Debt Capital Markets puzzles, solved step by step
- Puzzles
- 100
- Traced to a firm
- 16
- Topics
- 13
- Hard
- 30
095A company has EBITDA of Rs 300 crore and Rs 1,000 crore of debt, all floating at 10%. The benchmark rate rises by 150 basis points. What happens to its interest cover?Corporate bankingLeveraged finance
Try it first
Where does interest cover land?
Show the worked solution
Interest cover falls from 3.0x to about 2.61x. All the debt is floating, so the rate goes from 10% to 11.5% and interest from Rs 100 crore to Rs 115 crore. EBITDA is unchanged at Rs 300 crore, so cover is 300 / 115 = 2.61x. A 15% rise in the interest bill cuts cover by about 13%, with no change in the business at all.
Why does a small rate move matter so much?
A household on a floating home loan feels a rate rise in the very next EMI, even though nothing about its salary has changed. Companies with floating debt feel it the same way. Floating rate debt passes a benchmark rise straight into the interest bill, so coverage falls even when the business is doing exactly as well as before. Here 150 basis points on Rs 1,000 crore is Rs 15 crore a year, a 15% rise in interest.
A 150 basis point rise lifts interest on Rs 1,000 crore of floating debt from Rs 100 crore to Rs 115 crore, and with EBITDA unchanged at Rs 300 crore, interest cover falls from 3.0x to 2.61x. The relationshipEBITDA earnings before interest, tax, depreciation and amortisation, Rs 300 crore D floating rate debt, Rs 1,000 crore r the all-in floating rate, 10% before and 11.5% after What it says in wordsCoverage is earnings over the interest bill, and on floating debt the bill moves with the benchmark.What would a lender ask next?
Two questions: how much headroom is left, and how much is hedged. Cover would reach 2.0x only if interest rose to Rs 150 crore, a rate of 15%, so the benchmark would need to climb another 350 basis points from here. Hedging changes the answer more than anything else: if 60% of the debt were swapped to fixed, the same rise would add only Rs 6 crore of interest and cover would fall only to 2.83x. A banker who sees all-floating debt at 3.0x cover asks about hedging before anything else.
Where candidates lose it
The common slip is saying cover is unchanged because EBITDA did not move. The ratio has two sides, and floating debt makes the bottom one move.
The second is reporting 2.6x without the cause: interest up 15%, from Rs 100 crore to Rs 115 crore. The interviewer wants to hear that the business is unchanged and the capital structure did the damage.
What the interviewer asks next
- If covenants require cover of at least 2.5x, how far can the benchmark rise before the breach?
- What share of the debt would need to be fixed to keep cover above 2.8x after the rise?
- Why might EBITDA also fall when rates rise, and what does that do to the answer?
097You are selling a loan and will receive five bids one at a time, in random order. You must accept or reject each bid on the spot, and a rejected bid never comes back. What rule maximises your chance of accepting the single best bid, and what is that chance?Syndicate desksCorporate banking
Try it first
Which rule gives the best chance of ending with the top bid?
Show the worked solution
Reject the first two bids, then accept the first bid that beats both of them; you get the best bid 43.3% of the time. Taking the first or last bid wins only 20%. The two rejected bids set a benchmark, and the rule succeeds whenever the best bid comes later and the best of the bids before it sits among the first two. Checking all 120 orderings gives 52 wins, which is 43.3%.
Why reject bids you know nothing wrong with?
House hunting in a city you do not know, you would look at a couple of flats before signing anything, simply to learn what good looks like. Sign too early and you never had a benchmark; look too long and the best one may already be gone. The rejected bids are the price of information: they set the bar that later bids must clear, and the only question is how many to spend. With five bids, spending two is the best trade.
Rejecting the first two bids and then taking the first bid that beats them picks the best of five bids 43.3% of the time, against 20% for taking the first or the last bid and 41.7% or 35.0% for rejecting one or three. How do you get 43.3% without listing all 120 orders?
Ask where the best bid sits. If it is in the first two, you have already rejected it and lose. If it sits at position j, from 3 to 5, you take it only if no earlier bid after the first two already beat the bar, which happens when the best of the first j minus 1 bids lies in the first two. That chance is 2 out of (j minus 1), so the rule wins with probability one fifth of (2/2 + 2/3 + 2/4), which is 43.3%. Say the structure; the arithmetic takes ten seconds.
The relationship1/5 the chance the best bid is in any given position 2/(j-1) the chance that, with the best bid at position j, the best earlier bid is among the two rejected What it says in wordsAdd up, over each place the best bid could arrive, the chance the rule is still waiting when it gets there.What is the limitation for a real loan sale?
Two things. The rule maximises the chance of the very best bid, not the expected price; a seller who cares about the average price would behave differently. And real loan sales rarely force on-the-spot decisions: a desk runs a process that collects bids together, precisely to avoid this problem. With many bids, the rule becomes the well-known look at about 37% and then leap, and the success rate falls towards about 37% too.
Where candidates lose it
The common answer is to take the first good-looking bid. It wins only 20% of the time, because a good-looking bid with no benchmark is just a random bid.
The second loss is knowing the 37% rule and applying it blindly: 37% of five is 1.85 bids, and the candidate who rounds without checking may reject one instead of two. Compute the small case directly; it takes a few lines.
