Capital Budgeting: Choosing Between Projects

Capital budgeting is how a company decides which long-lived projects to fund. Sankalp Industrial Systems Limited, invented, has five numbered projects and one hurdle rate of 12.00 per cent. Five rules score them: net present value, internal rate of return, payback, discounted payback and the profitability index. The rules agree on most projects and disagree on two, and value comes from the rupees, not the percentages.

Begin somewhere small enough to picture. A household on an ordinary street runs a tiffin service out of one kitchen. There is some money put aside, and three things it could go into. A second gas connection and a bigger cooking range would let them take on the evening orders they keep turning away. A small second-hand van would cut the delivery charges they currently pay somebody else. A water tank and a filter would stop the two days a month they lose to the supply failing, and the housing society has told them that without one they will not be allowed to keep cooking at that volume at all.

Every one of those is a different kind of decision, and none of them is the kind of decision involved in buying rice. Rice is bought weekly, in a quantity that can be changed next week, out of money that comes back within days. The range, the van and the tank are large relative to the household, they last for years, and once the money has gone into them it is very hard to get back out. The difference between spending that can be adjusted next week and spending that locks a household or a company into a shape for years is the whole reason capital budgeting exists as a separate subject.

Notice also that the three are not the same kind of item even among themselves. The range and the van can both be bought, and neither stops the other. But if the kitchen has room for only one more appliance, then the range and something else in the same corner become a straight choice. And the tank is not a choice at all: without it the business stops, so the only real question about the tank is which tank, at what price, from whom. Hold on to those three shapes. A company's project list has the same three shapes, and they decide what kind of question is being asked long before any arithmetic starts.

Sankalp Industrial Systems Limited, a listed manufacturer of industrial valves, precision castings and the aftermarket parts and service that go with them, has five numbered projects in front of its board. The shape of the problem is real even where the company is not: a list of projects, one rate to judge them all against, and constraints that no arithmetic on the list reveals.

What is capital budgeting, and what makes it different from any other spending decision?

Capital budgeting is the process by which a company decides which long-lived projects to commit money to, and in what order. Capital budgeting is one of the three decisions a company makes, and it is the one that decides what the company will physically be in five years. The other two, how the money is raised and what comes back to shareholders, are settled elsewhere and are not this subject.

Three features mark a capital projectA large, long-lived, hard-to-reverse commitment of money to an asset, as against ordinary spending that can be adjusted from one week to the next. off from ordinary spending, and any proposal can be tested against all three in about a minute.

A capital project is large relative to the company. Sankalp's third valve line asks for Rs 2,00,00,00,000 at the start. Against a business whose whole traded enterprise value is Rs 22,40,00,00,000, that is close to a tenth of the company being pointed in one direction. Nobody signs that on a purchase order. A commitment that size goes to a board, in a paper, with figures attached.

A capital project is long-lived. The cash a project brings in arrives over years, not weeks, and it arrives after the money has gone out. The valve line pays Rs 65,00,00,000 a year for five years. The regional warehouse pays for ten. The gap between the money going out and the cash coming back is exactly why a rupee arriving in Year 5 has to be treated as worth less than a rupee today, and why the whole apparatus of discounting sits under this subject rather than beside it.

A capital project is hard to reverse. This is the feature people forget, and it is the one that hurts. A wrong order of steel is a bad week. A wrong factory line is a decade of running something nobody wanted, or a sale at a loss to a buyer who wants it even less. The money in a capital project is not merely spent; it is embedded in a physical thing whose second-hand value is usually a fraction of what it cost.

The three features together give the working definition. Capital budgetingDeciding which long-lived projects a company should fund, and in what order, when the money for them is finite. is the discipline for spending that is large, slow to pay back and hard to undo, and the reason it needs a discipline at all is that ordinary judgement is calibrated for the other kind of spending. A manager who is excellent at deciding whether to hire two more people is not, by that fact, calibrated to decide whether to commit Rs 2,00,00,00,000 for five years.

Why does a company need a hurdle rate before it can appraise anything at all?

Here is the fact this entire guide rests on. A company is a pool of capital that costs something to keep. Shareholders put money in and require a return for the risk of holding it there. Lenders put money in and charge interest. Neither of them is lending free. So the money sitting in Sankalp's business is not neutral, waiting to be used: it is running a meter.

