Reinvestment: How Much Growth Costs the Business

Reinvestment is the capital a business puts back in to grow: capital expenditure less depreciation, plus the movement in net working capital. Sankalp Industrial Systems Limited, invented, reinvests exactly Rs 1,00,00,00,000 every forecast year, and its operating profit after tax rises exactly Rs 18,00,00,000, so new capital is assumed to earn 18.00 per cent. Growth is the reinvestment rate multiplied by that return, and here the identity holds exactly.

The awkward part of this idea is easier to feel on a pavement than in a spreadsheet, so start with a food stall. A woman sells idlis outside a bus stand. She has one steamer, one gas cylinder, one table, and she sells out by half past nine every morning. People are still queueing when the last plate goes. So she decides to grow.

What does growing actually require of her? A second steamer, and steamers cost money. A second cylinder, and cylinders cost money. Enough rice and lentils soaking overnight to feed the bigger queue, which is money sitting in a bucket rather than in her hand. And because the office next door now takes fifty plates on account and settles at month end, some of her sales stop being cash the moment she makes them. She has to find all of that before a single extra rupee of profit shows up. Nobody gave it to her. The money came out of what she had already earned.

Growth is not a decision a business announces, it is a thing a business buys, and the price is paid in cash before the growth arrives. A forecast says the same thing in its own vocabulary, on an invented company with numbers built so that a reader can check them rather than take them on trust.

What is reinvestment, and how is it different from capital expenditure?

ReinvestmentCapital put back into a business to grow it, measured net of what merely replaces existing capacity. is the capital a business puts back into itself, measured net of whatever is merely holding the existing operation together. Measuring it net does almost all of the work, and that is why reinvestment and capital expenditureCash spent on long-lived assets in a period. are not the same number and must never be treated as one.

Take Sankalp Industrial Systems Limited, invented, a listed maker of industrial valves, precision castings and the aftermarket parts and service that go with them. Its Year 1 forecast carries capital expenditure of Rs 1,34,80,00,000. The word capital sits on that line, so a reader who wants to know what growth cost the business in Year 1 reaches for it. Capital expenditure is the wrong line, and it is wrong in two directions at once.

The capital expenditure line is too big. Part of it is replacement capitalSpending that keeps existing capacity running rather than adding to it.: money spent so that what already exists carries on existing. The line is also too small. A growing business has to fund a larger pile of stock and a larger pile of unpaid customer bills, and none of that appears on a capital expenditure line anywhere. Two corrections, in opposite directions, and only after both of them are made does the figure measure what growth cost.

Why does depreciation come out before the figure means anything?

Because a large part of what a manufacturer spends every year is not buying anything new. Furnaces wear out. Machine tools lose tolerance. A casting line that ran for eleven years does not run for a twelfth simply because nobody replaced it. Spending on that is the industrial equivalent of repainting the stall and buying a new gas cylinder when the old one cracks: it keeps the business where it is, and it buys nothing that was not already there.

Sankalp Industrial Systems Limited charges depreciation and amortisation at a flat 4.0 per cent of revenue, or Rs 52,80,00,000 in Year 1 against revenue of Rs 13,20,00,00,000. Whether that charge is the right measure of physical wear is a separate argument, settled elsewhere; the forecast uses it, so the forecast is read on its own terms. The role that charge plays is what matters here. Roughly Rs 52,80,00,000 of the Rs 1,34,80,00,000 is holding the existing Rs 1,80,00,00,000 of operating profit after tax exactly where it is, and a rupee that holds profit still has not bought a rupee of growth.

So the first correction subtracts it, and what survives is growth capitalSpending that buys capacity the business does not have yet.: Rs 82,00,00,000 of genuinely new productive capacity in Year 1. Crediting the company with the whole Rs 1,34,80,00,000 says the entire spend expanded the business. The existing furnaces would then run forever and never need a rupee. No manufacturer has ever been in that position.

Why does the movement in working capital go in?

Because capital in the ground does not have to look like a machine. Net working capitalReceivables plus inventory less payables, the money tied up in running the business day to day. is receivables plus inventory less payables, and every rupee of it is money the business has parted with and not yet got back. A valve sitting in a finished goods warehouse is cash converted into steel. An invoice a customer will settle in seventy days is cash the company has earned and does not have.

The idli stall shows it more plainly than any balance sheet. To sell twice as many plates she has to soak twice as much rice the night before. The rice is bought, it is paid for, and it is not yet food and not yet money. Soaked rice is exactly as much of an investment as the second steamer, and it appears on no capital expenditure line in any accounting system on earth.

Sankalp Industrial Systems Limited holds net working capital at a flat 15.0 per cent of revenue throughout the forecast, and revenue rises by exactly Rs 1,20,00,00,000 every year. Fifteen per cent of Rs 1,20,00,00,000 is Rs 18,00,00,000, and that is the movement in every one of the five years. The working capital movement is the second component of reinvestment, it is a fifth of the total, and a reader who watches only the capital expenditure line will never see it.

What happens when the three lines are run for all five years?

