Debt Capital Markets puzzles, solved step by step

40% debt, where WACC bottoms at 11.10%. After tax, debt costs 5.25%, 5.625%, 6.75% and 9% at the four levels. Weighting each with equity gives 12.00%, 11.365%, 11.10% and 12.20%. Cheap, tax-shielded debt pulls WACC down at first; by 60% the rise in both debt and equity costs outweighs the extra cheap debt.

Why does WACC fall at first?

Think of funding a house with a mix of a bank loan and money from relatives who expect a share of any gain. The bank is cheaper, and in this example the interest also cuts your tax bill. Replacing expensive equity with cheaper, tax-deductible debt lowers the blended cost, as long as neither cost rises too fast. Going from 0% to 20% debt, the after-tax debt cost is only 5.625% against equity at 12.8%, so WACC drops from 12.00% to 11.365%.

Why does it turn up again?

Every extra rupee of debt makes the company riskier for everyone. Lenders ask for more, and shareholders, now standing behind a bigger claim, ask for more too. Past some point the rising cost of both sources outweighs the benefit of shifting weight onto the cheaper one. From 40% to 60%, the debt weight rises by 20 points, but debt's after-tax cost jumps from 6.75% to 9% and equity's from 14% to 17%, and the blend climbs 1.10 points. That is the trade-off theoryThe idea that a company balances the tax saving from debt against the rising cost of financial distress as leverage grows. in four data points.

What does a lender add after the number?

Two caveats show judgement. The minimum is only as good as the cost schedule, and in real life that schedule is an estimate, especially the equity cost at high leverage. Only four points were given, so the true minimum could sit anywhere between 20% and 60%; say that you would want more points before recommending a structure. And a debt desk also cares about what the WACC table cannot show: whether 40% leverage keeps the rating in a band that keeps the market open in a bad year.

About 6% a year, forever. In a steady growth model the required return equals the dividend yield plus growth. The yield is 12 divided by 240, 5%, so growth must be 11% minus 5%, which is 6%. For a lender the useful point is fragility: if the market cut its growth view to 4%, the same formula gives a price of Rs 171, and the equity cushion under the debt shrinks by 29%.

How can a price contain a growth forecast?

Think of a shop rented out for Rs 12,000 a year that sells for Rs 2,40,000. A buyer who wants 11% a year gets only 5% from the rent, so the price only makes sense if the buyer expects the rent to rise about 6% a year. A price paid today is a bet on future cash, so you can run the valuation backwards and read off the growth the buyer has assumed. The Gordon growth modelA valuation for a cash flow that grows at a constant rate forever: price equals next year cash flow divided by the required return minus growth. does exactly that for a steady dividend payer.

Why should a lender care what the equity market assumes?

Because equity is the cushion that absorbs losses before the lender does. When a price rests on a growth assumption, a small change in that assumption moves the price a lot, so the cushion is thinner than the market value suggests. Here two points less growth takes the price from Rs 240 to Rs 171 without the dividend changing at all. A lender reading leverage on market value should also look at it on a more conservative growth view.

There is a second reading. Rs 12 a share paid out and growing 6% a year is cash leaving the company ahead of any debt repayment. A lender who sees a rich implied growth rate and a generous, rising dividend asks whether the business can fund both, and may want a covenant that limits payouts if leverage rises. State the limit too: the model assumes one growth rate forever and a cost of equity that is itself an estimate, so treat 6% as the market's rough view, not a forecast.

The levered beta is 1.4, and the cost of equity rises from 11.8% to 15.4%. Multiply the unlevered beta of 0.8 by 1 plus the after-tax debt-to-equity ratio, 0.75 x 1.0, which is 1.75. At a 7% risk-free rate and a 6% premium, equity then costs 7% plus 1.4 x 6%. Debt is cheaper than equity, but adding it makes the remaining equity riskier, so shareholders demand more.

Why does borrowing make the shares riskier?

Two friends each own half of a Rs 10 lakh tea stall. If sales drop and the stall's value falls 10%, each loses Rs 50,000. Now suppose the stall was bought with Rs 5 lakh of loan and only Rs 5 lakh of their own money. The same 10% fall costs Rs 1 lakh, and the lender still gets repaid in full, so the owners lose 20% of their stake. Debt does not change how risky the business is; it concentrates that risk onto a smaller slice of equity. Beta measures that sensitivity, so it rises with leverage.

