Capital Rationing: Choosing When There Is Not Enough Capital

Capital rationing is choosing projects under a fixed budget rather than against a hurdle rate alone. Sankalp Industrial Systems Limited, invented, has Rs 2,50,00,00,000 for the year. The mandatory effluent plant takes Rs 45,00,00,000, leaving Rs 2,05,00,00,000. Checking every feasible combination gives project 1 alone, worth Rs 34,31,00,000. Ranking by profitability index instead gives three projects worth Rs 28,95,00,000.

The awkward part of this subject is not the arithmetic, and it registers faster at home than in a board room. Start on a street. Picture a household with one salary and Rs 40,000 spare this month. The kitchen tap leaks. The scooter needs two tyres. The older child could join a coaching class that starts next week. The fridge has begun making a noise. Every one of those is worth doing. Every one of them, judged on its own, passes any sensible test that could be put to it. And all four still cannot be done. There is Rs 40,000 and there is no fifth envelope.

The shortage changes the shape of the question. When money is not scarce the question asked of each item is whether it is worth doing, and everything that answers yes gets done. When money is scarce that question stops working. The answer is yes four times over, and four yeses do not fit. A second question is forced, and it is a different shape. Which combinations of these fit inside Rs 40,000? Of the combinations that fit, the one worth the most is the answer. The moment the money runs out, the thing being chosen stops being an item and becomes a set of items.

What is capital rationing, and why ration when the money is there?

Capital rationing is the same squeeze with a board paper attached. A company writes down a total it will invest this year, and every proposal has to live inside that total. The total is called the capital budgetThe total a board approves for investment in a period, fixed in advance of the choosing., and once it is fixed it does something no hurdle rate does: it makes the projects compete with each other rather than with a rate. A project that clears the hurdle comfortably can still be turned down, not because anybody doubts it, but because something else fits better with the money available.

There are two ways a company arrives at that limit, and they look identical from inside the building. The first is hard rationingThe money genuinely cannot be raised on any terms the company would accept.. The money genuinely is not available. Lenders will not lend on terms anybody would sign, shareholders will not subscribe at a price anybody would accept, and the limit is a fact about the outside world. The second is soft rationingA limit the company sets on itself while the money is still available to raise.. The money is available and the company has decided not to take it. Only one of those two is a decision, and it is the second one. Soft rationing is the only one worth arguing about.

Why would a board hold a limit it could lift? Three reasons come up again and again, and none of them is about money. The first is attention. A company that approves nine projects at once is asking the same handful of senior people to supervise nine things, and supervision does not scale the way capital does. The second is execution capacity: engineers, commissioning teams and the plant floor itself are all finite, and a project approved into a queue is not a project running. The third is the most interesting. Every project on the list arrives with a forecast, and every forecast is written by somebody who wants the project approved. A fixed budget is a blunt way of taxing optimism. The limit forces the proposals to compete, and competition between forecasts is the only pressure most companies can actually apply to them.

What changes about choosing a project once the budget binds?

Sankalp Industrial Systems Limited, invented, makes industrial valves, precision castings and the aftermarket parts and service that go with them. Its board has set a capital budget of Rs 2,50,00,00,000 for the year. Five projects are in front of it, and all five have already been appraised at the company assumed cost of capital of 12.00 per cent. The 12.00 per cent is the hurdle rateThe return a project has to clear before it is worth doing at all, taken here as the company assumed cost of capital. every one of them was discounted at. How each of those appraisals was built is covered separately.

Two features of that table decide everything that follows. The first is at the bottom: the five outlays add to Rs 4,15,00,00,000 and the budget is Rs 2,50,00,00,000, so the list is more than half again as large as the money. The second is in the note column. Projects 1 and 2 are mutually exclusiveTwo proposals where taking one makes the other impossible, here because they need the same physical space.. The third valve line and the automation cell need the same floor of the same building, and only one of them can be built there. The exclusion is what turns a sorting exercise into a choosing exercise. It means the value of project 1 depends on what was decided about project 2.

