Equity Research puzzles, solved step by step
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009A retailer had 100 stores last year, each selling Rs 10 crore. This year existing stores grow 4%, and 20 new stores open half way through the year, each selling at 80% of a mature store's rate. What is total revenue growth?Sell-side equity researchIndian brokerage research
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Pick the total growth before you work it.
Show the worked solution
Total revenue grows 12%, from Rs 1,000 crore to Rs 1,120 crore. Existing stores add 4%, Rs 40 crore. The 20 new stores sell at Rs 8 crore a year but trade for only half the year, adding Rs 80 crore, 8 points. Split the two when you present it, because they tell different stories about the business.
Why split growth into old stores and new stores?
Think of a restaurant owner who opens a second branch. Total takings rise, but that says nothing about whether the first branch is doing better. Total growth mixes two different things: how the existing stores are trading, which is like-for-like growthSales growth from stores open for the whole of both periods, so new openings and closures do not distort it. Also called same store sales growth., and how many stores were added. A retailer can grow 12% on openings while every existing store shrinks.
Revenue rises from Rs 1,000 crore to Rs 1,120 crore, a 12% increase made of Rs 40 crore of like-for-like growth from existing stores and Rs 80 crore from 20 new stores trading for half the year. How do you work the new stores' contribution?
Three adjustments, one at a time. Twenty stores at a mature rate of Rs 10 crore would be Rs 200 crore. They run at 80%, so Rs 160 crore a year. They trade for half the year, so Rs 80 crore this year. Part-year openings and ramp-up each shrink a new store's first-year contribution, which is why store count growth overstates revenue growth in the year of opening.
Piece Working Rs crore Points of growth Existing stores, last year 100 x 10 1,000 Like-for-like growth 4% of 1,000 40 4 New stores 20 x 10 x 80% x half year 80 8 This year 1,120 12 The two engines of retail revenue growth kept apart, so each can be judged on its own. The follow-up an analyst should volunteer: next year, even with zero like-for-like growth and no openings, the 20 stores trade a full year and add another Rs 80 crore. That annualisation is growth already in the bag, and it is worth saying separately from the growth the business still has to earn.
Where candidates lose it
The trap is adding 20% and 4% to get 24%. It treats new stores as mature and open all year, which roughly doubles their real first-year contribution.
The second loss is giving only the total. An interviewer at a research desk wants to hear the like-for-like and new store pieces named separately, because that is how a retailer's results are read.
What the interviewer asks next
- What is next year's growth if like-for-like growth is zero and no stores open?
- How would you tell whether new stores are cannibalising old ones?
- Which matters more for the valuation of a mature retailer, like-for-like growth or store openings?
034A subscription app spends Rs 900 to acquire a user. Each user earns Rs 60 a month of contribution after direct costs, and 4% of users cancel every month. What are the lifetime value, the LTV to CAC ratio and the payback period?Sell-side equity researchBuy-side equity research
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What is the lifetime contribution of an average user?
Show the worked solution
LTV is Rs 1,500, LTV to CAC is 1.67x, and payback is 15 months per retained user, about 22 months for the cohort. Lifetime value is Rs 60 divided by 4% churn. CAC over monthly contribution, Rs 900 over Rs 60, gives the usual 15 month payback. Counting users who leave along the way, the cohort's cumulative contribution only reaches Rs 900 after about 22.4 months.
Why does churn set the lifetime value?
Think of a leaking water tank. If 4% of the water drains out every hour, a litre poured in stays, on average, 25 hours. With a constant monthly churn rate, the average customer life is one divided by churn, so lifetime value is monthly contribution divided by churn. Rs 60 over 0.04 is Rs 1,500. Halve churn to 2% and LTV doubles to Rs 3,000; that is why subscription analysts watch churn more closely than price.
A user who never cancels repays the Rs 900 acquisition cost in 15 months, but with 4% monthly churn the cohort's contribution bends towards a Rs 1,500 ceiling and only crosses Rs 900 at about 22.4 months, so churn caps value and stretches payback. Which payback number do you give the interviewer?
