Private Equity puzzles, solved step by step
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032A portfolio company has a loan of 300 at 9% with three years left. It can repay early at a 2% call premium and refinance at 7.5%. How much does refinancing save, net of the premium?Private creditMid-market buyout fund
Try it first
Ignoring discounting, what is the net saving?
Show the worked solution
About 7.5 before discounting, about 5.7 after. The rate falls 1.5 points on 300, saving 4.5 a year, or 13.5 over three years. The call premium is 2% of 300, which is 6, paid up front. Net, 13.5 less 6 is 7.5. Discount the savings at 7.5% and they are worth 11.7 today, so the net gain is about 5.7.
How should you think about a call premium?
Switching to a cheaper phone plan midway through a contract usually costs an exit fee. You switch only if the monthly saving, times the months left, beats the fee. A call premium is the lender's exit fee: it compensates the lender for losing a loan that pays above today's rate, so the borrower refinances only when the saving over the remaining term beats it. Here the fee is 6 and each year saves 4.5, so the fee is earned back in 1.33 years.
The borrower pays a premium of 6 at the refinancing date and saves 4.5 a year for three years, so the cumulative saving turns positive during year two and ends at 7.5, or about 5.7 discounted at 7.5%. When would refinancing not be worth it?
Work out the breakeven rate gap. Spread the premium over the years left: 6 over 3 years is 2 a year, which is 0.67% of 300. Refinancing pays only if the rate falls by more than the premium divided by the years remaining, about 67 basis points here. With one year left the breakeven gap would be the full 2 points, and refinancing at 7.5% would lose money.
The relationshipL the loan, 300 r_old - r_new the rate cut, 1.5 points n years remaining, 3 p the call premium, 2% What it says in wordsThe saving is the rate cut times the loan times the years left, less the premium paid to get out.Say what the sums leave out. A new loan carries its own arrangement fee and legal costs, often a point or more, which would eat most of the 7.5. Lenders also build call protection to step down over time, so waiting a year can cut the premium. And if the business improves, a lender may simply reprice the existing loan, which avoids the premium altogether.
Where candidates lose it
The common loss is quoting the gross saving of 13.5 and forgetting the premium, or quoting one year's saving of 4.5. The interviewer wants the full trade: saving over the remaining term against the one-off cost.
The second loss is ignoring the fees on the new loan. Mentioning them, even without a number, shows you know refinancing has a cost on both sides.
What the interviewer asks next
- With one year left, does refinancing at 7.5% still make sense?
- The new lender charges a 1% arrangement fee. What is the net saving now?
- Why do lenders insist on call protection in leveraged loans, and why does it usually step down?
061A sponsor can fund 4.5x EBITDA with senior debt of 3.0x at 7% plus second lien of 1.5x at 11%, or with a single unitranche loan of 4.5x at 8.5%. Which is cheaper, and why might the sponsor still choose the unitranche?Private credit
Try it first
What is the blended rate on the split stack?
Show the worked solution
The split stack is cheaper, at a blended 8.33% against 8.5%. Two thirds of the debt costs 7% and one third costs 11%, so the blend is 7% plus a third of the 4-point gap. On EBITDA of 100, that is 37.5 of interest a year against 38.25, a gap of only 0.75. Sponsors often pay that for one lender, one set of documents and a surer, faster close.
How do you blend two rates quickly?
If you borrow Rs 2 lakh from a bank at 7% and Rs 1 lakh from a relative at 11%, you are not paying 9% on the whole: most of the money is the cheap kind. A blended rate is a weighted average, so start from the cheaper rate and add the gap times the share of debt that is expensive. Here the second lien is a third of the stack, so the blend is 7% plus a third of 4 points, 8.33%.
The split stack of 300 senior at 7% and 150 second lien at 11% costs 37.5 a year, a blended 8.33%, while one unitranche of 450 at 8.5% costs 38.25, so the single lender costs 0.75 a year more. The relationship3.0/4.5 senior debt's share of the stack, two thirds 1.5/4.5 second lien's share, one third 4% the gap between the two rates What it says in wordsThe blended cost is the cheap rate plus the expensive tranche's share of the gap.Why would a sponsor pay more for one lender?
