Base Case vs Bull Case vs Bear Case: What Three Answers Mean

Three cases move the same four assumptions together and produce three enterprise values for one invented manufacturer. The lowest is Rs 16,54,93,67,166, the highest Rs 26,26,89,20,908, and Rs 21,28,13,79,094 sits between them. The two distances from that middle answer are not equal, and the lowest of the three puts the most cash on the table in Year 1.

All of that rests on one difference: a single valuation shows where a model lands, and three show how steeply it moves when the assumptions move. Steepness is the only thing the extra work produces. Every other figure in the three cases was already available from the base case alone. The moment three answers exist, the reader stops asking for a value and starts asking what would have to be true, and that is a better question.

What does a second and a third valuation actually add?

Think about a household deciding whether it can carry a loan repayment. One salary is coming in, and somebody works out that the repayment fits with a little to spare. The household now has a single answer, and the answer is not wrong. But it does not say how much has to go wrong before the repayment stops fitting. Rework it on a smaller salary and rework it again on a larger one, and the household learns something the first sum could never tell it: how much room there actually is.

A valuation works the same way. A second and a third case do not improve the first answer, they measure how fragile it is. The base case for Sankalp Industrial Systems Limited, an invented manufacturer of industrial valves and precision castings, is not made more accurate by the existence of a bull case. The base case is made legible. The three cases together show that a package of four favourable assumptions lifts the answer by roughly a quarter, and that a package of four unfavourable ones takes about a fifth off it.

The three cases must therefore move the same four assumptions. If each case moved a different set, the three answers would be three unrelated sums and the distance between them would mean nothing. Here the four movers are the terminal growth rate, the earnings before interest, tax, depreciation and amortisation (EBITDA) marginTrading profit before depreciation and interest, written as a share of sales, which strips out the effect of the company simply being bigger., the revenue step and the cost of capital, and everything else is pinned down. Because they are pinned down, the gap between the answers is attributable.

A second reason has nothing to do with arithmetic and everything to do with honesty. A single figure carried to the rupee looks settled. Rs 21,28,13,79,094 has eleven digits and every one of them looks earned. Put two more answers beside it and the eleven digits stop being the point. The eleventh digit is noise sitting on top of a gap of nearly ten thousand million rupees.

What is inside each of the three cases?

Before anything is compared, all three have to be stated in full, because a comparison between two things one of which has not been defined is just an assertion. Each case names four assumptions and produces one enterprise value. A fifth assumption, what a rupee of newly invested capital earns, stays pinned at 18.00 per cent across all three, and the block further down on what is held still gives the reason.

A column of the table read downwards is a complete case. A row read across is one assumption at three settings.

The three enterprise values in the bottom row are the whole output of the exercise, and the distance between them is the only new information any of it produced. How the four settings were chosen, and why those four rather than another four, is covered separately. Here they are inputs, restated so the answers can be read.

Why is the bull case further from the base case than the bear case is?

The bull case sits Rs 4,98,75,41,814 above the base case, or 23.44 per cent of it. The bear case sits Rs 4,73,20,11,927 below, or 22.24 per cent. The two distances differ by 1.20 percentage points, and the difference is not a slip.

A perpetuity divides by the rate less the growth, and dividing is not a straight line, so equal moves in the inputs never produce equal moves in the answer. Watch the divisor. In the base case it is 12.00 less 5.00, or 7.00 percentage points. In the bull case, 11.50 less 5.50 gives 6.00. In the bear case, 12.50 less 4.00 gives 8.50. Moving from 7.00 to 6.00 shrinks the divisor by one point and lifts the quotient by about a seventh. Moving from 7.00 to 8.50 grows it by one and a half points and cuts the quotient by about a sixth. Because the same rupee change in a divisor does more damage on the way down than on the way up, the two directions were never going to match.

A model that showed perfect symmetry would be the one to check. Symmetry in the output of a non-linear expression usually means somebody has moved the assumptions until the picture looked balanced. A balanced picture built that way is a decision about presentation dressed as a result.

The spread itself needs the same care. One gap of Rs 9,71,95,53,742 separates the two ends, and it has two correct percentage forms depending on what is put underneath it.

Any percentage spread must name what it was divided by, because two people quoting one range as 59 per cent and as 37 per cent are not disagreeing about anything at all.

Can the three multiples be read straight off one another?

Each answer can be restated as a multiple of Year 0 EBITDA, and doing so is the fastest way to make a valuation portable. The base case is 7.39 times, the bull case 8.76 times and the bear case 6.13 times. Three clean figures, and the temptation is immediate: subtract the outer two and call the spread 2.63 turns.

Subtracting one multiple from another is the subtlest error in the whole comparison. Each case re-cuts the margin on the same Rs 12,00,00,00,000 of Year 0 revenue, so each case has a different Year 0 EBITDA, and the three multiples are not sitting on the same denominator. At 22.5 per cent the bear case starts from Rs 2,70,00,00,000. At 24.0 per cent the base case starts from Rs 2,88,00,00,000. At 25.0 per cent the bull case starts from Rs 3,00,00,00,000. Part of what looks like the multiple moving is the number underneath it moving.

