Project Appraisal: Five Projects on Five Measures at Once

One calculator puts all five of Sankalp's numbered projects through all five appraisal measures at the same time, and the one number every measure depends on can be moved. At the company's own 12.00 per cent, four of the five clear. At 22.00 per cent only the automation cell is still standing. Three of the five columns move with the rate; two of them never move at all.

A grid like this stays honest rather than merely crowded only when very little sits underneath it. Each of the five projects on Sankalp Industrial Systems Limited's list is two numbers and a year count. There is an outlayDay one cash, handed over before anything has been produced. Each project below has exactly one, and it is the figure the four measured columns are compared against. at time zero, and there is a level annual amountSame figure, every year, for a stated number of years. Nothing steps up and nothing tails off. A single division can therefore stand in for a whole cash schedule. arriving at the end of each year until the project's life runs out. Twenty five cells of appraisal come out of ten numbers and one rate. So when two cells disagree, the disagreement cannot be about the facts. The disagreement has to be about the question each cell answers.

What is on the sheet these five projects arrive on?

Sankalp's engineering group has put five things forward. A third valve line, an automation cell for the machining shop, a tooling upgrade, a regional warehouse, and an effluent treatment plant at the main works. Every one of them has been reduced to the same shape before it reaches the appraisal desk, and that reduction is deliberate: it is what lets five unlike things be compared at all.

The reduction costs detail and buys comparability, and on this list it is a fair trade. A warehouse and a treatment plant have almost nothing in common as engineering. As cash they have exactly two features each, and those two features are enough to answer every question the five columns ask. Tax has already been taken out of all five sets of flows, at an effective 25.0 per cent that Sankalp assumes about itself. The 25.0 per cent is an assumption the company makes about its own tax position rather than a rate any authority has set.

The reduction throws four things away, and a reader who cannot name them will start trusting the grid further than it deserves. A valve line does not run at full output from its first month. A warehouse still has a building at the end of year ten, and the sheet gives it a value of nothing. The treatment plant's savings would drift with whatever the works is treating. Timing inside a year is gone as well: every rupee is placed at a year end whether it arrives in April or in March. None of that is on the sheet.

Keeping it off the sheet is a decision rather than an oversight. A first cut earns its place by being uniform. Five projects reduced the same way can be argued about in one room; five projects each described in its own engineering language cannot be compared at all, and the argument becomes a contest of whoever wrote the most confident paper. When a project survives this cut and the sum involved gets large enough, somebody goes back and puts the ramp, the residual and the seasonality in. Until that happens, an outlay and a level amount over a stated life is what the appraisal desk holds, and it is enough to answer every question the five columns ask.

The rate that all ten of those numbers meet is Sankalp's own 12.00 per cent. The figure is the company's weighted average cost of capitalBlended cost of the money a company runs on, shareholders and lenders together, each weighted by how much of the total it supplies. Building one from its inputs is a separate subject., and assembling one takes three ingredients: what shareholders expect, what lenders charge once tax relief has been counted, and how much of the total each side supplies. Assembling one is worked through under the cost of capital itself. Here the rate arrives as a given, in the same way an engineer receives a design load rather than deriving it, and it is used as the hurdle rateNothing gets funded unless it clears this figure. Each company sets its own, and where a particular one comes from is settled elsewhere; here it simply arrives ready made. for the whole sheet.

What does the grid say at the company's own 12.00 per cent?

Here is the whole thing, every cell computed from the ten inputs above and the 12.00 per cent rate. Read it as an instrument panel rather than as a verdict.

Four of the five clear. The fifth does not, and it is going to be built anyway. The grid has no column for that, and the reason is taken up below. Every figure in that table except one is already on the record. The exception is project 5's index of 0.6278, which had to be worked out: ten years of Rs 5,00,00,000 discounted at 12.00 per cent is worth Rs 28,25,11,151 today, and dividing that by the Rs 45,00,00,000 outlay gives 0.6278. The same present value, minus the outlay, gives the minus Rs 16,74,88,849 in the value column, so the two cells foot against each other.

Read down three of the columns in turn and three orderings come out. The value column ranks the four clearing projects 1, 2, 3, 4. The return column ranks them 2, 3, 1, 4. The index column ranks them 2, 3, 1, 4 as well. Two of those orderings put a different project at the top, and both are correct answers to questions that happen to be different. The value column is answering how many rupees of surplus a project adds. The other two are answering how hard each rupee committed is working. A big project can add more rupees while working each rupee less hard, and here one does.

