Debt Capital Markets puzzles, solved step by step

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100
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All topicsLeverage, coverage and cash flow9Mental maths and numeracy8Estimation and market sizing7Logic and brainteasers8Cost of capital and valuation riddles7Bond pricing and yield7Compounding, PIK and fees6Issuance and refinancing arithmetic8Credit spreads and default probability8Duration and convexity8Capital structure and recovery8Probability and expected value10Yield curve and forward rates6
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  1. 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.Estimation and market sizingHardCorporate 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.

    From riders to rupees of debt: five steps, one assumption eachRiders a day5 lakhassumedFares a yearRs 548 crx Rs 30 x 365Cash from opsRs 219 crx 40% marginDebt serviceRs 156 cr/ 1.4 coverDebt capacityRs 1,428 crx 9.13, 20 yrs 9%Debt capacity if ridership is lower or higher, every other assumption held, Rs crore3 lakh a day8575 lakh a day1,4287 lakh a day1,999Each lakh of daily riders supports about Rs 286 crore of debt
    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 relationship
    D=N×F×365×mDSCR×1−(1.09)−200.09≈547.5×0.401.4×9.129≈1,428D = \frac{N \times F \times 365 \times m}{\text{DSCR}} \times \frac{1-(1.09)^{-20}}{0.09} \approx \frac{547.5 \times 0.40}{1.4} \times 9.129 \approx 1{,}428
    Nriders a day, 5 lakh
    Faverage fare, Rs 30
    moperating margin on fares, 40%
    DSCRthe lender's debt service cover, 1.4x
    Ddebt 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?
  2. 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.Estimation and market sizingHardStructured 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.

    From people to rupees: one stated assumption per linkHouseholds30 crorean assumption:confirm censusTwo-wheelers in use19.8 crore55% own x 1.2 eachBought each year2.28 crore1.98 replace + 0.30 newBought on a loan1.37 crore60% financedNew loans a yearRs 1,02,600 crRs 75,000 eachRange when financed share runs 50% to 70% and the ticket Rs 65,000 to Rs 85,000, Rs crore74,1001,35,660central 1,02,60060,00090,0001,20,0001,50,000Only loans from lenders who sell pools reach the desk: at an assumed 30%, about Rs 30,780 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?