Final answer:
To find out which $1,000 face value security has the highest yield to maturity, one must consider interest payments and capital gains. For the bond purchased at $964 and yielding 12% to maturity, the total return includes the gains from the discount and interest earned. Market interest rate fluctuations affect bond prices and correspondingly yields.
Step-by-step explanation:
To determine which $1,000 face value security has the highest yield to maturity (YTM), we need to consider both the interest payments (coupon rate) and any capital gains or losses incurred by buying the bond at a discount or premium to its face value. In the scenario given, an investor receives the $1,000 face value at maturity plus an $80 interest payment for the last year. If the bond is bought at $964 and the market interest rates are at 12%, the yield to maturity can be calculated by the formula YTM = (Total Returns - Cost) / