Financial Analysis puzzles, solved step by step

It must reinvest 75% of operating profit at a 20% return, and 150% at a 10% return. Growth equals return on capital times the share of profit reinvested, so the reinvestment rate is 15% divided by the return. At 20% that leaves Rs 25 of every Rs 100 free. At 10% the company must invest Rs 150 for every Rs 100 it earns, raising Rs 50 from lenders or shareholders to keep growing.

Where does growth in operating profit come from?

Picture a tailor who earns 20% a year on every rupee of sewing machines she owns. If she wants next year's profit 15% higher, she needs 15% more machines' worth of profit, and each rupee of machines earns only 20 paise. Growth equals the return on new capital multiplied by the share of profit put back in. That share is the reinvestment rate, and it is the price the company pays today for tomorrow's growth.

What does the 10% case tell an analyst?

Below a 15% return, 15% growth cannot be paid for out of profit at all. At 10%, for every Rs 100 earned the company must invest Rs 150, so Rs 50 comes from new debt or new shares every year and free cash flow is negative. The table shows how the free cash left for owners changes with the return on capital.

Growth at a low return can still be worth having if the return beats the cost of capital, and it destroys value if it does not. Say the limitation: the formula assumes new capital earns what old capital earns. Price increases and efficiency gains are growth that needs no reinvestment, so real companies sometimes beat it.

Cover is 3.3x, falling to 1.7x. Take EBITDA of 100. Net debt of 300 at 10% costs 30 of interest, so EBITDA covers it 3.33 times. At 5x and 12%, net debt is 500 and interest is 60, so cover is 1.67x. Cover is one over leverage times the rate, and 0.30 doubling to 0.60 halves it.

Why is there no need for an actual EBITDA figure?

Think of a household whose loan EMIs are some multiple of monthly salary. Whether the salary is 50,000 or 5 lakh, the share of salary that goes on interest depends only on how many months of salary it borrowed and at what rate. Interest cover is EBITDA over interest, and interest is leverage times EBITDA times the rate, so EBITDA cancels and cover is one over leverage times the rate. Pick EBITDA of 100 only to make the arithmetic visible.

Why do leverage and rates tend to move together, and what does 1.7x mean?

A lender charges more to a borrower who owes more, so the second scenario is not a coincidence; it is how a stretched balance sheet usually looks. Because leverage and rate multiply, a company that adds debt while rates rise loses cover much faster than either change alone suggests. Cover of 1.7x also flatters the position: EBITDA is before tax, capex and working capital, so once maintenance capex is paid the cash left to service interest can be well under 1.7 times the bill. Say that limitation; credit analysts look at cover after capex for exactly this reason.

The competitor keeps more: Rs 25 against Rs 20 on every Rs 100 of sales. Cost plus 25% means a price of 1.25 times cost, so on Rs 100 of sales cost is Rs 80 and the margin is 20%. A 25% gross margin needs cost of Rs 75 on a price of Rs 100, which is a markup of 25 over 75, or 33.3%.

Why does the same 25% mean different money?

Think of a vegetable seller who buys tomatoes for Rs 80 a kilo and adds Rs 20. To him, that is 25% on what he paid. To his customer, Rs 20 out of the Rs 100 she paid is 20%. Same Rs 20, two percentages. Markup divides profit by cost; margin divides it by price, and price is always the bigger number, so a margin is always smaller than the markup that produced it. The distributor's 25% markup is a 20% margin; the competitor's 25% margin is a 33.3% markup.

Where does this mix-up cost real money?

In pricing conversations, sales teams often quote markups because the numbers sound larger, while finance teams report margins. If a target says 25% margin and the price list is built at cost plus 25%, every sale falls 5 rupees short per Rs 100, a fifth of the profit the plan assumed. Discounts make it worse: a 10% discount off a cost-plus-25% price leaves a price of Rs 90 on cost of Rs 80, an 11.1% margin, so half the profit per unit is gone. Say the conversion formula out loud whenever someone gives you a percentage of profit, and ask which base it is on.

14% today, rising to about 16.7% after B doubles, with no change in either division's own margin. Group EBITDA is 80 + 60 = Rs 140 crore on Rs 1,000 crore. When B grows to Rs 400 crore at 30%, EBITDA is 80 + 120 = Rs 200 crore on Rs 1,200 crore. The group margin is a revenue-weighted average, so it moves when the weights move.

Why is the group margin not the average of the two?

A cafe earns 30% on coffee and 10% on sandwiches. If it sells mostly sandwiches, its overall margin sits near 10%; if coffee takes off, the overall margin climbs, even though neither item is any more profitable. A group margin is a revenue-weighted average of segment margins, so it moves whenever the mix moves, even if no segment changes. Today B is a fifth of revenue, so the group sits a fifth of the way from 10% to 30%: 14%.

Can the group margin rise while every division gets worse?

