Final answer:
The question deals with calculating the yield to maturity of a bond with a 7% coupon rate in a market where interest rates have risen to 12%. As interest rates rise, existing bonds with lower rates are sold at a discount to offer a competitive yield. The yield to maturity accounts for both the interest payments and any capital gains or losses due to the bond being sold at a discount or premium.
Step-by-step explanation:
The subject of this question is related to the yield to maturity (YTM) of a bond. In finance, the yield to maturity is a critical concept that defines the total return that is expected on a bond if it is held until its maturity. This yield encompasses both the interest or coupon payments and the capital gains or losses resulting from the difference between the bond's purchase price and its face value at maturity.
When the interest rates in the economy rise after a bond has been issued, newly issued bonds will likely offer a higher interest rate. This makes older bonds with lower coupon rates, like the 7% bond in the question, less attractive since investors could get a higher return elsewhere. To compensate for this, the seller of the older bond has to discount its price below face value to make it yield a return competitive with the new interest rate environment, hence the yield to maturity will adjust to reflect the new market conditions.
In the example provided where the bond has only one year left until maturity, and the interest rates have risen to 12%, the bond with 7% coupon will be sold at a discount to attract investors. Therefore, if an investor is to receive the $1,000 face value plus $70 (note the typo in the example should be 7%, not 8%) for the last year's interest payment, the bond's selling price should be set so that the investor's yield matches the prevailing 12% rate. Once that price is found, it will be less than the bond's face value of $1,000 because the seller must offer a higher yield through a discounted price.