Every note yield is a yield to an assumed payoff month, and which month you assume decides whether you overpay.
An early payoff raises the yield on a note bought at a discount and lowers it on a note bought at a premium, because the discount or premium is realised over fewer months. A $100,000 note at 7.00 per cent, bought for 80 per cent of its balance, yields 9.64 per cent if it runs its full 25 years and 15.57 per cent if the borrower pays it off in month 36. The same note bought at 105 per cent yields 6.47 per cent to maturity and 5.16 per cent on the same payoff.
Worked in full in The Mortgage Note Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Most performing notes do not run to term. Borrowers sell, refinance or pay off a balloon, and on residential and owner-financed paper the payoff usually arrives years early. The yield you quote at purchase is therefore a yield to an assumed payoff month, and it is worth computing more than one.
| Input | Value |
|---|---|
| Unpaid principal balance | $100,000.00 |
| Note rate | 7.00% |
| Remaining term | 300 months |
| Monthly payment, principal and interest | $706.78 |
| Purchase price, discount case | $80,000.00 (80%) |
| Purchase price, premium case | $105,000.00 (105%) |
Price = Σt=1..k payment ÷ (1 + i)t + balancek ÷ (1 + i)k, yield = 12 × i
k is the payoff month. Solve for the monthly rate i that makes the cash flows worth the price. In Excel: the balance at month k is =FV(7%/12,k,706.78,-100000) and the yield is =RATE(k,706.78,-80000,Balance)*12.
Payoff in month 36. The balance after 36 payments is $95,070.79. The buyer receives 36 payments of $706.78, $25,444.05 in all, plus the payoff, $120,514.85 in total, for an outlay of $80,000.00. Solving gives a monthly rate of 1.30 per cent, 15.57 per cent a year.
Held to maturity. The buyer receives 300 payments, $212,033.76, a profit of $132,033.76 against $40,514.85 on the three-year payoff. More than three times the dollars, but spread over 25 years: the yield is 9.64 per cent.
| Payoff in month | Balance repaid | Yield at 80% | Yield at 105% |
|---|---|---|---|
| 12 | $98,470.19 | 30.63% | 1.91% |
| 36 | $95,070.79 | 15.57% | 5.16% |
| 60 | $91,162.15 | 12.62% | 5.80% |
| 120 | $78,633.40 | 10.50% | 6.27% |
| 300 (maturity) | $0.00 | 9.64% | 6.47% |
For the discount buyer every early payoff is good news, and the earlier the better: the $20,000.00 of discount is collected as a lump instead of slowly, as each payment repays principal bought below par. For the premium buyer the logic reverses. The $5,000 premium is lost the day the loan pays off, and a payoff in month 12 leaves a yield of 1.91 per cent on a 7.00 per cent note.
Maturity is the discount buyer's worst case, and the premium buyer's best. A discount note priced to its full term is priced conservatively; a premium note priced to its full term is priced on the one assumption least likely to hold.
The assumption also changes what you should pay. For a 12.00 per cent yield, the note is worth $81,953.46, 81.95 per cent of its balance, if you expect a payoff in month 60, and $67,106.25, 67.11 per cent, if you expect it to run to maturity: a gap of $14,847.21 on the same paper.
| Priced assuming | Price | Actually paid off | Realised yield |
|---|---|---|---|
| Maturity, month 300 | $67,106.25 | Month 60 | 17.21% |
| Payoff in month 60 | $81,953.46 | Never, held to month 300 | 9.34% |
A buyer who assumes an early payoff and pays for it loses 2.66 points of yield if the borrower stays. A buyer who assumes the full term and gets an early payoff gains 5.21 points. The asymmetry is why experienced note buyers price discount paper to maturity and treat the payoff as upside.
The common mistake is to look at the total profit instead of the yield. The note held to maturity makes $132,033.76 and the three-year payoff only $40,514.85, so the long hold looks better, but the shorter one earns 15.57 per cent against 9.64, and its cash can be redeployed. The second mistake is the premium buyer's: paying 105 per cent for a 7.00 per cent note on the strength of its coupon, with no view on how long the borrower will keep a loan that a refinance could replace.
The price for a target yield is set out in how to price a performing note, and the same timing logic drives the price of a partial.
A yield on a note is always a yield to a payoff month. At 80 cents, a 7.00 per cent note yields 9.64 per cent to maturity and 15.57 per cent on a payoff in year three; at 105 cents, 6.47 and 5.16. Compute the table before you bid, and price to the payoff month that hurts you. The free workbook for this case runs the price at any required yield and what prepayment, the balloon and an extension do to it.
If the note was bought at a discount, yes: the discount is collected at once. A $100,000 note at 7.00 per cent bought at 80 per cent yields 30.63 per cent on a payoff in month 12, against 9.64 per cent to maturity. If it was bought at a premium, an early payoff is the worst outcome: 1.91 per cent at 105 per cent.
The one that hurts you. For a discount note that is maturity, which gives the lowest yield; for a premium note it is an early payoff. In the illustrative case a buyer who pays $81,953.46 assuming a month-60 payoff earns 9.34 per cent if the loan runs to term instead of the 12.00 per cent targeted.
Because the profit is spread over more years. The illustrative note bought for $80,000.00 returns $132,033.76 of profit over 25 years, a 9.64 per cent yield, and $40,514.85 over three years if paid off in month 36, a 15.57 per cent yield. The shorter hold also frees the cash to be reinvested.
Prepayment, the balloon and an extension are worked on a performing note in Part I (chapters 2 to 5) of The Mortgage Note 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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