For Sankalp Industrial Systems Limited that meter runs at 12.00 per cent a year. The 12.00 per cent is the company's own weighted average cost of capital, built from a 14.00 per cent cost of equity and a 6.00 per cent after-tax cost of debt applied to weights of 75 per cent equity and 25 per cent debt. How that build works, where each input comes from and why the equity number is higher than the debt number are all covered separately. The 12.00 per cent is taken as given here, restated every time it is used, and never quietly changed.

The 12.00 per cent is the company's hurdle rateThe return a project has to beat before it is worth doing. Sankalp's is 12.00 per cent, its own weighted average cost of capital.: the rate a project has to clear before it is worth doing at all. Two things about it are commonly got wrong and both are worth being precise about.

First, it is a rate and not a target profit. A hurdle rate does not say a project must make Rs 10,00,00,000. The hurdle rate says that whatever the project makes must be enough to pay 12.00 per cent a year on the money it is using while it is using it. A project earning Rs 10,00,00,000 a year on Rs 30,00,00,000 clears easily. The same Rs 10,00,00,000 a year on Rs 300,00,00,000 does not clear at all. The rate makes those two comparable.

Second, the hurdle rate is what compensates the people who supplied the money for the risk of supplying it. The hurdle rate sits above the risk-free rate for exactly that reason. A government security pays the risk-free rate because a lender to a government carries very little chance of not being paid; an industrial valve business carries rather more. The 12.00 per cent is what that extra chance costs, expressed as an annual rate, and a project that does not beat it is a project that is destroying value while looking busy.

One practical consequence, and it is the reason project appraisal has any teeth at all. Asking whether a project will make a profit judges it against zero, and that sets a bar almost anything can step over. Judging it against 12.00 per cent sets a bar that a great many perfectly respectable proposals fail. Every rule in this guide is a different way of asking one question: does this project beat 12.00 per cent, and by how many rupees.

What are the capital budgeting decision rules, and what does each one measure?

There are five of them in common use, and Sankalp's board sees all five on every paper. The single most useful thing to notice about them is not what they say but what units they say it in. The unit reveals what question the rule was built to answer.

Read that row of units again. The units settle most of the arguments people have about these rules. One returns rupees. One returns a percentage. Two return years. One returns a bare ratio. Five different units means five different questions, so a disagreement between the rules is not a contest between a right answer and a wrong one; it is two questions being answered correctly at the same time.

Net present value: rupees added today

Net present valueThe rupees a project adds today, after discounting all the cash it will bring in and subtracting the money that goes out at the start. takes every rupee the project will bring in, discounts each one back to today at the hurdle rate, adds them up, and subtracts the money that goes out at the start. Whatever is left is what the project adds to the company in today's money.

Project 1, the third valve line, is the clean instance. An outlayThe money that goes out at the start of a project, before any of it comes back. of Rs 2,00,00,00,000 at the start, then Rs 65,00,00,000 a year for five years, all after tax at the company's own assumed effective rate of 25.0 per cent. Discount those five receipts at 12.00 per cent and they are worth Rs 2,34,31,04,532 today. Subtract the Rs 2,00,00,00,000 that went out and the project adds Rs 34,31,04,532.

The net present value is in rupees, and rupees are what the company banks. Net present value is the only one of the five measured in the unit the company actually keeps score in, and the other four defer to it whenever they disagree. A percentage cannot be spent. A number of years cannot be spent. Rs 34,31,04,532 can.

Internal rate of return: the rate that sets the value to zero

The internal rate of returnThe discount rate at which a project's net present value comes out at exactly zero. asks a different question: not how many rupees, but at what annual rate is the money inside this project growing. The internal rate of return is defined as the discount rate at which the project's net present value comes out at exactly zero, and for project 1 that rate is 18.72 per cent.

Net present value and the internal rate of return are not two calculations. The two measures are two readings off one line, and seeing that once removes most of the mystery from the pair.

Follow the line. Discount project 1's five receipts at nothing at all and it is worth Rs 1,25,00,00,000, being the plain sum of the receipts less the outlay. Charge it 12.00 per cent and it is worth Rs 34,31,04,532. Keep raising the rate and the value keeps falling. A higher rate punishes money that arrives later, and every rupee of this project arrives later. At 18.72 per cent the line touches zero. Push past that and the project is worth less than nothing.

