Debt Capital Markets puzzles, solved step by step
- Puzzles
- 100
- Traced to a firm
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- Topics
- 13
- Hard
- 30
003Estimate how much debt a new metro line could raise against its fare box. Build it from daily riders, average fare and operating margin, then apply a 1.4x debt service cover at 9% over 20 years.Corporate bankingIndian debt capital markets
Try it first
Once you have the yearly cash available for debt, which step turns it into a debt figure?
Show the worked solution
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.
Five lakh riders a day at Rs 30 is Rs 548 crore of fares; a 40% margin leaves Rs 219 crore, a 1.4x cover allows Rs 156 crore of debt service, and twenty years of that at 9% supports about Rs 1,428 crore, with each lakh of daily riders worth about Rs 286 crore of debt. 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.
The relationshipN riders a day, 5 lakh F average fare, Rs 30 m operating margin on fares, 40% DSCR the lender's debt service cover, 1.4x D debt capacity, Rs crore What it says in wordsYearly fares times margin gives cash; divide by the cover for the allowed payment; take twenty years of present value at 9% for the debt.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.
Where candidates lose it
Most candidates stop at revenue, or multiply one year's cash by twenty. The first ignores costs and the lender's cushion, the second ignores interest, and both overstate the debt by a wide margin.
The quieter loss is giving one number with no range. Ridership is the least certain input, so end with the answer at three ridership levels; an estimate without a sensitivity sounds like a guess.
What the interviewer asks next
- The authority raises the average fare to Rs 35 but ridership falls 10%. What happens to debt capacity?
- How would you size the debt if ridership ramps up over the first five years?
- Would you rather lend against the fare box or against a fixed availability payment from the authority, and why?
008Estimate the annual fee pool for debt capital markets bankers in a country from the number of bond issues, their average size and the fee rate. State your assumptions and give a range rather than a single number.Indian debt capital markets
Try it first
Which assumption will move your answer the most?
Show the worked solution
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.
At 1,100 issues a year, Rs 400 crore each and 10 basis points, the pool is about Rs 440 crore; moving the fee rate from 5 to 20 basis points swings it from Rs 220 crore to Rs 880 crore, far more than realistic ranges on issue count or size. 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.
The relationshipN issues a year, 1,100 S average issue size, Rs 400 crore f fee as a share of the amount raised, 10 basis points What it says in wordsVolume times the fee rate, with volume built from a count and an average size.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.
Where candidates lose it
The usual loss is spending the time on the issue count, the most visible input, and then picking a fee rate in one breath. The answer ends up precise on volume and arbitrary on the one input that decides it.
The second is giving one number. Low, base and high cases with the driver named, here Rs 175 to Rs 1,080 crore, show the interviewer that you know what you do not know.
What the interviewer asks next
- How would the pool change if a quarter of issuance moved to public issues paying twice the fee?
- How would you estimate one bank's share of the pool?
- Why might a bank accept a thin fee on a bond mandate?
028Size the annual flow of new two-wheeler loans in India that a securitisation desk could buy. Build it from households, ownership, the replacement cycle, the financed share and the ticket size, state every assumption, and do not rely on a remembered industry figure.Structured creditIndian debt capital markets
Try it first
Which link in the chain moves the answer most if you get it wrong?
Show the worked solution
About Rs 1 lakh crore of new two-wheeler loans a year, of which perhaps Rs 31,000 crore could reach a securitisation desk. Assume 30 crore households, 55% owning 1.2 vehicles each: 19.8 crore in use. Replacing them every 10 years plus 0.3 crore first-time buyers gives 2.28 crore sales. At 60% financed and Rs 75,000 a loan, that is about Rs 1,02,600 crore; the 30% pool-eligible share is an assumption.
Where do you start a sizing question without a known number?
Start from people and the things they own, then ask how often those things are bought. A family that runs one scooter for ten years buys a scooter every tenth year, so a street of a hundred such families buys about ten a year. Annual sales of a durable good are roughly the number in use divided by how many years each one lasts, plus whatever first-time buyers add. That structure lets you build the answer from facts you can defend instead of a figure half remembered from a newspaper.
