How to Build a Valuation Sensitivity Table

A sensitivity table moves one assumption at a time and writes down what happens to the answer. A two-way table moves two of them independently and prints the grid. For Sankalp Industrial Systems Limited, an invented manufacturer, a grid built on the cost of capital and terminal growth around 12.00 per cent and 5.00 per cent shows the rate carrying 2.59 times the weight the growth rate carries.

The 2.59 is the reason to build a grid at all. One valuation is already in hand. Missing from it is any account of where that valuation came from, and a grid of twenty-five numbers, read properly, supplies one. Read improperly, the same grid supplies a valuation range that has not been earned, and an unearned range is where sensitivity tables do their damage.

What is a sensitivity table actually for?

Consider a household running on one salary of forty thousand rupees a month. Rent is fourteen thousand. Somebody asks what happens if the landlord raises the rent by two thousand. No spreadsheet is needed: two thousand less in the pocket, every month, and the answer is exactly as big as the change. Nothing else moved. School fees did not move, the salary did not move, the electricity bill did not move. The rent question is a sensitivity. Only one thing moved, so the whole of the difference belongs to that one thing.

A sensitivity table exists to attribute an answer to its assumptions, one assumption at a time. Every valuation is a machine with inputs going in and one number coming out. The number by itself tells the reader nothing about which of the inputs it is leaning on. A sensitivity table takes the machine, jams every dial except one, turns that one dial through a stated range, and records the output at each setting. The record that comes back is not a better valuation. The record is a statement about how much of the valuation was resting on that dial.

A two-way table does the same thing with two dials instead of one, and it turns them independently. Every combination of the two therefore gets its own cell. Five settings on one and five on the other give twenty-five cells. Independence between the two dials is the whole design, and it is also the source of the trouble.

How is a sensitivity different from a scenario?

Go back to the household. Somebody now asks a different question: what happens if the earner changes jobs. A job change is not one dial. A job change moves the salary, and it probably moves the commute cost, and it may move the rent because the new office is across town, and the timing of the school admission may have to shift with it. Four things move, and they move together because one event is driving all of them. Four things moving off one event is a scenario.

A sensitivity holds everything still and moves one thing, and answers a narrow question precisely; a scenario moves several things together, as they would move together in the world, and answers a broad question loosely. Neither substitutes for the other. The sensitivity shows how much of the answer is sitting on the discount rate. The scenario shows what the business would be worth if a coherent, describable state of affairs came about. A sensitivity asked to describe a state of the world cannot. Nothing in it has checked whether its settings could happen at the same time. A scenario asked which assumption is doing the work cannot. Four assumptions moved at once, and the arithmetic cannot separate them.

The reason the two get confused so reliably is that they are drawn identically. Both arrive as a rectangle of numbers with axis labels. Nothing on the face of a sensitivity grid says which of the two objects a reader is looking at. A finished table has to say so in words. Building the cases, and holding the assumptions that move together inside them, is covered separately; mixing the two in one place is the fastest way to make a reader believe a corner cell is a case.

Which two variables belong on the axes?

A two-way table has room for exactly two. Choosing them is the first real decision, and it is where most weak tables go wrong. A badly chosen axis produces a grid that looks every bit as authoritative as a good one. An axis has to pass two tests, and failing either one produces a table that looks informative and is not.

The first test is mechanical. The variable must be something the model takes in, not something the model puts out. Moving an input makes the machine genuinely run again and hand back a different answer. Moving an output changes nothing. The model never reads that figure, so a different number has simply been written down. Somebody who puts a valuation multiple on an axis of a discounted cash flow has done exactly this. The multiple is a result of the model, not a lever inside it.

The second test is about argument. The variable has to be one that two reasonable, informed people could genuinely disagree about. An assumption that nobody disputes is swept on its axis through an invented range, and the table then measures the width of one analyst's imagination rather than the width of a real disagreement. On this model the number of shares outstanding is not a candidate. The share count is counted, not estimated, and sweeping it half a point in either direction would be theatre.

Why the cost of capital and terminal growth, and what does that pair leave out?

