Debt Capital Markets puzzles, solved step by step
- Puzzles
- 100
- Traced to a firm
- 16
- Topics
- 13
- Hard
- 30
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?Ares 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 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. Year Opening balance Cash interest, 8% PIK added, 4% Closing balance 1 100.00 8.00 4.00 104.00 2 104.00 8.32 4.16 108.16 3 108.16 8.65 4.33 112.49 4 112.49 9.00 4.50 116.99 5 116.99 9.36 4.68 121.67 Total 43.33 21.67 121.67 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 relationship8 x 1.04^(t-1) cash interest in year t, 8% of the opening balance 121.67 the accreted balance repaid at the end of year 5 1.12 one 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
093A Rs 1,000 crore fund charges a 2% management fee and a 20% performance fee on returns above fees, and earns a 10% gross return. Investors push the management fee down to 1.5%. What performance fee rate keeps the manager's revenue the same?Two SigmaNew York · 2026
Try it first
Roughly what performance fee replaces the lost 0.5%?
Show the worked solution
A performance fee of about 24.7%. Today the manager earns Rs 20 crore of management fee plus 20% of the Rs 80 crore return after fees, Rs 16 crore, for Rs 36 crore. At 1.5% the fixed fee is Rs 15 crore and the return after fees rises to Rs 85 crore, so the performance fee must bring Rs 21 crore: 21 / 85 = 24.7%. The swap is exact only at a 10% gross return.
Why does the performance fee base change?
Think of a salesperson paid a fixed salary plus a share of profit after salary. Cut the salary and the profit after salary goes up, so the share needed to make up the difference is smaller than a straight swap would suggest. The performance fee is charged on the return left after the management fee, so lowering the management fee enlarges the base the performance fee is charged on. That is why the answer is 24.7%, not 25%.
At a 10% gross return both fee terms pay the manager Rs 36 crore, but at 5% the old terms pay 26.0 against 23.6 and at 15% the new terms pay 48.4 against 46.0, so the trade shifts revenue from weak years to strong ones. The relationship100 the 10% gross return on Rs 1,000 crore, in Rs crore 15, 20 the new and old management fees, Rs crore x the new performance fee rate What it says in wordsSet the new fixed fee plus the new share of the bigger base equal to today's total.Is the manager really indifferent?
Only at a 10% gross return. At 5% gross, the old terms pay Rs 26.0 crore and the new pay Rs 23.6 crore; at 15%, the old pay Rs 46.0 crore and the new Rs 48.4 crore. Swapping fixed fee for performance fee moves the manager's revenue out of weak years and into strong ones, so the trade depends on the return you assume. Investors who push for it pay less when things go badly and more when they go well, which is often exactly what they want. A real fund would also have a hurdle rate, a high-water mark and fees charged on average rather than opening assets; each changes the arithmetic, not the logic.
Where candidates lose it
The common answer is 25% or 22.5%, from treating the two fees as if they sat on the same base. The management fee is on assets and the performance fee is on return after fees, so moving one changes the base of the other.
The second loss is saying the new terms are equivalent. They are equal at one assumed return only; say so, and give the 5% and 15% cases to show which way the risk moved.
What the interviewer asks next
- What performance fee keeps revenue the same if the assumed gross return is 15%?
- The fund adds a 5% hurdle, with performance fee only on returns above it. How does that change the answer at 10%?
- From the investor's side, which fee terms would you prefer in a year you expect to be weak, and why?
Asked at Two Sigma, Equity Capital Markets, New York, 2026 (Wall Street Oasis):
the 2/20 rule, and if one part of this equation changed, how would the other variable make up for it
