The Forecast Horizon: The Explicit Period and the Terminal Period

The explicit period is the run of years a model forecasts one at a time; the terminal period is everything after it, valued by a single formula. Sankalp Industrial Systems Limited, an invented manufacturer, is forecast for five years worth Rs 4,68,41,43,564 today, and the terminal period carries the other Rs 16,59,72,35,530. Stretching the explicit period moves the split far more than it moves the answer.

Underneath the split lies a division of labour and not a division of time. The explicit period is where the person building the model has something specific to say about a particular year: a plant coming on line, a contract ending, a margin recovering from a bad base. The terminal period is where they have nothing specific left, and one formula stands in for everything. The horizon is therefore not a length of time at all; it is a statement about where the modeller's knowledge runs out. Every argument about how many years to forecast is really an argument about how long a business takes to become ordinary. The answer differs by business and never by rule.

A household already runs this split without calling it anything. The notice for next year's school fee has arrived, so that fee can be named, and the year after it as well. Asked about the eighth year, the naming stops and the assuming starts: roughly the same, rising a bit. Nobody thinks that is a failure of planning. The stopping point is an honest report of where knowledge ends, and a discounted cash flow does exactly the same thing with a formula where the naming runs out.

What Is the Forecast Period, and What Makes a Year Explicit?

The forecast period is the span over which a model projects each line separately, year by year, rather than assuming them. On Sankalp Industrial Systems Limited it runs five years. Revenue stood at Rs 12,00,00,00,000 in the last completed year, and every projected year adds a further Rs 1,20,00,00,000 to it, arriving at Rs 18,00,00,00,000 by Year 5. The five revenue figures are not one assumption stretched across a decade. Each is a claim about a specific year that somebody can be argued out of.

A year is explicit when the model says something about that year that could be wrong. That is the whole test, and it is sharper than counting rows. A spreadsheet can produce forty rows in a second, and thirty-five of them can be a single assumption copied sideways. The test is not whether a row exists but whether the row carries information about the year it names.

The discount rate throughout is 12.00 per cent, the business's own assumed weighted average cost of capitalLenders want one return and shareholders want another; blend the two in the proportions the balance sheet actually uses and a single rate falls out.. Tax runs at an assumed 25.0 per cent effective rate, an assumption of this example rather than any published rate. How that 12.00 per cent gets built is settled separately and is not re-argued here.

What Must a Cash Flow Forecast Contain for a Year to Count?

A cash flow forecast is the set of projected lines that turns a year number into a forecast. On this model there are five of them, and a year that carries fewer is not an explicit forecast year at all. Take Year 3 in full. Revenue Rs 15,60,00,00,000. Earnings before interest, tax, depreciation and amortisation (EBITDA) at the flat 24.0 per cent margin, Rs 3,74,40,00,000. Depreciation at the flat 4.0 per cent of revenue, Rs 62,40,00,000. Capital expenditure Rs 1,44,40,00,000. And a movement in net working capitalMoney stuck in stock and in what customers have not yet paid, less what suppliers are still owed. Working capital swells as a business grows and somebody has to fund the swelling. of Rs 18,00,00,000, being 15.0 per cent of that year's extra revenue.

Read the third column and the point falls out. Five lines were forecast and four fell out of them. NOPATOperating profit with the tax on it taken off, and with nothing about borrowing anywhere in the line. Two businesses running identical operations show the same figure even where one carries far more debt. of Rs 2,34,00,00,000 is what the forecast produced, not what somebody typed in; free cash flow of Rs 1,34,00,00,000 is the output of the whole sheet and never an input to it. The long check foots: Rs 2,34,00,00,000 plus depreciation of Rs 62,40,00,000, less capital expenditure of Rs 1,44,40,00,000, less the working capital movement of Rs 18,00,00,000, is Rs 1,34,00,00,000.

Do that four more times and the explicit period is finished. Each year repeats the same five forecast lines, and because net new capital holds at Rs 1,00,00,00,000 throughout while NOPAT climbs Rs 18,00,00,000 a year, the cash flow climbs by the same Rs 18,00,00,000 every year.

The right-hand column is the whole of what five years of argument is worth today. Everything below turns on how small it looks beside the single figure standing in for every year after Year 5.

