Debt Capital Markets puzzles, solved step by step

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

Showing 71–80 of 84 · filtered from 100Clear filters

084A 5-year credit default swap trades with a standard running coupon of 100 basis points, but the market spread for the name is 400 basis points and the risky duration is 4.0. What upfront payment changes hands, and who pays it?Credit spreads and default probabilityHardSyndicate desksCredit research
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Who pays the upfront amount, and roughly how much?
Show the worked solution
The protection buyer pays about 12% of notional upfront. The contract's running coupon is 100 basis points but fair protection costs 400, so the buyer underpays by 300 basis points a year. Multiply by the risky duration of 4.0, the present value of one basis point a year until default or maturity, and the shortfall is 1,200 basis points, or 12 points: Rs 12 crore on Rs 100 crore of protection.
Why does a standard coupon create an upfront payment?
Think of a gym that charges every member the same Rs 1,000 a month but costs Rs 4,000 a month to run for some members. It can only take them if they pay the Rs 3,000 a month difference as a lump sum on joining. Standardised credit default swaps work that way. The running coupon is fixed by the contract rather than set to the market, so the gap between the market spread and the coupon, for every year the protection is expected to run, is settled as one payment on the first day.
Paying a running coupon of 100 basis points for protection the market prices at 400 leaves 300 basis points a year missing, and 300 times a risky duration of 4.0 is 12 points, which the protection buyer pays upfront.
The relationship
$\text{Upfront} \approx (S - C) \times RD = (400 - 100)\text{ bp} \times 4.0 = 1{,}200\text{ bp} = 12\%$
S the market spread, 400 bp a year
C the contract's fixed running coupon, 100 bp a year
RD risky duration: the present value of 1 bp a year, paid until default or maturity
What it says in wordsThe upfront payment is the yearly shortfall in the coupon multiplied by how many risky years it is paid for.
Why is the risky duration less than five?
Premiums on a credit default swap stop the moment the name defaults, so the expected number of payments is lower than five, and each one is discounted. A risky duration of 4.0 sits below the 4.33 of a plain five-year annuity at 5% because some of those payments will never be made. The riskier the name, the lower the risky duration, which is why a desk re-computes it rather than assuming it stays fixed as the spread moves. The formula above is the market's first approximation; the full calculation also nets accrued premium and uses a model of default timing.
What happens when the spread is below the coupon?
The sign flips. If the market spread were 50 basis points against a 100 coupon, the buyer would overpay by 50 a year and the seller would pay the buyer about 2 points upfront. Whoever is getting the better running deal pays the difference on day one.
Where candidates lose it
The common mistake is the sign. Candidates say the seller pays because the seller is taking the risk, but the seller is being underpaid at 100 basis points, so it is the buyer who owes the difference.
The second is forgetting the multiplication: 300 basis points is a yearly shortfall, and it has to be turned into a present value with the risky duration before it is a payment.
What the interviewer asks next
The spread widens to 500 the next day. Roughly what is the buyer's gain on Rs 100 crore?
Why would a market move to fixed coupons with upfront payments instead of quoting a running spread?
What default probability does a 400 basis point spread imply if you expect 40% recovery?
085You have two ropes. Each takes exactly 60 minutes to burn from one end to the other, but they burn unevenly, so half a rope does not take 30 minutes. With a lighter and nothing else, how do you measure exactly 45 minutes?Logic and brainteasersCoreSyndicate desks
Try it first
What is the one move that makes this possible?
Show the worked solution
Light rope A at both ends and rope B at one end at the same moment. Rope A burns out after exactly 30 minutes. At that instant, light the other end of rope B, which has 30 minutes of burn left. With two flames it finishes in 15 minutes, so rope B goes out at exactly 45 minutes.
Why does lighting both ends always give 30 minutes?
Two people painting a fence from opposite ends meet when the whole fence is painted, whatever the pace on each stretch; if the job is one hour for one painter, together they finish in half an hour. A rope's burn time behaves the same way: two flames consume the rope's 60 minutes of burn between them, so they must meet after 30 minutes, even though the meeting point is not the middle of the rope. Unevenness changes where they meet, never when.
Rope A, lit at both ends, burns out at 30 minutes; that is the signal to light rope B's other end, and the 30 minutes of burn left in rope B then finish in 15 minutes, at the 45 minute mark.
Why does rope B have exactly 30 minutes left?
Rope B has burned from one end for 30 minutes, so 30 of its 60 minutes of burn are gone and 30 remain, spread unevenly along whatever length is left. Lighting its other end applies the same halving trick to what remains: 30 minutes of burn with two flames takes 15. 30 plus 15 is 45. The trick works on any remaining burn time, not just a whole rope.
The relationship
$t_{\text{both ends}} = \frac{t_{\text{one end}}}{2} \qquad 30 + \frac{30}{2} = 45$
t one end burn time with one flame
