Debt Capital Markets puzzles, solved step by step

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

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063Which carries more interest rate risk: a 10-year floating rate note that resets every quarter, bought just after a reset, or a 2-year bond with a fixed 7% annual coupon yielding 7%? Estimate each one's duration.Duration and convexityWarm upFixed income asset management

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Which has the longer interest rate duration?

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The 2-year fixed bond carries far more rate risk: a duration of about 1.9 years against about 0.25 for the floater. The floater's coupon resets to the market every quarter, so a rate move can only hurt it until the next reset, three months away. The fixed bond is locked at 7% for two years, and its Macaulay duration is 1.93 years. A 1 point rise in rates costs the floater about 0.25 points and the fixed bond about 1.78.

Why is a 10-year floater so short on rate risk?

Think of two landlords. One has let a flat for two years at a fixed rent; the other has a ten-year lease whose rent is reset to the market every three months. If market rents jump, the first is stuck for two years and the second catches up within a quarter. A floater's coupon resets to the market rate on every reset date, so its value can only drift from par for the few months until the next reset, whatever its final maturity. Just after a reset, that is about a quarter of a year.

The 10-year floater's coupon is locked for only three months, a rate duration of about 0.25 years, while the 2-year fixed bond's coupon is locked for both years, a duration of 1.93 years, so the shorter bond carries about 8 times the rate risk.

The relationship

D_{fix} = \frac{1 \times \tfrac{7}{1.07} + 2 \times \tfrac{107}{1.07^{2}}}{100} = 1.93 \qquad D_{FRN} \approx 0.25

D_fix	Macaulay duration of the fixed bond, its value-weighted average time to the cash flows
7, 107	the fixed bond's two annual cash flows per Rs 100
D_FRN	the floater's rate duration, about the time to its next reset

What it says in wordsA fixed bond's duration runs to its cash flows; a floater's runs only to its next reset.

What does each lose if rates rise one point?

Reprice both at a rate 1 point higher: the fixed bond falls from 100 to 98.22, a loss of 1.78, while the floater loses only 0.25, because it earns the old coupon for one quarter and then resets. The fixed bond carries about 8 times the rate risk of a note five times its length. This is why a bank funding itself with three-month deposits is comfortable holding floaters: the asset and the liability reprice together.

Keep the other risk in view. The floater's short rate duration says nothing about credit: its spread duration runs to maturity, about 7 years here, so a widening in the issuer's spread hits it far harder than it hits the 2-year bond. Name both numbers if the interviewer pushes, because the claim that floaters are low risk is only half true. The limit: this assumes a flat 7% curve and an issuer whose credit does not change.

Where candidates lose it

The trap is equating maturity with rate risk. A 10-year floater sounds riskier than a 2-year bond, but its coupon catches up with the market every quarter, so a rate move can hurt it for a few months at most.

The second loss is stopping there and calling the floater safe. It has almost no rate duration but a long spread duration; say both, or the follow-up on credit will catch you.

What the interviewer asks next

Halfway between two resets, what is the floater's rate duration?
A bank funds itself with 3-month deposits. Which of the two bonds matches its funding better, and why?
Roughly what is the spread duration of the 10-year floater, and what does a 50 basis point widening cost it?

