Equity Research puzzles, solved step by step
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007A company has revenue of 100. Variable costs are 50% of revenue, fixed costs are 40, interest is 5 and the tax rate is 25%. Revenue rises 10%. By how much do EBIT and net income grow?Sell-side equity researchBuy-side equity research
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Revenue is up 10%. What happens to net income?
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EBIT grows 50% and net income 100%. Revenue of 110 leaves 55 after variable costs; less fixed costs of 40, EBIT is 15 against 10. Less interest of 5, pre-tax profit is 10 against 5, and after 25% tax net income is 7.5 against 3.75. Fixed costs magnify the change five times and interest doubles it again.
Why does a 10% revenue change become a 50% EBIT change?
Think of a tea stall with a fixed monthly rent. Once the rent is covered, every extra cup sold is almost pure profit, so a busy month feels far better than the extra sales alone suggest. Fixed costs do not grow with revenue, so the whole extra contribution lands in EBIT, and a thin EBIT makes that addition a large percentage. Here revenue up 10 adds 5 of contribution, and 5 on an EBIT of 10 is 50%.
Revenue rises from 100 to 110 while fixed costs stay at 40, so EBIT rises from 10 to 15; interest stays at 5, so net income rises from 3.75 to 7.5, a 100% increase from a 10% revenue gain. Why does net income grow twice as fast as EBIT?
Interest is a second fixed charge, sitting below EBIT. With interest of 5 taking half of an EBIT of 10, the next 5 of EBIT doubles pre-tax profit, and tax at a flat rate keeps that doubling intact. The shortcut: operating leverageHow much operating profit moves for a given change in revenue, driven by the share of costs that are fixed. is contribution over EBIT, 50 over 10, which is 5; financial leverage is EBIT over pre-tax profit, 10 over 5, which is 2. Together 5 x 2 = 10, and 10 x 10% = 100%.
The relationship50 contribution: revenue less variable costs 10 EBIT before the change 5 pre-tax profit before the change What it says in wordsOperating leverage times financial leverage times the revenue change gives the change in net income.The same arithmetic runs in reverse, which is the point a research analyst should add. A 10% revenue fall would halve EBIT and wipe out net income entirely. Leverage magnifies both directions, so a highly geared, high fixed cost company is the one whose earnings estimates move most on a small change in the top line. The limit of the shortcut: it holds only while costs behave as fixed, and over a few years most costs flex.
Where candidates lose it
The fast answer is 10% for everything, because it assumes every line scales with revenue. The question is built to see whether you notice which costs do not move.
The second loss is getting 50% for EBIT and stopping, forgetting that interest is a second fixed layer. Walk the income statement all the way to net income out loud.
What the interviewer asks next
- What happens to net income if revenue falls 10% instead?
- At what revenue does net income reach zero?
- How would you spot a company with high operating leverage from its annual report?
018A company's pre-tax profit is flat year on year, but its effective tax rate falls from 30% to 25%. How much does EPS grow, and should the stock's P/E multiple rise because of it?Sell-side equity researchHedge fund long/short
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By how much does EPS grow, with the share count unchanged?
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EPS grows 7.1%, and the multiple should not rise on that growth. Net income goes from 70 to 75 on flat pre-tax profit of 100. The price can reasonably rise about 7.1% at the same P/E, because each share now earns more. But the growth happens once: next year, with pre-tax profit still flat, EPS growth is zero.
Where does the 7.1% come from?
Think of a salaried employee whose tax bill falls. Take-home pay jumps once, but next year's take-home pay only grows if the salary does. A lower tax rate raises net income by the tax saved, here 5 on a base of 70, which is 7.1%, even though the business earned nothing more. Say the base out loud: people who answer 5% are measuring against pre-tax profit.
Pre-tax profit stays at 100 while tax falls from 30 to 25, so net income rises from 70 to 75, a 7.1% step in year one followed by zero growth in later years because the lower rate is already in the base. Why should the multiple stay where it is?
A P/E multiple pays for the level of earnings and for their future growth. The tax cut raises the level, so at an unchanged P/E of 20 the price rises 7.1% to match. It does not raise future growth, so a higher multiple would pay twice for the same one-off step. Re-rate to 22x on the back of 7% growth and the price would rise 17.9%, most of it paying for growth that will not repeat.
