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. 057A Rs 100 crore private credit loan pays 8% cash interest plus 4% PIK. The PIK compounds annually and the cash interest is paid on the accreted balance. What is owed at the end of year 5, how much cash interest has the lender received, and what is its IRR if it lent at par?Compounding, PIK and feesHardAres ManagementLos Angeles · 2026

    Try it first

    What IRR does the lender earn over the five years?

    Show the worked solution

    At the end of year 5 the borrower owes Rs 121.67 crore, the lender has received Rs 43.33 crore of cash interest, and the IRR at par is exactly 12%. The 4% PIK is added to the balance each year, so it grows to 100 x 1.04 to the fifth. Cash interest is 8% of each opening balance, rising from Rs 8.00 crore to Rs 9.36 crore. Both pieces earn on the full balance, so the lender earns 12% a year.

    What does PIK actually do to the balance?

    Think of a friend who borrows from you, pays part of the interest in cash each year, and says: add the rest to what I owe. Next year you charge interest on the bigger amount. PIKPayment in kind: interest settled by adding it to the amount owed instead of paying it in cash. interest is not paid; it is added to the loan, so the balance grows every year and every later charge is worked out on the bigger number. Here the balance grows 4% a year, from Rs 100 crore to 100 x 1.04 to the fifth, Rs 121.67 crore.

    The PIK builds the balance; the cash coupon is charged on the bigger balanceBalance owed, Rs crore (axis starts at 95)Rs 100 crore lent100.00104.00108.16112.49116.99121.67Year 0Year 1Year 2Year 3Year 4Year 5Cash interest each year, 8% of the opening balance: Rs 43.33 crore in total8.00Year 18.32Year 28.65Year 39.00Year 49.36Year 5IRR at par12.0%
    The Rs 100 crore balance accretes at 4% a year to Rs 121.67 crore by year five, and the 8% cash coupon charged on that growing balance rises from Rs 8.00 crore to Rs 9.36 crore, Rs 43.33 crore in total, for an IRR of 12% at par.
    YearOpening balanceCash interest, 8%PIK added, 4%Closing balance
    1100.008.004.00104.00
    2104.008.324.16108.16
    3108.168.654.33112.49
    4112.499.004.50116.99
    5116.999.364.68121.67
    Total43.3321.67121.67
    Rs crore. The lender receives Rs 43.33 crore of cash interest over five years and Rs 121.67 crore at maturity, of which Rs 21.67 crore is accrued PIK.

    Why is the IRR exactly 12% when only 8% arrives in cash?

    Each year the lender earns 12% on the whole balance: 8% arrives as cash and 4% is added to the balance, which then earns 12% itself. A lender earning 12% a year on every rupee outstanding, and repaid in full, has an IRR of 12%. The cash yield on the original Rs 100 crore starts at 8% and reaches 9.36% in year five, because the cash coupon is charged on the accreted balance.

    The relationship
    100=∑t=158×1.04t−11.12t+121.671.125  ⇒  IRR=12%100 = \sum_{t=1}^{5} \frac{8 \times 1.04^{t-1}}{1.12^{t}} + \frac{121.67}{1.12^{5}} \;\Rightarrow\; \text{IRR} = 12\%
    8 x 1.04^(t-1)cash interest in year t, 8% of the opening balance
    121.67the accreted balance repaid at the end of year 5
    1.12one plus the IRR that makes both sides equal
    What it says in wordsDiscounting the cash coupons and the accreted repayment at 12% gives back exactly the Rs 100 crore lent.

    What is the catch the interviewer wants you to name?

    A cash-plus-PIK loan earns the same 12% on paper as a 12% cash loan, but more of the return waits until year five. The lender collects Rs 43.33 crore in cash along the way against Rs 60 crore from a 12% cash-pay loan, and Rs 121.67 crore rides on the final repayment instead of Rs 100 crore. If the borrower defaults in year four, the PIK accrued so far is just a larger claim in the recovery, not cash in hand. That is why PIK paper is priced wider: the 12% holds only if the borrower pays at the end.

    Where candidates lose it

    The common mistake is to add the pieces as simple interest: 4% x 5 years is Rs 20 crore of PIK and 8% x Rs 100 crore x 5 is Rs 40 crore of cash. Both understate, because the PIK compounds and the cash coupon is charged on the growing balance: the right figures are Rs 21.67 crore and Rs 43.33 crore.

    The second is saying the IRR is below 12% because part of the interest arrives late. Late is not lost: the PIK earns the full 12% while it waits. Say that, then name the real cost, which is credit risk concentrated at maturity.

    What the interviewer asks next

    • The lender bought the loan at 97 instead of par. Roughly what is the IRR now?
    • What if the PIK is simple rather than compounding and cash interest is charged only on the original Rs 100 crore?
    • The borrower can choose each year between 12% in cash and 13% in PIK. When would it choose PIK, and what does that tell the lender?

    Asked at Ares Management, Credit, Los Angeles, 2026 (Wall Street Oasis): First 1v1 they said was mainly behavioral had PIK question

  2. 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?