Private Equity puzzles, solved step by step
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052A company carries debt of 600 against EBITDA of 100, so it is levered 6.0x. It repays 100 of debt every year and EBITDA grows 10% a year. What is leverage after three years?Mid-market buyout fundIndian mid-market PE
Try it first
Pick the closest figure for leverage at the end of year 3.
Show the worked solution
About 2.25x. Three repayments take debt from 600 to 300, and three years of 10% growth take EBITDA from 100 to 133.1. Leverage is 300 over 133.1, or 2.25x, down from 6.0x. Halving the debt alone would have left 3.0x; growth removes most of another turn, and that matters to a lender reading the covenant.
Why does leverage fall faster than the debt?
Think of a family loan measured against the family's income. Paying down the loan helps, and so does a pay rise, because the bank looks at how many years of income the loan represents. Leverage is debt divided by EBITDA, so it falls when the top shrinks and when the bottom grows, and here both are happening at once. Track both lines year by year rather than jumping to the end.
Debt falls from 600 to 300 while EBITDA rises from 100 to 133.1, so leverage drops from 6.0x to 2.25x; repayment alone would leave 3.0x and growth alone 4.51x. Year Debt EBITDA Debt / EBITDA 0 600 100.0 6.00x 1 500 110.0 4.55x 2 400 121.0 3.31x 3 300 133.1 2.25x Each year debt falls by a flat 100 and EBITDA rises by 10%, so the ratio drops from 6.00x to 4.55x, 3.31x and finally 2.25x. How much of the drop came from growth?
Split the move multiplicatively, which is exact for a ratio. Halving the debt divides leverage by 2.0; growing EBITDA by 33.1% divides it by 1.331. Six divided by 2.0 and then by 1.331 is 2.25x. Measured that way, repayment does about 71% of the work and growth about 29%, so growth is worth roughly three quarters of a turn here. Say the limit too: the 100 a year of repayment is an assumption, and in a real deal the cash for it comes from the same EBITDA that is growing.
Where candidates lose it
The common slip is answering 3.0x: halving the debt and stopping. It treats leverage as a debt number when it is a ratio, and it misses the 33% rise in EBITDA that does a large share of the work.
The other slip is compounding the debt reduction, as if debt fell 100 then a percentage. The repayment is a flat 100 each year; only EBITDA compounds. Keep the two lines apart and the ratio falls out.
What the interviewer asks next
- What leverage would a lender see at year 3 if EBITDA had fallen 10% a year instead?
- The covenant steps down to 2.5x at year 3. Is there headroom?
- Where does the 100 a year of repayment actually come from, and is it realistic at 6.0x?
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%?HPS 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.
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 relationshipr_E return on equity r_A return the asset earns before financing r_D interest rate on the debt D/E debt 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%
088A business has EBITDA of 100 and debt of 5x EBITDA at 10%. Capex is 20 and tax is ignored. What is interest cover, and how far can EBITDA fall before free cash flow after interest reaches zero?Private creditMid-market buyout fund
Try it first
How far can EBITDA fall before free cash flow hits zero?
Show the worked solution
Interest cover is 2.0x, and free cash flow reaches zero at EBITDA of 70, a 30% fall. Debt of 500 at 10% costs 50. EBITDA of 100 less capex of 20 and interest of 50 leaves 30 of free cash. That 30 is the cushion. At EBITDA of 70 the cover ratio still reads 1.4x, which looks fine just as the cash runs out.
Why is cover of 2.0x not the cushion it looks like?
A household earning Rs 1 lakh a month with a Rs 50,000 loan payment has income twice its instalment. But if it also spends Rs 20,000 on things it cannot skip, school fees and rent, only Rs 30,000 is truly spare. Interest cover ignores capex, so the real cushion is free cash flow after interest, 30 here, not the gap between EBITDA and interest. Cover would suggest EBITDA can halve; the cash says it can fall 30%.
EBITDA of 100 pays capex of 20 and interest of 50 and leaves 30 of free cash; at EBITDA of 70, a 30% fall, free cash is zero while interest cover still reads 1.4x. The relationship100 EBITDA 50 interest, 10% on debt of 500 20 capex the business must spend What it says in wordsCover compares EBITDA with interest; the breakeven adds the capex that must also be paid.What does a private credit lender do with this?
A lender tests the downside in cash, not in ratios: how far EBITDA can fall before the company must borrow more, cut capex, or miss a payment. Here the answer is 30%, and a lender would compare it with how far EBITDA fell in the sector's last downturn. If capex could be cut to 10 in a crisis, the cushion widens to a 40% fall, which is why lenders ask how much of capex is maintenance and how much is growth.
One limitation: with tax ignored the picture is generous. Tax would take a slice of the 30, and working capital swings in a downturn usually absorb cash too.
Where candidates lose it
Candidates say EBITDA can halve because cover is 2.0x. That forgets capex, which the business must pay whether or not EBITDA falls.
The second miss is giving the breakeven as an EBITDA level only. Say the percentage fall too, 30%, because that is the number a credit committee compares with history.
What the interviewer asks next
- Add tax at 25% on EBITDA less D&A of 20 less interest. Where is the breakeven now?
- If the rate rises to 12%, how much cushion is left?
- Which covenant would you set for this loan, and at what level?