Is the Terminal Period Simply the Sixth Year?

The terminal period is everything after the explicit forecast, valued by one expression instead of year by year. On this model the terminal period begins the instant Year 5 closes. Its terminal value is Rs 29,25,00,00,000, and discounted back five years that is Rs 16,59,72,35,530.

The commonest misreading is to treat the terminal period as a sixth year, and it is worth killing early. Year 6 appears in the arithmetic because a growing perpetuityA stream of payments with no end date whose size rises by a fixed percentage each period. How such a stream is valued belongs to time and money and is settled there. needs a starting cash flow, and the model builds one: NOPAT of Rs 2,83,50,00,000, free cash flow of Rs 2,04,75,00,000. But nobody projected Year 6. Nobody asked what Sankalp would be selling then, or to whom. The figure is a first term, not a forecast, and the same assumption prices Year 7 and Year 40 in exactly the same breath. There are no years on the far side of the join at all. There is one number standing for all of them.

Where Exactly Does One End and the Other Begin?

At an instant, and the instant has no width. An instant with no width sounds pedantic until the two sides are set out. The two sides disagree about two separate things at once, and both disagreements land at the same moment.

Two assumptions change at the same instant, and a model that hides either of them has misrepresented what it did. Growth falls. Reinvestment falls. Growth and reinvestment are not two independent choices but one choice seen twice, bolted together on this forecast by the 18.00 per cent that fresh capital is assumed to earn. Take each in turn.

At the Join, Does Growth Glide Down or Drop 2.14 Points?

A fixed Rs 1,20,00,00,000 lands each year on a base that keeps getting bigger, so revenue growth falls smoothly across the five explicit years: 10.00 per cent, then 9.09, then 8.33, 7.69 and 7.14. The fall is a glide, and a glide looks like the sort of thing that would carry on gliding. It does not. At the join the rate drops to 5.00 per cent and stays there, a fall of 2.14 points with nothing in between.

The step is not a defect somebody forgot to smooth; it is the defining feature of a two-stage shape. A model with one explicit stage and one terminal stage has exactly one boundary, and an assumption that changes at a boundary changes at an instant. The step could be removed by adding a stage that carries the rate down over several years, but that is a different model with different machinery, and what an extra stage is for and what it costs is covered separately. The point held here is only that the step must stay visible rather than get buried: a reader who cannot see it cannot ask whether 5.00 per cent forever is the right thing to step down to.

Why Does Reinvestment Drop 9.26 Points at the Same Instant?

The second step is larger than the first and almost nobody looks for it. In Year 5, net new capital of Rs 1,00,00,00,000 goes back into the plant against NOPAT of Rs 2,70,00,00,000, or 37.04 per cent of profit. From Year 6 onward the model assumes 27.78 per cent of profit, forever. The reinvestment ratio drops 9.26 points at the same instant growth drops 2.14, more than four times the size of the growth step.

Growth fell, so reinvestment fell with it, and the link between them is the 18.00 per cent that fresh capital is assumed to earn. If each rupee of new capital earns 18.00 per cent, then growing at 5.00 per cent a year requires putting back 5 divided by 18 of profit, or 27.78 per cent, and not one paisa more. Asking for 7.14 per cent growth instead requires 7.14 divided by 18, and Year 5 was carrying 37.04 for exactly that reason. The company is not becoming stingy at the join. The company is being asked to buy less growth, and less growth costs less.

The link matters more than it looks. Getting it wrong is expensive in a very specific way. Carry Year 5's 37.04 per cent reinvestment into perpetuity while also assuming 5.00 per cent growth, and the business has been asked to pay for growth it is not getting. On this model that mistake produces a terminal value of Rs 25,50,00,00,000 instead of Rs 29,25,00,00,000, a difference of Rs 3,75,00,00,000. Which of the two conventions a model should carry is covered separately; what belongs here is simply that the ratio has to move when the growth rate does.

Why Does the Length of a Forecast Measure Knowledge Rather Than Time?

Now put the two sides beside each other and ask what actually separates them. The calendar does not separate them. Year 5 and Year 6 sit the same distance apart as Year 2 and Year 3. The separation is that somebody had a claim about Year 5 and had none about Year 6.

