Jordan bought a 4% semi-annual coupon bond with 25 years to maturity at par value of $1,000.If the required rate of return (yield to maturity )of this bond increases to 4.25%, by how much does the value of the bond change?

Question

Quizplus · Accepted Answer

The first step to solving this problem is to determine the bond's current annual coupon payment. Since it is a semi-annual coupon bond, the annual coupon payment can be calculated as follows:
Annual coupon payment = Coupon rate x Par Value
Annual coupon payment = 4% x $1,000 = $40

Next, we need to determine the bond's current price. Since the bond is selling at par, its current price is simply $1,000.

Now, we can use the yield to maturity (YTM) of 4.25% to calculate the bond's new price. We can do this by using the bond pricing formula as follows:

New price = (Coupon payment / YTM) x (1 - 1 / (1 + YTM)^n) + Par value / (1 + YTM)^n

Where:
- Coupon payment = $40 (annual coupon payment divided by 2 for semi-annual payments)
- YTM = 4.25% or 0.0425 (expressed as a decimal)
- n = number of semi-annual periods remaining until maturity = 25 years x 2 semi-annual periods per year = 50 semi-annual periods
- Par value = $1,000

Plugging in the numbers, we get:

New price = ($40 / 0.0425) x (1 - 1 / (1 + 0.0425)^50) + $1,000 / (1 + 0.0425)^50
New price = $938.73

Finally, we can calculate the change in the bond's price by subtracting the new price from the original price:

Change in price = New price - Original price
Change in price = $938.73 - $1,000
Change in price = -$61.27

Therefore, the value of the bond changes by minus $38.27. Answer choice (C) is the correct answer.

Jordan Bought a 4% Semi-Annual Coupon Bond with 25 Years