Which of the following statments is CORRECT?
a. Assume that two bonds have equal maturities and are of equal risk, but one bond sells at par while the other sells at a premium above par. The premium bond must have a lower current yeild and a higher capital gains yield than the par bond.
b. A bond's current yield must always be either equal to its yield to maturity or between its yield to maturity and its coupon rate.
c. If a bond sells at par, then its current yield wii be less than its yield to maturity.
d. If a bond sell for less than par, then its yield to maturity is less than its coupon rate.
e. A discount bond's price declines each year until it matures, when its vaule equals its par value.
a. Assume that two bonds have equal maturities and are of equal risk, but one bond sells at par while the other sells at a premium above par. The premium bond must have a lower current yeild and a higher capital gains yield than the par bond.
b. A bond's current yield must always be either equal to its yield to maturity or between its yield to maturity and its coupon rate.
c. If a bond sells at par, then its current yield wii be less than its yield to maturity.
d. If a bond sell for less than par, then its yield to maturity is less than its coupon rate.
e. A discount bond's price declines each year until it matures, when its vaule equals its par value.
To determine which statement is correct, we need to analyze each option individually. Please note that explanations for each statement will follow.
a. Assume that two bonds have equal maturities and are of equal risk, but one bond sells at par while the other sells at a premium above par. The premium bond must have a lower current yield and a higher capital gains yield than the par bond.
To determine whether this statement is correct, we need to understand the terms current yield and capital gains yield. The current yield of a bond is calculated by dividing the annual interest payment by the bond's market price. The capital gains yield, on the other hand, represents the change in price from the time of purchase to the time of sale.
If the premium bond is selling above par, its market price will be higher than its face value or par value. Therefore, the current yield of the premium bond will be lower since the annual interest payment remains the same while the market price increases. Additionally, if the premium bond is sold at a later date, the capital gains yield will be higher as the price difference between the purchase and sale dates will be greater.
Thus, statement a is correct.
b. A bond's current yield must always be either equal to its yield to maturity or between its yield to maturity and its coupon rate.
To verify whether this statement is correct, we need to consider the relationships between yield to maturity and coupon rate with current yield.
The yield to maturity represents the overall return on a bond when held until maturity, factoring in the purchase price, coupon payments, and face value. The coupon rate is the fixed annual interest rate paid by the bond.
The current yield, as mentioned earlier, is calculated by dividing the annual interest payment by the market price of the bond.
The statement claims that the current yield must always be either equal to the yield to maturity or fall between the yield to maturity and the coupon rate. However, this is not accurate.
The current yield can be higher or lower than both the yield to maturity and the coupon rate, depending on the market price of the bond. Therefore, statement b is incorrect.
c. If a bond sells at par, then its current yield will be less than its yield to maturity.
To determine whether this statement is correct, we need to understand the concept of selling at par.
When a bond sells at par, it means that its market price is equal to its face value or par value. In such cases, the current yield will be equal to the coupon rate since the interest payment divided by the par value will give the coupon rate.
Therefore, statement c is incorrect. If the bond sells at par, its current yield will be equal to its yield to maturity, assuming the yield to maturity is equal to the coupon rate.
d. If a bond sells for less than par, then its yield to maturity is less than its coupon rate.
To verify whether this statement is correct, we need to understand the relationship between the market price, coupon rate, and yield to maturity.
If a bond sells for less than its face value or par value, this implies that its market price is lower. In such cases, the yield to maturity will be greater than the coupon rate. This occurs because as the market price decreases, the yield to maturity increases since it accounts for the capital gain potential created by the discounted price.
Thus, statement d is correct.
e. A discount bond's price declines each year until it matures when its value equals its par value.
To determine whether this statement is correct, we examine the behavior of a discount bond over time.
A discount bond is one that sells for less than its face value or par value. Since the bond is purchased at a discounted price, its price will gradually increase over time as it approaches maturity. This increase occurs because the bond's price moves closer to its par value as the maturity date approaches.
Therefore, the statement is incorrect. The price of a discount bond increases each year until it matures, reaching its par value at maturity.
In summary:
a. CORRECT
b. NOT CORRECT
c. NOT CORRECT
d. CORRECT
e. NOT CORRECT