Debt Capital Markets puzzles, solved step by step

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

Showing 11–20 of 100

011A 4-year bullet loan pays 10% a year and the borrower pays a 2% upfront fee. Roughly what yield does the lender earn, and how would you estimate it in your head?Compounding, PIK and feesWarm upCorporate bankingLeveraged finance
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Which is closest to the lender's yield?
Show the worked solution
About 10.6%, exactly 10.64%. The lender puts out Rs 98, receives Rs 10 a year and gets Rs 100 back in year 4. In your head: spread the 2 point fee over 4 years, about 0.5 a year, giving 10.5, then divide by the average money at work, about 99, which gives 10.61%. An upfront fee is extra yield spread over the life of the loan.
What does the fee actually change?
Imagine lending a friend Rs 1,000 for four years at 10%, but handing over only Rs 980 because you keep Rs 20 as a processing charge. Your interest is still on Rs 1,000 and you still get Rs 1,000 back. An upfront fee lowers the money the lender actually puts out, so the same coupons and repayment earn a higher yield on it. Look at the top of the figure: Rs 98 out, then 10, 10, 10 and 110 back.
The lender pays out Rs 98 and receives 10 a year plus 100 in year 4; the coupon alone is 10.00%, spreading the fee gives about 10.50%, adjusting for the smaller base gives 10.61%, and the exact yield is 10.64%.
How do you get close to 10.64% without a calculator?
Use the bond trader's approximation: yearly income over the average money at work. Yearly income is the coupon plus the fee spread evenly over the life, 10 plus 2 over 4, which is 10.5; the average money at work is halfway between 98 and 100, which is 99. 10.5 over 99 is 10.61%, within a few basis points of the exact 10.64%. Say the first step, 10.5, as your quick answer and the second as the refinement; interviewers like hearing both.
The relationship
$y \approx \frac{C + F/n}{(100 + P)/2} = \frac{10 + 2/4}{(100 + 98)/2} = \frac{10.5}{99} \approx 10.61\%$
C annual coupon, 10
F upfront fee, 2 points
n years to repayment, 4
P money actually lent after the fee, 98
What it says in wordsYield is roughly the yearly income, with the fee spread over the years, divided by the average money the lender has at work.
What if the loan is repaid early?
Then the fee is spread over fewer years and is worth more a year. If the borrower repays at par after 2 years, the same 2 points lift the yield to about 11.17%, because the fee is earned over half the time. This is why lenders care about expected life, not stated maturity, and why a loan that is likely to be refinanced early is priced partly on its fee. Say that one sentence and you have shown the interviewer you see the fee as yield, not as a one-off receipt.
Where candidates lose it
The two fast wrong answers sit either side. Saying 10% ignores the fee because it is paid once; saying 12% adds the whole fee to one year's coupon. Both miss that the fee belongs to the whole life of the loan.
The quieter loss is stopping at 10.5 when the interviewer asks for more precision. The base is Rs 98, not Rs 100, and that small adjustment is the difference between 10.50% and 10.64%.
What the interviewer asks next
What upfront fee would lift the yield on this loan to 11%?
Why does the same fee matter more on a 2 year loan than on a 7 year loan?
How should a bank book this fee in its income: all at once, or over the life of the loan?
012A Rs 800 crore bond carries an 8% coupon with a step-up of 25 basis points for each notch the issuer's rating falls below AA. It is downgraded two notches. What does that cost the issuer each year?Issuance and refinancing arithmeticWarm upIndian debt capital markets
Try it first
Answer in rupees, not basis points.
Show the worked solution
Rs 4 crore a year. Two notches below AA, from AA to AA- to A+, trigger two steps of 25 basis points, so the coupon rises from 8.00% to 8.50%. Half a per cent of Rs 800 crore is Rs 4 crore, taking annual interest from Rs 64 crore to Rs 68 crore for as long as the rating stays there. A step-up turns a downgrade into a cash cost.
How do you convert basis points into rupees quickly?
