The price of a bond will decrease when the yield to maturity increases due to rising market interest rates.
As the yield to maturity on Castles in the Sand Incorporated bonds went up from 8% to 15%, the bond must now sell for less than its face value in order to provide the newer, higher yield to investors.
The student inquired about how the market price of a bond would change when the yield to maturity increases from the initial rate at which it was issued. Previously issued at an 8% yield, the bond in question now must be sold at a price that reflects the new yield of 15%, since the interest rates in the market have risen.
To calculate the current price of the bond, we must discount the future cash flows, which are the annual coupon payments and the face value at maturity, by the new yield to maturity of 15%.
Let's use the example provided as a reference to explain the concept. Initially, the bond was sold at its face value of $1,000, earning an 8% coupon rate, indicating annual payments of $80 to the bondholder.
Now, due to increased market rates and the company's hard times, the attractiveness of this bond has decreased because investors can seek out other bonds with a 15% return.
So, this 8% bond must be sold for less than its face value to give a 15% yield to maturity to new investors.
The bond's price can be understood as the present value of future cash flows, including the face value and the interest payments, discounted by the new yield rate.
However, to get the exact current price of the bond, you'd need to perform present value calculations for each of the payments to be received over the next 8 years and sum them up after discounting each by the 15% rate.
Since the calculations are not shown, we cannot provide the precise price, but the concept is that the price of the bond will be lower than the face value due to the higher yield to maturity desired by investors.