Question

What condition must exist if a bond's coupon rate is to equal both the bond's current yield and its yield to maturity? Assume the market rate of interest for this bond is positive.

1) The clean price of the bond must equal the bond's dirty price.
2) The bond must be a zero coupon bond and mature in exactly one year.
3) The market price must exceed the par value by the value of one year's interest.
4) The bond must be priced at par.
5) There is no condition under which this can occur.

Answer 1

The bond's coupon rate, current yield, and yield to maturity are all equal when the bond is priced at par, meaning the bond's market price equals its face value.

Step-by-step explanation:

If a bond's coupon rate is to equal both the bond's current yield and its yield to maturity, then the following condition must exist: the bond must be priced at par. When a bond is priced at par, its market price is equal to its face value, meaning that investors will buy the bond for exactly what it is worth in terms of its face value. This scenario assumes that the market rate of interest is positive.

When the bond is sold at par value, the coupon rate (the interest rate stated on the bond) becomes the same as the current yield and yield to maturity because no gain or loss is experienced by the bondholder through changes in the market price of the bond. Hence, all three measures of return converge to the same value, which is the coupon rate set forth when the bond was issued.