Anchor on one basis point. One basis point of Rs 800 crore is Rs 8 lakh, so 50 basis points is 50 times Rs 8 lakh, Rs 4 crore. It works like a fuel surcharge on a bus ticket: a small percentage, but on a large base and paid every trip. Say the conversion out loud; desks talk in basis points and issuers pay in rupees, and the interviewer wants to hear that you can move between the two instantly.
Each notch below AA adds 25 basis points to the 8% coupon, so annual interest on Rs 800 crore climbs from Rs 64 crore at AA to Rs 66 crore at AA- and Rs 68 crore at A+, an extra Rs 4 crore a year after a two notch downgrade.
Why would an issuer agree to a step-up at all?
To get a lower coupon today. Investors worried about a downgrade will accept a tighter starting coupon if they are compensated when that fear comes true. A step-up couponA coupon that rises by a set amount if a trigger is hit, most often a downgrade of the issuer rating below a stated level. shifts rating risk back to the issuer: cheap while the credit holds, costlier exactly when the credit weakens. That timing is the catch, and it is what a good answer names next.
The relationship
$\Delta \text{Interest} = F \times n \times s = 800 \times 2 \times 0.25\% = 4 \text{ Rs crore a year}$
F face value outstanding, Rs 800 crore
n notches below the trigger, 2
s step-up per notch, 25 basis points
What it says in wordsThe extra interest is the face value times the number of notches times the step per notch.
What is the hidden danger in the structure?
It adds cost at the worst moment. A downgrade usually follows weaker cash flow, and the step-up then raises interest, which weakens coverage further and can invite another downgrade. On this bond, Rs 4 crore is small against Rs 64 crore of interest, but many issues carrying the same clause, or a larger step, can turn one downgrade into a spiral. Close with that, and add the limit: the terms of real step-ups vary, some step back down on an upgrade and some cap the total, so read the clause.
Where candidates lose it
The easy slip is counting the wrong number of notches. AA to AA- is one and AA- to A+ is two, so the step is 50 basis points, not 25 and not 75.
The second loss is answering Rs 68 crore, the new interest bill, when the question asked for the cost of the downgrade. Give the difference first and the new total second.
What the interviewer asks next
What does the step-up cost in present value terms if 5 years remain and the discount rate is 8.5%?
Why might investors prefer a step-up bond to a higher fixed coupon?
How does a step-up clause change the way a rating agency looks at a downgrade?
013An issuer's existing 8% bond trades at 102.00. The issuer taps the same line to raise Rs 500 crore of cash. How much face value must it issue, and what does it record as debt?Issuance and refinancing arithmeticCoreSyndicate desksIndian debt capital markets
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How much face value does Rs 500 crore of cash need?
Show the worked solution
About Rs 490.2 crore of face value, recorded initially at the Rs 500 crore received. At 102, every Rs 100 of face raises Rs 102, so 500 divided by 1.02 is Rs 490.20 crore. The issuer carries the debt at the cash received and amortises the Rs 9.8 crore premium down to face over the remaining life, so its interest expense sits below the Rs 39.22 crore coupon.
Why does a premium mean less face, not more?
Think of selling gift vouchers with a face value of Rs 100 that are so popular buyers pay Rs 102 for each. To collect Rs 50,000 you need to hand out fewer vouchers than 500. When a bond trades above par, each unit of face value brings in more than its face in cash, so the issuer creates less face than the cash it raises. The bond trades at 102 because its 8% coupon is above the yield investors now demand; the extra Rs 2 is them paying today for that above-market coupon.
At par, Rs 500 crore of face raises Rs 500 crore of cash with a Rs 40 crore coupon; at 102 only Rs 490.2 crore of face is needed, the Rs 9.8 crore premium makes up the rest, and the coupon on the new bonds is Rs 39.22 crore a year.
The relationship
$F = \frac{\text{Cash}}{P/100} = \frac{500}{1.02} \approx 490.20 \qquad \text{premium} = 500 - 490.20 \approx 9.80$
F face value to issue, Rs crore
P price per Rs 100 of face, 102.00
premium cash raised above the face value
What it says in wordsDivide the cash wanted by the price per rupee of face; the difference between the two is the premium.
What goes on the balance sheet?