t both ends burn time with two flames, always half
What it says in wordsTwo flames halve whatever burn time is left, so a half followed by a half of a half gives 45 minutes.
Say what the puzzle is testing, briefly: separating what you know (total burn time) from what you do not (where along the rope that time sits). A desk reading a bond's cash flows faces the same split: the total is fixed, the timing can be lumpy.
Where candidates lose it
The common wrong move is cutting a rope in half and assuming each half burns for 30 minutes. The question tells you the burn is uneven precisely to rule that out, and an interviewer will stop you there.
The second loss is lighting both ropes at both ends at once and then being stuck with two 30 minute timers. Keep one flame on rope B back until rope A tells you 30 minutes have passed.
What the interviewer asks next
How would you measure exactly 15 minutes with the same two ropes?
With only one rope, which times can you measure?
Using both ropes, list every time you can measure exactly.
086A holding company has Rs 200 crore of bonds and no other debt. Its only asset is an operating company worth Rs 700 crore, which has Rs 600 crore of its own loans. What do the holding company bondholders recover in a default, and what changes if the operating company guarantees the holding company bonds?Capital structure and recoveryHardRestructuringCredit research
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Without the guarantee, what do the holding company bonds recover?
Show the worked solution
Without the guarantee the bonds recover 50%; with it, about 87.5%. The operating lenders are paid first from the Rs 700 crore, so only Rs 100 crore reaches the holding company for Rs 200 crore of bonds. A guarantee gives the bonds a direct claim on the operating company, equal with its loans if both are unsecured: Rs 700 crore across Rs 800 crore of claims, Rs 175 crore to the bonds.
Why do holding company bondholders get only what is left?
Lend money to a friend whose only asset is a stake in the family shop. If the shop fails, its suppliers and its bank are paid out of the shop's till first, and your friend receives only what is left over, if anything. Holding company bonds sit in exactly that position. The holding company owns shares, not assets, so its lenders are paid only from the equity value of the operating company, after every creditor of the operating company has been paid in full. This is called structural subordinationBeing junior not because of a clause in the documents but because your borrower sits higher up a corporate chain than the assets., and no ranking clause in the bond documents can undo it.
Without a guarantee the operating lenders take their full Rs 600 crore and the holding company bonds recover Rs 100 crore of Rs 200 crore, 50%; with a guarantee both sets of creditors share Rs 700 crore across Rs 800 crore of claims and each recovers 87.5%.
What does the guarantee change, and for whom?
An upstream guarantee from the operating company gives the bondholders a second claim, this time directly against the operating assets. If that claim ranks equally with the operating loans, the two groups share Rs 700 crore across Rs 800 crore of claims: 87.5% each, Rs 175 crore to the bonds and Rs 525 crore to the loans. The bondholders' gain of Rs 75 crore is exactly the operating lenders' loss of Rs 75 crore; a guarantee does not create value, it moves the queue. That is why operating lenders often limit or prohibit such guarantees in their own documents.
The relationship
$R_{\text{no guarantee}} = \frac{\max(700 - 600,\,0)}{200} = 50\% \qquad R_{\text{guarantee}} = \frac{700}{600 + 200} = 87.5\%$
700 value of the operating company
600 operating company loans
200 holding company bonds
What it says in wordsWithout a guarantee the bonds get the leftover equity; with one they share the whole value pro rata.
What assumption would flip the answer back to 50%?
If the operating loans are secured on all of the operating assets, they are paid in full from the collateral before any unsecured guarantee claim, and the bonds are back to the Rs 100 crore residual. Label and security both matter: a guarantee only helps against creditors it can rank alongside. In real documents guarantees can also be capped or challenged, so a credit analyst reads the guarantee and the intercreditor terms before trusting a number like 87.5%.
Where candidates lose it
The common error is adding everything up, 600 plus 200 against 700, and giving the bonds a pro rata 87.5% with no guarantee in sight. That treats holding company bonds as if they were lenders to the operating company, which they are not.
The second loss is missing that the guarantee is a transfer. Candidates who say the bondholders are better off without adding that the operating lenders are worse off by the same Rs 75 crore have missed half of the answer.
What the interviewer asks next
If the operating company also had Rs 50 crore of trade creditors, what would each group recover with the guarantee?
Why would a holding company bond pay a higher coupon than an operating company loan from the same group?
What would the holding company bonds recover if the operating company were worth Rs 900 crore?
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.
Show the worked solution
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?
088The yield on a 10-year zero-coupon bond doubles from 3% to 6%. Does its price halve? Work out the old and the new price per Rs 100 of face value.Bond pricing and yieldCoreFixed income asset management