Say each assumption out loud as an assumption. Households: 30 crore, and say you would confirm the current census estimate. Ownership: 55% of households, with 1.2 vehicles each where they own one, which gives 19.8 crore two-wheelers on the road. Life: 10 years, so replacement demand is 1.98 crore a year. New owners: if ownership climbs one point a year, 0.3 crore households buy their first. Total: 2.28 crore a year.
Thirty crore households at 55% ownership and 1.2 vehicles each give 19.8 crore two-wheelers in use, a 10-year cycle plus first-time buyers gives 2.28 crore sales, and 60% financed at Rs 75,000 gives about Rs 1,02,600 crore of loans a year, within a range of Rs 74,100 to Rs 1,35,660 crore. How do you turn units into a rupee flow the desk can buy?
Two more links. Share financed: assume 60% of buyers borrow. Ticket: an average vehicle of Rs 1 lakh with a 75% loan-to-valueThe loan as a share of the price of the asset it buys. A 75% loan-to-value on a Rs 1 lakh scooter is a Rs 75,000 loan. is a Rs 75,000 loan. So 1.37 crore loans at Rs 75,000 each is about Rs 1,02,600 crore a year. Then cut to what a securitisation desk can actually buy: only loans made by lenders who sell pools, which at an assumed 30% is about Rs 30,780 crore. Banks that keep loans on their books never reach the desk.
How do you show the interviewer the number is sane?
Give a range and name the link that drives it. Moving the financed share between 50% and 70% and the ticket between Rs 65,000 and Rs 85,000 spreads the answer from Rs 74,100 crore to Rs 1,35,660 crore. A range with a named driver is more credible than a single precise figure. Then say the check you would run outside the room: compare 2.28 crore units with the industry body's published domestic sales, and the rupee total with the originators' disclosed disbursements. The chain is only as good as its weakest assumption, which here is the replacement cycle.
Where candidates lose it
The fast failure is quoting a figure you think you read somewhere and defending it. The interviewer asked for the build precisely to take memory out of it; a remembered number with no structure scores lower than a transparent chain that lands a little off.
The second failure is stopping at total loan volume. The question asked what a securitisation desk could buy, so the last link, the share of loans made by lenders who actually sell pools, is part of the answer and deserves its own stated assumption.
What the interviewer asks next
- Which of your assumptions would you test first with one phone call, and to whom?
- How does the answer change if electric two-wheelers push the average ticket to Rs 1.2 lakh?
- Why might a desk prefer these pools to a single corporate bond of the same size?
035Estimate the annual working capital credit demand of small grocery shops in a city of 1 crore people. State each assumption.Corporate bankingIndian debt capital markets
Try it first
What drives the size of a shop's working capital need most directly?
Show the worked solution
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.
A city of 1 crore gives about 25,000 grocery shops selling Rs 12,500 crore a year; with 30 days of stock and 10 days of supplier credit, 20 days of sales, Rs 685 crore, need funding, and banks at 40% provide about Rs 274 crore. How do stock days turn into a rupee need?
The relationship12,500 annual sales of all the shops, Rs crore 20 days of sales the shops must fund themselves, 30 of stock less 10 of supplier credit 0.4 assumed share of that gap funded by banks rather than owners or informal lenders What it says in wordsDaily sales times the days of funding gap gives the money tied up; the bank share gives the part that shows up as bank credit.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.
Where candidates lose it
Candidates often size annual sales and present that as the credit need. Rs 12,500 crore of sales is not Rs 12,500 crore of borrowing; only the days of sales tied up in stock need funding, and only part of that comes from banks.
The second loss is skipping the sanity check. Dividing sales back to a monthly spend per household takes ten seconds and shows the interviewer your chain holds together.
What the interviewer asks next
- Wholesalers extend supplier credit from 10 to 20 days. What happens to bank credit demand?
- How would you size the same market for a digital lender that underwrites on shop sales data?
- Which of your assumptions would a small-business lender know best?
059Estimate the debt needed to build 10 GW of new solar capacity, assuming a project cost of Rs 4 to 5 crore per MW and 75% debt funding. How sensitive is the answer to the cost assumption?Corporate bankingIndian debt capital markets
Try it first
Roughly how much debt is that?