Here is the shift in plain words. Without a budget, a project is measured against a rate, and the rate does not care how many other projects exist. Every proposal that clears 12.00 per cent gets funded, and the order in which they are considered makes no difference at all. With a budget, a project is measured against the other things the same rupees could have bought. The rate has not stopped mattering, but it has stopped being sufficient. A set now has to be named, and a set has properties that none of its members has: a total cost, a total value, and an internal consistency. Some members cannot sit beside others.

A second capital figure sits in the company forecast, and it is easy to mistake for a check on these five. The five projects are a list under consideration. The five projects are not inside the company published five year forecast. The forecast carries capital expenditure of Rs 1,34,80,00,000 in Year 1, rising to Rs 1,54,00,00,000 in Year 5 as the existing approved run rate. The project outlays and the forecast capital expenditure line are two different objects on two different bases, so neither can be added to the other and neither is a check on the other. Both are assessed against the same 12.00 per cent, and whether an approved project would be additional to that run rate or absorbed inside it is not settled by either of them.

Which claims on capital never reach the board as a project list?

Before the choosing starts, it is worth seeing how small the choosing actually is. A capital budget is not the whole of what a company puts into the ground in a year, and the part that arrives as a list of proposals with sponsors and slides is only one of three claims. The other two are real, they are large, and nobody ever votes on them.

Replacement Capital

Replacement capital is the spending that keeps the capacity the company already has. A furnace liner reaches the end of its life. A machine tool loses accuracy and has to be rebuilt. A roof leaks onto a finished goods store. None of that adds a single unit of output, and all of it has to happen for the output that exists to keep existing. The household again: replacing the tyres does not produce a second scooter, it keeps the existing one moving, and choosing not to do it is not a saving, it is a decision to stop riding.

The practical question is how much of a company spending is of that kind, and the working convention is to read depreciation as a stand in for it. Sankalp Industrial Systems Limited, invented, charges depreciation and amortisation of Rs 52,80,00,000 in Year 1 against capital expenditure of Rs 1,34,80,00,000. Read that way, roughly Rs 52,80,00,000 of the year spending is replacement capital. The company has to find that money before it has bought anything new at all. The convention is a convention and not a measurement: depreciation is an accounting charge on the cost of past assets, and what it actually costs to replace those assets today is a different number that this record does not carry. The frame of reading reinvestment as capital expenditure less depreciation plus the movement in working capital is the one set out by Koller, Goedhart and Wessels in Valuation, and by Aswath Damodaran in his valuation material.

Growth Capital vs Replacement Capital

Growth capital is what is left after replacement has been taken out, and that subtraction is the entire distinction. There is no separate measurement, no separate approval process and no line in any statement labelled with either name. There is one capital expenditure figure and one depreciation figure, and the gap between them is what a reader calls growth.

For this invented company in Year 1 the arithmetic is Rs 1,34,80,00,000 less Rs 52,80,00,000, leaving Rs 82,00,00,000. The Rs 82,00,00,000 of growth capital is the part that buys capacity the business does not have yet, and it is the only part of the capital expenditure line that behaves anything like a project list. The distinction matters here for one blunt reason: replacement capital is not really discretionary, so a budget that binds bites entirely on the growth half. Cut the budget and the furnace liner still has to be replaced. The third valve line is what gets cut.

Net Working Capital

The third claim is the one nobody proposes. Net working capital is receivables plus inventory less payables, the money tied up in simply running the business, and it grows when the business grows. As more valves are sold, more castings sit on the shop floor and more customers take longer to pay. Working capital is not a project. Nobody presents slides for it. The growth in it arrives as a movement in a cash flow statement after the fact.

Sankalp Industrial Systems Limited, invented, holds net working capital at 15.0 per cent of revenue and adds Rs 18,00,00,000 of revenue growth each year in the forecast, so the movement is Rs 18,00,00,000 in every one of the five years. Put the three claims together and the plan for Year 1 is Rs 52,80,00,000 of replacement, Rs 82,00,00,000 of growth and Rs 18,00,00,000 of working capital. The three come to Rs 1,52,80,00,000 of gross claims and, once depreciation is netted off, Rs 1,00,00,00,000 of net new invested capital. Only the Rs 82,00,00,000 of growth capital ever reaches a board as something to vote on, so a budget argument covers roughly half of the money and none of the people in it usually say so. The financing of the working capital cycle itself is covered separately, and so is the accounting for it.

