Financial Analysis puzzles, solved step by step

About Rs 157.5 crore. Start from potential rent of Rs 20 crore and take off 10% vacancy to reach effective gross income of Rs 18 crore. Operating expenses at 30% of that are Rs 5.4 crore, leaving net operating income of Rs 12.6 crore. Divide NOI by the 8% cap rate: Rs 12.6 crore over 0.08 is Rs 157.5 crore, which is 12.5 times NOI.

Why does a cap rate apply to net income and not to rent?

Think of a flat you rent out for Rs 30,000 a month. Some months it sits empty, and the society charges, repairs and property tax come out of your pocket. What you would pay for the flat depends on what is left, not on the rent written in the agreement. A cap rate is the yield a buyer wants on net operating income, the cash the building throws off after vacancy and running costs but before any loan payments. Applying it to gross rent values money the owner never receives.

How do you walk from potential rent to value?

Three steps, in order. Gross potential rent is what the building would earn fully let: Rs 20 crore. Take off vacancy first, because operating expenses here are a share of the income actually collected, not of the potential. 10% vacancy leaves effective gross incomeRent the building actually collects after vacancy and bad debts, before operating expenses. of Rs 18 crore. Expenses at 30% of 18 are Rs 5.4 crore, which leaves NOI of Rs 12.6 crore. Then divide by the cap rate.

What makes the exit cap rate the number to argue about?

Value is very sensitive to the cap rate: one point lower, at 7%, the building is worth Rs 180 crore; one point higher, at 9%, Rs 140 crore. That 1 point swing moves value by about Rs 40 crore on a Rs 157.5 crore building. Analysts usually set the exit cap rate a little above today's rate, because the building will be older when it is sold. Say the limit as well: a single cap rate assumes NOI is stable, so a building with large leases expiring soon needs a cash flow model, not one division.

Market capitalisation is Rs 2,000 crore. With no other liabilities, assets equal debt plus equity. A D/E of 0.5 means debt is half of equity, so assets are 1.5 times equity and book equity is Rs 1,500 crore over 1.5, which is Rs 1,000 crore, with Rs 500 crore of debt. At 2.0x book, the market values that equity at Rs 2,000 crore.

How does a debt-to-equity ratio split the balance sheet?

Think of a Rs 15 lakh car bought with a loan that is half the size of your down payment. If the loan is half the down payment, the car cost one and a half down payments, so the down payment was Rs 10 lakh and the loan Rs 5 lakh. A D/E of 0.5 does not mean half the assets are debt; it means debt is half of equity, so assets are 1.5 times equity. Rs 1,500 crore over 1.5 gives book equity of Rs 1,000 crore and debt of Rs 500 crore.

What assumptions sit under the answer, and what could you add?

The question rules out other liabilities, such as payables and provisions, and that matters: a real balance sheet has plenty, and then assets are not just debt plus equity. Say the identity you are using, assets equal liabilities plus equity, before you lean on it. You can also go one step further than asked. With Rs 500 crore of debt and no cash given, enterprise value is about Rs 2,500 crore. And a P/B of 2.0 says the market thinks the assets earn more than their cost of capital; read it next to return on equity rather than on its own.

Unlevered free cash flow is Rs 1,00,000 a year and the NPV is about Rs 1,43,308. Sales are Rs 4,50,000, goods Rs 2,70,000 and rent Rs 60,000, so EBITDA is Rs 1,20,000. Less Rs 40,000 of depreciation is EBIT of Rs 80,000; after 25% tax, NOPAT is Rs 60,000. Adding back depreciation gives Rs 1,00,000. Five years of that at 14% is worth Rs 3,43,308, less the Rs 2 lakh machine.

How do you get from sales to unlevered free cash flow?

Think of a tea stall owner counting what she can take home each year: takings, less tea and milk, less rent, less the tax man's share. The stall's old kettle wearing out is a cost on paper, but no cash leaves her purse for it each year. Unlevered free cash flow is the cash the asset throws off before any financing: operating profit after tax, plus non-cash charges, less the capital spending and working capital it needs. Here: sales of Rs 4,50,000 less goods of Rs 2,70,000 and rent of Rs 60,000 is EBITDA of Rs 1,20,000. Depreciation of Rs 40,000 gives EBIT of Rs 80,000, tax takes Rs 20,000, and NOPAT is Rs 60,000.

Why does depreciation matter only through tax?