The swap between those two orderings turns an academic difference into a live one. Projects 1 and 2 are mutually exclusiveTwo proposals that cannot both happen, usually because they want the same thing: one floor, one machine, one licence. Approving either kills the other.: one shed floor has been earmarked, and both proposals want it. Projects 3 and 4 are independent of everything else, so nothing about them forces a choice. Which of the two orderings should win when the pair collides is a genuine argument, and it is settled separately. The calculator marks the disagreement.

What happens to the whole list when the rate moves?

Everything above was one photograph taken at 12.00 per cent. The rate is not a fact about the projects; it is a number the company handed the appraisal desk, and it could have been different. Move it and a different photograph of the same five projects appears. A prediction is worth committing to before the control moves.

Which columns follow the slider, and which stand still?

Drag the control and three of the five columns respond: value, discounted payback and the index. Two do not move at all. Payback and the return column both sit perfectly still, and they do it for two entirely different reasons.

Payback is the outlay divided by the yearly amount. Two hundred crore of rupees over sixty five crore is 3.08 years, and there is no rate anywhere in that division. Nothing the slider does can touch it. The return column is different: it has a rate in it, but the rate is the project's own, found by asking what discount rate would drive the value column to exactly zero. The project's own return is a property of the ten input numbers, not of the control. So one column ignores the rate because it has none, and the other ignores the chosen rate because it is already using a rate of its own.

Where does each project drop out?

The count behaves in a way a reader rarely expects. Projects do not fade. Each one clears at every rate below a single number and clears at no rate above it, and the count falls in five clean steps rather than sliding down. A project's drop-out point and its return column are the same fact read two ways, so each of those five steps sits exactly at one project's own return.

Read the same information as a count instead of as five lines and it turns into a staircase. There is one more thing worth noticing in it. The company's own 12.00 per cent and the warehouse's drop-out at 12.11 per cent are eleven basis pointsCut one percentage point into a hundred slices and each slice is one. Eleven slices make 0.11 of a point. A margin that thin is about where anyone sensible stops calling it a margin. apart. At the width of this drawing those two lines land on top of each other, and that visual collision is the most accurate thing about the warehouse: it clears, and it clears by an amount too small to survive being wrong about anything.

Why do two projects tie in two columns and differ by three times in a third?

Look again at the middle of the grid. The automation cell and the tooling upgrade print identical figures in both duration columns, 2.50 years and 3.15 years, and then print Rs 22,09,55,240 and Rs 6,44,81,922 in the value column. The tie is not a coincidence and neither is the gap.

The tie comes from a ratio. Fifty crore of rupees divided by twenty crore is 2.50, and thirty crore divided by twelve crore is also 2.50. Both duration columns depend on the outlay only through that ratio, so any two projects sharing it will print the same two durations at any rate. Two food stalls, one twice the size of the other, both take two and a half years of takings to cover what they cost to fit out. The two stalls recover at the same speed. They do not earn the same money, and no measure of speed will ever say otherwise.

The gap in the value column then comes from two separate things, and it is worth pulling them apart rather than blaming the obvious one. Scale the tooling upgrade up until its outlay matches the automation cell's Rs 50,00,00,000. Its value column then reads Rs 10,74,69,869. The step up from where it stands today is Rs 4,29,87,948, and that step is pure size. The rest of the difference is a fifth year: the automation cell receives money for five years and the tooling upgrade for four, and that extra year's Rs 20,00,00,000 discounted five times is worth Rs 11,34,85,371. Two thirds of the gap is the extra year and one third is the extra size. Each of those pieces was rounded once for printing, so adding all three lands a rupee above the automation cell's own figure and subtracting two of them can land a rupee away from the third. The unrounded values agree exactly.

Why is a project that fails every column still on the sheet?

Project 5 is the effluent treatment plant, and it is the only row on the grid that fails everything. Minus Rs 16,74,88,849 of value. A return of 1.96 per cent against a hurdle of 12.00. Nine years of plain payback, and no discounted payback at all. Once each year's figure is shrunk, its Rs 5,00,00,000 of yearly cost savingsMoney a project stops the company from spending, rather than money it brings in. Arithmetically the two are the same rupee; the only difference is the line it appears on. never catch up with the outlay. An index of 0.6278. The company gets back about 63 paise of value for every rupee it puts in.

