Debt Capital Markets puzzles, solved step by step

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

    An undersecured lender takes its collateral, then joins the unsecured queueStage 1: the bank's own collateralplant 250short 150Bank claim 400joinsStage 2: 200 shared over 550 of unsecured claimsevery claim recovers 36.4%54.5claim 150Bank shortfall109.1claim 300Bonds36.4claim 100TradeBank: 250 + 54.5Rs 304.5 cr, 76.1%dashed outline = claim, filled = recovered, Rs 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
    ru=Aother(L−C)+B+T=200150+300+100=36.36%Bank=250+150×ru=304.5r_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_urecovery rate on unsecured claims
    L - Cthe bank's loan less the collateral value, its deficiency
    B, Tbonds and trade claims
    A_otherassets 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?
  2. 044A distressed bond trades at 55. It will either be repaid at 100 or restructured with a recovery of 30. Ignoring discounting, what probability of full repayment is the market pricing?Capital structure and recoveryCoreRestructuringCredit research

    Try it first

    The implied chance of full repayment is:

    Show the worked solution

    About 35.7%. Set the price equal to the probability-weighted payoff: p times 100 plus 1 minus p times 30 equals 55. The 30 is paid either way, so the price only has to cover 25 of the 70-point gap between recovery and par, and 25 over 70 is 35.7%. The market thinks restructuring is nearly twice as likely as repayment.

    How do you turn a price into a probability?

    Suppose a raffle ticket pays Rs 100 if you win and Rs 30 as a consolation prize if you lose, and it sells for Rs 55. Everyone gets the Rs 30, so you are really paying Rs 25 for a shot at an extra Rs 70. A price between two outcomes is a probability-weighted average of them, so you can solve for the weight. The consolation prize matters: ignore it and you would read the Rs 55 as a 55% chance.

    The relationship
    p⋅100+(1−p)⋅30=55  ⇒  p=55−30100−30=2570≈35.7%p \cdot 100 + (1 - p) \cdot 30 = 55 \;\Rightarrow\; p = \frac{55 - 30}{100 - 30} = \frac{25}{70} \approx 35.7\%
    pmarket-implied chance of full repayment
    100payoff if repaid in full
    30recovery if restructured
    55today's price
    What it says in wordsThe implied probability is how far the price sits above the recovery, as a share of the distance from recovery to par.
    The price tells you how far along the road from 30 to 100 the market sitsBond todayprice 55p = 35.7%1 - p = 64.3%Repaid in full100Restructuredrecovery 30305510025 of the 70 gapp x 100 + (1 - p) x 30 = 55 gives p = (55 - 30) / (100 - 30) = 25 / 70 = 35.7%
    A bond at 55 that pays either 100 or a recovery of 30 sits 25 points up a 70-point range, which implies a 35.7% chance of full repayment and a 64.3% chance of restructuring.

    What does ignoring discounting hide?

    Both payoffs arrive in the future, often a year or more away, and a distressed investor wants a high return for waiting. If the payoffs arrive in a year and the buyer demands 12%, the price must equal the expected payoff divided by 1.12, which lifts the implied repayment probability to about 45.1%. So the 35.7% is a floor: part of the discount to par is a charge for time and risk, not only for default. That is why desks quote these as risk-neutral probabilities, not forecasts.

    The other soft spot is the recovery of 30. It is an estimate, and the implied probability is sensitive to it: at a recovery of 40, p is 15 over 60, 25%. Before trading on the number, a credit analyst would test the recovery from the balance sheet and the claims ranking ahead of this bond.

    Where candidates lose it

    The instant wrong answer is 55%, reading the price as a probability. That would only be right if the bad outcome paid nothing. Here it pays 30, and the answer drops to 35.7%.

    The second miss is forgetting to say the assumption. Ignoring discounting makes the probability look low; one sentence noting that a required return would raise it shows you know the difference between a market price and a forecast.

    What the interviewer asks next

    • What price would imply a 50% chance of repayment?
    • If the recovery estimate falls to 20, what probability is implied at 55?
    • How would you set up the same calculation for a credit default swap spread?