Bond Price Calculator

Understanding Bond Price Valuation

The price of a bond represents the present value of all future cash flows expected from the security, discounted at the current market yield to maturity (YTM). Bond cash flows consist of two elements: periodic interest (coupon) payments throughout the life of the bond and the principal (face value) repayment at maturity.

Bond Price Formula

The present value formula for a bond paying $m$ coupon payments per year is:

$$P = \sum_{t=1}^{N} \frac{C}{(1 + y_p)^t} + \frac{M}{(1 + y_p)^N}$$

where $P$ is the bond price, $C$ is the periodic coupon payment ($M \cdot r / m$), $M$ is the par value, $y_p$ is the periodic yield ($y / m$), and $N$ is total compounding periods ($n \cdot m$).

Factors Influencing Bond Prices

• Market Interest Rates: Bond prices and interest rates move in opposite directions. When rates rise, existing bond prices drop, and when rates fall, bond prices increase.
• Coupon Rate vs Yield: If the coupon rate exceeds the required market yield, the bond trades at a premium ($P > M$). If the coupon rate is lower than market yield, it trades at a discount ($P < M$).
• Time to Maturity: As maturity approaches, a bond's price naturally converges toward its par value.