Guessing gets the distortion backwards, so work out which way it runs. The bull case has the largest denominator, so its multiple is pulled down. The bear case has the smallest, so its multiple is pushed up. Both are squeezed toward the middle. Put both enterprise values over the shared Rs 2,88,00,00,000 and the bull case reads 9.12 times against the bear case at 5.75 times, a gap of 3.37 turns. Subtracting the two published multiples gives 2.63 turns and therefore understates the real gap by about three quarters of a turnA single step in a multiple. Six times becoming seven times counts as one step, whatever amount happens to be sitting underneath it..

Strip the valuation out and the point survives. A trader prices one stall at four times monthly takings and another at six. The difference between four and six is not a fact about stalls, so nobody can subtract four from six until somebody says what a month brings in at each stall. Four against six is a fact about two ratios with different bottoms.

Which case puts the most cash on the table in the first year?

The bear case does, and it is not close. Set the three Year 1 figures in a column and the ranking inverts.

The order of the three cases in Year 1 is the exact reverse of the order of their answers.

Extend that across the whole explicit forecast and it holds. Add the five forecast years without discounting and the bear case throws off Rs 6,90,66,66,667 of cash. The base case manages Rs 6,70,00,00,000. The bull case finishes last again at Rs 6,43,12,50,000. So the case carrying the lowest valuation generates the most cash across the five years anybody has actually written down.

The lines do eventually cross, and where they cross is worth naming. The bear case slips below the base case between Year 3 and Year 4. The bull case does not pass the base case until Year 4, and even then by Rs 25,00,000 on a figure of about Rs 1,52,00,00,000, a rounding whisker. Only in Year 5 does the bull case pull clearly ahead, at Rs 1,75,87,50,000 against Rs 1,70,00,00,000. Four of the five forecast years give the bear case more cash than the bull case, and the bull case still finishes worth Rs 9,71,95,53,742 more.

Why does growing more slowly leave more cash in hand?

The reason is mechanical, and it deserves to be walked slowly because almost every reader guesses the other way. Two lines make the figure. Start with operating profit after taxWhat the trading operation earns once tax has been taken off, counted before anybody splits it between lenders and shareholders., the amount the trading year produces. Take away the net new invested capitalMoney the business must put in this year on top of replacing what wore out, so the total capital at work climbs instead of merely holding level. the same year swallows. Growth lifts the first line. Growth also lifts the second line, and early on it lifts the second faster.

Look at Year 1 in all three cases. The bull case earns Rs 2,12,62,50,000 of profit after tax and puts Rs 1,31,25,00,000 straight back into the business, leaving Rs 81,37,50,000. The base case earns Rs 1,98,00,00,000, reinvests Rs 1,00,00,00,000 and leaves Rs 98,00,00,000. The bear case earns the least of the three at Rs 1,77,60,00,000, but it only has to put back Rs 61,66,66,667, and it leaves the most at Rs 1,15,93,33,333.

Growth is bought with cash, and the bill arrives before the benefit does. Putting Rs 1,50,00,00,000 of extra sales through a business each year takes more capacity, more stock on the shelf and more credit extended to customers than putting through Rs 80,00,00,000. Because the return earned on new capital is pinned at 18.00 per cent in all three cases, the money each case has to put in is exactly the extra profit it wants divided by that return. The bull case wants Rs 23,62,50,000 more profit each year and must find Rs 1,31,25,00,000 to get it. The bear case wants Rs 11,10,00,000 more and needs Rs 61,66,66,667.

A caterer at the edge of a wedding season feels this in the same week it happens. Take the larger booking and the deposits for vegetables, gas and hired staff go out before a single plate is served. Take the smaller booking and less goes out, so more of the month's money is still in the tin on the last day. Nobody would call the smaller booking the better business. The smaller booking is simply the one that leaves cash lying around this month.

One note on precision before moving on. The bear case reinvests Rs 61,66,66,667 a year, a recurring figure rounded to the nearest rupee, and that same rounding runs through every bear case cash flow and into its answer. The base and bull cases land on exact rupees. The last two digits of an eleven digit answer carry no information either way, and any treatment that leans on them is selling precision the arithmetic does not have.

Where does the difference between the cases actually land?

Split each answer into two blocks. The first is the present value of the five years the model actually lists, the explicit forecast periodYears a model sets out one by one. Once they run out it stops listing and folds everything afterwards into a single closing figure.. The second is the present value of everything after those five years, valued as a growing perpetuityA stream with no end date that lifts by a fixed percentage every period, valued by dividing the next period amount by the rate less that percentage. and discounted back. Every case uses year end discountingA convention treating each year of cash as though it all landed on the closing day of that year, which keeps the arithmetic tidy and understates value slightly., so the split can be read straight across.