Show the worked solution
About Rs 30,000 to 37,500 crore of debt, with Rs 33,750 crore at the midpoint. 10 GW is 10,000 MW; at Rs 4 to 5 crore per MW the build costs Rs 40,000 to 50,000 crore, and 75% of that is debt. The answer moves one for one with the cost per MW: every Rs 0.5 crore per MW shifts the debt by Rs 3,750 crore, more than the effect of moving the gearing five points.
How do you structure the estimate before any arithmetic?
Estimating a home loan starts with the price per square foot, times the floor area, times the share the bank will fund. A project debt estimate is the same chain: capacity times cost per unit of capacity gives the project cost, and the debt share of that cost gives the borrowing. Say the chain out loud first, with its units: megawatts, crore per megawatt, then a percentage. The most common slip in this question is a units error, not an arithmetic one.
The relationship10,000 MW 10 GW of capacity, since 1 GW is 1,000 MW Rs 4 to 5 crore per MW the all-in project cost range given in the question 75% the share of project cost funded with debt What it says in wordsCapacity times cost per MW gives the project cost; the debt share of that is the borrowing.10,000 MW at Rs 4 to 5 crore per MW with 75% debt needs Rs 30,000 to 37,500 crore of borrowing, and the cost assumption swings the answer by Rs 7,500 crore against Rs 4,500 crore for a ten point swing in gearing. Which assumption moves the answer most?
Flex each input across a sensible range while holding the other at its midpoint. Moving the cost from Rs 4 to Rs 5 crore per MW swings the debt by Rs 7,500 crore; moving the gearing from 70% to 80% swings it by Rs 4,500 crore. So the cost assumption is the one to defend, or to ask about. A lender would also want to know how much of the cost is modules against land, grid connection and construction, because those pieces move for different reasons.
Close with the range, not a single number. An estimate built on a range of inputs should come out as a range, with the midpoint named and the driver identified. At the midpoint, Rs 33,750 crore at an assumed 9% would carry roughly Rs 3,038 crore of interest a year. The costs here are the question's assumptions, not current market figures; in a real pitch you would confirm the cost per MW and typical gearing against recent project financings before using them.
Where candidates lose it
The usual loss is units. Candidates multiply 10 by Rs 4 to 5 crore and answer Rs 40 to 50 crore, or forget the 75% and give the whole project cost as the debt.
The second is a single number with false precision. The cost input is a range, so the output is a range: say Rs 30,000 to 37,500 crore, name the midpoint, and say which assumption drives the spread.
What the interviewer asks next
- Roughly what annual interest bill does the midpoint debt carry at 9%, and what cash flow would cover it 1.3 times?
- How would you split this debt between bank loans and bonds, and why?
- Construction costs fall 20% while gearing rises to 80%. What is the new debt estimate?
090A truck financier wants to sell a Rs 1,000 crore pool of loans into an asset-backed securitisation. Its average truck loan is Rs 20 lakh. How many loans does it need, and what would stop it simply using its whole book?Structured creditCorporate banking
Try it first
How many Rs 20 lakh loans make Rs 1,000 crore?
Show the worked solution
About 5,000 loans, before any filters. Rs 1,000 crore is 1,00,000 lakh, and 1,00,000 divided by 20 is 5,000. The book cannot all go in because a pool takes only eligible loans: current on payments, held long enough to show a track record, and within concentration limits. If the notes must be overcollateralised by 10%, the pool needs about 5,500 loans.
How do you avoid a units slip?
If you are filling a Rs 1,000 box with Rs 20 notes, you need 50 notes; the only way to get it wrong is to mix up rupees and hundreds. Lakh and crore are the Indian version of that trap. Put both numbers in lakh before dividing: Rs 1,000 crore is 1,00,000 lakh, and 1,00,000 over 20 is 5,000. Say the conversion out loud; interviewers listen for it.
In this illustrative book of 12,000 truck loans, overdue, recently disbursed and over-concentrated loans fall away, leaving 7,200 eligible, enough for the 5,000 loans a Rs 1,000 crore pool needs, or 5,500 with 10% overcollateralisation. Why can the financier not just use the whole book?
