Equity Research puzzles, solved step by step
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059A company is growing its after-tax operating profit at 20% a year and earns a 15% return on every rupee of new capital it invests. What share of its profit must it reinvest to keep growing at 20%, and what does that do to its free cash flow?Buy-side equity researchLong-only asset management
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What share of profit must the company reinvest?
Show the worked solution
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%.
The relationshipg growth in after-tax operating profit RR reinvestment rate, the share of profit invested back in the business ROIC return earned on each rupee of new capital What it says in wordsThe share of profit a company must reinvest is its growth rate divided by the return it earns on new capital.To grow 20% at a 15% return on capital the company must reinvest Rs 133 crore against Rs 100 crore of profit, a bar a third taller, leaving free cash flow of minus Rs 33 crore that must be funded from outside. 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.
Return on new capital Reinvestment to grow 20% Free cash flow on Rs 100 crore profit 10% 200% of profit Rs -100 crore 15% 133% of profit Rs -33 crore 20% 100% of profit Rs 0 crore 30% 67% of profit Rs 33 crore 40% 50% of profit Rs 50 crore At a fixed 20% growth rate, a higher return on capital means less reinvestment and more free cash flow; at a 20% return the company exactly funds itself. 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.
Where candidates lose it
Candidates reach for a reinvestment rate below 100% out of habit, because it feels impossible to invest more than you earn. It is not impossible; it only means raising money every year, and that is exactly what the interviewer wants you to notice.
The second slip is concluding the business is bad. A 15% return on new capital is healthy against most costs of capital. Say that the value of growth depends on that return beating the cost of capital, and that the funding need, not the growth, is the risk.
What the interviewer asks next
- What growth rate can the company sustain while funding itself entirely from profit?
- If return on new capital falls to 8% and the cost of capital is 11%, is growth adding value?
- How would you spot, in the cash flow statement, a company growing faster than its returns can fund?
084Each year a company signs a new batch of customers who spend Rs 100 in their first year, and every batch keeps 70% of its previous year's spend each year after. With equal batches every year, what is revenue in year three, and what share of it comes from new customers?Sell-side equity researchBuy-side equity research
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Revenue is 100 in year one and 170 in year two. What is it in year three?
Show the worked solution
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.
Each year's batch adds Rs 100 and older batches keep 70% of the previous year's spend, so revenue climbs 100, 170, 219, 253 and 277, flattening towards a ceiling of Rs 333 as growth slows from 70% to 9%. 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.
The relationshipR_3 revenue in year three 0.7 the share of last year's spend each batch keeps R_infinity the ceiling revenue approaches with equal batches forever What it says in wordsRevenue is a geometric sum of shrinking layers, and it can never exceed new spend divided by the share lost each year.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.
Where candidates lose it
Candidates grow revenue at the year-two rate, 70%, and reach 289, or keep adding 70 and reach 240. Both treat the business as if customers never leave. The question is testing whether you see the layers.
The second loss is missing the ceiling. Saying that revenue tends to 100 over 0.3 shows you can read what retention does to the long-run size of the business, which is the real point.
What the interviewer asks next
- What retention would you need for revenue to reach 500 in the long run?
- If each batch spends 10% more in year two before decaying, how does the picture change?
- How would you spot deteriorating retention in reported numbers when the company does not disclose cohorts?