What the interviewer asks next
- With ten bids, how many would you reject first?
- If you are paid the bid you accept rather than rewarded only for the best, does the rule change?
- Rejected bidders may come back with 50% probability. How does that change your cut-off?
098You have 1,000 bottles of wine and exactly one is poisoned. The poison shows its effect after 24 hours, and you have one day to find the bottle. What is the fewest testers you need, and how do you assign the bottles to them?Syndicate desks
Try it first
How many testers do you need?
Show the worked solution
10 testers. Number the bottles 1 to 1,000 and write each number in binary with ten digits. Tester n drinks from every bottle whose n-th binary digit is 1. After 24 hours, the testers who fall ill spell out the poisoned bottle's number in binary. Ten testers give 1,024 possible patterns, enough for 1,000 bottles; nine give only 512.
Why is each tester worth a binary digit?
Think of the game twenty questions: every yes-or-no answer halves the possibilities, so twenty answers can pick out one thing in about a million. A tester is one yes-or-no answer: ill or fine. With one round of results, n testers can produce 2 to the power n different patterns, and you need at least as many patterns as bottles. 2^9 = 512 falls short of 1,000; 2^10 = 1,024 covers it. So ten is both enough and the minimum.
Each bottle number written in ten binary digits tells each tester whether to drink from it, and if bottle 613 is poisoned, testers 10, 7, 6, 3, 1 fall ill, whose place values add back to 613. How do you read the answer back?
Give tester n the place value 2 to the power (n minus 1): tester 1 is worth 1, tester 2 worth 2, up to tester 10 worth 512. Add the place values of the testers who fall ill and you have the bottle number. If bottle 613 is poisoned, its binary form is 1001100101, so testers 10, 7, 6, 3, 1 fall ill, and 512 + 64 + 32 + 4 + 1 = 613. Numbering 1 to 1,000 fits in ten digits because 1,000 is below 1,024, and the pattern where nobody falls ill is left spare.
The relationship2^n the number of distinct ill-or-fine patterns n testers can produce What it says in wordsTen testers are the fewest whose outcomes can label every bottle.The desk version of the lesson: design the test so that every outcome carries information. A tester who drinks from one bottle learns about one bottle; a tester who drinks from half of them splits the problem in two.
Where candidates lose it
The common answers are 1,000 testers, one bottle each, or some splitting scheme that needs several rounds. The 24 hour delay allows only one round, so the testers must be designed to answer in parallel.
The second loss is giving 10 without the proof that 9 is not enough. Say 2^9 is 512 in the same breath; it turns a remembered trick into an argument.
What the interviewer asks next
- You have two days instead of one, and a tester who falls ill on day one is out. How many testers do you need?
- Exactly two bottles are poisoned. Does the binary scheme still work?
- How many testers would a million bottles need?
099At initial price thoughts of 150 basis points over the benchmark, a bond's order book is 4 times covered. Each 5 basis points of tightening loses 10% of the original demand. How far can you tighten and still keep the book at least 2 times covered?Syndicate desks
Try it first
Where does the book hit 2 times cover?
Show the worked solution
You can tighten 25 basis points, to 125, and still be 2 times covered. Each 5 basis point step loses 10% of the original demand, which is 0.4x of cover. Going from 4.0x to 2.0x gives up 2.0x, or five steps, so 5 x 5 = 25 basis points. On a Rs 500 crore deal the book falls from Rs 2,000 crore to Rs 1,000 crore, and the issuer saves Rs 1.25 crore a year.
What is actually being traded off?
A shopkeeper with a queue of forty customers for twenty items can raise the price, and some customers will walk away; the question is how high to go before the queue gets too short to be comfortable. Book-building trades cover for price: each step tighter saves the issuer money and costs orders, and cover is the buffer against a weak aftermarket. Here every 5 basis points costs 0.4x, because the loss is 10% of the original book each time.
Starting at 4.0x cover at 150 basis points, each 5 basis points of tightening removes 0.4x, so the book reaches the 2.0x floor at 125 and any further tightening leaves it under-covered. The relationships the final spread in basis points 0.4 the cover lost per 5 bp step, 10% of the original 4.0x 2.0 the minimum cover you want to keep What it says in wordsCover falls by the same amount every step, so divide the cover you can spare by the cover each step costs.Would you really go all the way to 125?
Not automatically. The linear rule is a model of the book; real books drop in lumps, because price-sensitive orders carry limits and the orders that leave first are often the highest quality long-term investors. Landing exactly on the 2.0x floor leaves no margin if a few orders drop after the final terms. A syndicate desk might stop one step short, at 130 with 2.4x cover, giving up Rs 0.25 crore a year of saving on Rs 500 crore for a safer book and a better chance of a positive break. The arithmetic sets the limit; the judgement picks the point inside it.
Where candidates lose it
The common slip is treating 10% as 10% of the remaining book, which makes each step smaller and the answer wider than 25 basis points. The question says original demand, so the steps are equal.
The second loss is stopping at the number. The interviewer wants to hear what cover is for, why the real book is lumpier than the model, and why a desk might leave some tightening unused.
What the interviewer asks next
- If each step lost 10% of the remaining book instead, how far could you tighten?
- What else in the book, besides its size, would you look at before tightening?
- Why might an issuer prefer a larger deal at 130 to the planned size at 125?