067A company has assets worth Rs 100 crore today and a Rs 80 crore zero-coupon loan due in a year. Next year the assets will be worth either Rs 60 crore or Rs 140 crore. What do the lender and the shareholders get in each case, and which side would prefer the company to hold riskier assets?Capital structure and recoveryWarm upCredit research
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Which side wants the company to take on riskier assets?
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At Rs 60 crore the lender gets 60 and shareholders nothing; at Rs 140 crore the lender gets 80 and shareholders 60. Shareholders prefer riskier assets. The lender's payoff is capped at the Rs 80 crore it is owed, while shareholders keep everything above 80 and cannot fall below zero. Equity works like a call option on the assets with a strike of 80, so more volatility moves value from the lender to the shareholders.
Who gets what in each outcome?
A student borrows Rs 80,000 from a relative to start a small business and owes it back in a year. If the business ends up worth Rs 60,000, the relative gets Rs 60,000 and the student nothing; if it is worth Rs 1,40,000, the relative gets Rs 80,000 and the student keeps Rs 60,000. The lender's payoff is the smaller of the asset value and what it is owed; the shareholders' payoff is whatever is left above the debt, never below zero. Here that is 60 or 80 for the lender and 0 or 60 for the shareholders.
The lender's payoff rises with asset value only up to the Rs 80 crore it is owed, while the shareholders' payoff is zero below 80 and rises one for one above it, so widening the outcomes to 20 or 180 cuts the lender's average from Rs 70 crore to Rs 50 crore and lifts the shareholders' from Rs 30 crore to Rs 50 crore.
The relationship
$\text{Debt} = \min(V,\ 80) \qquad \text{Equity} = \max(V - 80,\ 0)$
V the value of the assets next year
80 the face value of the loan, the strike of the option
What it says in wordsThe lender is paid the asset value up to 80; the shareholders get the excess over 80, or nothing.
Why do shareholders like risk and lenders dislike it?
Keep the average at Rs 100 crore but widen the outcomes to Rs 20 or Rs 180 crore, each equally likely. The lender now gets 20 or 80, an average of 50 instead of 70, while shareholders get 0 or 100, an average of 50 instead of 30. Nothing about the business improved on average; Rs 20 crore of value simply moved from the lender to the shareholders. That is the shape of a call optionThe right, not the obligation, to buy something at a fixed price, so the holder keeps the upside above that price and loses nothing more below it.: capped loss, open-ended gain, so volatility helps the holder.
Case Asset value Lender gets Shareholders get Lender average Equity average
As planned 60 or 140 60 or 80 0 or 60 70 30
Riskier assets 20 or 180 20 or 80 0 or 100 50 50
Rs crore, each outcome assumed equally likely. Widening the outcomes leaves the asset average at Rs 100 crore but moves Rs 20 crore of expected value from the lender to the shareholders.
Say why a lender cares, because it is the point of the question. Loan documents restrict what a borrower can do with its assets, with limits on new debt, asset sales, dividends and changes of business, to stop shareholders swapping safe assets for risky ones after the loan is made. The pull is strongest near distress, as here, because shareholders have little left to lose. The limit: the 50/50 odds are an assumption, and the option view ignores that managers may also care about keeping the company alive.
Where candidates lose it
Candidates say nobody prefers more risk because the average asset value is unchanged. That treats both claims as if they shared outcomes equally, and they do not: the lender's payoff is capped and the equity's is floored.
The second miss is getting the payoffs right but never naming the option. Say equity is a call on the assets struck at the face value of the debt, and the follow-up on volatility answers itself.
What the interviewer asks next
With 50/50 odds, what is the loan worth today if investors discount at 10%?
The company can pay a Rs 20 crore dividend today out of its assets. Who gains and who loses?
Which covenants would you write into the loan to stop a switch to riskier assets?
073A company has EBITDA of Rs 200 crore, gross debt of Rs 900 crore and cash of Rs 300 crore. It uses Rs 200 crore of its cash to repay debt. What happens to its gross leverage and to its net leverage?Leverage, coverage and cash flowWarm upLeveraged financeCorporate banking
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What happens to net leverage?
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Gross leverage falls from 4.5x to 3.5x; net leverage stays at 3.0x. Gross debt drops from Rs 900 crore to Rs 700 crore against EBITDA of Rs 200 crore. Net debt is 900 minus 300 before and 700 minus 100 after, Rs 600 crore both times, because cash and debt fall together. The repayment cuts interest and tidies the balance sheet, but it does not change what the company owes net of what it holds.
Why does one ratio move and the other stay put?
If you owe a friend Rs 9,000 and have Rs 3,000 in your wallet, you are Rs 6,000 in the hole. Hand over Rs 2,000 and you owe Rs 7,000 with Rs 1,000 left: still Rs 6,000 in the hole. Net debt already counts the cash as if it could repay debt, so actually using the cash to repay debt changes nothing in the net figure. Gross debt ignores the cash, so it falls by the full Rs 200 crore.
Repaying Rs 200 crore of debt from cash takes gross leverage from 4.5x to 3.5x, but debt and cash fall together, so net debt stays at Rs 600 crore and net leverage stays at 3.0x.
The relationship
$\text{Gross: } \frac{900}{200} = 4.5\times \to \frac{700}{200} = 3.5\times \qquad \text{Net: } \frac{900-300}{200} = \frac{700-100}{200} = 3.0\times$
900, 700 gross debt before and after, Rs crore
300, 100 cash before and after, Rs crore
200 EBITDA, Rs crore, unchanged by the repayment
What it says in wordsGross leverage sees only the debt; net leverage sees debt less cash, and both fall by the same amount.
Why would a company repay debt with cash at all?
Because the money still changes: interest on Rs 200 crore of debt usually costs more than the same cash earns on deposit. If the debt costs 9% and the cash earns 6%, repaying saves about Rs 6 crore a year of net interest. It also matters where covenants are written on gross debt, as some loan documents are, and where the cash sits in a subsidiary or abroad and could not easily reach lenders in a crisis. That is why credit analysts ask whether cash is truly available before netting it.
Now look at the other side. Spending the cash also removes a cushion: a company with Rs 100 crore of cash has less room to absorb a bad quarter than one with Rs 300 crore, at the same net leverage. Lenders and rating analysts look at liquidity alongside leverage for this reason. The limit: this assumes EBITDA is untouched by the repayment, which holds, because interest sits below EBITDA.