Under amortised cost accounting, which Ind AS and IFRS use for most issued bonds, the debt starts at the cash received, Rs 500 crore before issue costs, not at the face value. The premium is then released over the bond's remaining life, so the carrying amount falls to Rs 490.2 crore by maturity and the interest expense is the effective yield on the carrying amount, below the cash coupon. Covenants that test debt may use face value instead, so check which number the documents count; the accounting details belong to the issuer's auditors.
What else must you check on a tap?
Three practical points. Taps usually settle between coupon dates, so buyers also pay accrued interest, which is cash in hand but not new debt, and it should not be counted in the Rs 500 crore. Face is issued in set denominations, so Rs 490.2 crore rounds to what the minimum lot allows. And the issuer should compare the tap with a fresh issue: tapping an existing line at 102 adds liquidity to one bond, which investors often value, while a new bond with a lower coupon might price differently.
Where candidates lose it
The instinctive wrong answer is Rs 510 crore, as if a premium meant issuing more. Candidates see 102 and add 2%. Get the direction first: buyers pay more than face, so less face is needed.
The second loss is recording debt at Rs 490.2 crore of face and booking a Rs 9.8 crore gain. The premium is not income; it is released over the life as a lower interest expense.
What the interviewer asks next
The tap settles 60 days after the last coupon. How much accrued interest do buyers pay?
What yield does a price of 102 imply if the bond has 5 years left?
Why might an issuer prefer to tap an existing line rather than launch a new bond?
014An issuer has a 2% chance of default in any year, independent of the past. What is the probability that it defaults at some point in the next 5 years, and why is it not 10%?Credit spreads and default probabilityCoreCredit researchRisk management
Try it first
Is the five year default probability above or below 10%?
Show the worked solution
About 9.6%. The chance of surviving one year is 98%, and surviving five independent years is 0.98 to the power 5, or 90.39%. Default at some point is everything else: 9.61%. It is below 10% because the 2% in each later year applies only to issuers still alive, a shrinking group, so simply adding the yearly rates double counts.
Why does adding 2% five times overstate it?
Think of a phone that has a 2% chance of breaking each year. A phone that broke in year 1 cannot break again in year 2. Default is a one-time event, so each year's 2% applies only to the issuers that survived until then, and that group shrinks every year. Seen from today, the chance of defaulting in year 2 is 98% times 2%, which is 1.96%; by year 5 it is 1.845%. Those five numbers sum to 9.61%, not 10%.
Seen from today, the chance of defaulting in each year falls from 2.00% to 1.84% as survivors shrink, summing to 9.61% over five years; over fifty years compounding survival gives 63.6% cumulative default while adding 2% a year would absurdly reach 100%.
What is the fastest correct route?
Go through survival. Survival over several independent years is the product of the one year survival rates, and cumulative default is one minus that product. 0.98 squared is 0.9604, times 0.98 again is 0.9412, then 0.9224, then 0.9039. Or use the shortcut that 0.98 to the fifth is about 1 minus 5 times 0.02 plus 10 times 0.0004, which is 0.904. Either way, default is about 9.6%.
The relationship
$P(\text{default by } n) = 1 - (1-p)^n = 1 - 0.98^5 \approx 1 - 0.9039 = 9.61\%$
p the default probability in any one year, 2%
n the number of years, 5
(1-p)^n the chance of surviving all n years
What it says in wordsCumulative default is one minus the chance of surviving every year.
Why does a credit desk care about a 0.4 point gap?
Over five years the gap is small, 10.0% against 9.6%. Over long horizons the difference becomes enormous: adding 2% a year says default is certain by year 50, while compounding survival says 63.6%. That matters for pricing long bonds, for reading a rating agency's cumulative default tables, and for turning a spread into an implied default rate. Say the limit too: real default rates are not independent from year to year, they cluster in recessions, so the 2% flat rate is a teaching simplification.
Where candidates lose it
Saying 10% is the whole trap, and it comes from treating the yearly probabilities as if they could stack. The interviewer is checking whether you see that default removes the issuer from later years.
The opposite slip is saying 2% because each year is independent. Independence means each year's odds are unchanged for a survivor, not that the risk over five years is the same as over one.
