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. 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