On a discounted cash flow these two are the usual pair, and there is an arithmetic reason rather than a habit behind it. The valuation of Sankalp Industrial Systems Limited comes to Rs 2,128.14 crore at the company's own weighted average cost of capitalLenders want one return and shareholders want another. Blend those two in the proportions the money was raised in, and what falls out is the single rate a whole business gets discounted at. of 12.00 per cent with terminal growth of 5.00 per cent. Of that, Rs 468.41 crore comes from the five explicit forecast years and Rs 1,659.72 crore is the present value of the terminal valueForecasts stop. Businesses carry on. One lump figure stands in for everything the company earns from the last forecast year onward, and on most models it is the biggest single item.. The terminal block is therefore 77.99 per cent of the answer, all of it sitting beyond Year 5.

The two axes were chosen because between them they price the block that carries seventy-eight per cent of the answer, and they do not carry equal weight even there. Terminal growth reaches only the terminal block: change it and the five forecast years are untouched. Those cash flows were fixed before any perpetuity was written. The cost of capital reaches everything. Every rupee in the model, in the forecast years and in the terminal block alike, gets divided by it. The asymmetry is not an opinion about which assumption is more important. The asymmetry is a structural fact about where each one enters the arithmetic, and it is why the comparison below comes out the way it does.

A grid on two variables is silent about every other variable in the model, so say honestly what the pair leaves out. The Rs 120.00 crore of extra revenue the company adds each year is held. The EBITDA margin of 24.0 per cent is held. The reinvestment rateOut of every hundred rupees of after-tax operating profit, this is the share ploughed straight back into machines and stock instead of being left available to whoever funded the business. that follows from Rs 100.00 crore of net new invested capital a year is held. The return on new capital of 18.00 per cent is held. The five-year horizon and the year-end discountingEvery rupee a year produces is treated as turning up on that year's final day. It overstates the wait a little, it is simple, and this guide holds to it in all twenty-five cells. convention are held. A reader who takes a two-way grid as a picture of the whole uncertainty in this valuation has taken it as a picture of two assumptions out of seven.

Where does the grid get centred, and why does the centre cell matter so much?

The centre of the grid is the base case: the cost of capital the valuation was actually built on, and the terminal growth rate it was actually built on. For this company that is 12.00 per cent down the side and 5.00 per cent across the top, and the cell where they meet must read Rs 2,128.14 crore.

The centre cell is the base case by construction, so if it does not reproduce the model's own answer the grid is being generated by something other than the model and every other cell is wrong in the same unknown way. The centre cell is the cheapest check available on a sensitivity table, and it is the one people skip. Nobody feels the need to look at the one cell whose answer is already known. A table built by hand from a copied block of formulas, or built off a stale link, or built with the discounting convention accidentally switched, will still produce twenty-five plausible looking numbers. The centre cell is the only place the fault becomes visible without redoing the whole model.

To the rupee, the base cell is Rs 21,28,13,79,094. The full rupee figure is the answer carried to full precision, and the grid rounds it to Rs 2,128.14 crore, the nearest lakh. When more than three quarters of an answer is a perpetuity, the final two digits of a rupee figure tell a reader nothing whatever. The point is that the same arithmetic produced both.

How wide should the steps be, and does that choice matter?

Once the grid is centred, the next decision is how far apart the gridlines sit. The grid below steps half a percentage point on both axes. The cost of capital runs 11.00 to 13.00 per cent down the side and terminal growth runs 4.00 to 6.00 per cent across the top. Five rows, five columns, twenty-five cells.

The step size is a presentation decision that looks exactly like an analytical one, and nothing on a finished table warns the reader of that. There is no correct step size. There is a convention: the sweep should cover the range a reasonable person might defend and no more. No rule turns that sentence into a number. Half a point on a cost of capital is a common choice because a cost of capital estimated to better than half a point is being over-claimed. A quarter point makes a tight, cautious-looking grid. A full point makes a dramatic one. The model underneath is identical in all three cases and so is the centre cell.

The control below redraws the same grid at all three step sizes, and the corners travel a long way while the centre cell does not move at all.

How is each cell actually built?

