Debt Capital Markets puzzles, solved step by step

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.

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.