Two caveats a research analyst adds. First, ask why the rate fell: a statutory cut is durable, while a one-time credit or a shift of profit to a lower-tax region may reverse, in which case even the level change deserves a discount. Second, check whether competitors got the same cut; if they did, some of it may be passed to customers through prices. Confirm any tax rate you use against the current rules rather than memory.
Where candidates lose it
The trap is treating the EPS jump like organic growth and arguing for a higher multiple because earnings grew faster. Growth that comes from a rate change is a step, and a step is paid for once.
The second loss is answering 5%, the change in the tax rate, instead of 7.1%, the change in net income.
What the interviewer asks next
- What if the lower rate comes from a one-time tax credit?
- How would you show this in an EPS bridge from last year to this year?
- How does the answer change if the company also buys back 5% of its shares?
032A company announces a 1-for-4 rights issue at Rs 80 a share when its shares trade at Rs 120. What is the theoretical ex-rights price?Indian brokerage researchSell-side equity research
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Pick the ex-rights price before you calculate.
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Rs 112. For every four shares worth Rs 120, a holder pays Rs 80 for one new share. The five shares then hold Rs 480 of old value plus Rs 80 of new cash, Rs 560 in all, so each is worth Rs 560 divided by 5, which is Rs 112. The right to buy one new share is worth Rs 112 minus Rs 80, or Rs 32.
Why does the share price fall when nobody has lost anything?
Picture four friends who each own a Rs 120 share in a shared tiffin business. A fifth friend joins by paying only Rs 80. The business is now worth Rs 560 and there are five equal owners, so each stake is worth Rs 112. After a rights issue the old and new shares are identical, so the price has to settle at the weighted average of the old value and the new cash per share. The fall from Rs 120 to Rs 112 is not a loss to existing holders, because they were offered the cheap share too.
The relationshipN_old, N_new old shares and new shares in the ratio, 4 and 1 P the price before the issue, Rs 120 S the subscription price, Rs 80 What it says in wordsThe theoretical ex-rights price is total value after the issue divided by total shares after the issue.Four old shares at Rs 120 and one new share bought at Rs 80 pool to Rs 560 across five shares, so each share is worth Rs 112 after the issue: a weighted average, not the old price. How do you prove an existing holder is no worse off?
Take a holder of four shares. If she subscribes, she had Rs 480 of shares and Rs 80 of cash; now she has five shares at Rs 112, still Rs 560. If she sells her right instead, she keeps four shares worth Rs 448 and receives about Rs 32 for the right, still Rs 480. Her wealth is unchanged either way; only a holder who ignores the right loses its value.
The analyst's follow-through: because the issue is priced below market, it carries a bonus element. Historical EPS is restated by dividing by the factor 120 over 112, or 1.0714, so per-share figures before and after the issue compare like with like.
Where candidates lose it
The fast wrong answer is Rs 100, halfway between Rs 120 and Rs 80. It treats the ratio as one for one. The weights are the share counts, four old to one new.
The second loss is calling the fall to Rs 112 a loss to shareholders. The interviewer wants to hear that the holder who takes up or sells the right is exactly where she started.
What the interviewer asks next
- What is the value of the right attached to each old share?
- How would you restate last year's EPS of Rs 12 for this issue?
- Why might a company price a rights issue far below the market price?
043A company whose shares trade at Rs 800 announces a 1:1 bonus issue. What happens to the share price, EPS and the P/E?Indian brokerage researchSell-side equity research
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What happens to the P/E after the bonus?
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The price falls to about Rs 400, EPS halves, and the P/E is unchanged. A 1:1 bonus gives one free share for each share held, so the share count doubles while the business, its profit and its value do not change. With EPS of, say, Rs 40, EPS becomes Rs 20 and the price Rs 400, leaving the P/E at 20x and the market value at Rs 8,000 crore.
If shareholders get free shares, why are they not richer?