What the interviewer asks next
What yearly default probability gives a 20% chance of default over 10 years?
If recovery is 40%, roughly what credit spread compensates for a 2% annual default rate?
Why would a rating agency's cumulative default table not fit a constant yearly rate?
015A Rs 500 crore bond portfolio has 60% in bonds with a modified duration of 4 and 40% in bonds with a modified duration of 9. The central bank surprises with a 25 basis point hike and the whole curve moves up in parallel. Roughly what is the mark-to-market loss?Duration and convexityCorePIMCOSan Diego · 2026
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What is the portfolio's modified duration?
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About Rs 7.5 crore, 1.5% of the portfolio. Portfolio modified duration is the value-weighted average: 0.6 times 4 plus 0.4 times 9 is 6.0. A 25 basis point parallel rise costs about duration times the move, 6.0 times 0.25%, or 1.5%, and 1.5% of Rs 500 crore is Rs 7.5 crore. The duration 9 block is only 40% of the money but carries 60% of the loss.
What does modified duration convert?
Think of duration as a lever length. A seesaw with a long arm moves more at the end for the same push. Modified duration tells you the approximate percentage fall in a bond's price for a one percentage point rise in its yield, so a duration of 4 means about 4% per 1% move, or 1% for 25 basis points. Once you have that, a rate shock converts straight into rupees: duration times the move times the value held.
How do you combine two blocks of bonds?
Weight each duration by the money in it. Portfolio duration is the value-weighted average of the holdings' durations, because each bond's loss is its own value times its own duration times the move. Rs 300 crore at duration 4 loses Rs 3.0 crore; Rs 200 crore at duration 9 loses Rs 4.5 crore. Together that is Rs 7.5 crore, exactly what Rs 500 crore at duration 6.0 gives. The figure makes the point visually: area is the loss.
With width for rupees held and height for duration, the Rs 300 crore block at duration 4 loses Rs 3.0 crore and the Rs 200 crore block at duration 9 loses Rs 4.5 crore for a 25 basis point rise, together Rs 7.5 crore, the same area as Rs 500 crore at a portfolio duration of 6.0.
The relationship
$\Delta V \approx -D_{p} \times \Delta y \times V = -(0.6 \times 4 + 0.4 \times 9) \times 0.0025 \times 500 = -6.0 \times 0.0025 \times 500 = -7.5$
D_p portfolio modified duration, the value-weighted average
\Delta y the parallel rise in yields, 0.25%
V portfolio value, Rs 500 crore
What it says in wordsThe rupee change is roughly minus duration times the yield move times the money held.
What would make the true loss differ from Rs 7.5 crore?
Three things, and naming them is what separates a desk answer from a formula. Convexity makes the true loss slightly smaller than the duration estimate for a rise in yields, though for a 25 basis point move the difference is tiny. Curves rarely move in parallel after a surprise hike: short yields usually jump more, which would hurt the duration 4 block more than this sum assumes. And spreads on corporate bonds can move on top of the base rate. Say that Rs 7.5 crore is the first-order answer to a parallel shift, then name which of these you would check first.
Where candidates lose it
The common error is averaging 4 and 9 to get 6.5, giving Rs 8.12 crore. Durations combine by money weight, and the interviewer set 60 and 40 precisely to see whether you use them.
The second loss is getting the percentage right and the rupees wrong: 6 times 0.25 is 1.5%, and 1.5% of Rs 500 crore is Rs 7.5 crore, not Rs 75 crore. Say the percentage first, then convert.
What the interviewer asks next
How much of the duration 9 bonds would you sell into cash to cut the loss for the same shock to Rs 5 crore?
If the short end rises 40 basis points and the long end only 10, which block loses more?
How would you hedge this portfolio's duration with a bond future or an interest rate swap?
Asked at PIMCO, Debt Capital Markets, San Diego, 2026 (Wall Street Oasis): Which is cheaper us bonds or us equities How does duration affect interest rtes
016Numerical reasoning: an issuer's bond volumes grow 12%, then 15%, then fall 10% over three years. What is the total change over the period, and what is the average annual growth rate?Mental maths and numeracyCoreCorporate banking
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What is the total change over the three years?