So the internal rate of return is not an extra fact about the project; it is the horizontal position of one specific point on the same curve the net present value is read off. That is why the two rules can never disagree about a single project taken on its own. If the curve is above zero at 12.00 per cent, then the point where it crosses zero must lie to the right of 12.00 per cent. Saying that is the same as saying the internal rate of return exceeds the hurdle. The two statements are one statement.

The reason a percentage feels more comparable than it is deserves a sentence of its own. A rate strips out size. Told that one project earns 28.65 per cent and another 18.72 per cent, almost everybody ranks the first ahead of the second. Percentages invite exactly that. But a percentage says nothing whatever about the size of the base it is a percentage of, and a lower rate on a much larger base can bank many more rupees. Scale is the hinge of the disagreement between the two rules.

Payback and discounted payback: how long the money is out

The payback periodHow many years pass before the outlay has come back, with no discounting applied at all. asks the simplest question anyone asks about money they have handed over: when do I get it back. For project 1, Rs 2,00,00,00,000 out and Rs 65,00,00,000 a year in means the outlay is recovered part way through the fourth year, at 3.08 years.

The discounted payback periodHow many years pass before the outlay has come back, once each year of cash has been discounted to today's money first. asks the same question but discounts each year's cash first, so it is asking when the outlay comes back in today's money rather than in face value. For project 1 that pushes the answer out from 3.08 years to 4.07 years. The later receipts are worth less once they are charged 12.00 per cent for the wait.

Both are useful and neither is a measure of worth. Speed and worth are different questions, and a project can come back quickly and still be small, or come back slowly and still be the most valuable thing on the list. A payback figure also says nothing at all about what happens after the break even year, which for a ten year project is most of its life. Both measures are covered separately.

The profitability index: value per rupee of outlay

The profitability indexThe present value of everything a project brings in, divided by the money that goes out at the start. divides the present value of everything coming in by the money going out. For project 1 that is Rs 2,34,31,04,532 over Rs 2,00,00,00,000, or 1.1716. Read it as rupees of present value per rupee of outlay: every rupee committed buys about Rs 1.17 of value in today's money.

Anything above 1.0000 is the same statement as a positive net present value, so as a straight accept or reject test it adds nothing the first rule does not already give. The profitability index earns its place in exactly one situation. Money runs short before the projects worth doing run out, and the question becomes how to get the most value out of a fixed sum. Capital rationing, and the ranking rule that goes with it, are covered separately.

What do the five rules say about Sankalp's own five projects?

Here is the whole list, restated from the invented company's own record and not recomputed to a different answer. Every project is discounted at the company's own 12.00 per cent hurdle rate. Every cash flow is after tax at the company's own assumed effective rate of 25.0 per cent. Cash arrives at the end of each year, and year end discounting is used throughout.

Two notes on precision before anything is read off that table. Both matter and neither is a defect. Every figure above is printed rounded for display, and every derived figure here is computed on the unrounded value and rounded only at the end. The company's own record carries the same five values in crore, as Rs 34.31 crore, Rs 22.10 crore, Rs 6.45 crore, Rs 0.40 crore and minus Rs 16.75 crore, and those are the rupee figures above rounded to the nearest lakh. Rebuilding a rupee figure by multiplying a crore figure back out gives a slightly different answer, so it is not done anywhere here.

The second note is about project 4 specifically. Project 4's internal rate of return prints as 12.11 per cent against a 12.00 per cent hurdle, or eleven basis points of clearance, and that is how the record states it. Carried unrounded the rate is 12.1094 per cent, so the true clearance is 10.94 basis points. Both are right, and which one is in use is always stated. The difference is not worth chasing. On a project this marginal the third decimal of the hurdle rate itself is doing more work than the third decimal of the answer.

Now read across. Four of the five clear the bar and the two headline rules agree on every single project taken on its own. Projects 1, 2, 3 and 4 each have a positive net present value and an internal rate of return above 12.00 per cent. Project 5 has neither. There is no project on this list where one of the two says accept and the other says reject, and that is not luck. Every one of these five is a single outlay followed by cash coming in and nothing else. For that shape the two rules always return the same verdict, and the curve above showed why they must: the two are readings of one line.

