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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 mathsCoreAMAres 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

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