Three lines, in a fixed order, and the order never changes: capital expenditure, less depreciation, plus the movement in net working capital. Run for Year 1 they give Rs 1,34,80,00,000 less Rs 52,80,00,000 plus Rs 18,00,00,000, and the answer is Rs 1,00,00,00,000. Then they run again for Year 2, and again for Year 3, and onward.

The answer is Rs 1,00,00,00,000 in every single year. The repetition is not an accident of the arithmetic, and it is what makes everything after it checkable. Capital expenditure climbs by Rs 4,80,00,000 a year and depreciation climbs by Rs 4,80,00,000 a year, so the two increases cancel exactly, and the working capital movement never moves at all. The forecast was built so that the company puts precisely the same amount of net new capital into the ground in each of the five years. Every change downstream therefore has to come from somewhere other than the reinvestment.

What does the new capital actually earn, and who checked it?

Now the other half of the question. The company put Rs 1,00,00,00,000 into the ground. What came back out? Operating profit after taxEarnings before interest and tax, taxed as though the company had no debt. runs Rs 1,80,00,00,000 in the base year and then Rs 1,98,00,00,000, Rs 2,16,00,00,000, Rs 2,34,00,00,000, Rs 2,52,00,00,000 and Rs 2,70,00,00,000 across the five forecast years. The tax used to get there is 25.0 per cent, and that is the company's own assumed effective rate, invented for this worked example rather than taken from any tax code.

The rise is Rs 18,00,00,000 a year, every year, without exception. Rs 1,00,00,00,000 goes in and Rs 18,00,00,000 of extra annual profit comes out, so the return on new invested capitalThe extra operating profit after tax a year of reinvestment produces, over the capital that produced it. is exactly 18.00 per cent in each of the five years. Meanwhile the capital already in the ground at the base year, Rs 12,00,00,00,000 of it, carries Rs 1,80,00,00,000 of operating profit after tax, or 15.00 per cent.

Eighteen against fifteen. Almost every treatment of this skips the sharpest point in the whole calculation. The eighteen-against-fifteen assumption is entirely an assumption about capital turnover and says nothing whatever about margin. The operating profit margin is a flat 15.00 per cent of revenue everywhere in this forecast, on old capital and new alike. How hard the capital works is what differs. Rs 1,00,00,00,000 of new capital is assumed to buy Rs 1,20,00,00,000 of revenue, or 1.20 turns, and 1.20 turns at a 15.00 per cent margin is Rs 18,00,00,000. The existing base carries Rs 12,00,00,00,000 of invested capital against Rs 12,00,00,00,000 of revenue, or 1.00 turn, and 1.00 turn at the same 15.00 per cent margin is a 15.00 per cent return.

Putting the gap as turnover changes what a reader can argue about. Saying that new capital earns more is a claim nobody can test. Saying that a rupee of new plant and stock will generate one rupee twenty of sales where the existing base generates one rupee is a claim an operations manager can be asked about directly. Is the new casting line faster? Does the aftermarket business tie up less inventory per rupee of sales? Both questions have answers.

And the honest position is that no evidence for the 1.20 turns is recorded anywhere. It is an assumption of the forecast, it is the single most load-bearing assumption in the whole model, and the arithmetic below asserts it rather than demonstrates it. For the 18.00 per cent to hold, the new capacity has to be genuinely more productive than the old, and nobody has produced an operating measurement showing that it is.

What is the fundamental growth equation, and does it hold here?

The fundamental growth equationGrowth equals the reinvestment rate multiplied by the return on new invested capital. says that growth equals the reinvestment rateNet reinvestment as a share of that year's operating profit after tax. multiplied by the return on new invested capital. Aswath Damodaran is the person who put this formulation at the centre of how a forecast is read, and Koller, Goedhart and Wessels build the same three quantities into one expression for growth, return on invested capital and value.

In plain words, before the formula gets used: a company grows by putting money back in. How much it grows depends on two things and only two: what share of its profit it puts back, and what a rupee put back earns. Half the profit put back at eighteen per cent grows about nine. All of it put back at nine per cent also grows about nine. Growth stops being an assumption typed into a cell and becomes an output of two other assumptions, and an output of two assumptions is exactly what makes a forecast checkable.

The reinvestment rate for Sankalp Industrial Systems Limited is the Rs 1,00,00,00,000 over each year's operating profit after tax: 50.51 per cent in Year 1, then 46.30, 42.74, 39.68 and 37.04 per cent. Now run the equation across the four year-pairs the forecast contains, and check every answer against the growth the forecast actually shows.

Anybody running the multiplication will notice something. The rates printed above are rounded to two decimal places for display. Multiplying the printed 50.51 by 18.00 gives 9.0918, not 9.0909. The agreement is exact on the unrounded reinvestment rate of 50.5050 and something, Rs 1,00,00,00,000 divided by Rs 1,98,00,00,000. Round at the end and never in the middle; the four agreements above are computed on the full values and printed to two decimals afterwards.

Why does the reinvestment rate fall while the reinvestment never moves?

