The current price of a $1,000 par value, 6-year, 4.2% semiannual coupon bond is $958.97. The bond's PVBP is closest to:
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A. B. C.Explanation
To calculate the bond's PVBP (Price Value of a Basis Point), we need to determine the change in price resulting from a 1 basis point (0.01%) change in yield. PVBP represents the bond's price sensitivity to changes in yield.
Here are the steps to calculate the PVBP:
Calculate the bond's yield to maturity (YTM): The yield to maturity is the discount rate that equates the present value of the bond's cash flows to its current market price. In this case, we are given the current price of the bond, $958.97, which is less than its par value of $1,000. The bond has a 6-year maturity and pays semiannual coupons, so it will have 12 periods (6 years * 2). We can use a financial calculator or spreadsheet function to find the yield to maturity. Let's assume the YTM is 4.5%.
Calculate the modified duration: Modified duration measures the percentage change in the bond's price for a 1% change in yield. It is given by the formula:
Modified duration = (1/(1+YTM/n)) * [(PV of cash flows * time period) / bond price]
Where YTM is the yield to maturity and n is the number of periods per year. In this case, n is 2 (semiannual payments). The PV of cash flows is the present value of the bond's cash flows, which can be calculated using the YTM. The time period is the number of years remaining until maturity. Let's calculate the modified duration.
PV of cash flows = (Coupon payment / (1+YTM/n)) + (Coupon payment / (1+YTM/n)^2) + ... + (Coupon payment + Par value / (1+YTM/n)^n)
PV of cash flows = (21 / (1+0.045/2)) + (21 / (1+0.045/2)^2) + ... + (21 + 1000 / (1+0.045/2)^12)
PV of cash flows = 995.3786
Time period = 6 years
Bond price = $958.97
Modified duration = (1/(1+0.045/2)) * [(995.3786 * 6) / 958.97]
Modified duration ≈ 5.023
PVBP = Modified duration * 0.01
PVBP ≈ 5.023 * 0.01
PVBP ≈ 0.05023
Therefore, the bond's PVBP is closest to $0.05. None of the given answer choices match exactly, but the closest option is A. $0.50.