Cut a pizza into eight slices instead of four and nobody gets more pizza. A bonus issue changes how many slices the company is cut into, not the size of the company, so each slice is worth proportionally less. A holder of 10 shares at Rs 800 had Rs 8,000; after the bonus she has 20 shares at Rs 400, still Rs 8,000. Nothing was paid and nothing was received.
The company is still worth Rs 8,000 crore after a 1:1 bonus, cut into 20 crore shares at Rs 400 instead of 10 crore at Rs 800, so EPS halves and the P/E stays at 20x: a bonus changes the slice count, not the pie. What happens in the accounts?
The company moves an amount equal to the face value of the new shares out of reserves and into share capital. Net worth is unchanged, because money only moves between two lines inside equity. No cash moves, profit is untouched, and the dividend per share usually halves unless the board chooses to keep it, which would then be a real increase in payout.
Before After 1:1 bonus Shares, crore 10 20 Price, Rs 800 400 EPS, Rs 40 20 P/E 20x 20x Market value, Rs crore 8,000 8,000 Every per-share number halves and every whole-company number stays the same. The analyst's housekeeping: restate past EPS, dividends per share and price charts for the bonus, otherwise the history shows a false halving. Say the limitation too. In practice the price can drift from the exact half, because a lower share price can widen the pool of buyers, but that is a market effect, not a change in value.
Where candidates lose it
The common slip is calling the stock cheaper after the bonus because the price halved. The P/E is the test, and it has not moved.
The second loss is forgetting to adjust history. A model that compares this year's EPS of Rs 20 with last year's unadjusted Rs 40 shows a collapse that never happened.
What the interviewer asks next
- How is a bonus issue different from a stock split in the accounts?
- Why might a board announce a bonus issue at all?
- If the company keeps the dividend per share the same after the bonus, what has changed?
057A company has 100 crore shares trading at Rs 50 and net income of Rs 500 crore. It uses Rs 1,000 crore of cash, which was earning 6% a year before tax, to buy back shares at Rs 50. The tax rate is 25%. What happens to EPS?Sell-side equity researchBuy-side equity research
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What is the new EPS?
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EPS rises 13.75%, from Rs 5.00 to about Rs 5.69. The cash was earning 6% before tax, Rs 60 crore, or Rs 45 crore after tax, so net income falls to Rs 455 crore. Rs 1,000 crore at Rs 50 retires 20 crore shares, leaving 80 crore. Rs 455 crore over 80 crore shares is Rs 5.69. The buyback helps because the earnings yield on the shares, 10%, beats the 4.5% after-tax yield on the cash.
Why does a buyback change EPS at all?
Four friends own a small shop and split its profit. One sells out to the other three, paid from the shop's savings account. Profit dips a little, because the savings no longer earn interest, but it is now split three ways instead of four. A buyback lowers earnings by the lost return on the cash and lowers the share count by the shares retired; EPS rises when the second effect is larger. Here the share count falls 20% and net income falls only 9%.
Retiring 20 crore shares adds Rs 1.25 to EPS and the lost after-tax interest of Rs 45 crore takes back Rs 0.56, so EPS ends at Rs 5.69, because a 10% earnings yield beats a 4.5% after-tax cash yield. The relationship500 net income before the buyback, Rs crore 1,000 x 6% x (1 - 25%) the after-tax interest the cash was earning, Rs 45 crore 1,000/50 shares retired, 20 crore What it says in wordsNew EPS is net income less the lost after-tax interest, divided by the shares left after the buyback.When does a buyback lift EPS?
Compare two yields. The earnings yieldEPS divided by the share price: the earnings each rupee spent on the shares buys. It is one over the P/E. is Rs 5 over Rs 50, 10%: what each rupee spent on shares buys in earnings. The after-tax yield on cash is 6% x (1 - 25%), 4.5%: what each rupee was earning where it sat. A buyback lifts EPS whenever the earnings yield beats the after-tax yield on the cash spent, which is the same as a P/E below one over that yield. Here the break-even P/E is 22.2x, so the same buyback would leave EPS flat at a share price of about Rs 111.
Does higher EPS mean each share is worth more?
