Private Equity puzzles, solved step by step

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  1. 040A company has floating-rate debt of 500 priced at a 5% base rate plus a 4% margin, and EBITDA of 110. The base rate rises by 200 basis points. What happens to interest cover?Credit and PIK mathsWarm upPrivate creditIndian mid-market PE

    Try it first

    Where does EBITDA interest cover go?

    Show the worked solution

    Interest cover falls from 2.44x to 2.0x. The all-in rate is 5% plus 4%, so 9% on 500 is 45 of interest, and 110 / 45 is 2.44x. After a 200 basis point rise the rate is 11%, interest is 55, and 110 / 55 is 2.0x. A two-point rise in the base rate lifts the interest bill by 22% and cuts cash left after interest from 65 to 55.

    Why does a two-point rate rise do so much damage?

    A household with a floating-rate home loan feels every rate rise in the next EMI, while one with a fixed rate does not. On floating-rate debt the borrower carries the rate risk, so a rise in the base rate goes straight into the interest bill. Two points on 500 is 10 more a year, which is 22% more than the 45 being paid today, with no change in how the business is running.

    The base rate rises 2 points; the interest bill rises 22%Today5% base + 4%interest 45left 65cover 2.44x110 / 45Base +200bp7% base + 4%interest 55left 55cover 2.00x110 / 55EBITDA 110 in both rowsExtra interest 500 x 2% = 10, which is 22% more on a bill of 45
    With EBITDA fixed at 110, a 200 basis point rise in the base rate lifts interest on 500 of floating debt from 45 to 55, so cover falls from 2.44x to 2.0x and the cash left after interest falls from 65 to 55.
    The relationship
    Cover=EBITDAD×(b+m)=110500×11%=2.0x\text{Cover} = \frac{EBITDA}{D \times (b + m)} = \frac{110}{500 \times 11\%} = 2.0x
    Dfloating debt, 500
    bthe base rate, now 7%
    mthe lender's margin, 4%
    What it says in wordsInterest cover is EBITDA over the interest bill, and on floating debt the bill moves with the base rate.

    What does a sponsor do about it?

    Most leveraged loans are floating, so sponsors usually hedge part of the debt. An interest rate swap fixes the rate on a portion of the loan, and a cap limits how high it can go in return for an upfront premium. Lenders often require a minimum hedged share in the loan agreement. The trade-off is cost and lost upside: a swap set before rates fall locks the borrower into the higher rate.

    Say what a credit analyst would look at next. EBITDA interest cover ignores capital spending and tax, so cash cover is tighter than 2.0x. A cover covenant set at, say, 2.0x would now be right at its limit, which turns a market move into a negotiation with lenders.

    Where candidates lose it

    The common loss is saying cover is unchanged because EBITDA is unchanged. Candidates forget that the coupon on floating debt resets with the base rate.

    The second loss is adding the 200 basis points to the margin and calling it a 2% rise in interest. The rate goes from 9% to 11%, which is a 22% rise in the bill. Say the percentage change in the bill, not in the rate.

    What the interviewer asks next

    • How much EBITDA growth would restore 2.44x cover after the rate rise?
    • If 60% of the debt is swapped to a fixed 7.5%, what is cover after the rise?
    • Why do lenders often insist on hedging, and who benefits when rates fall?
  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.