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A total rise of about 15.9%, or about 5.05% a year. Percentage changes multiply: 1.12 times 1.15 is 1.288, and a 10% fall from there leaves 1.1592. The steady yearly rate that gets to the same place is the cube root of 1.1592, about 1.0505. Adding the rates gives 17% and an average of 5.67%, both too high, because the fall hits a bigger base than the gains did.
Why can you not add the percentages?
A shop raises a price by 10% and later cuts it by 10%, and the tag ends below where it started, because the cut is taken on the higher price. Each percentage change is measured on the level it starts from, so a chain of changes multiplies rather than adds. Here the 10% fall comes after two good years, so it removes 12.88 points of the index, more than the 12 the first year added.
Indexed to 100, volumes rise to 112, then by 16.8 to 128.8, then fall by 12.88 to 115.92, a total change of 15.92% rather than the 17% that adding the three rates suggests.
How do you do it fast under test conditions?
Break each multiplication into easy pieces. 1.12 times 1.15 is 1.12 plus 15% of 1.12, which is 1.12 plus 0.168, so 1.288; taking 10% off is 1.288 minus 0.1288, which is 1.1592. For the yearly rate, test a round guess: 1.05 cubed is 1.1025 times 1.05, which is 1.1576, just under 1.1592, so the answer is a shade above 5%. On a timed test, that is enough to pick the right option in seconds.
The relationship
$1 + G = 1.12 \times 1.15 \times 0.90 = 1.1592 \qquad g = (1+G)^{1/3} - 1 \approx 5.05\%$
G the total change over three years
g the compound annual growth rate
1/3 one third, because there are three years
What it says in wordsMultiply the yearly growth factors for the total, then take the cube root for the steady yearly rate.
Why does the average of 5.67% overstate growth?
The simple average of 12, 15 and minus 10 is 5.67%, but three years at 5.67% would give 18.0%, not 15.9%. Whenever the yearly rates vary, the simple average is above the compound rate, and the gap grows with the swings. That is the same drag that makes a volatile bond fund's average return look better than what its investors actually earned. Say which average you are quoting: the compound rate describes the path, the simple average only describes the list of numbers.
Where candidates lose it
Adding the rates to get 17% is the trap the test is built around, and the wrong option is always on the list. Under time pressure the candidate recognises 17 as a number from the question and picks it.
The second trap is dividing 17 by 3 for the annual rate. Even after getting the total right at 15.92%, dividing by 3 gives 5.31%, which ignores compounding the other way. Take the cube root, or test 1.05 cubed.
What the interviewer asks next
What fall in year 4 would bring volumes back exactly to the start?
Volumes rise 20% and then fall 20%. Where do they end, and why?
Why do fund fact sheets report compound annual returns rather than simple averages?
017A one-year rating transition matrix says an A-rated issuer stays A with 92% probability, moves to BBB with 7.5% and defaults with 0.5%. A BBB issuer defaults with 2% in a year. Using the same matrix each year, what is the A issuer's cumulative two-year default probability?Credit spreads and default probabilityHardRisk managementCredit research
Try it first
Before working the tree: is the two year figure above or below 1.0%, twice the one year rate?
Show the worked solution
About 1.11%. There are three ways to be in default by the end of year 2. Default in year 1: 0.5%. Stay A, then default: 92% times 0.5%, which is 0.46%. Fall to BBB, then default: 7.5% times 2%, which is 0.15%. They add to 1.11%, more than twice the one year rate, because downgrades move issuers into riskier states.
Why can you not just double 0.5%?
Think of a student who might fail an exam this year or slip into a weaker class and fail next year from there. Multi-year default risk comes from migration as well as direct default: an issuer that is downgraded in year 1 faces a higher default rate in year 2. Doubling 0.5% assumes every survivor is still A, and the independent-survival answer, 1.00%, makes the same assumption. Both miss the 7.5% who drift to BBB.
An A issuer can default in year 1 (0.5%), stay A and default in year 2 (0.46%), or fall to BBB and then default (0.15%); the three paths add to a two year default probability of 1.11%.
How do you set it up so nothing is missed?
