Debt Capital Markets puzzles, solved step by step

Maximum debt is about Rs 872.7 crore, and the interest cover test binds. Cover of 2.5x on EBITDA of 240 allows interest of 96; at 11% that is Rs 872.7 crore of debt. Leverage of 4.0x would allow Rs 960 crore, but the rate is too high for the business to carry it. The two tests meet at a 10% rate; above that, coverage is the tighter limit.

Why run both tests instead of just the leverage one?

A household can be told it may borrow up to four years of income, but it also has to afford the monthly instalment. When interest rates are high, the instalment test fails first, long before the four-years rule does. Leverage measures how much debt there is; interest cover measures whether the business can pay for it, and the rate decides which one runs out first. A lender sizing debt computes both and lends the lower.

At what rate do the two tests swap?

Set them equal: 96 divided by the rate equals 960, so the rate is 10%. Above 10%, coverage binds; below it, leverage binds. That is the general rule to leave the interviewer with: the crossover rate is one over the leverage multiple times the cover multiple, 1 over 4.0 times 2.5, which is 10%. When rates rise, the same business can borrow less even though its EBITDA has not changed, and lenders who size on leverage alone find their borrowers failing cover tests a year later.

Say the limits. EBITDA interest cover ignores capex and tax, so a lender who worries about cash will also run a fixed charge test, which can bind lower still. And the effective leverage here is 3.64x, not the 4.0x the term sheet headline suggests; quoting 4.0x to the borrower would promise debt the second test will not allow.

Rs 25 lakh a year, Rs 6.25 lakh a quarter and about Rs 6,850 a day. A basis point is 0.0001, so Rs 2,500 crore times 0.0001 is Rs 0.25 crore, Rs 25 lakh a year. Divide by four for a quarter. Divide by 365 for a day, which gives Rs 6,849 on an actual/365 basis, or Rs 6,944 on a 360-day basis.

Why would a desk ask something this simple?

A shopkeeper who knows that one rupee off a product's price costs her Rs 3,000 a month in margin negotiates very differently from one who has to work it out after the customer leaves. Every pricing conversation in debt markets is in basis points, and the listener has to turn them into rupees on the deal in front of them instantly. An issuer who hears that 5 basis points is on the table wants to know that means Rs 1.25 crore a year, not to wait for a spreadsheet.

What changes when the basis point is on price instead of coupon?

The numbers above are one basis point of coupon or spread, paid each year. A basis point of yield on a bond's price is a different quantity. A one basis point move in yield changes a bond's value by roughly its duration times the notional times 0.0001, so on a five-year bond with duration near 4 it is about Rs 1 crore, not Rs 25 lakh. The two agree once you see why: five years of Rs 25 lakh, discounted at 8%, is worth about Rs 99.8 lakh today. Duration is roughly the present value of a stream of basis points.

Day counts are the last detail worth a sentence. Many rupee bonds count actual days over 365, while money market instruments and many floating rate loans elsewhere use 360; confirm the convention in the term sheet rather than assume it. The difference on one day is about Rs 95 here, trivial on a day and material over a large book, which is why the convention is always named in the documents.

Roughly Rs 270 crore of bank working capital credit outstanding, within a range of about Rs 150 to Rs 430 crore. A city of 1 crore has about 25 lakh households; at one shop per 100 households that is 25,000 shops. At Rs 50 lakh of sales each, they sell Rs 12,500 crore a year. Thirty days of stock less ten of supplier credit leaves 20 days to fund, Rs 685 crore, and banks fund an assumed 40%.

What exactly are you sizing?

A grocer pays the wholesaler for rice and oil before customers buy them. The money stuck on the shelves in between is the working capital, and a bank limit fills the part that the owner's own cash and the wholesaler's credit do not cover. The answer is a balance outstanding, the credit tied up at any moment through the year, not the total of every rupee drawn and repaid. Saying that first stops the interviewer wondering whether you are sizing sales or credit.

Now build it from people. A city of 1 crore at 4 people a household is 25 lakh households. Assume one small grocery shop per 100 households: 25,000 shops. Assume each sells Rs 50 lakh a year, so all of them sell Rs 12,500 crore. Check that against households: Rs 12,500 crore over 25 lakh households is about Rs 4,167 a month each at the local shop, a plausible share of a family's grocery bill. If it looked absurd, one of the first three links would be wrong.

How do stock days turn into a rupee need?

Each shop then carries about Rs 1.1 lakh of bank limit. A range is more honest than a point here, because the bank share is the weakest assumption: much small-shop credit comes from wholesalers, family and informal lenders. Moving net days between 15 and 25 and the bank share between 30% and 50% spreads the answer from about Rs 154 crore to Rs 428 crore. Customer credit, the running tab a grocer gives regular families, would add to the need; five days of it at the same bank share adds about Rs 68 crore.

