Payback vs Discounted Payback: When One Never Pays Back at All

Payback counts the years until a project’s outlay comes back. Discounted payback counts the same years after each receipt is discounted first, so it is never the shorter of the two. On Sankalp’s regional warehouse the figure moves from 5.63 years to 9.92 on a ten year asset. On the effluent treatment plant there is no discounted answer at all.

Underneath that sits one fact about arithmetic. Without discounting, every rupee that arrives retires one rupee of the outlay, and it makes no difference whether it turns up in Year 1 or Year 9. With discounting, each year’s rupee retires a little less of the outlay than the rupee before it did, and the shrinkage compounds. At Sankalp Industrial Systems Limited’s own hurdle rateEvery project on the list is measured against one required return, and 12.00 per cent is the figure Sankalp uses. Where a company gets that number from is settled separately; here it is simply the bar. of 12.00 per cent, a rupee arriving in Year 10 retires about 32 paise. So the further out the crossing already sat, the further out discounting pushes it, and past a certain point the crossing stops arriving at all. The gap between the two measures is not a correction bolted onto an answer. The gap is a different question with a different answer, and on one project on this list the second question has no answer to give.

What does the plain measure count?

Plain payback asks one question and nothing else: how many years pass before the money put in has come back in cash? The outlay is set down as a negative number, each year’s cash is added to it in turn, and the year in which the running total stops being negative is the one written down. If the crossing falls partway through a year, the fraction of that year’s cash that was still needed is added on, so the answer comes out as something like 3.08 years rather than a whole number of years.

Think about a household buying a water purifier for Rs 12,000 because it stops the household buying bottled water at about Rs 400 a month. Thirty months of saved bottle money adds back to Rs 12,000, so the purifier pays back in two and a half years. Nobody doing that sum in a kitchen adjusts the Year 3 saving downward because it is further away. The plain measure works exactly like the kitchen sum, and its appeal is that anybody can do it and everybody understands the answer.

The plain measure really reports a fact about liquidityHow soon committed money comes back and is free to be put somewhere else. Nothing to do with whether committing it was worth doing.: how long the company’s money is tied up before it is available again. Liquidity is a genuine question and a company with tight funding asks it constantly. How long money is tied up is simply not the same question as whether the project is worth doing, and the plain measure has no view on worth at all.

What does the discounted measure count instead?

The discounted measure runs the identical procedure with one substitution. Before a year’s cash is added to the running total, it is first restated as what it is worth today. A receipt of Rs 16,00,00,000 in Year 1 goes into the column as about Rs 14,28,57,143 at 12.00 per cent. The same receipt in Year 10 goes in as about Rs 5,15,15,718. Then the crossing is read off in exactly the same way, with the same fractional-year treatment, and the answer is again a number of years.

Notice what has and has not changed. The unit of the answer is unchanged: it is still years, not rupees. The procedure is unchanged: build a column, watch it climb, read the crossing. The weight each year carries on the way up has changed. In the plain column all ten years are equal contributors. In the discounted column the tenth year contributes roughly a third of what the first year does, so a project that leans on its later years has to wait much longer for its column to arrive.

Both measures, then, answer a question about duration. Neither answers a question about worth. The discounted figure is not simply the better of two attempts at the same number. Both are answers to the duration question, and neither attempts the question of worth.

So what actually separates the two?

Set them side by side and the difference is a single substitution in one step of a five-step procedure. Everything that follows comes from that one substitution, and the size of what follows is the surprise. A reader who has just met both measures usually expects the discounted answer to sit a bit above the plain one, in the way a tax-adjusted figure sits a bit below a pre-tax one. The expectation is wrong. On one of Sankalp’s five projects the discounted answer sits more than four years further out, and on another the discounted answer never arrives.

What do both measures say about all five of Sankalp’s projects?

Sankalp Industrial Systems Limited has five numbered projects under consideration. Each one is a single outlay at the start followed by the same amount of cash every year for a fixed number of years. Every one of those amounts is after the company’s own assumed effective tax rate of 25.0 per cent. Every project is measured against the same 12.00 per cent. Here are both measures on all five, with the difference between them in the last column.

All the years above are written to two decimal places, and each stretch in the last column is the difference between the two figures as printed. The stretch column makes the point on its own: 0.99, 0.65, 0.65, 4.29, and then a project where the second measure ceases to exist. As a share of the plain figure those are 32, 26, 26 and 76 per cent. Nothing about that column looks like a correction of a fixed size, and nothing about it supports a habit of adding a bit on.

What actually decides how far the crossing moves?

The usual explanation runs like this. A project with plenty of return above the rate barely notices being discounted. A project scraping the rate is nearly consumed by it. The explanation gets the right answer on four of these five projects and is still not quite the mechanism. Projects 2 and 3 settle the matter. Look at their returns: 28.65 per cent on the automation cell against 21.86 on the tooling upgrade, seven points apart, on different lives and different sums. Both stretch by 0.65 years, to the second decimal.