If debt is cheaper, why does the cost of equity go up?

Because shareholders are paid last. The cost of equity rises from 11.8% to 15.4%, and the 3.6 points added are the price of standing behind the lenders. The overall cost of capital may still fall, because half the funding is now debt that costs less and whose interest is tax deductible. That is the trade-off the desk is testing: cheaper money in, pricier equity as a result, and the tax shield decides the net.

Say the assumptions. This formula, usually credited to Robert Hamada, treats the debt as riskless, a beta of zero; for a heavily indebted company that overstates how much risk the equity carries alone. It also assumes the debt ratio stays at 1.0. Without the tax term the levered beta would be 1.6, so 1.4 sits between the unlevered 0.8 and that upper bound.

WACC is 8.0% before tax and 7.25% after. Read the cost of equity as the earnings yield, 1 over a P/E of 10, which is 10%. Half the capital costs 10% and half costs 6%, so the blend is 8.0%. The tax shield cuts debt to 6% x 0.75 = 4.5%, and the blend falls to 7.25%. The P/E shortcut assumes no growth; with growth the true cost of equity is higher.

Where does the cost of equity come from when you are not given a beta?

If a shop earns Rs 10,000 a year and sells for Rs 1 lakh, a buyer earns 10% on the price. Nobody would pay more unless they expected growth, so 10% is roughly what buyers of such a shop demand. A P/E of 10 means earnings are a tenth of the price, an earnings yield of 10%, and with no growth that is a quick proxy for the cost of equity. Say out loud that it is a proxy: it is the fastest honest route when the interviewer gives you only a multiple.

Why does tax only touch the debt half?

Interest is paid before tax and dividends after it. Every rupee of interest reduces taxable profit, so the government in effect pays a quarter of the interest bill at a 25% tax rate, and debt that costs 6% on paper costs 4.5% to the company. Equity gets no such relief. That is why the after-tax WACC is 0.75 points lower: half the capital times the 1.5 point shield. The difference compounds into valuation, since a lower discount rate raises the value of every future cash flow.

State the limit of the shortcut before the interviewer does. The earnings yield equals the cost of equity only for a company that does not grow and pays out all its earnings. If earnings grow at 3% a year, investors paying 10x are expecting roughly 10% plus 3%, about 13%, and the WACC rises with it. For a real company you would build the cost of equity from a risk-free rate, a beta and a market premium instead.

Worth more: about Rs 2,134 crore, Rs 134 crore above the unlevered value. Permanent debt of Rs 800 crore at a 25% tax rate creates a tax shield worth 0.25 x 800, Rs 200 crore, lifting value to Rs 2,200 crore. Distress would destroy 30% of that, Rs 660 crore, but with a 10% chance the expected cost is Rs 66 crore. The shield wins unless the distress probability passes about 30%.

Where does debt add value, and where does it take it away?

A family that takes a home loan gets a tax deduction on the interest every year, a steady saving. But if the loan is too big and a job is lost, they may have to sell the house in a hurry at a poor price. Debt adds value through the tax saved on interest and subtracts value through the expected cost of financial distress; the net of the two decides whether borrowing helps. That balance is the {term('trade-off theory', 'The idea that a company chooses its debt level by weighing the tax benefit of interest against the expected costs of financial distress.')} of capital structure.

Why is the tax shield worth t times D?

For permanent debt, the company pays interest of r times D every year forever and saves t times that in tax. Discounting a perpetual saving of t r D at the debt's own rate r gives t D. So Rs 800 crore of permanent debt at a 25% tax rate is worth Rs 200 crore in tax savings, whatever the interest rate, as long as the debt is truly permanent and the company always has profits to deduct against. Both conditions are generous, which is why real tax shields are usually worth less than t D.

Now find where the answer flips. The shield is 200; the distress cost is the probability times 660. The firm is worse off once the distress probability passes 200 over 660, about 30.3%, so debt at this level is value-adding only while distress stays well below a one-in-three chance. Adding more debt raises both lines, the shield in a straight line and the distress probability faster, which is why an optimal level exists. The limits: the 30% cost and the 10% probability are estimates, and indirect distress costs, lost customers and staff, are the hardest part to measure.

