Debt Capital Markets puzzles, solved step by step

About Rs 296 crore. A 1.3x cover means only 60 divided by 1.3, Rs 46.15 crore a year, can go to interest and principal. A level payment of that size for 10 years at 9% repays a loan equal to its present value: 46.15 times the annuity factor of 6.418, about Rs 296.2 crore. Debt capacity is the present value of the cash the lender lets you spend on debt.

What does the cover ratio actually limit?

Think of a family with Rs 60,000 a month to spare applying for a home loan. The bank will not let the whole Rs 60,000 go to the EMI; it wants a cushion in case a month goes wrong. A debt service cover of 1.3x means every rupee of loan payment must be backed by 1.3 rupees of cash, so the most the project can pay each year is 60 divided by 1.3, Rs 46.15 crore. The remaining Rs 13.85 crore is the lender's buffer against a bad year. It is not money you can borrow against.

How do you turn an allowed payment into a loan amount?

The loan is whatever amount those payments exactly repay with interest. A loan is the present value of the payments that service it, discounted at the loan's own rate. Ten level payments of Rs 46.15 crore at 9% are worth 46.15 times the ten year annuity factorThe present value of receiving 1 a year for a set number of years at a given rate. For 10 years at 9% it is about 6.42.. Look at the green bars: year 1's payment is worth Rs 42.3 crore today, year 10's only Rs 19.5 crore, because money further away is worth less now.

Check it out loud. Rs 296 crore at 9% is Rs 26.7 crore of first year interest, so the first payment of Rs 46.15 crore repays only about Rs 19.5 crore of principal. With a level payment, principal is repaid slowly at first and faster later, because interest takes the biggest bite while the balance is largest. If you can say that, the interviewer knows you understand what the annuity factor is doing rather than reciting it.

What would a lender push back on?

The Rs 60 crore is a forecast, and a forecast is exactly what a sponsor is paid to be optimistic about. The cover protects the lender only if the cash flow it is applied to is honest, so the real negotiation is over which forecast the 1.3x is applied to. Lenders often size on a downside case, shorten the tenor, or ask for a reserve account that holds some months of debt service in cash. Each of those moves the answer more than a quarter point on the rate would. State the limit too: the sum assumes the project runs all ten years and that nothing needs refinancing.

About 38 and about 0.026. A 1% daily gain doubles money roughly every 70 days, so a year holds just over five doublings: 2 to the power 5.2 is about 37.8. A 1% daily loss halves it about every 69 days, leaving about 0.026. The two outcomes end roughly 1,481 times apart: a tiny daily edge, held consistently, is enormous by year end.

Why is 365 times 1% the wrong way to think about it?

Picture a savings jar where every evening you add 1% of whatever is already inside. On day 1 that is one paisa per rupee; by day 200 the jar holds about seven times its start, so 1% of it is seven paise of the original rupee. Compounding means each day's 1% is earned on everything built so far, so the growth accelerates rather than adding up in a straight line. Simple addition, 365 times 1%, gives 4.65 and misses almost all of it.

How do you get to 38 without a calculator?

Use the rule of 70A shortcut: a quantity growing at r per cent a period doubles in about 70 divided by r periods.. At 1% a day, money doubles in about 70 days. A year of 365 days holds about 5.2 doublings, and 2 to the power 5 is 32 while 2 to the power 5.2 is about 37, so the answer is in the high thirties. The exact figure is 37.78. The same shortcut run backwards gives the loss: 1% down a day halves value about every 69 days, a little over five halvings in a year, which is one part in about 40.

Why does a markets interviewer care about this?

Because desks live on small edges repeated many times: a few basis points of carry every day, a slightly better fill on every trade, a small cost leak on every rebalance. An edge or a leak that looks trivial on one day decides the year, and it cuts both ways. Also notice that up 1% then down 1% does not get you back: 1.01 times 0.99 is 0.9999. Volatility on its own drags a compounding path downwards, which is worth one sentence after the numbers. The limit: real returns are not a steady 1% a day, so treat this as arithmetic about compounding, not a model of any market.

On my assumptions, about Rs 1,400 crore. Five lakh riders a day at an average Rs 30 fare is about Rs 548 crore of fares a year. A 40% operating margin leaves about Rs 219 crore of cash; a 1.4x cover allows Rs 156 crore a year of debt service. Twenty years of that at 9% is worth about Rs 1,428 crore. Every lakh of daily riders adds or removes about Rs 286 crore.

What structure do you say before any number?