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Roughly how much does the price fall?
Show the worked solution
No. The price falls from about 74.41 to 55.84 per Rs 100, a fall of 25.0%, not 50%. A zero's price is 100 divided by one plus the yield, compounded for ten years. Doubling the yield moves one plus the yield only from 1.03 to 1.06, so the price is divided by (1.06/1.03) to the tenth, about 1.33. Halving the price would need a yield near 10.4%.
Why is doubling the yield not doubling the discount?
A shop that raises its markup from 3% to 6% has doubled the markup, but the price tag only goes from 103 to 106. The thing that multiplies through is one plus the rate, not the rate. A bond's price depends on (1 + y) compounded over its life, so doubling y from 3% to 6% changes the base only from 1.03 to 1.06, about 2.9% a year. Ten years of that is a factor of 1.333, which takes about a quarter off the price.
A 10-year zero priced at 74.41 at a 3% yield falls to 55.84 at 6%, a 25.0% drop, well short of the 37.20 that halving would need, which would take a yield of about 10.4%.
The relationship
$P = \frac{100}{(1+y)^{10}}: \quad \frac{100}{1.03^{10}} = 74.41, \quad \frac{100}{1.06^{10}} = 55.84$
P price per Rs 100 of face value
y the annual yield
10 years to maturity, with nothing paid before then
What it says in wordsDiscount the single Rs 100 payment back ten years at each yield.
How does duration check the answer?
The modified duration of a 10-year zero at 3% is 10 / 1.03, about 9.71. Multiplied by a 3 point rise that predicts a fall of about 29.1%, against the true 25.0%. The straight-line estimate overshoots on a large move because the price curve bends: each extra point of yield takes off less than the one before. That bend is convexity, and a 3 point move is big enough to show it. For small moves duration is close; for large ones, reprice the bond directly.
Where candidates lose it
The trap is answering yes, because doubling feels proportional. Price is not inversely proportional to yield; it is inversely proportional to one plus the yield, compounded.
The second loss is getting 25% right and then being unable to say why duration gave 29%. One sentence on convexity turns a correct number into an understood one.
What the interviewer asks next
What yield would halve the price from 74.41?
If the yield falls from 3% to 0%, what happens to the price, and is the move bigger or smaller than the fall you just computed?
Would a 10-year bond paying a 6% coupon fall by more or less than the zero for the same move?
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
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?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?
092A high yield bond portfolio earns a spread of 450 basis points and an investment grade portfolio earns 120. Recovery on high yield defaults is 30%, and investment grade defaults are negligible. What annual default rate can the high yield portfolio absorb before it earns less than investment grade?Credit spreads and default probabilityCoreCredit researchFixed income asset management
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Roughly what default rate wipes out the extra spread?
Show the worked solution
About 4.71% of the portfolio defaulting each year. High yield earns 330 basis points more than investment grade. Each default costs 70% of face, since 30% is recovered, so each 1% of defaults costs 70 basis points. 330 divided by 70 is 4.71%. Below that default rate high yield still earns more; above it, less.
Why divide by the loss, not the default rate?
A shop that sells on credit loses less than the full bill when a customer fails to pay, if it can take back some of the goods. Bonds work the same way. The annual cost of defaults is the default rate times the loss given defaultThe share of face value lost when a borrower defaults, which is one minus the recovery rate., so the extra spread covers defaults up to the extra spread divided by the loss given default. With 30% recovered, each default loses 70%, and 330 basis points of extra spread covers 4.71% a year.
Annual credit loss rises by 70 basis points for each 1% of defaults and crosses the 330 basis points of extra spread at 4.71%, so high yield earns more than investment grade only while defaults stay below that rate.
The relationship
$d^{*} = \frac{s_{HY} - s_{IG}}{1 - R} = \frac{450 - 120}{0.70} = 471\text{ bp} = 4.71\%$
s_HY, s_IG the two portfolios' spreads, in basis points a year
R recovery on high yield defaults, 30%
d* the break-even annual default rate
What it says in wordsThe default rate that exactly uses up the extra spread is that spread divided by the loss on each default.
What does the number leave out?
A break-even default rate is a cushion, not a forecast: whether 4.7% is comfortable depends on how often default rates have run above it and for how long. It also assumes investment grade loses nothing; if investment grade lost 10 basis points a year, the break-even would rise to 4.86%. Recovery is the soft number: it tends to fall in exactly the years defaults rise, so a 30% assumption can flatter the cushion. And the calculation ignores price volatility, which matters to anyone who must mark the portfolio before the bonds mature.
Where candidates lose it
The frequent slip is saying 3.3%, treating every default as a total loss. With 30% recovery, each default costs 70%, and dividing by 0.7 is the whole point of the puzzle.
The second is using the full 450 basis points rather than the 330 excess over investment grade. The question compares two portfolios, so only the difference in spread buys the cushion.