Here is what those two have in common instead, and it is the only thing they share.

Identical plain paybacks, then. For a project whose cash arrives in equal annual amounts, the discounted payback is fixed entirely by the plain payback and the rate, and by nothing else at all. Not by the size of the project, not by its life, and not directly by its own rate of return.

The reason is short. A level cash flowThe same amount every year, no ramp at the front and no tail at the end. All five projects here were written that way so the arithmetic stays checkable by hand. means the plain payback is just the outlay divided by one year’s cash. The discounted crossing arrives when the annuity factorTen identical yearly receipts are not worth ten times one of them. Multiply a single year’s amount by this number instead. At 12.00 per cent over ten years it comes to 5.6502. for that many years, at that rate, has climbed to the same ratio. Two projects with the same ratio therefore have the same discounted answer, whatever else differs between them.

Stop on that last condition for a moment. The condition states project 5’s whole problem in advance. At 12.00 per cent, no project paying a level amount can ever have a discounted payback if its plain payback exceeds 8.33 years. Not in Year 20, not in Year 50. The discounted column climbs towards a ceiling and the ceiling is below the outlay.

How far does discounting push the regional warehouse?

Project 4 is where the size of the stretch stops being a curiosity. The regional warehouse takes Rs 90,00,00,000 out of the door once, and puts Rs 16,00,00,000 back at the end of each of the next ten years. Divide one by the other and the plain payback is 5.625 years, written 5.63. Look at that alone and the project reads as a steady middle-of-the-road commitment with roughly four and a half years of asset lifeThe number of years a project keeps producing cash before it stops. The warehouse runs ten of them and the tooling upgrade four. left over once the money is back.

Now build the discounted column. By the end of Year 9 the discounted column has climbed to about Rs 85,25,00,000. About Rs 4,75,00,000 of the outlay is still uncovered. Year 10 brings in about Rs 5,15,00,000 of present value, enough but only just: the crossing lands about 0.92 of the way through the final year. The discounted payback is 9.92 years on an asset that runs for ten, so the warehouse recovers its outlay in present value terms with about one month of life to spare. Those Year 9 and Year 10 amounts are stated as approximations, because what is locked on this case is the 9.92 year answer rather than the internals that produce it.

Two lines from the same project, the same ten receipts, and they part company further with every year that passes. The widening is the compounding described above made visible. Each year’s contribution to the discounted column is smaller than the last. The second line therefore flattens while the first keeps its slope.

What happens to the effluent treatment plant?

Project 5 is the case that breaks the habit entirely. Sankalp spends Rs 45,00,00,000 once on the effluent treatment plant, and the plant then takes Rs 5,00,00,000 a year off the company’s outgoings for ten years as a cost savingMoney that stops going out, rather than money that starts coming in. An appraisal counts both the same way.. Divide one by the other and the plain payback is exactly 9.00 years. On a ten year plant, that reads as a project which pays for itself with a year in hand. Tight, but a pass.

Discount those same ten receipts at 12.00 per cent and they come to about Rs 28,25,00,000 in total, against an outlay of Rs 45,00,00,000. The discounted column climbs for ten years and finishes about Rs 16,75,00,000 short, so there is no year in which it crosses and no fraction of a year to report. The answer is not a large number. There is no answer.

And the plant does not merely run out of years. Its Rs 5,00,00,000 a year, discounted at 12.00 per cent and continued without end, would come to about Rs 41,66,66,667 in total. The unending total is still about Rs 3,33,33,333 below what the plant cost. Give the plant a fifty year life or an unending one and the discounted column still never reaches the outlay. The ceiling it is climbing towards sits underneath the line it needs to reach.

What shows in advance whether a discounted payback exists at all?

The column need not be built to find out. There is one test, and it is exact on every project on this list. A discounted payback exists within a project’s life if and only if the project’s net present valueDiscount everything a project brings in, take away what it costs at the start, and whatever remains is this. The remainder is counted in rupees, never in years. over that life is positive. The two statements are the same statement wearing different clothes: the discounted column reaches the outlay exactly when the discounted receipts add to more than the outlay, and that second condition is the definition of a positive value.

For a project shaped like these five, where one payment goes out first and every later movement is a receipt, the same test can be read off the project’s internal rate of returnPush the discount rate high enough and a project’s worth today falls to nothing. The rate where it lands there is this one, and building it is covered separately. instead: the value is positive exactly when that rate is above the rate being discounted at. Both readings are used below, and both are properties of this cash flow shape rather than universal laws about every project a company might meet.