Look at the sequence of rates again: 50.51, then 46.30, 42.74, 39.68 and 37.04 per cent. A reader meeting that column cold will read it as a company easing off, deciding year by year to put less back in. Reading it that way is exactly backwards, and the reason is worth stating precisely.

The reinvestment rate is a fraction. The numerator is net reinvestment, fixed at Rs 1,00,00,00,000 in every single year and never moving by a rupee. The denominator is that year's operating profit after tax, climbing from Rs 1,98,00,00,000 to Rs 2,70,00,00,000. A fixed numerator over a growing denominator gives a falling fraction. The fall is arithmetic, not behaviour. The company does exactly the same thing in all five years. The same Rs 1,00,00,00,000 simply becomes a smaller share of a bigger profit.

How Growth, Reinvestment and ROIC Drive Firm Value

The three quantities stop being separate facts here and become one statement. Koller, Goedhart and Wessels put growth, return on invested capital and value into a single expression precisely so that nobody can talk about one of them without the other two, and the reason is a claim that sounds strange on first hearing: growth on its own says almost nothing about whether a business is becoming more valuable.

Watch it happen on this company. Sankalp Industrial Systems Limited grows operating profit at 9.09 per cent from Year 1 to Year 2 by putting back 50.51 per cent of its profit at an assumed 18.00 per cent. Now imagine a second business, invented in the same way, growing at exactly the same 9.09 per cent but earning only 6.00 per cent on its new capital. To grow at 9.09 per cent on a 6.00 per cent return it must reinvest 9.09 divided by 6.00, or 151.52 per cent of its operating profit after tax. The second business has to put back more than it makes. Every year, it hands nothing at all to anybody with a claim on it, and it borrows or issues shares to cover the shortfall.

Two businesses, one growth rate, and they are not the same object at all. The pair that carries information is growth alongside what the capital earns, never growth by itself. A business that grows fast on a return above what its capital costs is converting reinvestment into value. A business that grows fast on a return below what its capital costs is converting reinvestment into less of it, and growing faster makes that worse rather than better.

Sankalp Industrial Systems Limited carries a weighted average cost of capital of 12.00 per cent. The 12.00 per cent is the company's own locked assumption and is used only as a reference point. How a cost of capital is built, and where each of its inputs comes from, is covered under the cost of capital.

What does reinvesting more do to this year's cash?

Reinvesting more reduces this year's cash rupee for rupee, and the whole cost of growth is that one subtraction. Free cash flow to the firmOperating profit after tax less net reinvestment. is operating profit after tax less net reinvestment. On this forecast the reinvestment is Rs 1,00,00,00,000 in every year, so the cash the business generates is simply that year's operating profit after tax less Rs 1,00,00,00,000: Rs 98,00,00,000, then Rs 1,16,00,00,000, Rs 1,34,00,00,000, Rs 1,52,00,00,000 and Rs 1,70,00,00,000.

Year 1 can also be reached the long way, and it is worth doing once so the identity is not taken on faith. Operating profit after tax of Rs 1,98,00,00,000, plus depreciation of Rs 52,80,00,000 because it never left as cash, less capital expenditure of Rs 1,34,80,00,000, less the Rs 18,00,00,000 that went into working capital. The long route gives Rs 98,00,00,000, exactly as before. The short route and the long route are the same route.

The gap between the two series is the reinvestment, and the reinvestment never moves, so both rise by exactly Rs 18,00,00,000 a year and stay Rs 1,00,00,00,000 apart in every single year. The growth in the upper line was bought with the gap. Every rupee of the Rs 18,00,00,000 that operating profit gains next year was paid for out of the Rs 1,00,00,00,000 that did not reach anybody this year. The sentence is not a metaphor. The rupees are the same rupees.

Where does this calculation go wrong in practice?

Almost never through carelessness. The mistake is made by people being careful.

What does the equation not prove?

Almost everything a reader might want it to. The equation is a consistency check and not a proof, and the distinction is not a formality.

Four exact agreements across four year-pairs prove that the forecast is internally consistent. The agreements prove that the growth line and the reinvestment line in this model are telling the same story rather than two different ones. A great many forecasts fail exactly there, with growth typed in at one rate while the capital lines quietly support a different one, so the check earns its keep.

The agreements do not prove that any of it will happen. The check catches a model whose growth and reinvestment contradict each other; it cannot catch a model where both are wrong together. If the 1.20 turns of revenue per rupee of new capital is optimistic, the reinvestment rate is right, the multiplication is right, the agreement is exact, and every growth figure in this guide is still too high. A consistent forecast built on an unsupported 18.00 per cent return on new capital is still a forecast built on an unsupported 18.00 per cent return on new capital.

So the honest summary is narrow. Reinvestment is three forecast lines, its cost falls on the current year, and a growth number can be tested against a capital plan. None of that settles whether Sankalp Industrial Systems Limited will grow at 9.09 per cent, whether Rs 1,00,00,00,000 a year is the right amount to put back, or whether the company is worth more or less than anything.