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. 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

    Try it first

    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.

    PIK saves cash today, but the debt compounds faster than the cash doesCash pay at 11%500Debt owed0Cash kept500Net debtPIK at 12%, cash reinvested at 15%881Debt owed371Cash kept510Net debtPIK leaves net debt 10 crore higher at 15%. It wins only if the cash earns more than 16.4% a year.
    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=881.255⋅1.155−10.15=370.8881.2−370.8=510.3500(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)^5the PIK balance after five years
    55the 11% cash interest that PIK lets the company keep each year
    370.8that 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?