Financial Analysis puzzles, solved step by step

X carries more debt and owns a stake in an associate. Debt of Rs 750 crore at 8% costs 5.6% after tax, less than the 6.7% its operations earn on their value, so levering lowers the P/E. The associate adds Rs 22 crore to net income but nothing to EBITDA, while its Rs 300 crore value sits inside EV. Strip it out and X is 7.0x, like its peers.

Why can two multiples on the same company disagree?

Picture a house with a mortgage. Its price compared with the rent it earns is one ratio; your equity in it compared with the rent left after the mortgage payment is another. The two only agree if there is no loan. EV/EBITDA looks at the whole business before financing, while P/E looks at the shareholders' slice after interest, tax and anything non-operating. Every gap between them is explained by something that sits between EBITDA and net income, or between EV and equity value.

What numbers make both facts true?

Give both companies the same operations: EBITDA Rs 150 crore, depreciation Rs 50 crore, operating profit Rs 100 crore, tax 30%. The peer has no debt, earns Rs 70 crore and is worth Rs 1,050 crore: 15.0x earnings and 7.0x EBITDA. X borrows Rs 750 crore at 8%, so interest of Rs 60 crore leaves Rs 28 crore from operations, and it books Rs 22 crore as its share of an associateA company in which the group holds a significant minority stake, usually 20% to 50%. The group books its share of that company profit below operating profit, never in revenue or EBITDA.'s profit. Net income of Rs 50 crore at 12x is equity of Rs 600 crore, and with the debt that is an EV of Rs 1,350 crore, 9.0x EBITDA.

Which reason moves which multiple?

Separate them, because the follow-up always asks. Debt lowers the P/E when its after-tax cost is below the earnings yield of the operations. Here debt costs 8% times 0.7, which is 5.6%, while the operations earn 70 on 1,050, or 6.7%. Swapping expensive equity for cheaper debt leaves the operating slice at about 10.7x earnings. The associate does the other job: its Rs 300 crore of value sits inside EV while its profit sits below EBITDA, which lifts EV/EBITDA from 7.0x to 9.0x.

Name a third candidate if you have time: a lower tax rate than peers raises net income without touching EBITDA, so it also lowers P/E alone. Say what you would check to choose between them: the notes on debt, associates and the effective tax rate.

The implied tax rate is 37.5%. Market cap of 300 at 15x earnings gives net income of 20. Adding net debt of 180 gives EV of 480, so EBITDA at 6x is 80. Less D&A of 30 is EBIT of 50; less interest of 18 is pre-tax profit of 32. Tax is 32 minus 20, which is 12, and 12 over 32 is 37.5%, high enough to ask why.

Where do you start when six numbers arrive at once?

Think of working out a friend's take-home pay from what they spend and what they save. You do not start with their job title; you start with the two numbers that pin the answer. A tax rate is tax divided by pre-tax profit, so every other number in the question is a road to net income or to pre-tax profit. Say that first. Net income is one step: 300 over 15 is 20. Pre-tax profit needs EBITDA, which needs EV, which needs the net debt you were handed.

What does a 37.5% rate tell you, and what have you assumed?

You assumed there are no minority interests, no associates and no interest income on cash, so EV is just market cap plus net debt and every rupee of pre-tax profit belongs to shareholders. Say that. Then read the number. An effective rate well above the statutory rate usually means some costs are not tax deductible, some losses sit in units that cannot use them, or there are one-off tax charges. Compare it with the statutory rate the company actually pays, which you should confirm for the year in question. A second check: interest of 18 on net debt of 180 is 10%, which is plausible, so the inputs hang together.

About Rs 156 crore on cash flow, but a buyer will not pay much above Rs 150 crore, the cost of building the same plant. Revenue is Rs 100 crore and cash costs Rs 70 crore. Taking depreciation equal to the Rs 5 crore of capex, tax is 25% of Rs 25 crore, Rs 6.25 crore, leaving Rs 18.75 crore a year: over 12% that is Rs 156.25 crore. Replacement cost caps it.

How do you get from units to a value?

Valuing a factory is the same sum as valuing a flat you rent out: the rent left after upkeep and tax, divided by the return you need. A business with no growth is worth its steady yearly free cash flow divided by the discount rate. All the work is in getting the yearly cash right, and the two lines people forget are tax and the capex needed just to stand still.

Why does the rebuild cost set the ceiling?

Suppose someone asks Rs 25 lakh for a used car when the same model costs Rs 20 lakh new at the showroom. You walk to the showroom. No sensible buyer pays much more for an asset than it would cost to build an identical one, so replacement cost caps the price even when the cash flows say more. Here the gap is small, Rs 156.25 crore against Rs 150 crore, so a defensible answer sits close to Rs 150 crore.

The cap is loose in three ways, and naming them is what separates a good answer. Building takes time, perhaps two years with no cash coming in, so a working factory earns a premium for the lost years. Land, permits and trained staff may be hard to copy. And if cash flow value stays well above rebuild cost, rivals build plants, supply rises and prices fall, which pulls the cash flows back down. That last force is why the two numbers tend to converge over time.

What if the numbers pointed the other way?