For a level flow there is a third form of the same test, and it is the one that can be done in the head. The annuity factor over the life is compared with the plain payback. If the factor is the larger, a crossing exists.

Two decimals would hide project 4’s margin of 0.0252, so the plain payback figures in that table are written to four. The three readings agree on project 4: the factor clears the payback by 0.0252, the value is positive at Rs 40,35,685, and the rate of return is 12.11 per cent against a hurdle of 12.00. The three readings agree again on project 5, in the other direction: short by 3.3498, a value of minus Rs 16,74,88,849, and a return of 1.96 per cent.

Why does that test make the comparison honest?

Because it settles what the discounted measure inherits. The condition for the discounted measure to have any answer at all is the condition for the value to be positive. The discounted measure therefore cannot pass a project that the value rule rejects. It takes the accept-or-reject verdict as given and then adds a duration on top of it. The inheritance is a real improvement, and the only improvement one measure makes on the other.

The plain measure inherits nothing. The plain measure will happily report 9.00 years on project 5, a figure that sits comfortably inside a ten year life. Project 5 is worth minus Rs 16,74,88,849. A paper that carries only the plain column has a value-destroying project sitting on it looking like a pass, with no mark on the sheet to say otherwise.

What does the size of the gap say about a project?

Now that the mechanism is settled, the gap becomes readable. A project whose two figures sit close together has a plain payback that is short relative to what the rate can absorb. Short plain paybacks come from projects that recover their outlay quickly, and those projects earn well above the rate. A project whose two figures are far apart is the opposite. A narrow gap is a cushion and a wide gap is a warning, and reading the gap that way is the one genuinely useful thing this comparison produces beyond the two numbers themselves.

Say it carefully, though. The honest version has a condition on it. The gap is set by the plain payback and the rate. Within a group of projects that all run for the same number of years, a longer plain payback does mean a lower rate of return, so the gap and the cushion move together and the shorthand works. Across projects of different lives it can mislead, and projects 2 and 3 are the demonstration: identical gaps, and returns seven points apart.

What does the gap not show?

The gap does not show the project’s worth, and neither figure on either side of it does either. Both measures return a number of years, and a number of years cannot be added across a list, cannot be compared with a cost of capital, and cannot be turned into rupees of value. Project 2 stretches by 0.65 years and project 3 stretches by 0.65 years, and one of them is worth about three and a half times the other.

Nor does the gap rank projects. Project 1 returns 18.72 per cent and has a wider gap than project 2, and it is worth about half as much again in rupees. A reader who starts using the gap as a scoring column has quietly turned a diagnostic into a ranking. The mistake is the same as ranking by payback, made one layer further in.

Discounting does fix a specific and narrow defect: it stops the measure treating a Year 9 rupee as though it were a Year 1 rupee. The defect is worth fixing. Fixing the defect does not turn a duration into a valuation, and computing the duration more carefully will not either.

Which measure should a company reach for, and when?

Use the plain one when the question genuinely is about how long the money is out. A lender writing a covenant, a promoter funding an outlay from a facility that has to be renewed, a household deciding whether the purifier pays for itself before the household moves house: all of those are duration questions, and the plain measure answers them in a form everyone in the room can check. Its crudeness is the point. The plain payback is a rough, fast, universally legible number.

Use the discounted one when the figure is going to be used as a screen. A screening number has to carry a defensible rate inside it. An analyst who screens a list on plain payback is screening on an arithmetic that treats distant money as though it were near money. An analyst who screens on discounted payback has at least ruled out everything that destroys value. On this cash flow shape a project with no crossing is a project with a negative value.

How this gets used away from a textbook

A lender looking at Sankalp’s regional warehouse cares about the plain 5.63 years for one reason: it says roughly when the borrower’s cash position stops being under pressure from this outlay. The lender then looks at the discounted 9.92 and reads it as a warning about how little room the project has, and asks what happens if the annual cash comes in at Rs 14,00,00,000 instead of Rs 16,00,00,000. The pair is used that way in practice: not as two competing answers, but as a fast figure and a stress reading side by side.

An analyst writing this up does something similar with the gap. A list where the gaps run between a quarter and a third is a list of projects with room. A list where one project’s gap is three quarters is a list with one item that needs the value arithmetic done carefully and the assumptions behind its later years questioned. Those later years carry almost none of the weight, and yet the project depends on all of them.

And a household runs the same logic without the vocabulary. A shopkeeper putting in a second freezer that costs Rs 90,000 and saves Rs 1,500 a month of spoilage is looking at a five year plain payback on a freezer that might last seven. The freezer is exactly project 4’s shape, and the shopkeeper’s instinct to ask whether it will really still be running in Year 7 is precisely the question the discounted figure asks in a different unit.

Sankalp Industrial Systems Limited and its five projects are invented.
Educational material. Not advice on any investment, tax, budget or market position.