About 13.3x. Equity value is enterprise value less net debt: 8 x 100 = 800, less 300, is Rs 500 crore. Net income is EBITDA of 100, less depreciation of 20 and interest of 30, which leaves 50 before tax and 37.5 after 25% tax. Rs 500 crore over Rs 37.5 crore is 13.3x. The same business looks cheap at 8x EBITDA and dearer on earnings, because depreciation, interest and tax all sit between the two profit lines.

Why can the two multiples not be compared directly?

The price of a flat and the price of the owner's stake in it differ when there is a home loan: an Rs 80 lakh flat with a Rs 30 lakh loan leaves Rs 50 lakh of equity. EV/EBITDA prices the whole business against profit available to all funders; P/E prices only the equity against profit left after lenders and the tax authority are paid. To move from one to the other, bridge the value by taking off net debt, and bridge the profit by taking off depreciation, interest and tax.

Where does the gap between 8x and 13.3x come from?

Bridge it in two moves. Depreciation and tax alone turn 8x EBITDA into 13.3x earnings: with no debt, EBIT of 80 taxed at 25% is 60, and 800 over 60 is 13.3x. So the gap here comes from the lines between EBITDA and net income, not from the debt. A business with heavy depreciation or a high tax rate always looks dearer on P/E than on EV/EBITDA.

Does the debt change the P/E at all?

With these numbers, no, and that is worth noticing. Leverage raises the P/E when the after-tax cost of debt is above the business's unlevered earnings yield, and lowers it when the cost is below. The unlevered earnings yield is 60 over 800, 7.5%; the after-tax cost of debt is 10% x 0.75, also 7.5%. Swapping equity for debt removes value and earnings in the same proportion, so the P/E stays at 13.3x. At 8% interest it would be 11.9x; at 12%, 15.2x.

State the lesson for a credit desk. Never compare a P/E with an EV/EBITDA, or P/Es across companies with very different leverage, without bridging them first. The limit: this treats net debt as the only claim between enterprise and equity value; in real companies minority interests, leases and pension deficits also sit in that bridge.

Rs 30.5 per share with the discount and Rs 38.0 without it. The parts add to Rs 2,500 crore. A 15% discount takes off Rs 375 crore, leaving Rs 2,125 crore of enterprise value. Less Rs 600 crore of net debt gives equity of Rs 1,525 crore over 50 crore shares. With no discount equity is Rs 1,900 crore, or Rs 38.0. A 15% discount costs shareholders 19.7%.

Why does the discount come off before the debt?

Think of a house worth Rs 1 crore with a Rs 60 lakh home loan on it. If buyers suddenly pay 15% less for houses on that street, the house is worth Rs 85 lakh, the bank is still owed Rs 60 lakh, and the owner's share drops from Rs 40 lakh to Rs 25 lakh. A conglomerate works the same way. The holding company discount is a haircut on what the whole group is worth, and the lenders' claim is a fixed number that sits ahead of the shareholders, so the haircut is taken from enterprise value and passes through to equity untouched.

So the order is: value each business, add them to get the sum of the partsValuing each business on its own, usually against its own peers, and adding the values together., apply the holding company discountThe gap between what a group trades at and what its businesses would be worth separately, often blamed on head office costs, capital allocation or tax leakage. to the total, subtract net debt, and divide by shares. Rs 2,500 crore less Rs 375 crore is Rs 2,125 crore; less Rs 600 crore is Rs 1,525 crore; over 50 crore shares is Rs 30.5.

Why does a 15% discount cost the shareholders more than 15%?

Equity is the thin slice left after debt, so any fall in enterprise value is a bigger fall as a share of equity. The Rs 375 crore haircut is 15% of Rs 2,500 crore but 19.7% of Rs 1,900 crore. Push net debt to Rs 1,500 crore and the same haircut takes 37.5% of the equity. This is why a credit analyst reading a holding company cares about the discount even though no lender ever sees it on a statement: it is a measure of how much equity cushion the market will actually pay for.

What should you say about where the discount is applied?

Some desks apply the discount to equity value instead of enterprise value. On equity of Rs 1,900 crore, 15% gives Rs 1,615 crore and Rs 32.3 a share. The two conventions differ by Rs 1.8 a share here, so name your convention in the first sentence rather than let the interviewer find it. The enterprise value version is the more common reading when the discount is described as a discount to the sum of the parts, and it is the one that treats the lenders' claim as fixed.