Where candidates lose it
The fast wrong answer is that both ratios improve, because repaying debt sounds like deleveraging. Net leverage already assumed the cash could repay debt, so doing it changes nothing on that measure.
The opposite slip is saying the repayment achieved nothing. It lowers gross leverage, cuts net interest cost and spends liquidity; name all three.
What the interviewer asks next
The company instead raises Rs 200 crore of new debt and holds it as cash. What happens to each ratio?
Which leverage figure would you write into a covenant, and why?
When is it risky to net cash against debt?
087A company has an enterprise value of Rs 100 crore and debt of Rs 60 crore, and no cash. Its enterprise value falls 20%. By how much does its equity value fall?Capital structure and recoveryWarm upCredit research
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Answer in one breath.
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Equity falls 50%, from Rs 40 crore to Rs 20 crore. Enterprise value drops Rs 20 crore to Rs 80 crore, but the Rs 60 crore of debt does not shrink, so the whole Rs 20 crore comes off equity. Equity was only 40% of the business, so a 20% fall in the business is 20% x 2.5 = 50% of the equity.
Why does a 20% fall become a 50% fall?
Buy a Rs 1 crore flat with Rs 40 lakh of your own money and a Rs 60 lakh loan. If flat prices fall 20%, the flat is worth Rs 80 lakh, the bank still wants Rs 60 lakh, and your stake is Rs 20 lakh: half gone. Debt is a fixed claim, so every rupee lost in enterprise value comes off the equity, and the smaller the equity slice, the bigger the percentage fall. The multiplier is enterprise value over equity, here 100 over 40, or 2.5.
Enterprise value falls from Rs 100 crore to Rs 80 crore while debt stays at Rs 60 crore, so equity halves from Rs 40 crore to Rs 20 crore and the loan to value ratio climbs from 60% to 75%.
The relationship
$\%\Delta E = \%\Delta EV \times \frac{EV}{E} = -20\% \times \frac{100}{40} = -50\%$
EV enterprise value, Rs 100 crore
E equity value, Rs 40 crore
%Delta percentage change
What it says in wordsThe equity moves by the business's move times the leverage multiplier.
How does a lender read the same numbers?
From the lender's chair the question is how much cushion is left. The loan to value ratio climbs from 60% to 75%, so the equity buffer that protects the debt has halved even though the debt itself is untouched. Another 25% fall in enterprise value, to Rs 60 crore, would take equity to zero and put the lenders' own money at risk. That is why credit desks track enterprise value and covenants tied to it, not just whether interest is being paid.
Where candidates lose it
The instant answer is 20%, because the business fell 20%. It forgets that the debt claim is fixed and does not share in the fall.
The second slip is saying 33% by dividing 20 by 60, the debt, instead of by 40, the equity. Say the three numbers in order, 40, then 20, then half, and the answer is audible.
What the interviewer asks next
By how much would equity rise if enterprise value rose 20% instead?
What fall in enterprise value wipes out the equity completely?
The company holds Rs 10 crore of cash as well. How does the answer change?
089A 10-year government bond yields 7.0% and expected inflation is 4.5%. What is the real yield using the Fisher relation, and how far off is the quick subtraction?Yield curve and forward ratesWarm upFixed income asset management
Try it first
Is the exact real yield above or below the 2.5% you get by subtracting?
Show the worked solution
The real yield is about 2.39%, against 2.50% from simple subtraction. The Fisher relation divides one plus the nominal yield by one plus inflation: 1.07 / 1.045 - 1 = 2.39%. The shortcut overstates the real yield by about 11 basis points, because inflation also erodes the interest itself, and the gap widens as rates rise.
Why is subtraction only an approximation?
Lend Rs 100 for a year at 7% and get Rs 107 back. If prices have risen 4.5%, a basket that cost Rs 100 now costs Rs 104.50. Your Rs 107 buys 107 / 104.5 baskets, 1.0239 of them: a real gain of 2.39%, not 2.5%. Inflation shrinks the purchasing power of everything you get back, the interest as well as the principal, so the real yield is a ratio, not a difference.
At 7.0% nominal and 4.5% inflation the exact real yield is 2.39%, 11 basis points below the 2.50% shortcut, and with the same 2.5 point difference the gap grows from about 4 basis points at low rates to 32 at 15% and 12%.
The relationship
$1 + r = \frac{1 + n}{1 + \pi} \;\Rightarrow\; r = \frac{1.07}{1.045} - 1 = 2.39\%$
n the nominal yield, 7.0%
pi expected inflation, 4.5%
r the real yield
What it says in wordsReal growth is nominal growth divided by price growth.
When does the shortcut stop being good enough?
The error is roughly the real yield times inflation, divided by one plus inflation. At low rates it is a few basis points and nobody minds; at high inflation it is tens of basis points and it changes the conclusion. With nominal yields of 15% and inflation of 12%, subtraction says 3.0% but the true real yield is 2.68%. For a desk comparing an inflation-linked bond with a conventional one, a gap of that size is the whole trade. The rates here are illustrations; the relation, not the numbers, is the point.
Where candidates lose it
The fast answer is 2.5% with no comment. It is close enough on these numbers, but an interviewer asking for the Fisher relation wants the ratio, and wants you to say which way the shortcut errs.
The second loss is getting the direction backwards and saying the exact figure is higher. Anchor it with the basket example: Rs 107 buys fewer than 1.025 baskets once they cost Rs 104.50.
What the interviewer asks next
An inflation-indexed bond of the same maturity yields 2.0% real. What inflation is the market pricing in?
Why might the gap between nominal and indexed yields not equal expected inflation exactly?
If inflation is higher than expected, who gains: the holder of the nominal bond or the issuer?
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?Estimation and market sizingWarm upStructured creditCorporate banking
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How many Rs 20 lakh loans make Rs 1,000 crore?
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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?
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?Leverage, coverage and cash flowWarm upCorporate bankingLeveraged finance
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Where does interest cover land?
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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 relationship
$\text{Cover} = \frac{EBITDA}{D \times r}: \quad \frac{300}{1{,}000 \times 10\%} = 3.0\times \;\to\; \frac{300}{1{,}000 \times 11.5\%} = 2.61\times$
EBITDA 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?