Not by itself. EPS rose 13.75%, but the company also handed out Rs 1,000 crore of cash, and a buyback at a fair price leaves each remaining share worth the same. Before, the equity was worth Rs 5,000 crore over 100 crore shares; after, Rs 4,000 crore over 80 crore shares, still Rs 50 each. Holders own a bigger slice of a company that has less cash and so carries a little more risk, which is why the P/E often slips when EPS is lifted this way.
Where candidates lose it
Candidates forget the lost interest and divide Rs 500 crore by 80 crore shares, getting Rs 6.25 and a 25% rise. The cash was earning something, and that income disappears the day the cash is spent. The tax on it matters too: the lost income is Rs 45 crore, not Rs 60 crore.
The second loss is treating the EPS jump as value created. Say that a buyback at a fair price moves value between the shareholders who sell and those who stay; the EPS rise is the mirror image of a company that now holds less cash.
What the interviewer asks next
- At what share price would this buyback leave EPS unchanged? (about Rs 111)
- The company borrows the Rs 1,000 crore at 9% instead. What happens to EPS?
- Why might the P/E fall after a buyback that lifts EPS?
068A company's net income grows 8% a year, and every year it buys back 3% of its shares. How fast does its EPS grow, and how much higher is EPS after five years?Long-only asset managementBuy-side equity research
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What is EPS growth per year?
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About 11.3% a year, and about 1.71 times after five years. EPS is net income over shares. Net income is multiplied by 1.08 each year and the share count by 0.97, so EPS is multiplied by 1.08 / 0.97 = 1.113. Over five years that compounds to about 1.71x, against 1.47x for net income alone. Adding 8% and 3% to get 11% is close, but slightly understates it.
Why divide by 0.97 rather than add 3%?
Picture a pot of profit shared among a group of friends. If the pot grows 8% and one friend in every 33 leaves each year, each remaining friend's share grows by more than 8%, and a little more than 3% on top. EPS growth is (1 + net income growth) divided by (1 - buyback rate), minus one, because the share count sits in the denominator. Dividing by 0.97 is multiplying by 1.0309, a 3.09% boost, and that compounds with the 8%: 1.08 x 1.0309 = 1.1134.
The relationship1.08 net income growth factor per year 0.97 share count factor per year after a 3% buyback g_EPS EPS growth per year What it says in wordsEPS grows by the net income growth factor divided by the share count factor, compounded each year.Net income rises from 100 to 146.9 over five years while the share count falls to 85.9, so EPS rises to 171.1 and the gap between the two lines widens every year. Is buyback-driven EPS growth as good as profit growth?
Not automatically. EPS growth from a shrinking share count is paid for with cash that could have been reinvested or paid out, and it adds value for the remaining holders only when the shares are bought below what they are worth. A company buying back stock at a high multiple can show fast EPS growth while transferring value to the shareholders who sell. The question to ask is what the cash would have earned elsewhere.
What would an analyst check before trusting the 11.3%?
Two things. First, whether the 8% net income growth already carries the cost of funding the buyback: interest lost on cash, or interest paid on new debt. Second, whether staff share awards are quietly adding shares back. What matters is the net fall in the share count: if awards add 2% a year, EPS growth drops to about 9.2%. The share count line in the notes to the accounts settles both.
Where candidates lose it
Most candidates say 11% by adding the two rates, which is close enough to pass but misses the point the interviewer is testing: growth rates in a ratio combine by multiplying and dividing, not by adding.
The costlier slip is saying 5% by subtracting, on the instinct that buying shares uses money. The buyback reduces the denominator, so it adds to EPS growth; whatever it costs in lost interest is already inside the net income figure given.
What the interviewer asks next
- Staff share awards add 2% to the share count each year. What is EPS growth now? (about 9.2%)
- Net income is flat and the company buys back 5% a year. What is EPS growth? (about 5.26%)
- Why might the P/E fall even while buybacks lift EPS growth?
082A company earns net income of Rs 200 crore on 100 crore shares. It has a Rs 300 crore convertible bond paying 8% that would convert into 15 crore shares, and the tax rate is 25%. What is diluted EPS?Sell-side equity researchBuy-side equity research
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Which diluted EPS is right?
