Case 001Private credit and direct lendingCore

A Rs 300 crore senior secured loan to Tamrika Water Tech is offered to you at 94 with a 10% coupon and three years left. Defaults run at 4% a year with 60% recovery. What is the yield, the loss-adjusted yield, and would you buy it?

The situation

A bank wants to sell its Rs 300 crore share of a senior secured term loan to Tamrika Water Tech, a maker of water treatment plants for industrial parks. The loan pays a 10% coupon once a year and repays in full at the end of three years. The bank is asking 94, so Rs 282 crore for the Rs 300 crore of face value.

Your credit team estimates that a borrower of this quality defaults about 4% of the time each year. If it defaults, a lender secured on the plant and receivables recovers about 60 paise on the rupee, paid at the end of the year of default. Your fund needs a loss-adjusted return of at least 10% on senior secured loans.

Your task

Work out the yield to maturity at 94, the yield after expected default losses, and say whether you would buy the loan and at what price you would stop.

Quick check

Before any maths: after expected losses, where does the yield land?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The loan yields about 12.5% to maturity at 94, but only about 10.5% after expected defaults, so it clears a 10% hurdle by half a point. I would buy at 94 only if diligence supports the 4% default estimate: the hurdle breaks if defaults run above about 5.1% a year, and the most I would pay is about 95.2.

Step 1What does the price of 94 promise if nothing goes wrong?

Start with the promised cash: Rs 10 of coupon in each of three years and Rs 100 back at the end, for every Rs 94 you pay. The yield to maturity is the one rate that discounts those promised cash flows back to 94, and here it is 12.5%. The discount adds about 2.5 points a year on top of the coupon, because the 6 points you gain as the price climbs back to par are spread over three years and earned on a smaller outlay. That is the number a seller quotes. It assumes every payment arrives on time.

Step 2How much of that yield do expected defaults take away?

Think of lending to a friend who, one year in twenty-five, cannot pay you back and hands over his scooter instead. You have to price the scooter years in, not just the good years. The loss-adjusted yield uses expected cash flows, each promised payment weighted by the chance the borrower is still paying, plus the recovery in the years it is not. At 4% a year the loan survives all three years 88.5% of the time. Expected cash flows per Rs 100 are 12.00, 11.52 and 99.53, and the rate that discounts them to 94 is 10.5%.

The discount looks generous until expected losses come offCoupon on par10.0%Yield to maturity at 9412.5%Expected default losses-2.0 pointsLoss-adjusted yield10.5%fund hurdle 10.0%0%
The loan's 10% coupon becomes a 12.5% yield to maturity at a price of 94, but expected defaults at 4% a year with 60% recovery take off 2.0 points, leaving a loss-adjusted yield of 10.5%, only just above the fund's 10% hurdle.
The relationship
94=∑t=13E[CFt](1+yL)tE[CFt]=St c+(St−1−St) R  ⇒  yL≈10.5%94 = \sum_{t=1}^{3} \frac{E[CF_t]}{(1+y_L)^t} \qquad E[CF_t] = S_t\,c + (S_{t-1} - S_t)\,R \;\Rightarrow\; y_L \approx 10.5\%
S_tthe chance the borrower is still paying at year t, 0.96 to the power t
cthe coupon, 10 per 100, plus the 100 of principal at year 3
Rthe recovery, 60 per 100, received in the year of default
y_Lthe loss-adjusted yield
What it says in wordsWeight each promised payment by the chance it is paid, add the recovery in the years it is not, and find the rate that makes that stream worth the price.

There is a quick version you can do out loud: yield minus default rate times loss severity, 12.5% minus 4% times 40%, gives 10.9%. The shortcut is useful for a first read but flatters this loan by about 0.4 points, because a default also takes that year's coupon and the pull to par you were counting on. Say the shortcut, then say which way it errs.

Step 3How wrong can the default estimate be before the trade fails?

This is the question that turns a yield into a decision. At 94 the loan clears the 10% hurdle only while defaults stay below about 5.1% a year, a cushion of roughly one point over the base case. At 6% the loss-adjusted yield falls to 9.5%. Run it the other way and the most you could pay for a 10% loss-adjusted return is about 95.2, so a counter-offer at 94 or a touch below is the right place to stand.

How much default the price can absorb before the hurdle breaks9%10%11%12%Base case, 4%: 10.5%Hurdle breaks at 5.1%0%2%4%6%8%Yearly default probability, recovery fixed at 60
The loss-adjusted yield on the loan at 94 falls as the yearly default probability rises and crosses the fund's 10% hurdle at about 5.1%, so the trade has roughly one point of default cushion over the 4% base case.

Close with the question the price is asking you. A bank selling at 94 when fresh loans of similar quality price near par may know something: a covenant waiver request, a delayed receivable, a customer walking away. A discount is only attractive after you know why it exists and after expected losses are taken off. The view: buy at 94 if the credit work confirms the 4% estimate, and walk away if it points nearer 5%.

Where candidates lose it

The common loss is quoting the 12.5% yield to maturity as the return. That number assumes every coupon is paid and every rupee of principal comes back. For a secured loan with real default risk, the promised yield is a ceiling, not an expectation.

The second is using the shortcut and stopping. Yield minus default rate times severity gives 10.9% here, which overstates the answer by about 0.4 points. On a trade that clears the hurdle by half a point, that error is most of the margin.

What the interviewer asks next

  • The seller drops to 92. What is the loss-adjusted yield now?
  • Recovery falls to 40% because the plant is specialised. What price clears the hurdle?
  • Why might a bank sell a performing loan below par at all?
  • How would a two-year remaining life change the value of the discount?

Company names and figures are illustrative.