Financial Analysis puzzles, solved step by step

The reported yield is 5.0%; with stock pay treated as a cost it is 3.1%. Market value is 10 crore shares at Rs 800, Rs 8,000 crore. Rs 400 crore over that is 5.0%; Rs 250 crore is 3.1%. You do not need a future share price: deduct stock pay as if it were cash salary, because whatever the price, the shares handed to staff are worth Rs 150 crore.

Why is stock pay a real cost when no cash leaves?

Think of a family shop that pays its manager with a slice of the business instead of a salary. The till looks fuller, but the family now owns less of the shop. Stock-based compensation is wages paid in ownership rather than cash, and adding it back to free cash flow counts the saving without counting the slice given away. For this company, Rs 150 crore of the Rs 400 crore reported, 37.5%, exists only because staff were paid in shares. Put the other way, the reported yield is 60% higher than the yield an owner actually earns.

How does stock pay reach equity value if you do not know the future share price?

There are two consistent routes. Treat stock pay as a cash expense in the DCF, leave it out of the add-backs, and divide the equity value by today's diluted share count. Or keep the add-back and forecast every share that will be issued in future, which needs the future share price you do not know. The first route avoids the circle, because the rupee value handed to staff is fixed by the grant, Rs 150 crore a year, whatever the price turns out to be. Only the number of shares depends on the price: at Rs 400 the grant is 37.5 lakh shares, at Rs 800 it is 18.75 lakh, at Rs 1,600 about 9.4 lakh. Owners give up Rs 150 crore of value each time.

What is the one line that shows you understand it?

The gap between the two yields, 5.0% less 3.1%, is 1.9%, exactly the share of the company given to employees each year. An investor who takes the 5.0% at face value is being paid partly in their own dilution. The limit to say: stock pay retains staff and may cost less than the cash salary it replaces, so it is a real expense rather than a waste. The only point is that it must be counted once, as a cost.

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.

Both hold when the two stocks share a slow driver that changes month to month, while their day-to-day moves push in opposite directions. On any one day the shared drift is a small part of each move and the opposing noise wins, so the daily correlation is negative. Over a month the drift adds up 21 times while the noise partly cancels, so the shared part dominates and the correlation turns positive.

How can two stocks move apart by the day but together by the month?

Take two neighbours' electricity meters. On a given day one runs high because guests are staying while the other family is away, so daily readings look opposed. But both bills climb every summer when the air conditioners come on. Correlation is not a fixed property of two assets; it belongs to a horizon, because different forces drive short moves and long moves. Daily returns are dominated by trading noise and stock-specific news; monthly returns by sector and macro trends.

Why does the shared driver win over a month?

Write each daily return as a shared drift plus the stock's own noise. Over 21 days the drift adds up in a straight line, so a month's drift is 21 times a day's and its variance is 21 x 21 = 441 times larger. Noise does not line up day after day, so its variance grows only 21 times. Whatever the two stocks share pulls harder the longer you hold them, because shared moves stack while unshared moves wash out. With daily noise variance of 1, a noise correlation of minus 0.3 and a drift variance of 0.107, the monthly correlation comes out at exactly plus 0.6.

The model also shows how sensitive the result is. Halve the drift variance and the monthly correlation drops from 0.6 to 0.39. Read across the whole year, daily returns would show a correlation of about -0.17: still negative, because on any single day the drift is too small to matter.

What else could cause it, and what would you check?

Two other mechanisms produce the same pattern. A lead-lag, where one stock reacts to shared news a day later, hides co-movement in daily data that monthly data captures. And short-term trading that pushes money from one stock into the other, such as a pairs or index rebalancing flow, creates opposing daily moves inside a shared trend. Then question the evidence. Twelve monthly points give a correlation of 0.6 a standard error of about 0.19, so the true figure could plausibly be anywhere from about 0.2 to near 1. Check other years before building a hedge on it, because a hedge ratio estimated on daily data can have the wrong sign for a position held for months.