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Diluted EPS is about Rs 1.90, against basic EPS of Rs 2.00. Assume the bond converts. Earnings rise by the after-tax interest no longer paid: Rs 300 crore at 8% is Rs 24 crore, Rs 18 crore after tax. Shares rise by 15 crore. Rs 218 crore over 115 crore shares is Rs 1.90, a dilution of 5.2%. Check first that the bond dilutes at all.
Why do earnings go up when the bond converts?
Imagine a friend who lent you money and agrees to take a share of your business instead of repayment. From that day you stop paying them interest, so your profit rises, but you now split it with one more owner. A convertible works the same way: conversion removes the coupon and adds the shares, and the if-converted methodThe standard way to include a convertible in diluted EPS: assume it converts at the start of the year, add back its after-tax interest and add the new shares. captures both. The add-back is after tax, because the interest was saving tax: Rs 24 crore of interest cost only Rs 18 crore of profit.
Assuming conversion adds Rs 18 crore of saved after-tax interest to Rs 200 crore of earnings and 15 crore shares to 100 crore, so diluted EPS is Rs 1.90 against basic Rs 2.00, and forgetting the add-back gives Rs 1.74. When would you leave the bond out altogether?
When including it would raise EPS. Work out what the bond costs per new share: Rs 18 crore of after-tax interest over 15 crore shares is Rs 1.20 a share. If that figure is below basic EPS, conversion dilutes and the bond goes in; if it is above, the bond is antidilutiveA security whose assumed conversion would increase EPS. Accounting standards exclude it from diluted EPS. and is left out. Here Rs 1.20 is below Rs 2.00, so it goes in. If the same bond converted into only 5 crore shares, its cost per share would be Rs 3.60 and it would be excluded.
The relationship200 net income, Rs crore 300 x 8% x (1 - 25%) after-tax interest saved if the bond converts, Rs 18 crore 115 existing 100 crore shares plus 15 crore from conversion What it says in wordsAssume conversion: earnings rise by the interest no longer paid, after tax, and the share count rises by the conversion shares.An analyst uses diluted EPS for valuation because a convertible that is in the money will convert, and the market prices the stock on the larger share count. The limit is that diluted EPS is a snapshot: it counts only securities that dilute at today's numbers, and a rise in the share price can bring more of them in.
Where candidates lose it
The fast wrong answer is 200 over 115, Rs 1.74: counting the new shares but forgetting that the coupon goes away. The second wrong answer adds back the full Rs 24 crore of interest instead of the Rs 18 crore after tax.
The third miss is skipping the antidilution test. Saying the per-share cost of the bond, Rs 1.20, against basic EPS of Rs 2.00 takes five seconds and shows the interviewer you know when the rule flips.
What the interviewer asks next
- The bond converts into 5 crore shares instead. What is diluted EPS?
- The company also has 10 crore options at a strike of Rs 20 with the share at Rs 40. How do they enter diluted EPS?
- Why might an analyst use diluted shares in a valuation even when the accounts show basic?
093A company reports consolidated net income of Rs 100 crore. That includes a 60% owned subsidiary which earns Rs 50 crore. What profit is attributable to the company's own shareholders?Sell-side equity researchIndian brokerage research
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What profit belongs to the parent's shareholders?
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Rs 80 crore. Consolidation adds 100% of a controlled subsidiary's profit, even though the parent owns only 60%. The outside shareholders' 40% of Rs 50 crore, Rs 20 crore, is then deducted as the non-controlling or minority interest. Rs 100 crore less Rs 20 crore leaves Rs 80 crore, which is the figure to use for EPS and P/E.
Why does consolidation count profit the parent does not own?
Think of two brothers who run a shop together, one owning 60% and the other 40%. The elder brother runs it, signs for it and reports its full takings in his family budget, then sets aside his brother's share. Accounting does the same: a parent that controls a subsidiary shows all of its revenue, costs and profit, then carves out the part owned by others as the non-controlling interestThe share of a subsidiary owned by shareholders other than the parent. Also called minority interest.. Control decides consolidation; ownership decides who keeps the profit.
