10. Bond prices and interest rate An 8 percent coupon bond with 15 years to maturity is priced to offer a 9 percent yield to maturity. You believe that in one year, the yield to maturity will be 6.5 percent. What is the change in price the bond will experience in dollars? (Assume annual interest payments and par value is $1,000.)
To calculate the change in the bond's price, you need to follow these steps:
1. First, calculate the current price of the bond using the given yield to maturity. The yield to maturity (YTM) is the rate of return anticipated on a bond if it is held until it matures. In this case, the bond has an 8% coupon rate, so the annual coupon payment is $80 (8% of $1,000).
The current price of the bond can be calculated using the present value formula:
Price = Coupon payment * [(1 - (1 + YTM)^(-n)) / YTM] + (Par value / (1 + YTM)^n)
In this formula, n is the number of periods until maturity (15 years), and YTM is the yield to maturity (9% or 0.09).
Price = $80 * [(1 - (1 + 0.09)^(-15)) / 0.09] + ($1,000 / (1 + 0.09)^15)
= $1,020.04
Therefore, the current price of the bond is $1,020.04.
2. Next, calculate the future price of the bond after one year using the new yield to maturity (6.5% or 0.065).
Using the same present value formula as above:
Price = $80 * [(1 - (1 + 0.065)^(-15)) / 0.065] + ($1,000 / (1 + 0.065)^15)
= $1,125.51
Therefore, the future price of the bond after one year is $1,125.51.
3. Finally, calculate the change in price by subtracting the current price from the future price:
Change in Price = Future Price - Current Price
= $1,125.51 - $1,020.04
= $105.47
Therefore, the bond will experience a change in price of $105.47.
Note: The change in price is positive because the new yield to maturity (6.5%) is lower than the current yield to maturity (9%), which means the bond will become more valuable.