Read the first row across and the three cases are almost the same. Rs 4,50,78,85,795, Rs 4,68,41,43,564 and Rs 4,82,57,85,681 lie within about Rs 32,00,00,000 of one another, and the order is reversed there as well. Read the second row and the three cases are barely related. The bear case finishes Rs 4,73,20,11,927 below the base case despite being Rs 14,16,42,117 ahead over the explicit five years, so the whole gap and another Rs 14,16,42,117 on top of it opened up after the forecast stopped.

The bull case tells the same story from the other side. The bull case is Rs 17,62,57,769 behind the base case across the five explicit years and finishes Rs 4,98,75,41,814 in front, all of it and more earned in the terminal block. The terminal block is what a scenario is really testing. Not the next twelve months. The shape of everything after the model stops writing years down.

How is a scenario different from a sensitivity?

A scenario and a sensitivity are two different exercises, not two sizes of the same one. A sensitivity moves one assumption and freezes everything else, and a scenario moves several together because they are believed to travel together in the world.

In the base case one thing is nudged: terminal growth, 5.00 per cent up to 5.50. Nothing else moves at all. The answer goes from Rs 21,28,13,79,094 to Rs 21,95,24,70,471, a move of Rs 67,10,91,377 and 3.15 per cent. Moving one assumption on its own is a sensitivity. Only one thing was allowed to cause the change, so the cause of the change is known precisely.

Now take the bull case. Revenue steps up, the margin widens, the cost of capital falls and terminal growth rises, all at once, and the answer is Rs 26,26,89,20,908. Four assumptions moving together is a scenario, and a scenario says something a sensitivity cannot. The same underlying conditions that lift growth also widen a margin and cheapen borrowing, so a company growing faster probably does all three at once. No single sensitivity can reach the bull case answer. Both exercises exist for precisely that reason, and neither replaces the other.

The cost of the scenario is attribution. When four things move and the answer moves Rs 4,98,75,41,814, none of that Rs 4,98,75,41,814 can be assigned to any one of the four. In the world the four rarely move alone, so the cost of the sensitivity is realism. Run both and read them for different things.

Why is the return on new capital held still in all three cases?

Every case assumes that a rupee of newly invested capital earns 18.00 per cent. The 18.00 per cent does not budge when the revenue step changes, when the margin changes or when the cost of capital changes. Holding that return still is a deliberate modelling choice, and it is the reason the three cases are readable at all.

With four assumptions moving and a fifth held still, every difference between the answers has four possible causes; let the fifth move and it has five, and no reader can attribute anything. Holding it still also does something quieter. A pinned return fixes the relationship between growth and reinvestment, so a case that grows faster is forced to pay for that growth at the same rate as the others. The bull case cannot buy its extra Rs 23,62,50,000 of annual profit cheaply. The bull case must find Rs 1,31,25,00,000 a year, and that outlay is exactly why its Year 1 cash flow is the lowest of the three.

Stated plainly, this is an assumption, not a finding. A real business does not earn a constant return on every rupee it puts in, and presenting 18.00 per cent as a property of Sankalp Industrial Systems Limited rather than as a setting inside a constructed example would be a claim with no basis.

What is a range for, once it exists?

A range is not a softer answer. A range is a different kind of answer, and in one important respect the more decisive of the two. A point estimateOne figure handed over as the answer, carrying no width around it and saying nothing about how far it would travel if an input changed. tells a reader what a model produced; a range with its assumptions printed at each end tells a reader what would have to be true for each end to hold. The second is the thing anybody can actually argue with.

So the form matters. Reported properly, the output of this exercise reads: Rs 16,54,93,67,166 to Rs 26,26,89,20,908, where the low end assumes Rs 80,00,00,000 of revenue added a year at a 22.5 per cent margin, a 12.50 per cent cost of capital and 4.00 per cent terminal growth, and the high end assumes Rs 1,50,00,00,000 at 25.0 per cent, 11.50 per cent and 5.50 per cent. Anybody reading that can disagree with a specific number instead of with a mood.

Reported badly it reads: about Rs 21,00,00,00,000, plus or minus a bit. The assumptions were the only part anybody could check, and that version has thrown them away and kept the digits, the part that never mattered.

What may anybody say about the traded figure?

Shares in Sankalp Industrial Systems Limited change hands at an enterprise value of Rs 22,40,00,00,000. Where does that fall against a range with a low end of Rs 16,54,93,67,166 and a high end of Rs 26,26,89,20,908? Between them. Falling inside the range is the whole of what the comparison establishes about the traded figure.

Three further sentences do not follow from that placement: that the company is fairly valued, that anybody agrees with the base case, or that the bull case is being priced in. A range with its assumptions named is an output of an exercise; a verdict about a price is a different claim, needing evidence of a different kind.

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