Depreciation is subtracted to reach EBIT and added back to reach cash flow, so on its own it washes out. Its only cash effect is the tax it saves: Rs 40,000 of depreciation at 25% cuts tax by Rs 10,000 a year. That is why taxing EBITDA directly is wrong: it would give Rs 90,000 a year and lose the shield. The answer leans on assumptions you should say out loud: no working capital for stock in the machine, no repairs, no salvage value, a steady 50 sales a day, and a 14% rate that reflects the risk of the location. The NPV is positive by a wide margin, so the decision is most sensitive to daily volume, the one number nobody can check in advance.

On earnings yield alone equities look dear, 4% against 7%, but that ignores growth; on expected return they offer about 12% against 7%, a premium of about 5 points. The dividend yield is half of 1/25, 2%, and growing it at 10% gives roughly 12%. Whether 5 points is enough to pay for equity risk is the judgement the question is really after.

Why is 4% against 7% the wrong comparison?

A flat that rents for 3% of its price looks poor next to a 7% fixed deposit, yet people still buy flats, because rents rise over time and the deposit's interest never does. A bond's yield is close to its whole return if held to maturity, while an earnings yield is only the first year of a stream that grows, so setting one against the other treats a growing payment as a fixed one. The 4% earnings yield is 1 / 25; it says nothing yet about the 10% growth in the question.

How do you turn a multiple into an expected return?

Use the dividend growth relation: the return on a share held for the long run is the dividend yield plus the growth rate of the dividend. The payout is 50%, so the dividend yield is 0.5 / 25 = 2%. Growth is 10%, so the expected return is about 12%. Using next year's dividend, 2% grown by 10%, gives 12.2%; the difference does not change the verdict.

What does the growth assumption have to survive?

Growth carries the whole verdict, so test it. Retaining half the earnings and growing 10% forever requires a 20% return on every rupee reinvested, which is a demanding assumption for an entire market. If growth is 7% instead, the expected return is 9% and the premium shrinks to 2 points; at 5% growth equities offer no more than the bond. The answer to 'which is cheaper' is a statement about growth: at 25 times earnings, equities beat bonds by a healthy margin only if 10% growth is believable. Say that, and resist a one-word verdict.

In the year it happens, the capex cut: it adds the full Rs 10 crore to free cash flow, while more revenue or lower cost of goods sold adds Rs 7.5 crore after 25% tax. Capex is a direct cash item. If the change repeats every year, lower capex means lower depreciation and more tax, so all three converge on Rs 7.5 crore a year, and an exit multiple on EBITDA favours revenue and cost.

Why does capex hit cash harder than revenue or cost?

If you earn Rs 10,000 more, you keep what is left after income tax. If you decide not to buy a Rs 10,000 laptop, you keep all Rs 10,000, because buying it was never a deduction in that year. Revenue and cost changes reach free cash flow after tax; a capex change reaches it in full, because capex is subtracted below the tax line. So with a 25% tax rate, Rs 10 crore more revenue or Rs 10 crore less cost of goods sold adds Rs 7.5 crore, and Rs 10 crore less capex adds Rs 10 crore.

One assumption sits under the revenue answer: that the extra Rs 10 crore comes with no extra cost and no extra working capital. In practice more revenue usually needs more receivables and stock, which takes a little more away. Say so in one clause.

What changes when the change repeats every year?

Capex becomes depreciation. Spend Rs 10 crore less every year on assets depreciated over five years, and depreciation falls by Rs 2 crore more each year until it is Rs 10 crore lower, which raises tax by Rs 2.5 crore. In steady state a recurring capex cut adds Rs 10 crore of cash less Rs 2.5 crore of lost tax shield, Rs 7.5 crore a year: exactly the same as the revenue and cost changes. The capex cut's edge is timing, worth something in present value, but not a permanent advantage.

Even a one-off cut keeps only part of its edge. Discounted at 10%, Rs 10 crore saved next year is worth Rs 9.09 crore, but the depreciation shield given up over the following five years is worth Rs 1.72 crore, leaving Rs 7.37 crore against Rs 6.82 crore for a one-year revenue gain. Still ahead, by much less than Rs 2.5 crore.

How does the terminal value change the ranking?

If the terminal value uses an exit multiple of EBITDA, a permanent Rs 10 crore of extra revenue or lower cost raises terminal EBITDA by Rs 10 crore and the terminal value by Rs 80 crore at 8x, while a capex cut does not touch EBITDA and adds nothing through the multiple. With an exit multiple, recurring revenue and cost changes beat capex by a wide margin; with a perpetuity growth terminal, all three are equal in steady state. Name which terminal method you are assuming before you rank them. And add the business limit: capex cut without consequence is rare, because the assets usually drive future revenue.