Give both and say which is which. The common convention is CAC divided by monthly contribution, 15 months, which describes a user who stays. A cohort of acquired users earns less than that each month because some have left, so the money spent on the cohort comes back later, after about 22.4 months. By month 15 only 54% of the cohort is still paying.
Measure Working Result Average life 1 / 4% 25 months LTV Rs 60 / 4% Rs 1,500 LTV / CAC 1,500 / 900 1.67x Payback, retained user 900 / 60 15 months Payback, cohort 1,500 x (1 - 0.96^n) = 900 22.4 months Every figure uses contribution after direct costs and is undiscounted; discounting would lower LTV and stretch both paybacks. Then give a view. A ratio of 1.67x is thin: the business keeps Rs 600 per user over the user's life before any overhead, and a common rule of thumb looks for about three times. The two levers are churn and acquisition cost, and the numbers show churn is the stronger one.
Where candidates lose it
The common loss is multiplying Rs 60 by some chosen number of months instead of letting churn set the life. The second is quoting 15 months as if every acquired user repays it; with churn the cohort takes about half as long again.
Say that the figures are undiscounted and use contribution, not revenue. LTV built on revenue flatters the ratio because it ignores the cost of serving the user.
What the interviewer asks next
- If churn falls to 3%, what are LTV and LTV to CAC?
- How would a 1% monthly discount rate change the lifetime value?
- Why might churn be higher in the first three months than later, and what does that do to the formula?
070An airline's load factor rises from 80% to 85% while its yield, the revenue it earns per passenger kilometre flown, falls 4%. What happens to its revenue per available seat kilometre, RASK?Sell-side equity researchIndian brokerage research
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What happens to RASK?
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RASK rises about 2%. RASK is yield times load factor: revenue per passenger kilometre times the share of seat kilometres that carry a passenger. The load factor rises by 85/80 = 1.0625, a 6.25% gain, not 5%, and yield is multiplied by 0.96. Together 1.0625 x 0.96 = 1.02, so RASK is up 2.0%.
Why is RASK yield times load factor?
Think of a 50-seat bus. Revenue per seat on a trip is the fare each rider pays times the share of seats with a rider in them. Fill more seats at a lower fare and revenue per seat can go either way, depending on the sizes. Revenue per available seat kilometre splits exactly into what each flown passenger kilometre earns, the yield, and the share of available seat kilometres that are flown, the load factor, so percentage changes in the two multiply.
Drawn as an area, the higher load factor adds a green strip worth 6.25% and the lower yield removes a thin red strip worth 4%, so RASK rises from 80 to 81.6, a gain of 2.0%. The relationshipRASK revenue per available seat kilometre yield revenue per revenue passenger kilometre, the price actually earned LF load factor, revenue passenger kilometres over available seat kilometres What it says in wordsRevenue per seat offered is the price per seat sold times the share of seats sold.Why is the load factor gain 6.25% and not 5%?
Because 5 is the change in percentage points, and the question needs the percentage change. A move from 80% to 85% is 5 points, but 5 on a base of 80 is a 6.25% increase in seats filled, and it is the percentage change that multiplies through to revenue. Get that wrong and you add +5 and -4 to say +1%, which halves the true answer. The break-even is useful too: with yield down 4%, RASK stays flat at a load factor of 83.3%.
What should an analyst ask next?
Whether the two changes are linked, and what happened to cost. Airlines often fill seats by cutting fares, so a higher load factor and a lower yield can be one decision, not two pieces of news. RASK only matters against CASK, the cost per available seat kilometre: a 2% gain in RASK is a margin gain only if cost per seat kilometre rose by less. A change in the average trip length also moves yield, since longer flights earn less per kilometre, so check the route mix before reading the fall in yield as weaker pricing.
