Basic, lesson 1 of 3
Bond prices and yields
A bond's price is the present value of its coupons and principal. The yield is the single discount rate that makes that present value equal the price.
9 min, 3 checks
1Price is the present value of the cash flows
A plain bond promises fixed coupons and the face value at maturity. Discount each payment back at the market yield and add them up. That sum is the price. Prices are quoted per 100 of face value, so a quote of 98.5 on a $1,000 bond means $985.
Price = C / (1 + y) + C / (1 + y)^2 + ... + (C + Face) / (1 + y)^n
C is the coupon per period, y the yield per period, n the number of periods.
Worked example
Halvorsen Industries 5% bond, three years, annual coupons
- 1Coupon: 5 per 100 face each year. Market yield: 4%.
- 2Year 1: 5 / 1.04 = 4.808.
- 3Year 2: 5 / 1.04^2 = 4.623.
- 4Year 3: 105 / 1.04^3 = 93.345.
- 5Sum: 4.808 + 4.623 + 93.345 = 102.78 (102.775 unrounded).
The bond trades at about 102.78. It pays 5% when the market only asks 4%, so buyers pay up for it.
Check 1
A two year bond pays a 6% annual coupon. The market yield is 5%. What is its price per 100 of face, to two decimals?
2Par, premium, and discount
Yield to maturity, YTM, is the one rate that sets the present value of every cash flow equal to today's price. It assumes you hold to maturity, get paid in full, and reinvest each coupon at the same yield. Compare it with the coupon and you know where the price sits.
| Relationship | Price | What happens over time |
|---|---|---|
| Coupon = yield | Par, 100 | Price stays near 100 |
| Coupon > yield | Premium, above 100 | Price drifts down to 100 by maturity |
| Coupon < yield | Discount, below 100 | Price drifts up to 100 by maturity |
Check 2
A Corrigan Foods bond has a 3% coupon and the market yield for its risk is 5%. Where does it trade?
3Current yield and accrued interest
Current yield is the annual coupon divided by the price. It ignores the pull to par, so it overstates the return on a premium bond and understates it on a discount bond. It is a quick income number, not a return number.
Current yield = Annual coupon / Price
Bonds trade between coupon dates. The buyer pays the seller the interest earned since the last coupon, the accrued interest, on top of the quoted clean price. Clean price plus accrued is the dirty price, the cash that actually changes hands.
Worked example
Accrued on a semiannual bond
- 16% annual coupon, paid 3 every six months.
- 2Two months since the last coupon: 6 x 2 / 12 = 1.00 per 100.
- 3Clean price 99.00. Dirty price 99.00 + 1.00 = 100.00.
The buyer pays 100.00 per 100 of face and receives the full 3.00 coupon four months later.
Check 3
A bond with a 5% coupon trades at 95. What is its current yield, in percent, to two decimals?
Terms in this lesson: Yield to maturity, Basis point.
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