 crore. The free cash flow to equityOnce the interest is paid and the borrowing balance has moved, the cash still sitting there has only shareholders left holding it. route, discounting Rs 87.00, 103.50, 120.00, 136.50 and 153.00 crore at 14.00 per cent, gives Rs 1,441.38 crore. The two routes are Rs 146.76 crore apart, being 9.24 per cent of the firm route, and no amount of checking the arithmetic will close the difference.

Why they differ is pinned down and treated separately: it turns on the borrowing schedule the model actually runs against the funding mix the beta was levered on. The check itself is simply this. Both routes are run. If they disagree, the disagreement is something learned about the model's assumptions, and the number it puts on that disagreement is worth writing in the file.

Step three: is the rate in the same currency as the cash flow?

A rate carries the inflation expectation of the currency it was built in. Carrying that expectation is not a convention somebody chose. Step one already forces it. If the rate has inflation inside it, that inflation belongs to one particular currency, and prices do not rise at the same speed everywhere. So the rate travels with the cash flow's currency and never with the analyst's habits.

On this model the check passes without argument. Every cash flow is in rupees. The 12.00 per cent was built on a rupee risk-free rate of 7.75 per cent and a rupee-relevant equity premium, so both sides of the pairing are denominated the same way. Discounting these rupee cash flows at a rate assembled somewhere else would import a foreign inflation expectation into an Indian forecast without a single line in the file saying so, and the answer would look entirely normal.

The everyday version is a wedding budget quoted partly in one currency and partly in another, with one exchange rate assumed at the top of the sheet and a different one assumed halfway down. Nothing looks wrong. The total is simply not a number.

Step four: does the terminal growth rate sit below the discount rate?

Step four takes ten seconds, and it saves a model from printing a figure that arithmetic never produced. The perpetuity form puts a cash flow over the difference between the rate and the growth rate. If growth equals the rate, that divisor is nil. If growth exceeds the rate, the divisor turns negative and a positive cash flow produces a negative terminal value. A model whose growth rate reaches its discount rate does not produce a very large answer, it produces no answer at all, and any figure printed there has been invented by the spreadsheet.

Here it passes with a wide margin: 5.00 per cent against 12.00 per cent. The check still passes at the reverse-engineered growth rate of 5.7976 per cent that comes out of running the arithmetic backwards. Growth stays below the rate in the slower case at 4.00 per cent against 12.50 per cent, and in the faster case at 5.50 against 11.50. Four settings, and the check clears all four.

What about the loop in the weights that every reader spots?

The four checks are done. Now the thing a sharp reader has been holding since the first paragraph. The 12.00 per cent is weighted using equity at Rs 1,800.00 crore beside debt of Rs 600.00 crore. The weights put 75.0 per cent of the capital in equity and 25.0 per cent in debt. But the model itself produces an operating equity value of Rs 1,588.14 crore. The equity weight is an input to the rate, and the rate produces a value, and that value is an equity number too, so the input and the output are the same quantity measured twice.

The ruling that settles it

Here is how this worked model resolves the loop, and it is a ruling rather than a dodge. Sankalp Industrial Systems Limited is a listed manufacturer whose equity carries a quoted price, so the weights are read from the capital structure the market can already see. A figure somebody can look up beats a figure a model produced. Whatever the model itself outputs is treated as a second, separate estimate of the same quantity, and the two are allowed to disagree. Nothing is re-solved to force them together.

A ruling like that is easy to assert and hard to defend, so the defence has to be a measurement of what the ruling costs. If iterating the loop moved the answer a lot, the ruling would be indefensible whatever its logic. If it moves the answer very little, the ruling is simply the sensible choice. So the cost is computed.

How the loop is run to a settled point

Each pass does the same four things. Take the equity value the model produced last time. Set it against gross debt of Rs 600.00 crore to get a debt to equity ratio. Relever the beta off an unlevered betaMarket sensitivity with the effect of the borrowings taken back out, leaving only what the operations themselves contribute. of 1.00 with a relevering factor of 0.75. Rebuild the cost of equity from a 7.75 per cent risk-free rate with the total premium of 5.00 per cent on top, reweight against the after-tax cost of debtThe coupon a lender charges, net of the tax a borrower no longer pays once that interest has come off first. of 6.00 per cent, then discount the same five cash flows and the same terminal build at the rate that comes out.