If the cash flow value were Rs 100 crore against a Rs 150 crore rebuild cost, the factory would be worth about Rs 100 crore. Replacement cost is a ceiling, not a floor: nobody pays Rs 150 crore for a plant whose cash flows justify only Rs 100 crore. The floor is what the land and machinery would fetch if sold off, which is a third number worth asking for before you commit.

Enterprise value stays at Rs 1,000 crore at every step; only the split between lenders and shareholders moves. Raising Rs 200 crore and holding it leaves net debt at 300 and equity at 700. Paying it out takes net debt to 500 and equity to 500, with shareholders holding the Rs 200 crore in cash. As PIK interest accrues at 10%, the notes grow to 242 after two years and equity falls to 458, value moving to the lenders.

Why does borrowing not change enterprise value?

Suppose your house is worth Rs 1 crore and you take a Rs 20 lakh loan against it, keeping the money in the bank. The house is still worth Rs 1 crore; you owe 20 lakh more and hold 20 lakh more, and your net position is unchanged. Enterprise value is the value of the operating business and does not depend on how it is funded; a financing step only changes who has a claim on that value. Here the PIK notes add 200 of debt and 200 of cash, so net debt stays 300, equity stays 700, and EV stays 1,000.

What does the dividend do?

The cash leaves the company and lands in shareholders' pockets. Net debt rises from 300 to 500 because the cash that offset the notes is gone, and equity value falls from 700 to 500. Shareholders are no richer and no poorer: they hold Rs 500 crore of shares plus Rs 200 crore of cash, 700 in all, exactly the 700 they started with. What changed is that the lenders now have a 500 claim ahead of them on the same Rs 1,000 crore of operations, so the equity is riskier and the dividend was financed by that risk.

What happens as the PIK interest accrues?

A PIK noteA loan whose interest is paid in kind: added to the principal each period instead of paid in cash, so the amount owed compounds. charges no cash interest; the coupon is added to the principal. At 10%, the Rs 200 crore becomes 220 after a year and 242 after two. With operations unchanged, EV is still 1,000, so equity is 1,000 - 542 = 458: the 42 of accrued interest is value transferred from shareholders to lenders without a rupee moving. In practice EV does move, but for operating reasons: earnings grow or shrink. Two second-order effects can touch EV through financing: interest that is deductible lowers tax and adds a shield, and heavy leverage raises the chance of distress, which costs value; confirm whether accrued but unpaid interest is deductible under the current tax rules before counting the shield.

The trap in the question is the word increase. A candidate who hears PIK and reaches for a bigger EV is adding debt to a number that already includes it. The market capitalisation does fall, from 700 to 500 and then 458, and adding net debt of 500 back to a market cap of 500 gives 1000, the same 1,000. The limit: this holds the operating business fixed to isolate the financing; a real company's EV changes every day for other reasons.

About 10.4% a year, forever, with the company paying out 48% of its earnings. A forward P/E equals the payout ratio divided by the cost of equity less growth, and with a fixed ROE the payout is set by growth: payout = 1 minus g/ROE. So 30 = (1 minus g/0.20) / (0.12 minus g). Multiply out: 3.6 minus 30g = 1 minus 5g, so 25g = 2.6 and g = 10.4%. Check: a dividend yield of 48% / 30 = 1.6% plus 10.4% growth is the 12% cost of equity.

Where does a multiple hide a growth forecast?

If someone offers to sell you a shop for thirty years of its current profit, they are not quoting a price; they are telling you how fast they expect the profit to grow. The multiple is the forecast. Under the Gordon growth model a share is worth next year's dividend over (r minus g), so dividing by next year's earnings gives P/E = payout / (r minus g), and a given P/E can be solved for g. The one thing people forget is that the payout is not free to choose: growth has to be paid for with retained profit.

With a fixed return on reinvested profit, growth equals ROE times the retention rate, so retention is g/ROE and payout is 1 minus g/ROE. At a 20% ROE, growing at 10% means keeping half the earnings. Put that into the multiple: 30 = (1 minus 5g) / (0.12 minus g). Cross-multiply: 3.6 minus 30g = 1 minus 5g, so 2.6 = 25g and g = 10.4%. The implied payout is 1 minus 0.104/0.20 = 48%, and the implied dividend yield is 48% of a 3.33% earnings yield, 1.6%.

Why does the ROE matter as much as the growth rate?

Because the ROE sets how much growth costs. At a 15% ROE the same 30x needs 11.1% growth, since a bigger share of earnings has to be retained to fund each point of it. At an ROE equal to the cost of equity, 12%, the multiple is 1/r = 8.3x whatever the growth rate, because every retained rupee earns exactly what shareholders could earn elsewhere. Growth adds value only when the reinvested profit earns more than the cost of equity; the multiple prices the spread between ROE and r as much as it prices g. The curve is also steep near the answer: at 10% the multiple is 25x, at 11% it is 45x, so a 30x stock is one point of growth away from either 25x or 45x.

Now say the limitation. 10.4% growth forever, only 1.6 points below the discount rate, is not a forecast anyone would defend; no company outgrows the economy indefinitely. The honest reading is that 30x prices a long period of fast growth that will fade, and a two-stage model, say 10.4% for a decade and a lower rate after, is the next thing to build. The one-line solve is still worth doing, because it converts a multiple into a sentence you can argue with: the market expects this company to compound earnings at about 10% for a very long time while earning 20% on what it retains.