The picture is doing something the table cannot. On one honest linear scale, project 4's Rs 40,35,685 is a hairline, and that hairline is the finding rather than a drawing problem. Project 1 is worth 85 times what project 4 is worth. When a proposal clears by that little, the answer stops depending on the project and starts depending on whether the 12.00 per cent estimate is itself right, and no rule on the list can settle that.

The other thing worth seeing is that outlay and value are two genuinely different axes, and the project that sits highest on one is not the project that sits highest on the other.

Project 2 costs a quarter of what project 1 costs and is worth about two thirds as much. Project 3 is the smallest thing on the list and is worth more than project 4, at a third of project 4's outlay. Project 5 is the only one below the line. There is no rule anywhere in this subject for reading value off size, and a list where the biggest project happened to be the most valuable would be a coincidence rather than a pattern.

Which are the mutually exclusive projects on this list, and what does that change?

Everything so far has treated the five as if they were five separate questions. The five are not independent of one another. A list of projects has a shape before it has any numbers, and that shape decides what kind of decision is being made.

Two projects are mutually exclusiveTwo projects where taking one makes the other impossible, usually because they need the same space, the same team or the same permission. when taking one makes the other impossible. Sankalp's projects 1 and 2 are exactly that: 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. Nothing in either appraisal says so. Both come out positive, both clear the hurdle comfortably, and the constraint lives in the building rather than in the arithmetic.

The shared floor changes the question being asked. For an independent projectA project whose acceptance neither requires nor prevents any other project on the list. such as project 3 or project 4, the question is a test: does this clear 12.00 per cent, yes or no, and the answer for one has nothing to do with the answer for another. For a mutually exclusive pair the question is a choice: which of these two, given that both are not available. A test needs only a bar; a choice needs a ranking, and ranking is the only place in this whole subject where the rules can fall into opposite orders.

The household makes the difference easy to feel again. If the tiffin household has room and money for both the range and the van, then each is judged on its own and both can be bought. If the corner of the kitchen holds one appliance, then the range and the second refrigerator become a choice, and now somebody has to say which is better rather than whether each is good. The arithmetic did not change. The room did.

What does a company do about a project that has to be built whatever its value?

Project 5 is the effluent treatment plant. Rs 45,00,00,000 out, Rs 5,00,00,000 a year of cost savings for ten years. Discount those savings at 12.00 per cent and they are worth Rs 28,25,11,151, so the project has a net present value of minus Rs 16,74,88,849 and an internal rate of return of 1.96 per cent against a 12.00 per cent bar. The plant never pays back on a discounted basis at all: the discounted savings across its whole ten year life come to less than the money that went out at the start, so there is no year in which the line crosses.

By every rule set out here it fails, and it is built anyway. Project 5 is a mandatory projectOne that must be done for the business to keep operating at all, whatever an appraisal says about its value., required under the plant's own consent to operate. And here is where a good analyst goes wrong in an interesting way, by running the correct calculation on the wrong comparison.

The usual rule compares building the plant with keeping the money, and that is not the comparison anybody at this company faces. The alternative to spending Rs 45,00,00,000 on an effluent plant is not having Rs 45,00,00,000. The alternative is not being allowed to run the plant that produces the valves. Once the alternative is stated correctly, the negative figure stops being a verdict and becomes a price: this is what continuing to operate costs.

The remaining question is real but different. The board is not choosing whether to comply. The board is choosing which way of complying costs least, and that is a comparison between compliance routes rather than between a project and nothing. The comparison needs a costed quotation for each compliance route, and none is priced in this record. Naming the right question is itself more than the appraisal rules on their own supply.

How does approving a project change what the whole company is worth?

How Capital Budgeting Affects Long-Term Firm Value

One connection makes capital budgeting more than an internal procedure, and it is simpler than it looks. The value of a company is the value of everything it will do with its money. A project is a thing it will do with its money. So the value of the company and the value of the projects inside it are not two objects that need reconciling; they are one object counted twice.

Which gives a clean statement. Approving a project with a positive net present value moves the value of the company by that net present value, on the day it is approved, on the assumptions the appraisal was built with. Approving project 1 adds Rs 34,31,04,532 of value. Not over five years. A present value is already stated in today's money.