Every cell in the grid is a full re-run of the model at that row's rate and that column's growth rate, and each one is built the same disciplined way. The free cash flow to the firmTake what operations earn, pay the tax, pay for the growth, and stop there. Nothing has yet gone to a lender or a shareholder, which is why the whole capital base is entitled to it. stream is unchanged at every setting: Rs 98.00, Rs 116.00, Rs 134.00, Rs 152.00 and Rs 170.00 crore across the five forecast years. The five figures get discounted at the row's rate under the year-end convention.

The terminal block is where the column does its work. The block uses the growing perpetuityPicture a payment that never stops arriving and gets slightly larger every time. One short division puts a price on the whole endless stream. form that Gordon set out, and its reinvestment rate is made to follow the growth rate of that column. Damodaran is the name that argument travels under. A company that intends to grow at 6.00 per cent forever on capital that earns 18.00 per cent has to plough back a third of its operating profit forever to pay for that growth; a company growing at 4.00 per cent has to plough back only two ninths. Making the terminal reinvestment follow the column is what stops any cell in the grid quietly assuming growth it has not paid for, and a grid built without it produces a right-hand edge that is generous by an amount nobody can see.

The rounding rule, stated once so it applies to all twenty-five

Two decimals of a crore is the nearest lakh, and every cell below is rounded once, straight from the exact enterprise value. Rounding an already rounded intermediate a second time puts a cell out by a lakh nobody can trace, so every difference and every percentage is worked out on the unrounded values first and rounded afterwards. On this particular grid the two routes happen to agree to the last digit. The agreement cannot be assumed in general: on other tables built off the same model, subtracting two printed figures and subtracting the two exact ones land a paisa apart.

What does the finished grid look like?

Rows are the weighted average cost of capital. Columns are the terminal growth rate. Every figure is an enterprise value of the operating business in rupees crore, and none of them has been bridged to an equity value. The base cell is shaded green and the four corners are shaded red, because the base can be read on its own and the corners cannot.

The centre comes first. The centre cell says Rs 2,128.14 crore, the model's own locked answer, so the grid is coming from the right machine. Every reading that follows depends on that one agreement holding.

How is the grid read honestly?

Read the row through the base and the column through the base, and read nothing else. The row and the column through the base are the only readings on the whole grid where exactly one assumption has moved. No other reading on the table is one the table can actually support.

The row through the base: what terminal growth alone is worth

Along the 12.00 per cent row, terminal growth from 4.00 to 6.00 per cent takes the answer from Rs 2,017.49 crore to Rs 2,272.83 crore. The movement is Rs 255.34 crore across two full percentage points of growth. The cost of capital never moved. Nothing in the forecast moved. So the whole of that Rs 255.34 crore belongs to terminal growth and to nothing else, and it can be said so without hedging.

The column through the base: what the rate alone is worth

Now stay on the 5.00 per cent column. The cost of capital from 11.00 to 13.00 per cent takes the answer from Rs 2,506.58 crore to Rs 1,845.06 crore, a movement of Rs 661.52 crore across the same two percentage points. Note the direction: the rate moves the answer the other way. A higher discount rate makes every future rupee worth less today, and a higher growth rate makes there be more of them.

The comparison, which is the point of the whole exercise

Two percentage points of rate is worth Rs 661.52 crore. Two percentage points of growth is worth Rs 255.34 crore. Over moves of the same size in percentage points, the rate is worth 2.59 times what the growth rate is worth on this model, and that single comparison is the most useful thing the grid produces. The comparison is also completely invisible in the corners.

Both figures are computed on the unrounded cell values; on this grid the printed cells happen to subtract to the same two answers. The ratio itself is 2.5907, printed here as 2.59, and a reader who has met it described elsewhere as roughly two and a half times is looking at the same number rounded less finely.

Be careful about what that ratio is and is not. The ratio is a fact about this model at this centre point with these steps, and not a law about discounted cash flows. The ratio comes out at 2.59 here because 77.99 per cent of the answer sits beyond Year 5, and because the rate divides both blocks while the growth rate multiplies only one of them. Change the shape of the forecast, or the horizon, or where the centre sits, and the ratio changes with it. The method is what travels between models: work the row, work the column, compare the two.