List where the issuer can be after year 1, then ask for each state what happens in year 2. Default is an absorbing state, so a year 1 default stays counted; the other states each carry their own year 2 default rate. The A branch contributes 0.92 times 0.005 and the BBB branch 0.075 times 0.02. A small matrix multiplication does the same thing: square the one year matrix and read off the A to default cell.
The relationship
$P_2(A \to D) = p_{AD} + p_{AA}\,p_{AD} + p_{AB}\,p_{BD} = 0.5\% + 0.92 \times 0.5\% + 0.075 \times 2\% = 1.11\%$
p_AD one year default rate from A, 0.5%
p_AA chance of staying A for a year, 92%
p_AB chance of moving from A to BBB, 7.5%
p_BD one year default rate from BBB, 2%
What it says in wordsAdd every path that ends in default within two years, each path's probability being the product of its steps.
What does the migration path tell a credit investor?
The downgrade path is only 7.5% likely but supplies 14% of the two year default risk. For a high rated issuer, most of the medium-term risk is the chance of becoming a weaker credit, which is why investors watch outlooks and migration as closely as default rates. Downgrades also cost money before any default, through wider spreads. Say the limits: real matrices are estimated from history, the same matrix is unlikely to hold every year, and defaults cluster in downturns, so treat this as the arithmetic, not a forecast.
Where candidates lose it
The fast wrong answer is 1.0%, doubling the one year rate, or 0.9975%, compounding it as if the issuer could only ever be A. Both are the same error: ignoring that the issuer's rating can change before it defaults.
The second loss is forgetting the year 1 default path, adding only the two year 2 paths to get 0.61%. Default is absorbing: once in, the issuer stays counted.
What the interviewer asks next
BBB issuers can also fall to BB, which defaults at 8% a year. What else would you need to add a third year?
How would you compute the same answer with a matrix multiplication?
Why might a transition matrix estimated from a calm decade understate this risk?
018A 3-year bond with a 10% annual coupon is priced at an 8% yield. What is its price today, and what will it be after one and two years if the yield never moves? Why is the holder's income less than the coupon?Bond pricing and yieldCoreFixed income asset management
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The yield stays at 8% for a year. What happens to the bond's price?
Show the worked solution
105.15 today, 103.57 after one year and 101.85 after two, then 100 at maturity. The bond pays 10 a year when the market wants 8, so it trades at a premium, and the premium shrinks as the high coupons are used up. Each year the holder gets 10 of coupon but gives back part of the premium, so true income is 8.41 in year 1, exactly 8% of the 105.15 paid.
Why is the bond above 100 in the first place?
Imagine a flat rented at Rs 10,000 a month on a three year lease when similar flats rent for Rs 8,000. A buyer pays extra for that lease, but the extra is only worth the months left on it. A bond paying a coupon above the market yield trades above par, and the premium is the present value of those extra coupons still to come. Priced at 8%, three coupons of 10 and the 100 repayment are worth 105.15.
At an unchanged 8% yield the price falls from 105.15 to 103.57, 101.85 and 100, and each year's coupon of 10 splits into a fall in price and a true income of 8.41, 8.29 and 8.15, 8% of each year's opening price.
How do you get the three prices quickly?
Price the premium, not the bond. Each year the bond pays 2 more than the market rate would, so the premium is 2 times the annuity factor for the years left, at 8%. With three years left the factor is 2.577, so the premium is 5.15; with two years left it is 1.783, a premium of 3.57; with one year left, 0.926, a premium of 1.85. That is quicker than discounting every cash flow and makes the pull to par obvious.
The relationship
$P_n = 100 + (C - y \times 100) \times \frac{1-(1+y)^{-n}}{y} \qquad P_3 = 100 + 2 \times 2.577 = 105.15$
P_n price with n years left
C annual coupon, 10
y market yield, 8%
n years to maturity
What it says in wordsPrice is par plus the present value of the coupon's excess over the market rate for the years left.
Why does it matter that income is less than the coupon?
