Equity Research puzzles, solved step by step

Puzzles: 100
Traced to a firm: 19
Topics: 11
Hard: 30

Topic

All topics Probability and brainteasers12 Expected value and decisions8 Market sizing and estimation12 Returns and compounding9 Valuation riddles12 Three statement riddles10 EPS and share count9 Cost of capital and rates8 Growth, mix and unit economics8 Mental maths6 Data and reasoning traps6

Level

Any Warm up Core Hard

Source

Any Reported at a firm Standard

Showing 1–5 of 5 · filtered from 100Clear filters

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?EPS and share countCoreSell-side equity researchHedge fund long/short
Try it first
By how much does EPS grow, with the share count unchanged?
Show the worked solution
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?EPS and share countCoreIndian brokerage researchSell-side equity research
Try it first
Pick the ex-rights price before you calculate.
Show the worked solution
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 relationship
$\text{TERP} = \frac{N_{old} \times P + N_{new} \times S}{N_{old} + N_{new}} = \frac{4 \times 120 + 1 \times 80}{5} = 112$
N_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?
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?EPS and share countCoreSell-side equity researchBuy-side equity research
Try it first
What is the new EPS?
Show the worked solution
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 relationship
$\text{EPS}_{new} = \frac{500 - 1{,}000 \times 6\% \times (1-25\%)}{100 - 1{,}000/50} = \frac{455}{80} = 5.69$
500 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?EPS and share countCoreLong-only asset managementBuy-side equity research
Try it first
What is EPS growth per year?
Show the worked solution
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 relationship
$g_{EPS} = \frac{1.08}{0.97} - 1 = 11.3\% \qquad \left(\frac{1.08}{0.97}\right)^{5} = 1.71$
1.08 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?
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?EPS and share countCoreSell-side equity researchIndian brokerage research
Try it first
What profit belongs to the parent's shareholders?
Show the worked solution
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?

N_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

500	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

1.08	net income growth factor per year
0.97	share count factor per year after a 3% buyback
g_EPS	EPS growth per year

Try it first

Where does the 7.1% come from?

Why should the multiple stay where it is?

Where candidates lose it

What the interviewer asks next

Try it first

Why does the share price fall when nobody has lost anything?

How do you prove an existing holder is no worse off?

Where candidates lose it

What the interviewer asks next

Try it first

Why does a buyback change EPS at all?

When does a buyback lift EPS?

Does higher EPS mean each share is worth more?

Where candidates lose it

What the interviewer asks next

Try it first

Why divide by 0.97 rather than add 3%?

Is buyback-driven EPS growth as good as profit growth?

What would an analyst check before trusting the 11.3%?

Where candidates lose it

What the interviewer asks next

Try it first

Why does consolidation count profit the parent does not own?

How do you check the answer another way?

What goes wrong if you use the Rs 100 crore?

Where candidates lose it

What the interviewer asks next