Final answer:
The student's question concerns the calculation of a bond's current yield at the time of purchase, with information on the YTM and coupon rate provided. To calculate current yield, one would need to divide the annual coupon payment by the bond's purchase price. An example calculation was given assuming a purchase price and the known coupon rate.
Step-by-step explanation:
The student is asking about calculating the current yield of a bond at the time of purchase. Current yield is a concept in finance that refers to the annual income (interest or dividends) divided by the current price of the security. This calculation is important in understanding the return on investment from the bond's coupon payments relative to its market price. The Yield to Maturity (YTM) is a related concept that represents the total return anticipated on a bond if the bond is held until it matures.
To find the current yield at the time of purchase, you need to know the annual coupon payment and the price at which the bond was bought. The bond's coupon rate was 7%, making semiannual payments, and was purchased at a YTM of 9%. Unfortunately, the bond price at purchase is not provided, but typically it would be below its face value since the YTM of 9% is higher than the coupon rate of 7%. The current yield would be calculated by dividing the bond's annual coupon payment by its purchase price.
If the bond was bought for a price of $964 with an $80 annual coupon payment (7% of $1000 face value), the current yield would be calculated as $80 divided by $964, which gives approximately 8.3%. The current yield provides an idea of the income return on the bond at the purchase price but does not account for capital gains or losses if the bond is sold before maturity or if the market interest rates change.