What free cross-check does the grid supply?

Sankalp Industrial Systems Limited has a traded enterprise valuePut a price on the operating business by itself, before anybody asks who paid for it. Lenders and shareholders are both looking at this same figure and both have a claim on it. of Rs 2,240.00 crore. Along the 12.00 per cent row that figure lands between two cells: the 5.50 per cent cell at Rs 2,195.25 crore and the 6.00 per cent cell at Rs 2,272.83 crore.

The grid shows where the traded figure sits, and nothing beyond that. Turning that position into a statement about the assumptions a buyer must be carrying is covered separately. Reading the position as the market being wrong, or as the model being wrong, or as anything about whether the shares are worth buying, is a conclusion the grid does not support. The grid is a set of arithmetic results with a traded number laid against it, and the honest sentence is simply that the traded figure falls between those two cells.

Why are the corners not a valuation range?

Here is the temptation. The bottom left cell reads Rs 1,773.03 crore and the top right reads Rs 2,746.04 crore. The spread is Rs 973.01 crore, or 54.88 per cent of the low corner. The two numbers look exactly like a range, both came out of a correct model, and writing the sentence takes four seconds. The sentence is wrong twice over, for two separate reasons, and the second reason is the real argument.

The first reason: nothing on the grid attached a likelihood to anything

A range implies that the ends are in some sense equally worth taking seriously. A sensitivity grid has never made that claim and cannot. A grid is twenty-five arithmetic results, each one the answer to a completely determinate question of the form: what would the model say at exactly this rate and exactly this growth. Nothing anywhere in the construction weighted one cell against another, and the centre is not more likely than the corner because it sits in the middle of a rectangle somebody chose the size of. If a reader wants a distribution, a grid is not one, and dressing a grid up as one is a claim about probability that no part of the arithmetic supports.

The second reason, and this is the one that actually settles it: the two axes are not independent

The whole design of a two-way table is that it turns the two dials independently. Turning them independently is fine as arithmetic. As a description of the world it is only fine if the two things really can move independently, and here they cannot, because both of them have inflation inside them.

A cost of capital contains the risk-free rate, and the risk-free rate contains expected inflation. A terminal growth rate stated in nominalMeasured in the rupees of the day, with inflation still sitting inside the number rather than stripped out of it. A real figure is the same measurement with inflation taken away. rupees also contains expected inflation. The top right corner pairs a cost of capital of 11.00 per cent with terminal growth of 6.00 per cent. The pairing asks inflation expectations to fall enough to take a whole point off the discount rate and to rise enough to add a whole point to nominal growth, on the same day, in the same economy. The bottom left corner asks for the mirror image of that. Neither is a state of the world anybody could stand up and describe.

Terminal growth of 5.00 per cent sits against expected inflation of 5.00 per cent on this company, so the model has already handed it nothing in real terms once Year 5 is past, and the growth axis is very nearly an inflation axis. Moving along that axis is, to a first approximation, moving expected inflation while pretending the discount rate has not noticed.

What does the step size do to a grid that has not changed?

The model now holds completely still. Same five free cash flows, same return on new capital, same horizon, same discounting convention, same centre cell of Rs 2,128.14 crore. One thing changes that is not in the model at all: how far apart the gridlines are drawn.

Same company. Same model. Same day. Same centre cell. The corner to corner spread runs from 23.73 per cent of the low corner to 169.74 per cent of it, and the only thing that changed was how far apart the gridlines were drawn. Every figure in that table is in rupees crore except the last column, and every share is measured against that row's own low corner. The low corner is the base the whole comparison is quoted on.

The step size does not feel like an assumption; it feels like formatting. An analyst can therefore produce almost any range they like from an entirely unchanged model by choosing how wide to draw the grid, and will usually do it without meaning to. The record of what changed sits in the axis labels, where nobody reads it.

What must a finished table carry beside it?

A grid on its own is an invitation to misread. Four short lines beside it close almost every route to a misreading, and the fourth is the one that does the real work.

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