Why Do Bonds Trade at a Premium, Discount, or Par?
Contractual coupons stay fixed while required returns change. Price brings the two back into balance.
Try it and see the difference
What if required returns change, but coupons do not?
Face value 1,000, 5% coupon, ten years to maturity and semiannual payments. Change only YTM.
Coupon rate and YTM are both 5%. In this fixed-coupon model on a coupon date, all future payments have a present value of 1,000.
Coupon PV 389.73 + Principal PV 610.27 ≈ 1,000.00
Why does this happen?
The same 50 annual coupon looks attractive when the market requires only 3%, so buyers pay above face value. When it requires 7%, a 5% coupon is less attractive: a lower price lets the complete payment stream offer that required yield.
Purchase premium or discount is part of YTM
Maturity still repays face value of 1,000. A premium purchase receives less principal than its purchase price; a discount purchase receives more. YTM includes coupons, that difference and timing, so it need not equal the coupon rate.
Show formal definition and formula
Premium, par and discount describe price relative to face value. For a fixed-coupon bond valued on a coupon date, a coupon rate above, equal to or below YTM corresponds to premium, par or discount.
Coupon and number of periods
Present value of all payments
- P
- Current price
- F = R
- Face value, also maturity repayment
- C
- Coupon per period
- c
- Annual coupon rate, decimal
- y
- Nominal annual YTM, decimal
- m
- Coupon frequency; 2 here
- T / N
- Maturity years / total coupon periods
Fixed scheduled payments, valued on a coupon date with decimal rates. Default, taxes, fees and calls not defined in the example are excluded.
A common misconception
Discount does not necessarily mean a bargain, and premium does not necessarily mean poor value. This lesson isolates fixed payments and market yield, without assessing credit, liquidity or contract options.