Where candidates lose it
The fast wrong answer is plus 1%: five up, four down. It adds percentage points to percentages, and it adds changes that should be multiplied. Both slips point the same way, which is why the answer comes out at half the truth.
The second loss is stopping at revenue. Say that the number means little without cost per seat kilometre, and that a fuller plane at lower fares may be a pricing choice, and you sound like an airline analyst rather than a calculator.
What the interviewer asks next
- With yield down 4%, what load factor keeps RASK flat? (83.3%)
- Cost per seat kilometre is unchanged. What happens to the operating margin if it started at 8%?
- Why might yield fall when the airline adds long-haul routes, even if fares are unchanged?
095A 10 million tonne cement plant runs at 70% utilisation. Fixed costs are Rs 700 crore a year and each tonne sold brings in Rs 1,200 of contribution. What happens to EBITDA if utilisation rises to 80%?Indian brokerage researchSell-side equity research
Try it first
Volume rises about 14%. Roughly how much does EBITDA rise?
Show the worked solution
EBITDA rises from Rs 140 crore to Rs 260 crore, up about 86%. At 70%, 7 million tonnes earn Rs 840 crore of contribution, less Rs 700 crore of fixed cost. At 80%, 8 million tonnes earn Rs 960 crore, less the same Rs 700 crore. Volume rises 14.3%, but because the plant runs just above its 58% breakeven, EBITDA nearly doubles.
Why does profit move so much more than volume?
An autorickshaw driver pays a fixed daily rent for the vehicle. On a slow day the fares barely cover the rent; one extra long ride can double what he takes home, because the rent was already paid. When most costs are fixed, every extra tonne adds its full contribution to profit, so profit grows far faster than volume. This is operating leverageHow strongly profit responds to a change in volume, because fixed costs do not move with sales.. A cement plant is almost all fixed cost: the kiln, the staff and the depreciation are there whether it runs at 60% or 90%.
EBITDA for the 10 million tonne plant crosses zero at 58.3% utilisation, reaches Rs 140 crore at 70% and Rs 260 crore at 80%, so a 14% rise in volume near breakeven lifts EBITDA by 86%. How do you get the percentage quickly?
Use the degree of operating leverage: contribution over EBITDA. At 70% that is Rs 840 crore over Rs 140 crore, 6 times. So a 14.3% rise in volume becomes roughly 6 times 14.3%, about 86%. The multiplier falls as utilisation rises, because EBITDA grows while fixed cost stays the same, so the next 10 points would add less in percentage terms. The breakeven, Rs 700 crore over Rs 120 crore per million tonnes, is 58.3%, and the closer a plant runs to it, the bigger the multiplier.
The relationshipu utilisation, the share of capacity sold 10 x 120 10 million tonnes of capacity at Rs 120 crore of contribution per million tonnes 700 fixed costs, Rs crore a year What it says in wordsEBITDA is contribution on the tonnes sold less a fixed cost that does not move, so the percentage change is large when EBITDA starts small.What does an analyst take from this?
Utilisation is the swing variable for cement earnings. EBITDA per tonne moves from about Rs 200 to Rs 325 as utilisation rises from 70% to 80%, even though price and cost per tonne have not changed. That is why cement analysts track regional demand and capacity additions so closely. The limit runs both ways: the same leverage cuts EBITDA by the same Rs 120 crore if utilisation falls to 60%, and in practice contribution per tonne also moves with prices and fuel costs, which can swamp the volume effect.
Where candidates lose it
The instinctive answer is that EBITDA rises in line with volume, about 14%. It ignores the fixed cost, which is the whole point of the question.
The second miss is getting 86% and presenting it as a general rule. It is large because the starting EBITDA is small; say that the multiplier shrinks as the plant fills up and grows as it approaches breakeven.
What the interviewer asks next
- What EBITDA does the plant make at 60% utilisation?
- If contribution falls to Rs 1,000 a tonne, where is breakeven?
- Why do cement stocks often move before utilisation data confirms a recovery?