Because the 0.75 a year buys simplicity that has real value. With two tranches there are two lender groups and an intercreditor agreementThe contract between two groups of lenders to the same company that sets who is paid first, who controls enforcement and what each may do without the other. between them, and every waiver or amendment means two negotiations. A unitranche puts one lender across the table, which usually means a faster close, fewer parties who can block a change, and more certainty in a competitive auction. The limit: compare all-in costs, because upfront fees and call protection can differ between the two and move the answer by more than 0.17 points.
Where candidates lose it
The usual slip is a simple average: 7% and 11% make 9%, so the unitranche looks cheap. Senior is twice the size of the second lien, so the blend sits much nearer 7%.
The other loss is stopping at cheaper means better. The interviewer wants the second half: a gap of 0.17 points is small, and a sponsor will often pay it for speed and a single counterparty.
What the interviewer asks next
- At what unitranche rate would the sponsor be indifferent on interest alone?
- What changes if the second lien pays 11% as PIK rather than cash?
- Why might a unitranche lender split the loan into first-out and last-out pieces behind the scenes?
092A private credit fund makes a 3-year loan of 400 at 10%. The borrower has a 5% chance of default each year and lenders would recover 60%. What is the expected annual loss rate, and what does the loan earn after expected losses?Private credit
Try it first
What is the expected loss each year, as a share of the loan?
Show the worked solution
Expected loss is about 2% a year, 8 on 400, so the loan earns about 8% after losses. The chance of default is 5% and a default costs the 40% not recovered: 5% times 40% is 2%. That takes a fifth of the 10% coupon. Assuming a 5% base rate, the 5 point spread shrinks to about 3 points once expected losses are paid for.
Why multiply the default chance by the loss, not use it alone?
If you lend a friend Rs 1,000 and think there is a one in twenty chance they cannot repay, but you know you would get Rs 600 back from them anyway, your expected loss is not Rs 50 but one twentieth of Rs 400, Rs 20. Expected loss is the probability of default times the loss given defaultThe share of the loan a lender loses when a borrower defaults, after recoveries. A 60% recovery means a 40% loss given default., so recovery matters as much as the chance of default. Here: 5% times 40%, which is 2% a year.
With a 5% chance of default and 60% recovered, a 400 loan loses 160 if the borrower defaults and nothing otherwise, an expected loss of 8, or 2% a year, a fifth of the 10% coupon, leaving about 8% after losses. The relationshipPD probability of default in a year, 5% LGD loss given default, one minus the 60% recovery EL expected loss each year, as a share of the loan What it says in wordsExpected loss is how often default happens times how much it costs when it does; subtract it from the coupon to get the loss-adjusted yield.What changes over the full three years?
Default can happen in any year, so the chance of at least one default over three years is 1 minus 0.95 cubed, about 14.3%. Expected loss in rupees falls slightly each year because a loan that has already defaulted cannot default again: 8, then 7.6, then 7.2, about 22.8 over the life. The simple 2% a year is a good approximation. It also ignores the coupon lost in the year of default, which a fuller model would include.
A credit interviewer then asks whether 8% is enough. Compare it with the fund's cost of capital and with what safer loans pay. If senior loans to stronger borrowers yield 9% with expected losses of 0.5%, this loan is the worse risk-adjusted deal despite its higher coupon.
Where candidates lose it
The common slip is using the 5% default probability as the loss, which ignores recovery and overstates the expected loss by two and a half times.
The second is forgetting that expected loss is an average. A single loan either loses 160 or nothing; the 2% only describes a large, diversified book of loans like it.
What the interviewer asks next
- What coupon would give the same 8% loss-adjusted yield if recovery fell to 30%?
- Why do recoveries tend to fall exactly when defaults rise?
- How would a PIK toggle change the expected loss on this loan?