Say the chain first, so the interviewer can follow every assumption: riders, fares, cash, allowed debt service, debt. Debt capacity is a cash flow estimate divided by a cover ratio and turned into a present value, so the whole answer is only as good as the riders and the margin you assume. A tea stall owner asking for a loan gets the same treatment: cups a day, price a cup, what is left after milk and rent, and how much of that the bank will let go to the EMI.

Where do the assumptions come from, and which one matters most?

Each is an illustration you should defend in a sentence. Five lakh daily riders is a busy urban line, not a flagship. Rs 30 is an average across short and long trips. Forty per cent is the margin after staff, power and maintenance, before depreciation. Ridership drives everything, because it multiplies straight through: at 3 lakh riders the capacity falls to about Rs 857 crore, at 7 lakh it rises to about Rs 1,999 crore. Say the range out loud; it shows you know which input moves the answer.

What would a lender say about this number?

Three things. First, ridership on a new line ramps up over several years, so the early payments are the riskiest and a lender may want a grace period or a lower cover test in the first years. Second, a fare box alone rarely funds the build: the debt it supports is usually a slice of the cost, with the rest from grants, equity or land and advertising income. Third, fares are often set by a public authority, so the lender is exposed to a fare decision it does not control. Closing on that shows you see the loan as a credit, not a spreadsheet.

7.5 degrees. The minute hand at 15 minutes points exactly at the 3, which is 90 degrees from 12. The hour hand moves half a degree every minute, so at 3:15 it sits at 3 times 30 plus 15 times 0.5, which is 97.5 degrees. The gap is 97.5 minus 90, or 7.5 degrees.

Why is zero the wrong answer?

Zero comes from picturing a clock as two independent pointers that jump. The hour hand moves continuously: it covers 30 degrees between one number and the next over 60 minutes, so it moves half a degree every minute. At quarter past, it has done a quarter of its journey from 3 to 4. Think of a train between two stations: fifteen minutes into an hour long run, you are not still standing on the first platform.

What is the general method, so any time works?

Measure both hands from 12 in degrees. The minute hand sits at 6 degrees times the minutes; the hour hand sits at 30 degrees times the hours plus half a degree times the minutes. Subtract, and if the result is over 180, take 360 minus it to get the smaller angle. Saying the method before the number is what the interviewer is listening for, because the next question will be a harder time.

Why does a capital markets desk ask this?

It is a speed and care test, not a clock test. The question checks whether you notice that two things are moving when the obvious reading has only one moving. The same slip in a desk setting is quoting a yield as if the price had not moved since the morning, or pricing accrued interest as if the settlement date were today. After the answer, one sentence on the 5.5 degrees a minute rule shows you can generalise.

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.

About 7.14%. The buyer pays Rs 98.25 and gets Rs 100 back 91 days later, a gain of Rs 1.75 on Rs 98.25 invested, which is 1.781% for the period. Scaling by 365 over 91 gives 7.14% a year. It beats 1.75 times four for two reasons: the return is earned on the price paid, not the face value, and a year holds a little more than four 91 day periods.

Why divide by 98.25 and not by 100?

Lend a friend Rs 98 and get Rs 100 back: you made Rs 2 on Rs 98, not on Rs 100. A yield is always the gain divided by the money you actually put in, and on a discounted bill that is the price, not the face value. Dividing by 100 gives the discount rate, a quoting convention that understates what the buyer earns. On a Rs 1.75 gain the difference is small, but interviewers ask this precisely to see whether you know which base is which.

Why 365 over 91 instead of 4?

A quarter is not exactly 91 days: 365 divided by 91 is 4.011. On a 365 day basis a 91 day return is scaled by 365 over 91, so the days in the bill's life, not the word quarter, set the multiplier. That adds only about two basis points here, but on bills of 182 or 364 days, or where day counts differ between markets, getting the multiplier right is exactly what a desk checks.

Is 7.14% what the buyer really earns over a year?

Only if the gain is not reinvested. If the buyer rolls into a new bill at the same price every 91 days, interest earns interest and the effective annual rate is about 7.34%. Simple and compounded yields answer different questions, so say which one you are quoting. The simple formula here is the convention commonly used to quote Treasury bills; confirm the convention and day count of the market you are pricing in before comparing a bill yield with a bond yield, which may be stated on a different basis.

On my assumptions, roughly Rs 175 crore to Rs 1,080 crore a year, with a base case near Rs 440 crore. Base case: 1,100 issues a year at an average Rs 400 crore is about Rs 4.4 lakh crore of issuance, and a 10 basis point fee on that is Rs 440 crore. The fee rate drives the range far more than volume does.