Goodwill is Rs 250 crore. Fair value of net assets is book equity of Rs 500 crore plus the Rs 200 crore brand, less a Rs 50 crore deferred tax liability (25% of 200): Rs 650 crore. Price paid less that is 900 - 650 = 250. On the combined balance sheet cash falls Rs 900 crore, the target's assets arrive with the brand and goodwill, a Rs 50 crore liability appears, and the target's equity disappears.

What exactly is goodwill?

Buying a running restaurant for Rs 90 lakh when its kitchen, furniture and stock are worth Rs 50 lakh, and its name alone could be sold for Rs 20 lakh, leaves Rs 20 lakh paid for things you cannot list: the regulars, the location's habit, the team. Goodwill is the plug: price paid less the fair value of every asset and liability you can identify, including the tax that comes with them. So the work is in the identifiable side, and the brand and its tax are the two lines people miss.

Why does the brand create a tax liability?

The brand goes onto the books at Rs 200 crore, but in a share purchase the tax authorities see no new asset: its tax base stays at zero. As the brand is amortised in the accounts, no matching tax deduction arrives, so future tax bills will be higher than the book profits suggest. That future tax is a real liability, 25% of the Rs 200 crore gap, Rs 50 crore, and it is booked on day one. A liability reduces net assets, so it increases goodwill by the same Rs 50 crore. In an asset purchase where the step-up is tax-deductible, there would be no liability and goodwill would be Rs 200 crore; check which structure and which tax rules apply.

What happens to these numbers after the deal?

The target's equity vanishes because the acquirer now owns it; only the acquirer's equity survives, unchanged by a cash deal. Afterwards the brand, if it has a finite life, is amortised, and the deferred tax liability unwinds in step, which softens the hit to net income. Goodwill is not amortised under Ind AS and IFRS; it is tested for impairment at least once a year, so a disappointing acquisition shows up later as a write-down. Confirm the treatment under the standard the company reports in. The interviewer is checking that you can make the balance sheet balance and explain why each new line exists.

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.

Roughly Rs 70,000 to 75,000 crore a year, on the assumptions below. Start from an assumed 1.8 crore two-wheelers sold a year, assume a little over half are bought on credit, and lend about three quarters of the price. Splitting the market into commuter motorcycles, scooters and premium bikes gives about 99 lakh loans averaging Rs 73,600, or Rs 72,832 crore. Every input is an assumption to state and then confirm.

What is the structure before any number?

To estimate what a college canteen sells on credit, you would count meals, the share put on a tab, and the average tab. Loans work the same way. A finance market size is units times financing penetration times ticket size, and saying that structure first lets the interviewer follow every number after it. Here the units are new two-wheelers sold in a year, penetration is the share bought on a loan, and the ticket is the price less the down payment.

Assume about 1.8 crore two-wheelers are sold in India a year. Treat that as an assumption to confirm against the industry body's current sales data, never a fact to quote. Prices range from a basic commuter bike to a premium motorcycle, so one average price is fragile; split the market three ways instead.

How do you check it a second way?

Run it top-down in one line: 1.8 crore units x 55% financed x 75% of an average Rs 1,00,000 price is Rs 74,250 crore. Two routes landing within about 2% of each other is the check, and the segment split earns its place by showing where the uncertainty lives. The softest input is the financed share: every 5 points on it moves the answer by about Rs 6,621 crore. Then a feel check: 99 lakh loans a year is about 27,123 loans a day across the country, which is plausible for a mass market sold through thousands of dealers.

Say what the number is not. It is a yearly flow of new loans. The loan book outstanding at any time is a stock: with loans running about two and a half years and repaid evenly, the average loan is half outstanding for that period, so the book is roughly 1.25 times a year's disbursement, about Rs 91,041 crore. Used-vehicle loans are excluded.

A's lenders are in trouble and B's are merely uncomfortable; both sets of shareholders take a far bigger hit than revenue. A's EBIT swings from Rs 100 crore to minus Rs 40 crore and cannot cover Rs 50 crore of interest. B's falls to Rs 60 crore and covers it 1.2 times. Profit before tax falls 280% at A and 80% at B: operating and financial leverage multiply.

Why do identical profits hide very different risks?