Case	Asset value	Lender gets	Shareholders get	Lender average	Equity average
As planned	60 or 140	60 or 80	0 or 60	70	30
Riskier assets	20 or 180	20 or 80	0 or 100	50	50

900, 700	gross debt before and after, Rs crore
300, 100	cash before and after, Rs crore
200	EBITDA, Rs crore, unchanged by the repayment

EV	enterprise value, Rs 100 crore
E	equity value, Rs 40 crore
%Delta	percentage change

n	the nominal yield, 7.0%
pi	expected inflation, 4.5%
r	the real yield

Try it first

Why is a 10-year floater so short on rate risk?

What does each lose if rates rise one point?

Where candidates lose it

What the interviewer asks next

Try it first

Who gets what in each outcome?

Why do shareholders like risk and lenders dislike it?

Where candidates lose it

What the interviewer asks next

Try it first

Why does one ratio move and the other stay put?

Why would a company repay debt with cash at all?

Where candidates lose it

What the interviewer asks next

Try it first

Why does a 20% fall become a 50% fall?

How does a lender read the same numbers?

Where candidates lose it

What the interviewer asks next

Try it first

Why is subtraction only an approximation?

When does the shortcut stop being good enough?

Where candidates lose it

What the interviewer asks next

Try it first

How do you avoid a units slip?

Why can the financier not just use the whole book?

What would change the count?

Where candidates lose it

What the interviewer asks next

Try it first

Why does a small rate move matter so much?

What would a lender ask next?

Where candidates lose it

What the interviewer asks next