The yield method on a floating-rate direct loan: the calibrated spread, the market move, the life assumption, and why the base rate hardly matters.
Discount the loan's contractual cash flows at the base rate plus the spread a market participant would now demand, with that spread calibrated to the price at which the loan was struck. An illustrative 50 million term loan at a margin of 575 basis points, issued at 98, implies a discount spread of 637. A year later, with comparable spreads 125 basis points wider, the same calculation gives 95.33, or 47.66 million. A 200 basis point move in the base rate changes that price by only 0.14 of a point.
Worked in full in The Private Markets Valuation Specialist by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Most private credit funds mark performing loans with a yield, or discounted cash flow, method. The method itself is uncontroversial. The two judgments inside it decide the mark: which spread the cash flows are discounted at, and over what life. Both are worked below on one loan.
| Term | Value |
|---|---|
| Face amount, EUR millions | 50.0 |
| Margin over the base rate | 575 bp |
| Base rate, assumed flat | 4.00% |
| Original term, quarterly interest, bullet repayment | 4 years |
| Issue price | 98.0 |
| Widening in comparable loan spreads over the first year | 125 bp |
Price = Σ coupont ÷ (1 + (base + s)/4)t + 100 ÷ (1 + (base + s)/4)n
Solve for the discount spread s that returns the issue price of 98.0 on 16 quarters: s = 637 bp, 62 above the contractual margin.
In Excel, put the quarterly cash flows in a row and use Goal Seek on the spread cell until =NPV((base+s)/4, flows) equals 98.
The 62 basis points are the original issue discount expressed as spread. They are part of what the lender was paid for the risk on day one, and they belong in the discount rate. Discounting at the contractual margin instead makes the loan worth par on the day it was bought at 98, which is the credit version of failing the day-one test.
Current discount spread = calibrated spread + change in comparable spreads
637 + 125 = 762 bp. With three years left, the discount yield is 4.00% + 7.62% = 11.62% against a coupon of 9.75%.
Price on 12 remaining quarters: 95.33, a value of 47.66 million.
At an unchanged spread, the passage of a year would have pulled the price from 98.0 to 98.43. The widening takes it to 95.33, a loss of 1.55 million that has nothing to do with the borrower. The check on the arithmetic is spread duration: at 2.55, a 125 basis point move should cost about 3.19 per cent of the price, roughly 3.1 points, and it does.
Move the base rate up 200 basis points and the price goes to 95.46; move it down 200 and it goes to 95.18. The change is 0.14 of a point either way, 0.07 million. The coupon resets with the base rate, so the loan carries almost no interest rate risk. The residual movement exists only because the discount spread, 762, differs from the margin, 575: the gap between them is discounted at a slightly different rate. A floating-rate loan's fair value is a credit spread instrument. If a quarter's mark moves materially and the only change is the base rate, the model has a fixed coupon in it somewhere.
| Remaining life | No change | +50 bp | +125 bp | +200 bp | +300 bp |
|---|---|---|---|---|---|
| 1.5 years | 99.15 | 98.47 | 97.46 | 96.47 | 95.16 |
| 2.0 years | 98.90 | 98.02 | 96.71 | 95.42 | 93.74 |
| 3.0 years | 98.43 | 97.17 | 95.33 | 93.52 | 91.18 |
The life assumption is the second judgment. Direct loans are rarely held to maturity: borrowers refinance or are sold. If the evidence supports an expected life of two years rather than the contractual three, the price is 96.71, 1.38 points or 0.69 million higher. Shortening the life always helps a loan below par, because the discount is recovered sooner. That makes it a judgment that needs support, such as the fund's own repayment history for comparable loans, not one adopted because it lifts the mark.
The method above is for a performing loan. Once recovery is in doubt, the question stops being what spread to apply and becomes what the enterprise is worth and what ranks ahead of the loan. A yield method applied to a loan that is impaired will keep returning a price near par for a borrower that cannot repay.
Calibrate the spread to the issue price, move it with comparable spreads, and support the life you discount over. Here that is 762 basis points and 95.33. The free workbook marking a credit across the cycle takes a similar loan from performing into a recovery analysis, and a related article applies the same calibration discipline to an equity mark.
Barely. The coupon resets with the base rate, so the price moves only through the small gap between the discount spread and the margin. On an illustrative loan priced at 95.33, a 200 basis point rise in the base rate moves the price to 95.46, and a fall moves it to 95.18. Spreads, not rates, drive the mark.
The spread that makes the discounted cash flows equal the price actually paid at origination. A four-year loan at a 575 basis point margin bought at 98.0 implies 637 basis points. Subsequent marks move that spread with comparable loan spreads, so the original issue discount stays in the risk premium.
It shortens the period over which a below-par loan recovers its discount. With 762 basis points of discount spread, a loan priced at 95.33 over three remaining years is worth 96.71 over two, 0.69 million more on 50.0 of face. The shorter life needs evidence, such as repayment history on comparable loans.
The companion workbook for chapter 10 of The Private Markets Valuation Specialist marks a senior secured loan across the cycle, from performing into trouble. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: private equity and private markets → · All 324 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.