Debt Capital Markets puzzles, solved step by step
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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
065In a trading game you are asked to make a two-way market on the sum of three fair dice. Quote a bid and an offer. The first die is then shown to be a 6. Where do you move your market, and why?Belvedere TradingChicago · 2022
Try it first
After the 6 is shown, where should the middle of your market be?
Show the worked solution
Start around 10.5, say 9.5 bid and 11.5 offered, then move to about 12.2 bid, 13.8 offered once the 6 is shown. Each fair die is worth 3.5 on average, so three are worth 10.5. After the reveal the value is 6 plus 3.5 plus 3.5, which is 13.0. The market should also narrow, because one die's uncertainty has gone: the standard deviation falls from 2.96 to 2.42, so the width shrinks by about a fifth, not a third.
Where does the first quote come from?
A shop that buys and sells used phones offers to buy below what it thinks a phone is worth and to sell above it, and earns the gap. A market maker quotes around the expected value, with a bid below and an offer above, and the width reflects how uncertain that value is. Each fair die averages 3.5, so three dice average 10.5. A quote of 9.5 bid, 11.5 offered straddles that value; the sum can still land anywhere from 3 to 18, so the market cannot be tight.
Before any die is shown the sum centres on 10.5 with a standard deviation of 2.96; once a 6 is shown it centres on 13.0 with a standard deviation of 2.42, so the quote moves up 2.5 and narrows from 9.5 to 11.5 to about 12.2 to 13.8. What changes when the first die is shown?
Two things, and candidates usually say only one. The expected value jumps to 6 plus 3.5 plus 3.5, which is 13.0, and the uncertainty shrinks because only two dice are still hidden. Variance adds across independent dice, 35/12 for each, so it falls from 8.75 to 5.83, a third lower; the standard deviation falls from 2.96 to 2.42, about 18% lower. Scale the width by that: 2 points becomes about 1.6, so quote roughly 12.2 bid, 13.8 offered.
The relationship3.5 the expected value of one fair die 35/12 the variance of one fair die sigma the standard deviation of the part of the sum still unknown What it says in wordsThe expected value adds the known die to the average of the hidden ones; the uncertainty comes only from the dice still hidden.What does the interviewer want to hear beyond the numbers?
Move the market the moment information arrives, because a stale quote is a free option for everyone else at the table. If you stay at 9.5 to 11.5 after a 6 shows, every player buys your offer at 11.5 against a fair value of 13.0. Then say what you would do if you suspected the other side knew more than you, for example had seen a second die: widen, or lean your quote towards the risk. The limit: the width here is a choice; a real desk sets it by competition and by how much risk it can hold, not by a formula.
Where candidates lose it
The common loss is leaving the market where it was, or moving the middle and forgetting the width. Fair value jumps to 13.0 the moment the 6 is shown and the uncertainty is smaller, so both the level and the width should change.
The second is narrowing the width by a third because one of three dice is known. Variance falls by a third, but the standard deviation falls by only about 18%, so the market narrows by about a fifth.
What the interviewer asks next
- Someone lifts your 13.8 offer three times in a row. What do you do next?
- Before any die is shown, what is the probability that the sum is 13 or more?
- How does your market change if the second die is also shown to be a 6?
Asked at Belvedere Trading, Equity Capital Markets, Chicago, 2022 (Wall Street Oasis):
superday with two 1-1s and a group trading game