What the interviewer asks next
If recovery falls to 20% in a downturn, what is the new break-even default rate?
What default rate does the full 450 basis point spread cover if investors demanded no extra return for risk?
Why do recoveries tend to fall when default rates rise?
094A borrower can pay 11% in cash or 12% as payment-in-kind on a Rs 500 crore five-year loan. Any cash it does not pay out can be reinvested in the business at a 15% return. Which option leaves the equity better off after five years, and when would the answer flip?Compounding, PIK and feesHardLeveraged financePrivate credit
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The business earns 15%, more than the 12% PIK rate. Does PIK win?
Show the worked solution
Paying cash leaves the equity about Rs 10 crore better off. PIK debt compounds at 12% to Rs 881 crore. The Rs 55 crore a year that PIK keeps in the business, reinvested at 15%, grows to only Rs 371 crore, so net debt is Rs 510 crore against Rs 500 crore with cash pay. The answer flips if the business earns more than about 16.4% on the cash, or if paying cash would starve it.
What exactly is being compared?
Deferring a credit card bill and investing the money instead only pays if your investment grows faster than the card's balance. PIKPayment in kind: interest is added to the loan balance instead of being paid in cash, so the debt compounds. interest is that deferral, made formal. Under PIK the whole loan compounds at the PIK rate, while only the cash you did not pay compounds at your own return, so the two piles grow on different bases. Line up where each option leaves the company at year 5: debt owed, less any cash built up by reinvesting what was not paid.
Paying 11% in cash leaves Rs 500 crore of debt, while PIK at 12% grows the debt to Rs 881 crore against Rs 371 crore of reinvested cash, so PIK ends Rs 10 crore worse unless the cash earns above 16.4%.
The relationship
$500(1.12)^5 = 881.2 \qquad 55\cdot\frac{1.15^5 - 1}{0.15} = 370.8 \qquad 881.2 - 370.8 = 510.3$
500(1.12)^5 the PIK balance after five years
55 the 11% cash interest that PIK lets the company keep each year
370.8 that cash reinvested at 15% for five years
What it says in wordsNet debt under PIK is the compounded loan less the compounded cash that was kept.
When does the answer flip?
Solve for the return that makes the kept cash worth exactly the extra Rs 381 crore of PIK debt: about 16.4%. PIK is cheap only if the cash it saves earns more than the PIK rate, and here more still, because the PIK rate carries a one point premium over cash pay. At a 12% reinvestment return the kept cash reaches only Rs 349 crore. Two further reasons can flip the answer in practice: a borrower whose cash is scarce may not be able to pay 11% without cutting investment it needs, and a borrower expecting to refinance or be sold early carries the PIK compounding for less time. Tax treatment of PIK interest can also differ; confirm it rather than assuming.
Where candidates lose it
The trap is comparing 15% with 12% and declaring PIK the winner. The PIK rate applies to the whole Rs 500 crore; the 15% applies only to Rs 55 crore a year. Rates on different bases cannot be compared directly.
The second loss is ignoring the one point PIK premium. It is why the break-even is near 16%, not 12%, and it is the number a leveraged finance desk would negotiate hardest.
What the interviewer asks next
If both options were priced at 11%, what reinvestment return would make them equal?
The company is sold at the end of year 3. Does that help or hurt the PIK option?
Why would a lender accept PIK at all, and what does it ask for in return?

S	the market spread, 400 bp a year
C	the contract's fixed running coupon, 100 bp a year
RD	risky duration: the present value of 1 bp a year, paid until default or maturity

t one end	burn time with one flame
t both ends	burn time with two flames, always half

700	value of the operating company
600	operating company loans
200	holding company bonds

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

Try it first

Why does a standard coupon create an upfront payment?

Why is the risky duration less than five?

What happens when the spread is below the coupon?

Where candidates lose it

What the interviewer asks next

Try it first

Why does lighting both ends always give 30 minutes?

Why does rope B have exactly 30 minutes left?

Where candidates lose it

What the interviewer asks next

Try it first

Why do holding company bondholders get only what is left?

What does the guarantee change, and for whom?

What assumption would flip the answer back to 50%?

Where candidates lose it

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

How does a lender read the same numbers?

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Why is doubling the yield not doubling the discount?

How does duration check the answer?

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Why is subtraction only an approximation?

When does the shortcut stop being good enough?

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How do you avoid a units slip?

Why can the financier not just use the whole book?

What would change the count?

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Why is the answer not five days?

What does this tell you about liquidity?

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Why divide by the loss, not the default rate?

What does the number leave out?

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What exactly is being compared?

When does the answer flip?

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