The plant is still going ahead. The works runs under a consent to operatePermission a plant needs in order to keep running at all. The consent is granted on conditions, and losing it stops production rather than merely slowing it down. that requires the treatment plant, so the choice is not between building it and keeping the money. Compliance is not a return and cannot be made into one, so the grid has no column for a thing that simply has to happen and never will have one. A household faces the same shape when a roof leaks: nobody computes a return on the repair, they compare quotations. Comparing quotations is the honest question for project 5 too. Not whether to build it, but which of the available ways of meeting the condition costs least. The same arithmetic can run that comparison once somebody supplies a second option.

Project 5's discounted payback cell looks like an error and is not. There is a ceiling on how long a level stream can take to pay back once each year is discounted, and at 12.00 per cent it is 8.33 years, being one divided by the rate. A project whose undiscounted payback already sits past that ceiling can never reach the outlay however many years are allowed, and project 5's 9.00 years sits past it. The proof of that ceiling is given where the discounted column is built, and the calculator prints the word rather than a number.

What the control cannot show

One slider drives all five rows, and that is a real limitation rather than a design shortcut. The panel applies the same 12.00 per cent to a warehouse and to an effluent treatment plant, and there is no honest reason to think those two carry the same risk. A company that believes one project is riskier than its own average business has to say so by discounting that project at something higher than the company rate, and this panel has no way to hear it. If Sankalp's board took the view that the regional warehouse deserved 14 per cent of its own, the warehouse would stop clearing and nothing on this screen would say why. The judgement about how risky one project is lives with the people who set rates, not with the grid.

The cash figures are frozen too. Moving the control from 8 to 28 per cent leaves every one of the ten input numbers unchanged to the rupee. Holding them still is exactly right for showing what a rate does on its own and quite wrong as a picture of the world. Rates rarely move by themselves. A cost of capital rising usually travels with borrowing costing more, customers spending less carefully, and a warehouse full of stock that is suddenly harder to shift. The panel isolates one variable because isolating one variable is how its effect becomes visible, and a reader who forgets the isolation will overread the staircase.

And there is no money in the calculator. Not a rupee of budget, no limit, no total. Every row is judged on its own against the rate, and clearing a rate is not the same as being able to pay for what clears. The four rows clearing at 12.00 per cent carry Rs 3,70,00,00,000 of outlay between them, before anyone even mentions that two of them want the same floor. Affordability is a real question with a real answer, and it is settled where capital rationing is taught. The same goes for the collision between projects 1 and 2: the panel shows that the columns disagree, and which one wins is settled separately.

Who actually reads a grid like this, and what do they read first?

Nobody reads all five columns with equal attention, and which one a reader goes to first is a reliable clue to what they are worried about. A working knowledge of that is more useful than a rule about which measure is best.

A loan has an end date and a project does not care about it, so a lender reads the duration columns before anything else. If a bank has lent against the warehouse on a seven year facility, the number that matters is the 9.92 years of discounted payback, not the Rs 40,35,685 of value. The project can be worth having and still not return the money inside the tenure, and those are two different conversations with two different departments. A credit officer looking at project 5 sees a discounted payback of never and stops there; whatever the compliance argument is, it is not a repayment argument.

An equity analyst reads the value column, then immediately asks what rate produced it. The instinct to ask about the rate is right, and the control above is exactly what it is for. If the analyst thinks Sankalp's cost of capital is nearer 15 than 12 per cent, the warehouse stops clearing before the argument even starts, and the analyst has learned something about the company's approval process rather than about the warehouse.

A board reads the count. Four of five is a comfortable sentence to put in a paper, and it hides the fact that one of the four clears by eleven basis points. Asking how far the rate has to move before the count changes is a far better question than asking whether a particular project is good, and any board shown this staircase once starts asking it. A household uses the same instinct when it works out how many months of expenses its savings cover rather than whether one purchase was wise: the useful number is the one that says how much room is left.

Strip the company away and the same reading order shows up at street level. A vegetable seller with one lump of saved money and two ideas, a second cart and a cold box, will ask how long before I have my money back. A person with no cushion has to ask that question first. A shopkeeper who has been trading for twenty years and has a cushion asks the other question. How much am I better off at the end? Neither of them is being naive. The first is answering a survival question with a duration measure and the second is answering a wealth question with a value measure, and the grid is simply both of those people sitting at the same table.

The private equity habit is different again. A sponsor's binding constraint is money rather than opportunity, and a ratio is the right shape of answer when the constraint is money. So a sponsor reads the index column first. Reading the index first is correct in its own setting and it is the habit that goes wrong here, for one reason only: this sheet has two projects on it that cannot both be built, and a ranking rule looks at one project at a time. Capital rationing, where a fixed amount of money runs out before the good projects do, is a separate subject with its own answer, and this calculator has no amount of money in it at all.