Because the coupon overstates what the holder earns. Of the 10 received in year 1, 1.59 is really the holder's own money coming back as the premium runs off, so the income is 8.41, exactly the 8% yield on the price paid. A bank or fund that booked the full 10 as income would show a loss of the same size in the price. This is why accounts amortise premiums and why a desk compares bonds on yield, not coupon. The limit: it all assumes the yield stays at 8%, and any move in rates adds a gain or loss on top.
Where candidates lose it
The common wrong answer is that the price stays put because the yield did not move. Candidates link price changes only to yield changes and forget that time alone moves a premium or discount bond towards 100.
The second slip is calling the 10% coupon the return. The return at purchase is the 8% yield; the coupon is higher only because part of it hands back the premium you paid.
What the interviewer asks next
What does the same path look like for a 6% coupon bond at an 8% yield?
If the yield falls to 7% after one year, what is the one year return?
Why do insurers sometimes prefer premium bonds with high coupons?
019A bank lent Rs 400 crore secured on a plant now worth Rs 250 crore. Unsecured bonds are Rs 300 crore and trade creditors Rs 100 crore. Other assets are worth Rs 200 crore. In a liquidation, what does the bank recover in total, and what do the bondholders get?Capital structure and recoveryCoreRestructuringCorporate banking
Try it first
What do the bondholders recover?
Show the worked solution
The bank recovers about Rs 304.5 crore, 76.1%; the bondholders get about Rs 109.1 crore, 36.4%. The bank takes the plant, Rs 250 crore, and is still owed Rs 150 crore. That shortfall ranks as an unsecured claim beside Rs 300 crore of bonds and Rs 100 crore of trade claims. The Rs 200 crore of other assets is shared across Rs 550 crore of claims at 36.36% each.
What does security actually give the bank?
A pawnbroker holding your watch gets the watch first. If the watch sells for less than you owe, you still owe the rest, but now as an ordinary debt. Security gives a lender first call on the pledged asset, up to its value; for any shortfall the lender becomes an ordinary unsecured creditor. Here the plant covers Rs 250 crore of the Rs 400 crore loan, so the bank is undersecuredOwed more than the value of the collateral pledged against the loan, so part of the claim is effectively unsecured. by Rs 150 crore.
The bank takes the Rs 250 crore plant and carries its Rs 150 crore shortfall into the unsecured pool, where Rs 200 crore of other assets is shared across Rs 550 crore of claims at 36.4%, giving the bank Rs 304.5 crore in total and the bondholders Rs 109.1 crore.
How is the unsecured pool shared?
Pro rata, by the size of each claim. All unsecured claims of the same rank share the unencumbered assets in proportion to what they are owed, and the bank's deficiency counts in full. The pool is 150 plus 300 plus 100, which is Rs 550 crore, against Rs 200 crore of assets, a recovery of 36.36%. The bank receives 36.36% of 150, Rs 54.5 crore, the bonds Rs 109.1 crore and trade creditors Rs 36.4 crore.
The relationship
$r_u = \frac{A_{\text{other}}}{(L - C) + B + T} = \frac{200}{150 + 300 + 100} = 36.36\% \qquad \text{Bank} = 250 + 150 \times r_u = 304.5$
r_u recovery rate on unsecured claims
L - C the bank's loan less the collateral value, its deficiency
B, T bonds and trade claims
A_other assets not pledged to anyone, Rs 200 crore
What it says in wordsUnsecured claims, including the secured lender's shortfall, share the free assets pro rata.
What would change the numbers in a real case?
Several things the puzzle strips out, and naming one or two shows judgement. Insolvency costs and any claims the law ranks ahead of unsecured creditors, such as some employee and statutory dues, come out of the pool first, so the real unsecured rate would be lower than 36.4%. Plant values in a forced sale are often below appraisal. And the priority rules differ by country and by process, so check the regime that applies. The core mechanics, collateral first and deficiency pari passu, hold widely.
Where candidates lose it
The first trap is ignoring the bank's shortfall, sharing Rs 200 crore over only the bonds and trade claims at 50%. That gives the bonds Rs 150 crore and quietly treats the bank as if its Rs 150 crore had vanished.
The opposite slip is letting the bank take everything because it is the secured lender. Security attaches to the plant, not to every asset, so the other assets are shared.