What does a mandatory project do to the money that is left?

Project 5 is the effluent treatment plant. The plant costs Rs 45,00,00,000 and saves Rs 5,00,00,000 a year of operating cost for ten years, and discounted at 12.00 per cent that comes to a net present value of minus Rs 16,75,00,000. The plant never pays back on a discounted basis. On every rule taught for choosing between projects it is a reject, and it is going to be built.

The plant is going to be built because it is a mandatory projectOne that has to be done for the business to keep operating at all, whatever its own value comes to. under the plant consent to operate. The alternative to spending Rs 45,00,00,000 is not keeping Rs 45,00,00,000. The alternative is not running the plant at all, and that removes every rupee of revenue the plant produces and every project that depends on it. Asking whether a mandatory item clears the hurdle rate compares the project against a state of the world that is not on offer. The answer comes back clean, defensible and completely useless.

The right question about project 5 is narrower and much more useful. Which of the ways of complying that are actually available costs least? The comparison between compliance routes is a real one with real alternatives in it, and the answer to it is a number somebody can act on. The minus Rs 16,75,00,000 is the honest price of compliance and should be visible rather than buried. The number is not a decision variable.

The mandatory item does something simple and severe to everything else. The plant takes Rs 45,00,00,000 off the top. The budget of Rs 2,50,00,00,000 becomes Rs 2,05,00,00,000, and every combination considered from here has to fit inside Rs 2,05,00,00,000. One item that nobody chose has removed eighteen per cent of the money before the choosing began.

How is the best set found inside what is left?

By listing every set that fits and adding up what each one is worth. That is it. The method is called enumerationListing every combination that fits the budget and taking whichever one is worth the most.. Enumeration feels too simple to be a technique, and that is precisely why it gets skipped in favour of something that looks more like analysis. Four discretionary projects give sixteen possible sets including the empty one. Both project 1 and project 2 cannot be built, so strike out the four sets that contain the pair. Strike out the ones that cost more than Rs 2,05,00,00,000. Nine sets survive, and one of them is the answer.

Read the last row. The best set inside Rs 2,05,00,00,000 is project 1 on its own, worth Rs 34,31,00,000, and it hands Rs 5,00,00,000 of the budget back unspent. Two combinations would have beaten it and neither fits: projects 1 and 3 would be worth Rs 40,76,00,000 but cost Rs 2,30,00,00,000, and projects 1 and 4 would be worth Rs 34,71,00,000 but cost Rs 2,90,00,00,000. Both are out of reach by a margin the budget cannot close.

Two things make enumeration the right tool here rather than a lazy one. The first is that it is exact. Enumeration is not an approximation of the answer. Once every combination has been checked there is nothing left to check, so enumeration is the answer. The second is that with five projects it is trivial. Sixteen sets, minus the impossible and the unaffordable, leaves nine rows anybody can write on one side of paper in ten minutes. Enumeration stops being practical when the list is long. The number of sets doubles with every project added, and at thirty projects the count runs past a billion. A long list is the case a ranking rule exists for, and five projects is not that case.

What does the profitability index measure, and when is it a rule?

The profitability index is the present value of what a project brings in divided by what it costs. Project 2 brings in about Rs 72,09,55,000 of present value, rounded to the nearest thousand rupees, for Rs 50,00,00,000 of outlay. The division gives 1.4419. The index is a sensible measure and it answers a sensible question: how much value does a project produce per rupee of the budget it consumes? Under a budget that question sounds exactly like the right one. The index is therefore reached for at precisely the moment it is least safe.

Look at what the picture makes obvious. Project 2 sits on the steepest line, so it has the highest index. Project 1 sits furthest to the right and highest up, so it produces the most value and consumes the most budget. The index ranks by slope. The budget constrains along the bottom. A ranking by slope answers which project is most efficient per rupee. Efficiency per rupee picks the same set as a budget limit only when two specific conditions hold.