Investors and rating agencies buy a pool with rules attached. Eligibility criteriaThe conditions every loan must meet to enter a securitised pool, such as being current on payments and having a minimum repayment history. typically exclude loans that are overdue, loans too new to have shown a repayment record, and loans that would push the pool over limits on any one borrower, region or vehicle type. So the pool size starts with simple division and ends with eligibility: the question is not how many loans exist but how many qualify. India's securitisation rules also set a minimum holding period and a minimum retention by the originator; confirm the current figures in the RBI's directions rather than relying on memory.
What would change the count?
Two things. First, Rs 20 lakh may be the average loan at disbursal; loans that have been repaying for a year or two have smaller outstanding balances. If the average outstanding is Rs 14 lakh, the pool needs about 7,143 loans. Second, structures often require the pool to exceed the notes sold, so Rs 1,000 crore of notes might need Rs 1,100 crore of loans. The financier also has a reason not to strip its best loans out: what remains on its own balance sheet gets worse.
Where candidates lose it
The common loss is a zero: 500 or 50,000 loans from mixing lakh and crore. Convert both figures to lakh before you divide.
The second is stopping at 5,000. The follow-up is always about eligibility, and a candidate who can name three filters and the difference between disbursed and outstanding balance shows they know how a pool is actually put together.
What the interviewer asks next
- If 20% of the book is overdue or unseasoned, how large must the book be to fill the pool?
- Why would investors want a cap on the share of loans from any one state?
- Would you expect the pool's average loan to be larger or smaller than the book's, and why?
091A fund wants to buy Rs 5,000 crore of a bond segment where average daily trading is Rs 1,000 crore, and it will not take more than 2% of each day's volume. How long does it take to build the position, and what does that say about liquidity?Fixed income asset managementSyndicate desks
Try it first
Roughly how long does the fund need?
Show the worked solution
About 250 trading days, roughly a year. The fund may buy 2% of Rs 1,000 crore, which is Rs 20 crore a day, and Rs 5,000 crore divided by Rs 20 crore is 250. The position is five full days of the whole market's trading, which makes it illiquid for this fund: it would take about as long to sell as to buy.
Why is the answer not five days?
Imagine wanting to buy 500 kilos of tomatoes from a village market that sells 100 kilos a day. In theory it is five days of the market's supply; in practice, if you take everything, prices jump and the regular buyers go home empty handed. So you decide to take no more than a couple of kilos a day. The limit on your share of daily volume, not the market's total volume, sets how fast you can trade, and here that limit is Rs 20 crore a day. Rs 5,000 crore at Rs 20 crore a day is 250 days.
At 2% of Rs 1,000 crore a day the fund buys Rs 20 crore daily and needs 250 trading days, about a year, while a 10% share of volume would take 50 days and a segment ten times as liquid 25 days. The relationshipPosition the amount to buy, Rs 5,000 crore ADV average daily volume, Rs 1,000 crore participation the most of each day's volume the fund will take, 2% What it says in wordsDivide what you want to trade by what you are allowed to trade each day.What does this tell you about liquidity?
Liquidity belongs to a position, not to a market: the same bonds are liquid for a Rs 50 crore holder and illiquid for a Rs 5,000 crore holder. Days to trade is the simplest honest measure. At 250 days, the fund carries a year of market risk while it builds, and faces the same year if it ever needs to sell, which matters most exactly when others are selling too. Daily volume also falls in a stressed market, so the exit could take longer than the entry. A desk would size the position down, accept a higher participation rate and more price impact, or look for a block trade or a new issue where it can take size in one go.
Where candidates lose it
The fast wrong answer is five days, dividing the position by the whole market's volume. It ignores the participation limit that the question hands you.
The second loss is giving 250 days and stopping. The interviewer wants the implication: this position is illiquid for this fund, the exit is the real risk, and there are ways to get size faster, each with a cost.
What the interviewer asks next
- If the fund accepts 5% of daily volume, how long does it take, and what does it give up?
- Daily volume halves in a sell-off. How long would it take to exit the full position at 2%?
- Why might a new issue be a better way to build this position than the secondary market?