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.

Loan B, with an expected loss of Rs 0.45 crore against Rs 0.10 crore for Loan A. Expected loss is exposure times default probability times loss given default. Loan A: 50 x 1% x 20% is Rs 10 lakh. Loan B: 20 x 3% x 75% is Rs 45 lakh, 4.5 times as much on a loan less than half the size. Security and borrower quality matter more than the headline amount.

What goes into expected loss?

Imagine lending your bicycle to two friends. One borrows the expensive one but always returns things and leaves his phone as a deposit; the other borrows a cheap one, loses things often, and leaves nothing. What you expect to lose depends on how much you lend, how likely it is to go wrong, and how much you get back if it does, multiplied together. Lenders write those three as EAD, PD and LGD.

What does the answer mean for pricing?

Express each loss as a rate on the loan. Loan A costs 0.2% a year in expected losses; Loan B costs 2.25%, so B needs roughly two points more of spread just to break even on credit losses. Two factors did that. The default probability tripled, and the lack of security nearly quadrupled the loss when things go wrong. Security is why a secured loan to a weaker borrower can be safer than an unsecured loan to a stronger one.

Say the limit. Expected loss is an average; it covers the cost of doing business, not the bad year. A credit portfolioA book of many loans, where losses depend on how many default together, not only on each loan alone. with a few large loans can lose far more than its expected loss when one of them fails. Loan A's Rs 10 lakh expected loss hides a Rs 10 crore hit if it defaults, which is why lenders hold capital for unexpected loss as well.

The implied one-year rate a year from now is about 8.20%. Rs 100 at 7.6% for two years grows to 115.78. Rs 100 at 7% for one year grows to 107, so the second year must turn 107 into 115.78: a rate of 8.20%. It is above both spot rates because the two-year rate is an average, and the second year has to be high enough to pull the 7% first year up to 7.6%.

What does a forward rate actually mean?

You can reach the next town by the highway in one go or by a side road with a stop halfway. If both leave at the same time and arrive at the same time, the second leg of the side road must make up whatever speed the first leg lost. A forward rate is the rate for the second leg that makes lending for two years in one go pay exactly the same as lending for one year and rolling over. If the two routes paid differently, everyone would take the better one until they did not.

Why must the forward sit above both spot rates?

Because the two-year rate is roughly the average of the two one-year legs. If the first leg earns 7% and the average is 7.6%, the second leg must earn about 7.6% plus the 0.6 the first leg fell short, roughly 8.2%. The quick approximation is two times 7.6 less 7, which is 8.2%; compounding adds the last few hundredths to give 8.20%. On an upward sloping curve, forwards always sit above the spot rates, and the steeper the curve, the further above.

Say what the forward is not. It is not a forecast of where one-year rates will be; it is the break-even rate that makes the two routes equal today. If investors demand extra yield for locking money up longer, a term premium, the forward will sit above what the market truly expects. A desk uses it to price a forward starting loan or to judge whether rolling short or locking long is cheaper.

The price is 125 at 6.4% and 83.33 at 9.6%: a gain of 25 against a loss of 16.67. A perpetuity is worth its coupon divided by the yield, so 8 over 0.064 and 8 over 0.096. The price-yield curve is bowed, not straight, which is convexity: for the same move either way, the price rises more than it falls, and the gap grows with the size of the move.

How do you price a bond that never matures?

Think of a shop that pays you Rs 8 of rent every year forever. If you want an 8% return, you will pay Rs 100 for it; if 6.4% is enough, you will pay Rs 125, because 6.4% of 125 is 8. A perpetuity's price is simply its annual payment divided by the yield investors demand. No maturity, no final repayment, no discounting table: one division does all the work.

Why is the gain bigger than the loss?

Because the price curve bends toward you. When yields fall, each extra basis point lifts the price more than the last, and when yields rise, each basis point cuts it less than the last, so equal moves produce unequal price changes in the holder's favour. That bend is convexityThe curvature of the price-yield relationship; positive convexity means prices gain more when yields fall than they lose when yields rise by the same amount.. The average of 125 and 83.33 is 104.17, above the starting 100, which is the whole idea in one number.

A perpetuity has a lot of it, because its cash flows stretch to infinity. At 8% its duration is 1 over the yield, about 12.5 years, so a straight-line estimate would say 1.6 points moves the price about 20 either way. The truth, +25 and -16.67, shows how badly a duration-only estimate does on large moves for long bonds. The limit is that convexity helps only a holder of an option-free bond; a callable perpetual would lose most of that upside.