What the interviewer asks next
The plant sells for Rs 400 crore instead. What do the bondholders now recover?
The bank also holds a second charge on the other assets. How does that change the split?
Why would a bank lend against a plant knowing it might be worth less in a forced sale?
020Senior debt of Rs 300 crore, subordinated notes of Rs 200 crore and trade claims of Rs 100 crore are all unsecured, but the notes are contractually subordinated to the senior debt only. Enterprise value is Rs 300 crore. Who gets what?Capital structure and recoveryHardRestructuringCredit research
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What do the trade creditors recover?
Show the worked solution
Senior debt gets Rs 250 crore, the subordinated notes nothing, and trade creditors Rs 50 crore. All three are unsecured, so first share Rs 300 crore pro rata across Rs 600 crore of claims: 150, 100 and 50. The notes then turn their Rs 100 crore over to the senior debt, which is still owed 150, leaving senior at 250. Trade creditors signed nothing, so they keep their 50.
What is contractual subordination, in plain terms?
Two siblings borrow from their parents and from a neighbour. The younger sibling promises the elder that any repayment the younger receives will be handed over until the elder is repaid. The neighbour never heard about that promise and is unaffected. Contractual subordinationAn agreement by one class of creditors to be paid only after a named senior class, enforced by handing over anything received until the senior class is paid in full. is a promise between two classes, so it moves value between them and leaves every other creditor exactly where the law puts them.
Rs 300 crore shared pro rata over Rs 600 crore of claims gives senior 150, notes 100 and trade 50; the notes then hand their 100 to the senior debt, ending at senior 250, notes 0 and trade 50, so trade recovers the same 50% either way.
Why share pro rata first, before applying the subordination?
Because in the eyes of the insolvency law all three claims are unsecured and of equal rank. The legal waterfall treats them pari passu; the subordination agreement then works on what the noteholders receive, not on the waterfall itself. So compute the pro rata split, 50% each on Rs 600 crore of claims, then apply the turnover: senior is still owed Rs 150 crore, and the notes' Rs 100 crore goes to it in full. Had the notes' share exceeded what senior was owed, the surplus would stay with the notes.
The relationship
$\text{Senior} = 150 + \min(300 - 150,\ 100) = 250 \qquad \text{Notes} = 100 - 100 = 0 \qquad \text{Trade} = 50$
150 senior's pro rata share, 50% of 300
100 the notes' pro rata share, turned over to senior
300 - 150 what senior is still owed after its own share
What it says in wordsSenior takes its own share plus the notes' share, up to the amount it is still owed; trade keeps its pro rata share.
What would a wrong reading cost each class?
Reading the notes as subordinated to everyone, a straight ladder, would pay senior 300 in full, trade nothing and notes nothing, a strict waterfall that takes Rs 50 crore from trade creditors who never agreed to it. The difference between subordinated to a named class and subordinated to all creditors is worth real money, so a credit analyst reads the subordination clause before building any recovery table. In real cases, check also whether senior's post-filing interest counts in the turnover, which the documents decide.
Where candidates lose it
The common error is building a simple ladder: senior first, then trade, then notes. That pays senior 300 and trade 0, and misses that the notes promised to stand behind the senior debt only.
The second is applying pro rata and stopping, leaving the notes with 100. The agreement exists precisely to move that 100, so finish the turnover step and say what it is.
What the interviewer asks next
Enterprise value rises to Rs 480 crore. Who gets what now?
How would the answer change if the notes were subordinated to all senior obligations, including trade?
Why do senior lenders value a subordination clause in a creditor that ranks equally with them by law?

C	annual coupon, 10
F	upfront fee, 2 points
n	years to repayment, 4
P	money actually lent after the fee, 98

F	face value outstanding, Rs 800 crore
n	notches below the trigger, 2
s	step-up per notch, 25 basis points

F	face value to issue, Rs crore
P	price per Rs 100 of face, 102.00
premium	cash raised above the face value

p	the default probability in any one year, 2%
n	the number of years, 5
(1-p)^n	the chance of surviving all n years

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Why share pro rata first, before applying the subordination?

What would a wrong reading cost each class?

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