Alex purchased a $1,000 par value bond one year ago at a price of $1,016. At the time of purchase, the bond had 12 years to maturity and a 5%, semiannual coupon. Today, the bond has a yield to maturity of 5.25%. What is his realized yield as of today?

Question

Quizplus · Accepted Answer

The realized yield is the difference between the current market value of the bond and the purchase price, divided by the purchase price. The current market value of the bond can be calculated using the following formula:```Current market value = Present value of future cash flows + Present value of face value```The present value of future cash flows can be calculated using the following formula:```Present value of future cash flows = (Coupon payment / (1 + Yield to maturity / 2)^n) + (Coupon payment / (1 + Yield to maturity / 2)^(n-1)) + ... + (Coupon payment + Face value / (1 + Yield to maturity / 2)^2n)```where:* Coupon payment = $1,000 * 5% / 2 = $25* Yield to maturity = 5.25% / 2 = 2.625%* n = 12 * 2 = 24Plugging these values into the formula, we get:```Present value of future cash flows = $25 / (1 + 0.02625)^1 + $25 / (1 + 0.02625)^2 + ... + ($25 + $1,000) / (1 + 0.02625)^48``````Present value of future cash flows = $997.40```The present value of the face value is simply the face value of the bond, which is $1,000.Therefore, the current market value of the bond is:```Current market value = $997.40 + $1,000 = $1,997.40```The realized yield is:```Realized yield = ($1,997.40 - $1,016) / $1,016 = 1.32%```Therefore, the correct answer is D.

Alex Purchased a $1,000 Par Value Bond One Year Ago