The five cash flows never move. Terminal growth never moves. Nor does the 18.00 per cent that new capital is assumed to earn. The only thing that moves is the equity figure the weights are read from, and everything downstream of it.

The same passes are tabled below. Nobody has to move the control to see all of them.

Follow the enterprise value column down the table and watch what it does. Pass 1 overshoots to Rs 2,151.91 crore. Pass 2 undershoots to Rs 2,148.99 crore. Pass 3 comes back over at Rs 2,149.34 crore, pass 4 goes under at Rs 2,149.30 crore, and the sequence closes on Rs 2,149.31 crore from alternating sides. The passes do not march towards the answer. Each pass swings across it by less than the one before, and a shrinking swing is itself the evidence that a settled point exists. The distance readout in the panel above makes it explicit: Rs 21.17 crore, then Rs 2.60 crore, then Rs 0.32 crore, then Rs 0.04 crore, and then a step of under Rs 0.01 crore. Every one of those is measured against the unrounded settled figure. The last two are therefore smaller than subtracting the printed column would suggest.

The implied debt share is worth a glance too. The headline model is read off 25.00 per cent debt. The settled model produces 27.16 per cent. A debt share of 27.16 per cent is a real difference in what the model believes about the funding mix, and it moves the answer by 1.0 per cent.

Which is worth more: the loop, or the sentence nobody wrote?

Two numbers that almost never get set beside each other belong beside each other here. Running the loop to its settled point is worth Rs 21.17 crore. Moving terminal growth by eighty basis points, from 5.00 per cent to 5.80 per cent, is worth Rs 112.24 crore on the same model, holding the rate at 12.00 per cent and rebuilding the terminal cash flow at the reinvestment that growth requires. The assumption with no note against it is worth more than five times the defect that gets one.

How is this actually run, and by whom?

An equity analyst runs all four steps before the model goes to a reviewer, and the run takes about ten minutes. The output is not a corrected model. Four lines go into the assumptions tab: which kind of rupee, which claimant, which currency, and how much room the growth rate has. As far as the next reader is concerned, a check nobody can see was not run. The value of the run is the written record that it happened.

A credit reviewer at a lender reads the same four lines for a different reason. A borrower's own valuation arriving with a rate that pairs with the wrong stream tends to overstate what is left for shareholders, and the reviewer wants to know which stream was discounted before reading a single output. Step two is the one they turn to first.

An investment committee uses the four steps as a filing standard rather than as arithmetic. Any model reaching the table states its four answers, so a discussion about whether the assumptions are sensible does not have to start by working out what the assumptions were. When step two fails, the committee expects the size of the failure stated in rupees and left open, not closed.

And a student or a candidate sitting an exam gets the cheapest version of all. Given a cash flow and a rate, ask the four questions in order before touching a calculator. Most marks lost on discounting questions are lost to a mismatched pairing rather than to arithmetic, and the pairing is decided before any arithmetic starts.

What does a failed check tell a reader, and what does it not?

A failed check is a statement about the pairing and nothing more. A failed check says the rate and the cash flow in front of the reader do not belong together. The check never says which of the two carries the wrong assumption, and reading it as though it did is how the wrong side gets adjusted.

On this model that distinction is the whole difference between two afternoons. Reading the Rs 146.76 crore as a defect sends an analyst hunting through formulas for an error that was never made. Reading it as a finding produces one sentence: the two routes rest on different assumptions about how growth is funded, and here is what that is worth. The second afternoon produces something a reader can use.

There is one more thing a failed check does not tell, and it is the reason the checks end where they do. A check that passes is not a verdict on the model. Three of these four passed on a model whose largest single assumption is that a manufacturer stops growing in real terms forever. Consistency is a floor and never a ceiling: it confirms the arithmetic is asking a coherent question, and stops there. Whether the answer to that question is any good is a separate matter entirely, and consistency never reaches it.

Sankalp Industrial Systems Limited is invented.
Educational material. Not advice on any investment, tax, budget or market position.