Bond A has a coupon rate of 10% and a yield of 13%. Bond B has coupon rate of 5% and sells for the same price as Bond A. Both bonds have the same face value and maturity. From this, which of the followings is the most inappropriate statement? A. The yield of Bond B is greater than 5%. B. The yield of Bond B is less than 10%. C. Bond A is a discount bond. D. Both bonds are discount bonds.
Question
Bond A has a coupon rate of 10% and a yield of 13%. Bond B has coupon rate of 5% and sells for the same price as Bond A. Both bonds have the same face value and maturity. From this, which of the followings is the most inappropriate statement? A. The yield of Bond B is greater than 5%. B. The yield of Bond B is less than 10%. C. Bond A is a discount bond. D. Both bonds are discount bonds.
Solution
The most inappropriate statement is D. Both bonds are discount bonds.
Here's why:
A. The yield of Bond B is greater than 5%. This statement is appropriate because if Bond B sells for the same price as Bond A but has a lower coupon rate, then its yield must be higher than its coupon rate to make it as attractive to investors as Bond A.
B. The yield of Bond B is less than 10%. This statement is also appropriate. Given that Bond B has a lower coupon rate than Bond A, it's reasonable to assume that its yield would also be less than that of Bond A.
C. Bond A is a discount bond. This statement is appropriate. A bond is considered a discount bond when its yield to maturity is higher than its coupon rate. Since Bond A has a yield of 13% which is higher than its coupon rate of 10%, it is indeed a discount bond.
D. Both bonds are discount bonds. This statement is inappropriate. We can't assume that Bond B is a discount bond just because it sells for the same price as Bond A. A bond is considered a discount bond when its yield to maturity is higher than its coupon rate. We don't have enough information to determine if this is the case for Bond B.
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