The yield to three-year takeout worked on a direct loan, the five lives that change the answer, and OID against extra spread.
On a floating-rate direct loan quoted to a three-year life, one point of original issue discount is worth about 39.5 basis points a year of spread, not the 33 that dividing by three suggests. A loan at S+600 issued at 98 yields 10.79 per cent to a three-year takeout, a pickup of 79 basis points over par. The value of the same 2 points ranges from 215 basis points if the loan is repaid after one year to 45 if it runs to maturity.
Worked in full in The Private Credit Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A direct lender is offered a six-year senior loan at the reference rate plus 600 basis points with quarterly coupons. The sponsor proposes to issue it at 98, two points of OID, and the question on the credit committee's desk is what that discount is worth in the only currency the committee compares across deals: spread per year. The reference rate is held flat at an illustrative 4.00 per cent so that the coupon is a fixed 10.00 per cent and the calculation isolates the discount.
| Input | Value |
|---|---|
| Reference rate, held flat (illustrative) | 4.00% |
| Spread | 600 bp |
| Coupon | 10.00% |
| Issue price | 98.0 |
| OID | 2.0 points |
| Contractual maturity | 6 years |
The shortcut divides the discount by the assumed life: 2 points over three years is 67 basis points a year, or 33 per point. It understates the value because it ignores that the lender invests 98, not 100, so every coupon is earned on a smaller outlay. The correct approach is a yield: solve for the rate that discounts the coupons and the redemption at par back to the price paid.
98 = Σ (2.50 / (1 + y/4)k) for k = 1 to 12, + 100 / (1 + y/4)12
y = 10.79%; at par the yield is 10.00%, so the OID adds 79 bp a year, or 39.5 bp per point
Excel: =RATE(12, 2.5, -98, 100)*4
The market convention of quoting to a three-year life, sometimes called the yield to three-year takeout, exists because few direct loans run to maturity. They are refinanced, repriced or repaid on a sale. The convention is a guess about life, and the value of the discount depends on that guess more than on anything else.
| Life (years) | Yield | Pickup over par | Per point of OID | Shortcut (OID / life) |
|---|---|---|---|---|
| 1 | 12.15% | 215 bp | 108 bp | 200 bp |
| 2 | 11.13% | 113 bp | 56 bp | 100 bp |
| 3 | 10.79% | 79 bp | 39 bp | 67 bp |
| 4 | 10.62% | 62 bp | 31 bp | 50 bp |
| 6 | 10.45% | 45 bp | 23 bp | 33 bp |
Two readings follow. First, the shortcut is always low, by about 12 to 15 basis points of pickup on this loan, because it leaves out the effect of buying below par. Second, and more important, the value of a discount falls steeply with life. A lender who assumes three years and is repaid in one earns 215 basis points of pickup; one who is held to six earns 45. The discount pays most exactly when the lender keeps the loan least.
The question usually arrives as a choice. The sponsor offers either the two points of OID or 50 basis points more spread at par, S+650. The undiscounted cash count says they are equal at four years: 2.0 points of discount against 50 basis points a year for four years. The yield says otherwise.
| Life (years) | OID route | Spread route | OID advantage |
|---|---|---|---|
| 1 | 12.15% | 10.50% | +165 bp |
| 2 | 11.13% | 10.50% | +63 bp |
| 3 | 10.79% | 10.50% | +29 bp |
| 4 | 10.62% | 10.50% | +12 bp |
| 6 | 10.45% | 10.50% | −5 bp |
The two routes tie at a life of about 5.3 years, not four. The discount is received on day one and works for the lender from then on, while the extra spread arrives quarter by quarter. On a loan that is likely to be refinanced inside three years, the OID is clearly the better currency for the lender. On a loan to a business with no obvious exit, which the lender may hold to maturity, extra spread is close to a tie and is the safer one: it also accrues on any extension and is not lost if the borrower refinances at a discount of its own.
Call protection changes this arithmetic. A soft call at 101 in year one adds a point to the one-year outcome and protects the lender in exactly the scenario where the OID is consumed fastest. Price the OID and the call schedule together, as one package of upfront economics.
The frequent error is to compare deals on the shortcut figure, OID divided by an assumed life, and then to fix the life at three years for every loan regardless of its profile. The shortcut always understates the yield; fixing the life at three years overstates it for a six-year loan and understates it for a one-year loan. So the two errors run in opposite directions for long-lived loans and in the same direction for short ones. A pipeline ranked on three-year yields will systematically favour loans with heavy discounts and expected short lives, which tend to be the ones with the most refinancing risk on the borrower's side, because the borrower plans to take them out early.
Two corrections cost nothing. Quote the yield at the life the deal team actually expects, alongside the three-year convention. And for any loan where OID makes up more than about a third of the pickup, show the yield to maturity too: if the deal only clears the hurdle on the three-year figure, the committee is approving an assumption about repayment, not a credit.
The second of the three new cases in the free workbook for this case extends the book's Calloway pricing example: the same loan earning a different yield depending on the year it is repaid, and a spread cut priced against OID over different lives. For the fee arithmetic one level up, at the fund, see what a subscription line actually does to the IRR.
It is the yield of a loan assuming it is repaid at par after three years, the usual market convention for leveraged and direct loans because few run to maturity. For a loan at a 10.00 per cent coupon bought at 98, the yield to three-year takeout is 10.79 per cent, against 10.45 per cent if it is held for the full six years.
It depends on how long the loan stays outstanding. Two points of OID beat 50 basis points of extra spread by 165 basis points of yield if the loan is repaid after one year, by 29 after three, and lose by 5 if it runs six years. The break-even life in the example is about 5.3 years, longer than the four years a simple cash count suggests.
Because the lender pays 98, not 100, so each coupon is earned on a smaller outlay and the discount is received at the start rather than spread over time. On the worked loan the shortcut gives 67 basis points a year for 2 points, while the true yield pickup over par is 79 basis points.
This article is one calculation from The Private Credit Investor. 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.
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