How do you structure it before any number?

Say the formula first: issues a year, times average size, times the fee as a share of the amount raised. A fee pool is a small percentage of a large volume, so the rate you apply matters more than how precisely you count the volume. Think of a wedding planner's income: the number of weddings and the average budget are easy to guess roughly, but whether the planner takes 2% or 10% of the budget changes the answer five times over.

Where do the assumptions come from?

Each should be defended in one line and flagged as an assumption to check. The issue count and size here are guesses for a bond market where banks, finance companies and public sector issuers place large issues with institutions; public issuance data and league tables would replace them in real work. The fee rate is the least observable input, because arranger fees on privately placed, top rated issues can be a few basis points while complex or lower rated deals pay much more. So the range runs from 5 to 20 basis points around a 10 basis point base.

What do you say after the range?

Test it against something you know. A pool of a few hundred crore rupees shared across many arrangers means each bank's domestic bond fee income is modest, which is why desks care about volume, league table rank and the other products a mandate brings. Then name what would change the view: a shift from private placements to larger public issues, or more lower rated issuance, would push the average fee up. Say clearly that every figure here is an illustrative assumption for the method, not a market statistic.

Rs 5.075 crore. The annual coupon is 7.25% of Rs 350 crore, Rs 25.375 crore. On actual/365, 73 days is exactly one fifth of a year, because 73 times 5 is 365. One fifth of Rs 25.375 crore is Rs 5.075 crore, which a buyer settling on day 73 pays the seller on top of the clean price.

What do you look for before you multiply?

A friendly fraction. Mental maths on a desk is mostly spotting which number makes the rest easy. 73 is exactly a fifth of 365, so the whole calculation collapses to one fifth of the annual coupon. It is like splitting a Rs 25,375 bill between five friends: nobody reaches for a calculator once they see it is a clean fifth. Say the fraction out loud first, so the interviewer hears the shortcut rather than watching you grind through 7.25 times 350 times 73.

How do you get the annual coupon quickly?

Split the rate. 7% of 350 is 24.5 and a quarter per cent of 350 is 0.875, so the annual coupon is Rs 25.375 crore. Breaking an awkward rate into a round rate plus a small piece keeps each multiplication in your head. Then divide by five: 25 divided by 5 is 5, and 0.375 divided by 5 is 0.075, so Rs 5.075 crore. Another route is 350 divided by 5 first, which is 70, and 7.25% of 70 is 5.075. Either way, two steps.

Why does accrued interest matter on a trade?

Because the seller has earned 73 days of coupon but the buyer will receive the whole next coupon. The buyer pays the accrued interest to the seller at settlement, so the cash that changes hands is the clean price plus accrued, the dirty price. On Rs 350 crore, Rs 5.08 crore is real money. Also say the limit: the day count convention varies by market and by instrument, and actual/365, actual/actual and 30/360 give slightly different answers, so check the bond's terms before you settle.

Principal of about Rs 115.76 and a year 3 coupon of about Rs 2.32. The principal is lifted by inflation each year and compounds: 100 times 1.05 cubed is Rs 115.7625. The 2% real coupon is paid on that indexed principal, so the year 3 coupon is Rs 2.315. Both the coupon and the principal keep their buying power, which is what the investor is paying for.

What exactly is being indexed?

Think of a rent agreement where the rent rises with inflation every year and the deposit is topped up by the same percentage. On an indexed bond the principal is scaled up by inflation, and the fixed real coupon rate is then applied to that scaled principal, so both the income and the repayment keep pace with prices. After one year of 5% inflation the principal is Rs 105 and the coupon is 2% of 105, Rs 2.10, not Rs 2.

Why does the principal compound instead of adding 5 a year?

Because the index is a price level, and price levels compound: 5% in year 2 is 5% of the already higher year 1 prices. The indexed principal is the original principal times the ratio of today's index to the index at issue, which after three years of 5% is 1.05 cubed. Adding 5 a year gives 115, off by Rs 0.76, small here but large over a 10 or 20 year bond.

What does that mean for the yield an investor sees?

Bought at Rs 100, the cash flows 2.10, 2.205 and 118.08 give a money return of about 7.1% a year, which is 1.02 times 1.05 minus 1: the real 2% plus inflation plus a small cross term. The investor has locked in a real return of 2% whatever inflation turns out to be, and that certainty is the product. Say the limits: actual indexed bonds use a lagged index, some protect principal from falling below par, and the tax treatment of the uplift varies, so check the specific bond's terms.