The first condition is that projects are divisible. If any fraction of a project could be bought for that fraction of its value, then spending the last rupees on a part of the highest ranked remaining project would always be optimal, and working down the index order until the money runs out would be exactly right. The second is that projects are independent. Taking one does not remove another from the list. Where both hold, ranking by the index is not a heuristic, it is a proof. Where either fails it is a guess wearing the clothes of a rule.

Neither holds here. The projects are indivisibleA project is taken whole or not at all, so there is no such thing as buying three quarters of one.: a third valve line is a building with machines in it, and three quarters of one produces nothing. And projects 1 and 2 are mutually exclusive by construction. So the index is not wrong as a measure of anything. The index is being used outside the conditions that make it a rule. The fault is a different one and much harder to notice because the arithmetic never misbehaves.

Where does the ranking rule fail, and what does it cost?

The fault is at step one and nowhere else. Taking project 2 first removes project 1 for two separate reasons, and each maps onto one of the two conditions the index quietly assumed. Independence fails: the two need the same floor, so approving the automation cell means the third valve line cannot be built at all. Divisibility fails: Rs 50,00,00,000 spent leaves Rs 1,55,00,00,000. The remainder cannot buy a Rs 2,00,00,00,000 line, and cannot buy three quarters of one either. Project 1 was the largest single source of value on the list, and the rule discarded it in its first move without ever comparing it to anything.

The one-at-a-time procedure is why the failure is so hard to catch by review. A reviewer reads the ranking and it is correctly computed. Reads the picks and they follow the ranking. Reads the totals and they add up. Every line is right. The error is not in a line, it is in the choice of a procedure that looks at one project at a time, applied to a problem where the projects are not independent of one another. A rule that can only see one item cannot see an exclusion between two, and it will never report that it could not see it.

Notice also what the leftover money does to the intuition. The index answer returns Rs 35,00,00,000 and the enumerated answer returns Rs 5,00,00,000, and a reader who has absorbed the idea that a budget should be used will reach for the fuller one. The instinct to spend the budget is wrong in both directions. Unspent budget is not a cost, and spending a budget is not an achievement. A set that spends everything and returns Rs 22,50,00,000 is worse than a set that spends half and returns Rs 34,31,00,000. The measure is the value of the set. How full the budget looks is information about the shape of the list, not a score.

What is one more crore of budget worth?

Almost always nothing, and occasionally an enormous amount. The value of an extra crore is the least intuitive quantity in capital rationing, and the easiest to see once it is drawn. A budget feels like a dial: turn it up a little and get a little more. A budget is not a dial. A budget is a staircase, and the height of each step is set by the size of the project it makes affordable rather than by the size of the increase.

Walk the steps. Below Rs 75,00,00,000 nothing beyond the mandatory item is affordable and the discretionary value is Rs 0. At Rs 75,00,00,000 project 3 comes into reach and the answer jumps to Rs 6,45,00,000. At Rs 95,00,00,000 project 2 becomes affordable and the answer jumps to Rs 22,10,00,000. At Rs 1,25,00,00,000 both fit together at Rs 28,55,00,000. Then a long flat stretch of ninety crore rupees of budget that buys nothing whatever, until Rs 2,15,00,00,000 makes projects 2, 3 and 4 fit for Rs 28,95,00,000, a step of only Rs 40,00,000 for ninety crore rupees of extra budget. Then at Rs 2,45,00,00,000 project 1 becomes affordable on its own and the answer jumps from Rs 28,95,00,000 to Rs 34,31,00,000, so one crore rupees of budget buys Rs 5,36,00,000 of value at that single step and nothing at all on either side of it.

The staircase is the discontinuity, and it has a practical edge. If somebody asks what an extra crore of capital is worth to this invented company this year, there is no general answer. There is only an answer at a particular budget. At Rs 2,44,00,00,000 it is worth Rs 5,36,00,000. At Rs 2,15,00,00,000 it is worth almost nothing. At Rs 2,50,00,00,000, where the board actually set it, Rs 5,00,00,000 of the budget is already going unspent, so the next crore is worth nothing at all. Whether the company should raise more money so that the limit binds less tightly is a question about the funding mix and is covered separately.

Who outside a board room ever needs this?