The parent's own business earns Rs 50 crore and consolidation adds all Rs 50 crore of the 60% owned subsidiary to reach Rs 100 crore, then deducts the outside owners' 40%, Rs 20 crore, leaving Rs 80 crore for the parent's shareholders. How do you check the answer another way?
Build it from the parent's side. The parent's own business earns Rs 100 crore less the subsidiary's Rs 50 crore, which is Rs 50 crore. Add its 60% share of the subsidiary's Rs 50 crore, Rs 30 crore, and you reach the same Rs 80 crore. Two routes that agree are what the interviewer wants to hear, and the second route also shows you which business drives the parent's profit.
What goes wrong if you use the Rs 100 crore?
Every per-share number is overstated. If the company is worth Rs 1,200 crore, the P/E on Rs 100 crore is 12x, but on the Rs 80 crore that shareholders actually own it is 15x. Using consolidated profit makes the stock look 20% cheaper than it is. The same logic runs through enterprise value: EBITDA includes all of the subsidiary, so EV must add the value of the minority stake to stay consistent. Indian groups with listed subsidiaries make this a frequent test.
Where candidates lose it
Candidates either take the Rs 100 crore as it stands or subtract the whole subsidiary and answer Rs 50 crore. The first ignores the outside owners; the second ignores the parent's 60% share.
The quieter miss is doing the profit correctly and then forgetting the knock-on to P/E and EV/EBITDA. Name both, because the interviewer usually asks next.
What the interviewer asks next
- Why must enterprise value add minority interest when EBITDA is consolidated?
- If the parent owned 40% with no control, how would the subsidiary appear instead?
- The subsidiary is listed and worth Rs 900 crore. How would you value the parent?
100A company starts its April to March financial year with 100 crore shares and issues 20 crore new shares on 1 October. Net income for the year is Rs 330 crore. What is EPS?Indian brokerage researchResearch KPO and GCC
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Which share count goes under the Rs 330 crore?
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Rs 3.00, on 110 crore weighted average shares. The 100 crore opening shares count for the full year. The 20 crore new shares existed only from 1 October, half the year, so they count as 10 crore. Rs 330 crore over 110 crore is Rs 3.00. Dividing by the year-end 120 crore would understate EPS at Rs 2.75.
Why weight the shares by time?
A flat shared by two people for six months and three people for the next six has housed two and a half people on average over the year, and splitting the annual electricity bill by three would overcharge the one who arrived late. EPS divides a full year's profit by the shares that were outstanding while it was earned, so shares issued mid-year count only for the part of the year they existed. The money raised on 1 October only helped earn profit in the second half.
The company had 100 crore shares from April to September and 120 crore from October to March, a time-weighted average of 110 crore, so Rs 330 crore of net income gives EPS of Rs 3.00. The relationshipN bar the weighted average number of shares, crore 6/12 the share of the year the new shares were outstanding 330 net income for the year, Rs crore What it says in wordsCount each share for the fraction of the year it existed, then divide the year's profit by that average.When is the time weighting not used?
When no new money comes in. A bonus issue or a share split changes the number of shares without changing the company's resources, so it is applied to the whole year and to comparative years as if it had always happened. If the 20 crore shares had been a bonus issue, the count would be 120 crore for the full year and EPS Rs 2.75, with last year's EPS restated on the same basis. Confirm the exact treatment against the current accounting standard on earnings per share, Ind AS 33 in India.
Why does an analyst care about the difference?
Because next year's EPS starts from 120 crore shares for the full twelve months. If profit stays at Rs 330 crore, EPS falls to Rs 2.75 next year even though nothing got worse, simply because the new shares count for a full year. An analyst forecasting growth in EPS has to model the share count forward, not just the profit, or the forecast will look better than the business.
Where candidates lose it
The common slips are dividing by the closing 120 crore, which gives Rs 2.75, or by the opening 100 crore, which gives Rs 3.30. Both ignore when the shares were issued.
The follow-up catches the rest: candidates who time-weight a bonus issue as if it were a fresh issue for cash have missed the one case where the rule changes.
What the interviewer asks next
- The 20 crore shares were a bonus issue instead. What is EPS?
- If the issue had been on 1 January, what would the weighted count be?
- What will EPS be next year if net income stays at Rs 330 crore?
