Equity Research puzzles, solved step by step

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.

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.

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.

About 6.7%. Revenue is price times volume, so the growth factors multiply: 1.12 = 1.05 x (1 + v). Dividing, 1.12 / 1.05 = 1.0667, so volume grew about 6.67%. Subtracting 5 from 12 gives 7%, which overstates volume by the small cross term, 0.33 points.

Why divide instead of subtract?

Think of a tea stall that raises the price of a cup and also sells more cups. The takings grow for both reasons, and the extra cups are also sold at the higher price, which is a little extra neither change produces alone. Revenue is price times volume, so growth factors multiply, and the way to back one out is to divide. 1.12 divided by 1.05 is 1.0667.

When does the shortcut of subtracting matter?

The error from subtracting is the corner of the rectangle, price growth times volume growth. At single-digit rates the corner is small, about 0.33 points here, but it grows quickly with the rates, and in high-inflation markets it becomes the whole story. With 30% price rises and 40% revenue growth, subtracting says 10% volume growth; dividing says 7.7%.

For an analyst this split is the first question on any results call: how much of the growth was price and how much was volume. Volume growth says whether the company is winning customers; price growth says whether it has pricing power or is passing on costs. The limitation: reported price growth often mixes true price changes with shifts in product mix, so ask how the company defines it.

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.

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.

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.

About 20.7%. Set the market at 100. The company's sales go from 20 to 22.4 and the market from 100 to 108, so its share is 22.4 over 108, or 20.74%. The gain is only 0.74 of a point, because share moves with relative growth: 1.12 divided by 1.08, about 3.7% more share, on a 20% base.

Why does growing 4 points faster add less than 1 point of share?

A student who scored 20 out of 100 last term and improves her marks by 12% while the class average improves by 8% has done a little better relative to the class, not a lot. Market share is a ratio, so it changes by the ratio of the two growth rates, 1.12 over 1.08, applied to the share you started with. A 3.7% relative gain on a 20% share is about 0.74 of a point.

How do you use this the other way round in a model?

Analysts often forecast a company as market growth plus a share assumption. If you forecast 12% growth in an 8% market, you are assuming a share gain of about 0.74 points a year, and five years of that takes 20% to about 24.0%. Saying that out loud tests whether the forecast is believable: which competitor is giving up that share, and why? The limitation: this assumes the market figure and the company's sales are measured the same way, which is often not true when companies report by segment.

It must reinvest about 133% of its profit, so free cash flow is negative. Growth equals the reinvestment rate times the return on invested capital, so the reinvestment rate is 20% divided by 15%, or 1.33. On Rs 100 crore of after-tax operating profit the company must invest Rs 133 crore, leaving free cash flow of minus Rs 33 crore, which has to come from lenders or shareholders.

Where does the rule that growth equals reinvestment times return come from?

A tailor earns Rs 15 a year for every Rs 100 of sewing machines she owns. To earn 20% more next year she needs 20% more machines, and buying them takes cash. Profit grows only as fast as the capital that produces it, so growth equals the share of profit reinvested times the return that capital earns. Turn it round and the reinvestment rate is growth divided by the return on invested capitalAfter-tax operating profit divided by the capital tied up in the business, fixed assets plus working capital.: 20% over 15% is 133%.

Does negative free cash flow mean the business is bad?

Not on its own. The check on the right of the figure proves the arithmetic: Rs 100 crore of profit on Rs 667 crore of capital is 15%; add Rs 133 crore and capital is Rs 800 crore, which earns Rs 120 crore next year, exactly 20% more. Negative free cash flow from growth creates value as long as the return on new capital beats the cost of that capital, and destroys value when it does not. The questions an analyst asks are how long the gap can be funded, and at what price.

What does this tell you about a growth story pitched in an interview?

That growth is never free, and its cost depends on returns. Two companies growing 20% can have opposite cash profiles: one earning 40% on new capital throws off half its profit, one earning 10% needs twice its profit again every year. When someone pitches a fast grower, ask for its return on new capital before you ask for its growth rate.

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.

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.

Revenue is Rs 219 in year three, and Rs 100 of it, 46%, comes from new customers. The three layers are the new batch at 100, the year-two batch at 70 and the year-one batch at 49. Growth falls from 70% to 28.8% even though the company signs just as many customers, because revenue creeps towards a ceiling of Rs 333, which is new spend divided by the share lost each year.

Why do you build revenue layer by layer?

Picture a gym that signs 100 members every January, where 30% of any class drops out each year. Its member count is not 100 a year times the years open; it is this year's class plus what is left of every earlier class. Revenue built from customers is a stack of cohortsA group of customers who joined in the same period, tracked together over time., each decaying at the retention rate, and the total is the sum of the layers. Writing the layers down stops you from projecting last year's growth rate forward, which is the mistake the question is set up to catch.

Why does growth slow when the company is signing just as many customers?

Because the loss grows with the base. In year three the company loses 30% of 170, which is 51, and adds 100, so net growth is 49. Revenue stops growing when the spend lost each year equals the spend added, which here is at Rs 333: 100 divided by 0.3. Retention sets that ceiling. At 80% retention, year-three revenue would be Rs 244 and the ceiling Rs 500; at 60% the ceiling is Rs 250.

What does an analyst do with the 46%?

It tells you how much of the business must be won again every year. When nearly half of revenue comes from customers signed in the last twelve months, sales hiring and marketing spend are carrying the top line, and any slowdown in new wins shows up in revenue almost at once. By year five the share from new customers falls to 36% as the older layers pile up. The limitation of the model is equal batches: a company that grows its sign-ups each year will show faster growth, and one that spends more per customer in year two, through upsell, can see a batch grow rather than decay.

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%.

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.

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.