Yes. Suppose that while B doubled, A's margin slipped to 9% and B's to 28%. Group EBITDA would be 72 + 112 = Rs 184 crore on Rs 1,200 crore, 15.3%, still above the 14% start. Both divisions got less profitable and the group margin still rose, because the shift towards B outweighed the decline inside each. Statisticians call this pattern Simpson's paradox, and a management commentary that cites only the group margin can hide it.

What should an analyst do with a reported margin gain?

Split it into mix and rate. The mix effect is the margin you would get with the new weights and the old divisional margins, less the starting margin: 16.67% less 14% is 2.67 points. The rate effect is the rest. In the puzzle the rate effect is zero; in the deteriorating version it is -1.33 points, which is the story a reader needs. The limit: segment data is often reported only twice a year and with shared costs allocated by management, so the split is only as clean as the allocation.

12% a year at a 40% payout, and 6% at 70%. With no new equity and fixed leverage, the only fuel for growth is retained profit. Equity grows by ROE times the share of profit kept: 20% x 60% = 12%. Debt grows in step to hold the ratio, so assets, and at a steady asset turnover sales, can grow 12%. Keep only 30% and the ceiling halves to 6%.

Why is retained profit the only fuel?

A family shop that refuses outside partners and refuses to borrow more than it already does relative to its size can grow only on the profit it leaves in the till. With new equity ruled out and leverage fixed, equity can grow only by retained profit, and debt can grow only as fast as equity. So the whole balance sheet is capped at the rate equity compounds.

Put numbers on it. Opening equity of Rs 100 crore earns Rs 20 crore at a 20% ROE. Rs 8 crore is paid out and Rs 12 crore kept, so equity closes at Rs 112 crore, 12% higher. Next year's profit on Rs 112 crore is Rs 22.4 crore, also 12% higher, and the pattern repeats.

What assumptions are hiding inside the formula?

The formula, often taught through Robert Higgins' sustainable growth rate, assumes the 20% ROE holds on every new rupee of capital. Split ROE the DuPont way and it could be a 5% net margin x 2.0 asset turnover x 2.0 assets to equity. Growth above 12% therefore needs one of five things: a better margin, faster asset turnover, more leverage, new equity, or a lower payout. That list is the useful part of the answer, because it is exactly the set of levers a finance team argues about when a plan grows faster than its funding.

The limitation is worth one sentence: ROE rarely stays flat as a company grows, because new projects are usually less profitable than the best existing ones. The 12% is a ceiling under today's economics, not a forecast.

Depreciation and amortisation rose from Rs 60 crore to Rs 90 crore, up Rs 30 crore or half again. D&A is exactly the gap between EBITDA and EBIT: 180 minus 120 last year, 200 minus 110 this year. The usual causes are a burst of capex now being depreciated, an acquisition bringing amortisation of intangibles, or an accounting change, such as lease accounting, that moves a cash cost out of operating expenses and into depreciation.

How do you find D&A from two margins?

If your take-home pay rises but your savings fall, something between the two lines got bigger: rent, EMI, school fees. You find it by looking at the gap, not the lines. EBITDA and EBIT differ by exactly one thing, depreciation and amortisation, so when the two margins move in opposite directions, D&A has grown by the sum of the two moves. Here, 2 points up and 1 point down is 3 points of Rs 1,000 crore of revenue, or Rs 30 crore.

Convert to rupees to be sure. EBITDA is Rs 180 crore last year and Rs 200 crore this year; EBIT is Rs 120 crore and Rs 110 crore. D&A is Rs 60 crore, then Rs 90 crore. Revenue is flat, so D&A went from 6% to 9% of revenue.

What could explain a 50% jump in D&A on flat revenue?

Three stories, each with a different meaning. First, a capex burst: a new plant or system has come into use and is being depreciated, but has not yet lifted revenue. That is a timing story, and the question is when revenue arrives. Second, an acquisition: buying a business brings customer lists and brands onto the balance sheet, and amortising them raises D&A without any new cash spend. Third, an accounting change. Under lease accounting standards such as Ind AS 116, rent stops being an operating expense and becomes depreciation plus interest, which raises EBITDA and D&A together without changing the cash the company pays.

The lease story fits the EBITDA rise neatly, since rent leaving operating expenses lifts EBITDA directly. But EBIT usually edges up under that change too, because part of the old rent now sits in interest, below EBIT. EBIT falling here suggests at least some genuine new depreciation as well.

Which margin should an analyst trust?

Neither on its own. EBITDA ignores the cost of the assets that produce the profit, so a company can raise its EBITDA margin simply by buying capacity or by reclassifying rent. EBIT charges for those assets, but through accounting depreciation that may not match their real wear. The honest check is cash: EBITDA less capex less lease payments, compared across both years, tells you whether the business really earns more. Ask management which of the three stories is true before praising the higher EBITDA margin.