Private Equity puzzles, solved step by step

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  1. 012A company's enterprise value is 800. It has 500 of senior debt, 400 of subordinated notes and equity beneath both. In a restructuring, what does each class recover? What changes if enterprise value is 1,000 instead?Leverage and capital structureWarm upKKRNew York · 2025

    Try it first

    At an enterprise value of 800, what do the subordinated notes recover?

    Show the worked solution

    At 800, senior recovers 100%, the notes 75% and equity nothing. Value is paid strictly by priority. Senior takes its 500 first, leaving 300 for the 400 of notes, which is 75%. At 1,000, value covers all 900 of debt, so both classes recover in full and equity is left with 100. The 200 increase in value goes 100 to the notes and 100 to equity.

    In what order does the value get paid out?

    Think of a row of buckets under one tap, each bucket overflowing into the next. The first fills completely before a drop reaches the second. A capital structure works the same way: each class is paid in full before the class below it receives anything. With 800 of value, the senior bucket takes 500 and is full. The remaining 300 flows into the notes bucket, which holds 400, so it is 75% full. Nothing reaches equity.

    Value fills claims in order of priority; the line cuts one trancheEV of 800Senior 500Sub notes 400EquityEV 800EV of 1,000Senior 500Sub notes 400EquityEV 1,000RecoverySenior 500 (100%)Sub 300 (75%)Equity 0Each extra 1 ofEV goes to thenotes until 900Senior 100%, sub 100%, equity 100the notes are the tranche the line cuts
    At an enterprise value of 800 the senior debt of 500 is paid in full, the subordinated notes get the remaining 300 of their 400, a 75% recovery, and equity gets nothing; at 1,000 both debt classes are whole and equity keeps 100.

    Which security does the interviewer care about most?

    The one the value line cuts through. That tranche is the fulcrum securityThe most senior class of claims that is not repaid in full, and so typically ends up owning the restructured company., here the subordinated notes at an EV of 800. Every change in enterprise value between 500 and 900 lands entirely on the notes, so they are the class whose price moves with the valuation argument while senior sits at par and equity sits at zero. In a restructuring the fulcrum holders usually swap their claim for the new equity, which is why distressed investors spend their time on it.

    What changes if enterprise value is 1,000?

    The line clears the debt. Senior is still paid 500, the notes are now paid their full 400, and the 100 left over belongs to equity. The 200 of extra value is split 100 to the notes and 100 to equity, and none of it reaches senior, which was already whole. That asymmetry is the lesson: a senior lender's upside is capped at par, while the junior classes capture the swing. Say the limitations too: real cases add administrative claims ahead of senior debt, and negotiated outcomes sometimes give junior classes a little value to secure their agreement.

    Where candidates lose it

    The usual slip is sharing value pro rata, giving every creditor 800 over 900, about 89%. That ignores priority, which is the whole point of having senior and subordinated claims.

    The second miss is stopping at the recoveries. The follow-up about 1,000 is there to see whether you notice which tranche absorbs the change in value.

    What the interviewer asks next

    • At what enterprise value does equity start to recover anything?
    • If the senior debt were secured on assets worth only 400, how would the answer change?
    • Why might a distressed fund buy the notes at 60 when they recover 75?

    Asked at KKR, Distressed Debt, New York, 2025 (Wall Street Oasis): What are your weaknesses? A capital structure question with enterprise value.

  2. 076An investment is funded half with debt at 7% and half with equity. The asset earns 12% a year before financing, and tax is ignored. What return does the equity earn? What if the asset earns only 5%?Leverage and capital structureCoreHPS Investment Partnersnew york · 2024

    Try it first

    Before you calculate: with the asset at 12%, what does the equity earn?

    Show the worked solution

    Equity earns 17% when the asset earns 12%, and only 3% when it earns 5%. Per Rs 100 of asset, lenders take a fixed 3.5. At 12% equity keeps 8.5 on its 50; at 5% it keeps 1.5 on its 50. Leverage adds the spread between the asset return and the cost of debt, times debt over equity, in both directions.

    Why does borrowing push the equity return above the asset return?

    Think of buying a flat for Rs 100 lakh with Rs 50 lakh of your own money and a Rs 50 lakh loan at 7%. If the flat earns 12 lakh a year in rent and value, the bank takes 3.5 lakh and everything else is yours. Lenders get a fixed amount whatever the asset earns, so any return above the cost of debt on the borrowed half lands on the equity. The borrowed 50 earns 12% and costs 7%; that 5 point spread on 50 is 2.5, added to the 6 the equity's own half earns.

    Lenders take a fixed 3.5; equity keeps whatever is leftAsset earns 12%12Lenders: 7% x 50 = 3.5Equity keeps 12 - 3.5 = 8.58.5 on equity of 50= 17% return on equityUnlevered 12%, levered 17%: +5 pointsAsset earns 5%5Lenders: 7% x 50 = 3.5Equity keeps 5 - 3.5 = 1.51.5 on equity of 50= 3% return on equityUnlevered 5%, levered 3%: -2 pointsEach bar is Rs 100 of asset: Rs 50 of debt at 7%, Rs 50 of equity
    On Rs 100 of asset funded half with debt at 7%, lenders take 3.5 whatever happens: at a 12% asset return equity keeps 8.5 on 50 for 17%, and at 5% it keeps only 1.5 on 50 for 3%.
    The relationship
    rE=rA+(rA−rD)DE=12%+(12%−7%)×1=17%r_E = r_A + (r_A - r_D)\frac{D}{E} = 12\% + (12\% - 7\%)\times 1 = 17\%
    r_Ereturn on equity
    r_Areturn the asset earns before financing
    r_Dinterest rate on the debt
    D/Edebt over equity, here 50 over 50, which is 1
    What it says in wordsEquity earns the asset return plus the spread over the cost of debt, scaled up by how much debt there is for each rupee of equity.

    What happens when the asset earns less than the debt costs?

    The same formula runs backwards. At 5%, the spread is minus 2 points, and with one rupee of debt per rupee of equity the equity return falls to 5 minus 2, which is 3%. Leverage is not a return booster; it is a multiplier on the spread, and the spread can be negative. Below a 3.5% asset return equity earns nothing at all, and below zero it loses money faster than the asset does.

    In the room, give both numbers and then the rule in one sentence. A private credit interviewer is checking that you see the downside as clearly as the upside, because their job is to sit on the other side of that fixed 3.5.

    Where candidates lose it

    The fast wrong answer is 24%, doubling the asset return because equity is half the funding. That forgets the lenders are paid first. The other slip is subtracting the 7% rate from 12% and calling 5% the equity return, which treats the whole asset as if it were borrowed.

    Work in rupees on Rs 100 of asset: asset income, less interest, over equity. Then give the 5% case without being asked; that is the half of the answer that shows judgement.

    What the interviewer asks next

    • What equity return do you get at 70% debt and the same 12% asset return?
    • At what asset return does the equity earn exactly the same as the asset, and why?
    • Now add tax at 25%. What happens to the 17%?

    Asked at HPS Investment Partners, Financial Sponsors, new york, 2024 (Wall Street Oasis): I was asked to calculate the returns of an investment that consisted of 50% debt with an interest rate of 7%