Debt Capital Markets puzzles, solved step by step

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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. 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

    Try it first

    Which side wants the company to take on riskier assets?

    Show the worked solution

    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 is capped at 80; the shareholders keep everything above it040801201602004080120Value of the assets next year, Rs croreloan of 80Lender: the smaller of V and 80Shareholders: V - 80, never below 0V = 60: lender 60, equity 0V = 140: lender 80, equity 60Same average of 100, wider outcomes60 or 140: lender 70, equity 3020 or 180: lender 50, equity 50
    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
    Debt=min⁡(V, 80)Equity=max⁡(V−80, 0)\text{Debt} = \min(V,\ 80) \qquad \text{Equity} = \max(V - 80,\ 0)
    Vthe value of the assets next year
    80the 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.

    CaseAsset valueLender getsShareholders getLender averageEquity average
    As planned60 or 14060 or 800 or 607030
    Riskier assets20 or 18020 or 800 or 1005050
    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?
  2. 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

    Try it first

    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.

    Debt keeps its size, so the whole fall lands on equityDebt 60Equity 40EV 100BeforeDebt 60Equity 20EV 80After a 20% fallunchangedEV falls20%Equity falls50%Loan to value60% to 75%Multiplier EV / equity2.5x20% x 2.5 = 50%
    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
    %ΔE=%ΔEV×EVE=−20%×10040=−50%\%\Delta E = \%\Delta EV \times \frac{EV}{E} = -20\% \times \frac{100}{40} = -50\%
    EVenterprise value, Rs 100 crore
    Eequity value, Rs 40 crore
    %Deltapercentage 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?