Private Equity puzzles, solved step by step

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  1. 024A company has a 500 toggle note that pays either 10% in cash or 11% in kind. It toggles to PIK for three years. What is the note worth at the end, and what is total leverage if there is 300 of other debt and EBITDA stays flat at 100?Credit and PIK mathsCoreAres ManagementLos Angeles · 2026

    Try it first

    After three years of PIK at 11%, the note is

    Show the worked solution

    About 684, and leverage of about 9.8x. Each year 11% is added to the balance rather than paid: 500 grows to 555, then 616, then 683.8. Add the 300 of other debt and total debt is 984 against EBITDA of 100, so 9.8x, up from 8.0x today. The company has kept 150 of cash over the three years and taken on 184 of extra debt to do it.

    What does toggling to PIK actually do?

    Think of a credit card where you can skip the monthly payment and let the interest be added to the balance. Nothing leaves your account this month, but next month's interest is charged on a bigger number. A toggle noteA bond or loan whose issuer can choose each period to pay interest in cash or to add it to the principal, usually at a higher rate for the in-kind option. lets the borrower choose that every period, and the price of choosing it is a higher rate charged on a balance that compounds. Here the cash option costs 50 a year. The PIK option costs 55 in year one, and because that 55 is added to the note, 61.05 in year two and 67.77 in year three.

    Three years on PIK: the note grows and leverage climbs with itother debt 300note 500debt 8008.00xtodayother debt 300note 500PIK +55debt 8558.55xyear 1other debt 300note 500PIK +116debt 9169.16xyear 2other debt 300note 500PIK +184debt 9849.84xyear 3Cash interest avoided over three years: 150. Debt added instead: 184, because 11% compounds on a growing note.EBITDA held flat at 100, so every unit the note grows is a unit of leverage with nothing to cover it.
    With 300 of other debt and EBITDA flat at 100, three years of 11% PIK on the 500 note take total debt from 800 to 984 and leverage from 8.0x to 8.55x, 9.16x and 9.84x, while the 150 of cash interest avoided is less than the 184 of debt added.

    How does the leverage climb, year by year?

    Start at 800 of debt on 100 of EBITDA, 8.0x. After year one the note is 555 and total debt 855, so 8.55x. After year two the note is 616.05 and leverage 9.16x. After year three it is 683.82 and leverage 9.84x. Because EBITDA is flat, every unit the note accretes is a unit of leverage with no new earnings to carry it, and the ratio rises by almost two turns in three years without the business doing anything. That is the whole point of the question: PIK is deferred cash, not free cash, and it is deferred at a compounding rate.

    The relationship
    N3=500×1.113≈683.8Leverage=683.8+300100≈9.8xN_3 = 500 \times 1.11^3 \approx 683.8 \qquad \text{Leverage} = \frac{683.8 + 300}{100} \approx 9.8x
    N_3the note balance after three years of in-kind interest
    1.11one plus the PIK rate, applied to the growing balance each year
    300the other debt, which does not accrete
    What it says in wordsThe note grows at the in-kind rate compounded, and leverage is all the debt divided by an EBITDA that has not moved.

    When is toggling sensible, and what should you add?

    When the cash has a better use than paying interest: a short period of heavy investment, or a downturn the company expects to come out of. The toggle buys time at a known price, and the question for the lender and the sponsor is whether the EBITDA that eventually has to carry 984 of debt will be there when the time runs out. Say the things the simple version leaves out: the 1-point premium over the cash coupon is what the lender charges for the option, PIK interest is often still a tax deduction even though no cash moves, and a 9.8x company usually needs an equity cure, a sale or growth, because refinancing at that level is hard.

    Where candidates lose it

    The common error is simple interest, three years of 55, which gives 665. PIK compounds on the accreted balance, so the answer is about 684, and the gap is the interest on interest.

    The second loss is to say 684 and stop. The interviewer asked about leverage because that is what the toggle changes: convert to total debt over EBITDA, show the climb from 8.0x to 9.8x, and say that flat EBITDA is what makes the climb dangerous.

    What the interviewer asks next

    • If EBITDA instead grows 10% a year, what is leverage after three years?
    • What would the lender want in exchange for the toggle option, beyond the extra 1%?
    • How does three years of PIK change the recovery for the 300 of other debt if the company is worth 7x EBITDA at the end?

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

  2. 098A PIK note of 200 accrues 12% a year, compounded annually, for 5 years, with nothing paid until maturity. How much is owed at maturity, and how much more is that than five years of the same 12% paid in cash?Credit and PIK mathsWarm upAres ManagementNew York · 2026

    Try it first

    Roughly how much is owed after five years?

    Show the worked solution

    About 352.5 is owed, about 32.5 more than a cash-pay note's 320. PIK interest is added to the balance each year: 224, 250.9, 281.0, 314.7, then 352.5. A cash-pay note returns 24 a year plus 200 at the end, 320 in all. The extra 32.5 is interest on interest, which is why a PIK claim grows faster than its coupon suggests.

    What does paid in kind actually mean for the balance?

    A PIKPayment in kind: interest that is not paid in cash but added to the amount owed, so the loan balance grows instead. note pays its interest with more debt. It is like a credit card where you pay nothing and the interest is added to the bill each month, so next month's interest is charged on the bigger bill. Because each year's interest joins the balance, the 12% is earned on a growing base, and the claim compounds. After one year the balance is 224, after two 250.9.

    PIK interest earns interest, so the claim outruns the coupon200Yr 0224.0Yr 1250.9Yr 2281.0Yr 3314.7Yr 4352.5Yr 5At year 5PIK owed 352.5Cash-pay total 320PIK extra+32.5Bars: PIK balanceDashed: principal pluscash interest received
    A 200 PIK note at 12% compounds to 224, 250.9, 281.0, 314.7 and 352.5 over five years, while a cash-pay note's principal plus interest received rises in a straight line to 320, so the PIK claim ends 32.5 higher.
    The relationship
    200×1.125=352.5200+5×24=320352.5−320=32.5200 \times 1.12^5 = 352.5 \qquad 200 + 5 \times 24 = 320 \qquad 352.5 - 320 = 32.5
    1.12^5five years of 12% compounding, about 1.762
    24the yearly cash interest on 200 at 12%
    What it says in wordsPIK compounds the balance; cash-pay adds the same interest each year without compounding, and the gap is the interest on interest.

    Why does a private credit lender or a sponsor care?

    The borrower keeps its cash today, which helps a company that is growing or stretched. The price is a claim that grows every year, so at exit the sponsor's equity sits behind a bigger debt than the original 200. For the lender, PIK means more risk: nothing is received for five years, and if the company fails the larger balance may not be recovered. Lenders usually charge a higher rate for PIK than for the same loan paid in cash.

    Where candidates lose it

    The common slip is 320: adding five years of simple interest. That treats PIK as if the interest were paid in cash, missing that it compounds on the balance.

    The other is calling the 32.5 free money for the lender. It is compensation for waiting five years with nothing in hand, and for the risk that the balance is never paid.

    What the interviewer asks next

    • What is owed after 5 years if the PIK compounds semi-annually at 6% a half-year?
    • If the cash-pay interest could be reinvested at 12%, how do the two compare?
    • How does a PIK toggle option change who bears the risk?

    Asked at Ares Management, Generalist, New York, 2026 (Wall Street Oasis): Asked me basic behaviorals as well as some technicals around accounting as well as PIK interest.