50% with a fair coin, and about 64.6% with a 55% win rate. With a fair coin, your capital is a fair bet, so the chance of reaching 6 from 3 is 3 over 6. With an edge, the chance is 1 over 1 plus (q over p) cubed, where q over p is 0.45 over 0.55. That gives 1 over 1.548, or 64.6%. Spread the same edge over walls ten times further away and it rises to about 99.8%.

Why is the fair-coin answer simply 3 over 6?

Picture a game where you and a friend toss a coin for Rs 1 until one of you is broke; you start with Rs 3, the friend with Rs 3. Every toss is fair, so on average nobody gains, and your expected wealth at the end must still be Rs 3. If the game ends at 0 or 6 and your expected ending wealth is 3, you must reach 6 exactly half the time. In general the fair-coin chance of reaching N from i is i over N.

How does a 55% edge change it?

This is the classic gambler's ruinA random walk that stops at two walls, used to find the chance of hitting one wall before the other. set-up. A 55% edge on each trade turns into a 64.6% chance of doubling before going broke, a modest lift because the walls are only three steps away. The fair game takes 9 trades on average to finish, so the edge only gets a handful of chances to work.

That is the lesson a desk wants. The same edge, bet in smaller pieces relative to capital, almost removes the risk of ruin: starting at 30 with a target of 60 and 1-unit trades, the chance of success is 99.8%. Betting a large share of capital on each trade throws the edge away, because variance gets to end the game before the edge shows. The limit is the model itself: real trades do not win or lose exactly one unit, and edges are estimated, not known.

Pre-funding costs about Rs 13 crore of negative carry, before tax. The issuer pays 8.2% on the new bond while earning 6.9% on the parked cash, a 1.3% gap on Rs 1,000 crore for twelve months. In return it removes refinancing risk: it no longer needs the market to be open, spreads to hold and its rating to survive the final year. On a five-year deal, waiting would have to cost more than about 26 basis points a year for pre-funding to lose.

What exactly does pre-funding cost?

A family renting a flat signs a new lease a year before the old one ends because rents are rising and good flats are scarce. For twelve months they pay a little extra holding the new flat, but they are not searching in a panic the week the old lease ends. Pre-funding costs the gap between what the new money costs and what the parked cash earns, for as long as both exist: the negative carryThe cost of holding a position whose income is lower than its funding cost, here cash earning less than the bond that raised it.. Here 8.2% less 6.9% is 1.3%, on Rs 1,000 crore for a year, Rs 13 crore, about Rs 1.08 crore a month.

What does that Rs 13 crore buy?

Certainty. Without pre-funding, the issuer must refinance in a narrow window before maturity, and if markets are shut, spreads have widened or its rating has slipped in that window, it either pays far more or cannot repay. Pre-funding is insurance with a known premium. A useful breakeven: spread over a five-year replacement bond, Rs 13 crore is about 26 basis points a year before discounting and about 33 after. If waiting risked a rise larger than that, or a missed maturity, the premium was cheap.

Say the refinements. Interest paid is usually tax deductible and interest earned is taxable, so at an assumed 25% rate on both the after-tax carry is about Rs 9.75 crore. The issuer also carries a bigger balance sheet for a year, gross debt rises before the old bond goes, which can briefly worsen reported leverage. And the parked cash must be invested safely and kept liquid; reaching for yield on it defeats the purpose of paying for certainty.

About 35.7%. Set the price equal to the probability-weighted payoff: p times 100 plus 1 minus p times 30 equals 55. The 30 is paid either way, so the price only has to cover 25 of the 70-point gap between recovery and par, and 25 over 70 is 35.7%. The market thinks restructuring is nearly twice as likely as repayment.

How do you turn a price into a probability?

Suppose a raffle ticket pays Rs 100 if you win and Rs 30 as a consolation prize if you lose, and it sells for Rs 55. Everyone gets the Rs 30, so you are really paying Rs 25 for a shot at an extra Rs 70. A price between two outcomes is a probability-weighted average of them, so you can solve for the weight. The consolation prize matters: ignore it and you would read the Rs 55 as a 55% chance.

What does ignoring discounting hide?

Both payoffs arrive in the future, often a year or more away, and a distressed investor wants a high return for waiting. If the payoffs arrive in a year and the buyer demands 12%, the price must equal the expected payoff divided by 1.12, which lifts the implied repayment probability to about 45.1%. So the 35.7% is a floor: part of the discount to par is a charge for time and risk, not only for default. That is why desks quote these as risk-neutral probabilities, not forecasts.

The other soft spot is the recovery of 30. It is an estimate, and the implied probability is sensitive to it: at a recovery of 40, p is 15 over 60, 25%. Before trading on the number, a credit analyst would test the recovery from the balance sheet and the claims ranking ahead of this bond.