Debt Capital Markets puzzles, solved step by step

Puzzles: 100
Traced to a firm: 16
Topics: 13
Hard: 30

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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.Estimation and market sizingCoreIndian 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 relationship
$\text{Pool} = N \times S \times f = 1{,}100 \times 400 \times 0.0010 = 440\text{ Rs crore}$
N 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?

035Estimate the annual working capital credit demand of small grocery shops in a city of 1 crore people. State each assumption.Estimation and market sizingCoreCorporate bankingIndian debt capital markets

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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 relationship

\text{Bank credit} = \text{Sales} \times \frac{\text{stock days} - \text{supplier days}}{365} \times \text{bank share} = 12{,}500 \times \frac{20}{365} \times 0.4 \approx 274

12,500	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?Estimation and market sizingCoreCorporate bankingIndian debt capital markets
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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 relationship
$\text{Debt} = 10{,}000\ \text{MW} \times \text{Rs } 4 \text{ to } 5\ \text{crore per MW} \times 75\% = \text{Rs } 30{,}000 \text{ to } 37{,}500\ \text{crore}$
10,000 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?
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?Estimation and market sizingCoreFixed income asset managementSyndicate desks
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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 relationship
$\text{Days} = \frac{\text{Position}}{\text{ADV} \times \text{participation}} = \frac{5{,}000}{1{,}000 \times 2\%} = 250$
Position 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?

N	issues a year, 1,100
S	average issue size, Rs 400 crore
f	fee as a share of the amount raised, 10 basis points

10,000 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

Position	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%

Try it first

How do you structure it before any number?

Where do the assumptions come from?

What do you say after the range?

Where candidates lose it

What the interviewer asks next

Try it first

What exactly are you sizing?

How do stock days turn into a rupee need?

Where candidates lose it

What the interviewer asks next

Try it first

How do you structure the estimate before any arithmetic?

Which assumption moves the answer most?

Where candidates lose it

What the interviewer asks next

Try it first

Why is the answer not five days?

What does this tell you about liquidity?

Where candidates lose it

What the interviewer asks next