Moving the horizon is not moving a date; it is moving a declaration about what is known. This is why a rule imposed from outside can never set it. One business has an order book stretching to Year 3. Another has a plant coming on line in Year 7 that changes the shape of everything after it. Two businesses in the same trade, in the same market, in the same week can therefore honestly warrant a three year forecast and a nine year one. A house convention that says five years applies one knowledge claim to both, and no single claim can be true of both.

When Should a Forecast Stop, and What Test Answers That?

There is a usable test underneath all this, and it has a testable form. Forecast until the business is doing ordinary things at an ordinary rate of return, and stop there. Ordinary means two things at once: growing at a rate that could plausibly carry on without end, and earning a return on new capital that competition has finished pushing down. When both are true, an extra explicit year only repeats what the formula already says, so it adds nothing.

Now run the test on Sankalp and be honest about the answer. Return on invested capitalProfit from operations set against the money tied up producing it, so a business needing less capital for the same profit scores higher. is 15.00 per cent in the last completed year, on invested capital of Rs 12,00,00,00,000 against NOPAT of Rs 1,80,00,00,000. By Year 5, after five years of Rs 1,00,00,00,000 put in, invested capital is Rs 17,00,00,00,000 and NOPAT is Rs 2,70,00,00,000, so the return has risen to 15.88 per cent. The business is not converging across the forecast; it is drifting slightly further from ordinary. That is a fact about this example, and any claim that five years was therefore the right number would be a justification invented after the event.

Name that 18.00 per cent properly before going further. The whole convergence test turns on it, and it is not a claim about profitability at all. Profitability sits at 15.00 per cent of sales throughout, whichever vintage of capital produced the sales. Capital turnoverRevenue per rupee of capital in the ground. At 1.20, each rupee put in spins up one rupee and twenty paise of sales in a year. is where the two vintages part company.

Read the last column and the number stops being a number. The last column is a sentence somebody has to defend: fresh machinery will spin one and a fifth times where the installed base spins once. No evidence for that sits anywhere in this record. Anybody wanting to argue with this valuation should start there and not with the discount rate.

What Does Every Length from One Year to Five Actually Produce?

Enough principle. Here is the ladder, computed for this business at every length the record supports. At each length the same terminal build is applied to that year's NOPAT: terminal value is that year's NOPAT times 1.05, times thirteen eighteenths, divided by 0.07. The build comes to 10.8333 times NOPAT. The discount factorMultiply a future rupee by this and what comes out is what that rupee is worth on the day the valuation is made. The factor shrinks the further out the rupee sits. for that year then brings it back, at 12.00 per cent with year-end discountingA convention that books every rupee of a year as arriving at the close of the year, not spread over the twelve months. The alternative convention is settled under time and money. throughout.

And here is what each of those produces once the explicit cash flows are discounted and added.

Each cell is rounded to the nearest rupee on its own, and the four year row therefore prints an enterprise value one rupee above its two neighbours added together. Neither figure is wrong. Nor does the final digit of any cell mean anything: where four fifths of an answer falls out of a single formula, rupee precision is a display habit and not a claim about accuracy.

The ladder stops at five years, and a sixth length would need figures this forecast does not contain. Years 6 to 10 do not exist in the record, and inventing them would contradict the terminal assumption already in use. The forecast adds Rs 1,20,00,00,000 of revenue a year and the terminal period assumes 5.00 per cent growth, and those are different worlds. The honest treatment of a number nobody has is to leave it out.

Read the two columns against each other and the point is hard to miss. The terminal share falls 17.64 points across the ladder. The answer itself spans Rs 20,02,67,85,714 at one end of the ladder and Rs 21,28,13,79,094 at the other, a range of Rs 1,25,45,93,379, or 6.3 per cent. Lengthening the forecast changes where the value is recorded far more than it changes how much of it there is. A modeller who goes from three explicit years to five has moved 8.77 points of the answer out of the terminal formula and into the forecast, and has moved the answer itself by Rs 48,42,19,382, or 2.3 per cent. Five argued years are far easier to defend in a room than one formula, so the move is worth making for confidence. The move is not worth making for accuracy.

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