Redemption Value

Study guide: Exam FM-2

The redemption value $C$ is the amount paid to the bondholder at maturity (when the bond is "redeemed"). For most bonds, the redemption value equals the Face Value ( $C = F$ , called redemption at par). However, redemption can occur at a premium ( $C > F$ ) or discount ( $C < F$ ). That describes $C$ against $F$ ; whether the bond is bought at a premium or discount compares the price $P$ with $C$ .

The basic bond price formula uses $C$ as the terminal payment:

$P = Fr \cdot a_{\overline{n}|j} + C \cdot v^n$

For Callable Bonds, the redemption value may vary by call date, and the buyer must calculate the worst-case yield (minimum yield) to determine the appropriate price.

Bond Redeemable at a Premium A $1{,}000$ face bond with 6% annual coupons matures in 5 years with redemption at $1{,}050$ . Price at yield $7\%$ .

Answer $P = 1000(0.06) \cdot a_{\overline{5}|7\%} + 1050(1.07)^{-5} = 60(4.1002) + 1050(0.712986)$ $= 246.01 + 748.64 = 994.65$

The bond is redeemable at a premium ( $C = 1{,}050 > F$ ) but is bought at a discount ( $P = 994.65 < C$ ): its modified coupon rate $g = 60/1{,}050 = 5.71\%$ is below the 7% yield.