And now the honest part. Sankalp's traded enterprise value is Rs 22,40,00,00,000. Rs 34,31,04,532 against that is 1.53 per cent. Rs 34,31,04,532 is real money and it is not a transformation, and saying so plainly is more useful than either exaggerating it or waving it away. The largest project on the list moves a company of this size by about one and a half per cent. Capital budgeting is mostly the accumulation of decisions that size, made repeatedly, in the right direction.

One boundary travels with that figure. The five numbered projects are a list under consideration, and they do not sit inside the company's locked 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, and that is the existing approved run rate, the ordinary replacing and extending the business already does. The project list is assessed against the same 12.00 per cent hurdle the forecast is discounted at, and whether it is additional to that run rate or part of it is a question the record does not settle. The two are therefore not added together, and no value for this company after approval follows from the list.

Where the value comes from, and it is an assumption rather than a finding

Ask the awkward question. Why should any project on this list be worth anything at all? If a company could put money into new capacity and earn exactly what that money costs, every project would come out at a net present value of zero and this whole subject would be arithmetic without a purpose.

Sankalp's forecast assumes that new capital earns 18.00 per cent while the company's capital costs 12.00 per cent. The six point gap between what new capital earns and what capital costs is the entire reason any project on this list is worth anything, and it is an assumption of the forecast rather than an observed fact about the business. Nothing in the record is evidence that new valve capacity will earn more than the capacity already in the ground. The forecast simply assumes it, as forecasts do.

Saying so is not a caveat bolted on at the end. The gap is the most load-bearing assumption in the model. Every rupee of value in the table above is downstream of that gap, so a reader who accepts the arithmetic and forgets the assumption has accepted a choice as though it were a finding. Gaps like that one also tend not to last. A business earning six points above its cost of capital on new investment attracts competitors who would like some of it, and the competitive erosion of returns is covered separately.

Why can two rules rank the same pair of projects in opposite orders?

Everything above said the two headline rules agree on every project taken on its own, and that is true. Now put two of them side by side and ask which is better.

Net present value puts project 1 ahead of project 2: Rs 34,31,04,532 against Rs 22,09,55,240, a lead of Rs 12,21,49,291 computed on the unrounded pair. Internal rate of return puts project 2 ahead of project 1: 28.65 per cent against 18.72 per cent, a lead of 9.93 points. The two rankings are not two mistakes. Both are correct, and they point in opposite directions.

The cause is scale. Project 1 costs four times what project 2 costs. A high percentage return on Rs 50,00,00,000 can be worth fewer rupees than a lower percentage return on Rs 2,00,00,00,000, and rupees are what the company banks. The falling curve above made the same point, arriving from a different direction: a rate strips out the size of the base, and when the bases differ by four times, stripping out size is exactly the wrong thing to do.

Projects 1 and 2 are the mutually exclusive pair, so the disagreement matters here rather than being an academic curiosity. If they were independent the company would simply take both and no ranking would be needed. Since only one floor exists, one of the two rules has to lose.

Which one loses, and the reason it loses, is covered separately. There is a determinate answer, found by asking at what discount rate the two projects would be worth exactly the same, and that crossover rate, with the reasoning behind the choice, is covered separately. The useful part is smaller: the disagreement is to be expected rather than startling, it appears only when a ranking is forced, and it is a question about scale rather than a sign that one of the rules is broken.

How does this go wrong when the arithmetic is faultless?

What order do the four steps have to be run in?

The correction to that failure is an order of operations, and it is short enough to memorise.

Settle the structure. Which projects can coexist, which exclude each other, which one is mandatory and therefore not being chosen at all. Then settle the rate: one hurdle for the whole list, this company's own 12.00 per cent, applied consistently rather than negotiated project by project. Then appraise each project against that rate, on its own. Only then rank what is left, and only among the projects that survived the first step.

Ranking feels like analysis and structure feels like admin, so running that sequence backwards causes more capital budgeting errors than any misuse of a formula. Steps one and two also cost almost nothing. Establishing that two projects share a floor is a phone call. Establishing that the hurdle rate is 12.00 per cent is a restatement. The expensive part of the process, the appraisal, is the part that protects least when the cheap parts have been skipped.