Take two tea stalls that each clear Rs 10,000 a month. One rents a shop for Rs 60,000 a month and buys cheap; the other rents a cart for Rs 10,000 and pays more per cup. In a good month they look the same. In a bad month the shop's rent is still due while the cart's costs fall with its sales. Fixed costs do not shrink when revenue does, so the higher the fixed share of costs, the more of every lost rupee of revenue comes straight out of profit. That sensitivity is operating leverage.

Work out each company's variable cost. A spends Rs 900 crore to make Rs 100 crore of EBIT; Rs 600 crore of that is fixed, so Rs 300 crore, or 30% of revenue, is variable. B's Rs 900 crore is Rs 100 crore fixed and Rs 800 crore variable, 80% of revenue. So a lost rupee of revenue costs A 70 paise of EBIT and B only 20 paise. Revenue falls by Rs 200 crore: A loses Rs 140 crore of EBIT, B loses Rs 40 crore.

What does each lender actually face?

Each lender is owed Rs 50 crore of interest a year, 10% on Rs 500 crore. B's lender is paid out of operating profit with Rs 10 crore to spare: thin, and a rating analyst would note coverage dropping from 2.0x to 1.2x, but no default. A's lender is not paid from operations at all. A must find Rs 90 crore of cash, Rs 50 crore of interest plus the Rs 40 crore operating loss, from its cash balance, an asset sale or new borrowing, so its lender's safety now depends on liquidity, not earnings. A's break-even revenue to cover interest is Rs 929 crore, just 7% below today; B's is Rs 750 crore, 25% below.

Why do shareholders and lenders feel operating leverage differently?

Run revenue up 20% as well as down. A's profit before tax jumps from Rs 50 crore to Rs 190 crore and B's to Rs 90 crore. A's shareholders get the steep line both ways, and their loss is capped at the value of their shares. The lender gets the same Rs 50 crore in the good year and the base year, and loses only in the bad year, so operating leverage hands the upside to equity and the downside to debt. That is why credit analysts ask about the fixed cost base before they ask about margins, and why lenders to high fixed cost businesses ask for lower debt or tighter covenants.

The limitation: real fixed costs are not perfectly fixed. A could cut overheads, defer maintenance or renegotiate rent within a few quarters, so the first year is the dangerous one. Say that, and the answer moves from a formula to a judgement.

The zero falls more: about 8.8% against about 6.4% for the coupon bond. Price sensitivity follows duration, the present-value-weighted average time to each cash flow. The zero's only cash flow is at year 10, so its duration is 10 years. The coupon bond returns part of its value early, so its duration is 7.25 years. Modified duration predicts falls of 9.26% and 6.71%; convexity makes the actual falls slightly smaller.

Why does the timing of cash flows decide the sensitivity?

Two friends each owe you Rs 1,000 in total. One will repay it all in ten years; the other pays Rs 80 a year and the rest at the end. If prices start rising faster and money loses value faster, which IOU loses more value? The one where every rupee is ten years away. The second friend's early payments are already in your hands and can be reinvested at the new higher rates. A bond's price sensitivity to yield depends on when its value arrives on average, not on its final maturity date. That average, weighted by present value, is the Macaulay duration.

How big is each fall?

Use modified duration, Macaulay duration divided by one plus the yield, as the percentage price change per point of yield. For the zero, 10 / 1.08 = 9.26; for the coupon bond, 7.25 / 1.08 = 6.71. So a one point rise should cut prices by about 9.3% and 6.7%. Repricing exactly: the zero goes from 46.32 to 42.24, down 8.80%; the coupon bond goes from par, 100.00, to 93.58, down 6.42%.

Why are the actual falls smaller than duration predicts?

Duration is the slope of the price curve at today's yield, a straight-line estimate. The real curve bows outward, so as yields rise each further step hurts a little less, and as yields fall each step helps a little more. That curvature, convexity, makes a plain bond fall less than duration predicts when yields rise and gain more than predicted when they fall. For a one point move the gap is small, under half a point here; for larger moves, add the convexity term or simply reprice the bond.

Two practical notes. Most Indian government bonds pay coupons twice a year, which shortens the duration slightly but leaves the answer unchanged. And the gap between the bonds widens with maturity and narrows as coupons fall: a coupon bond's duration always sits below its maturity, while a zero's always equals it.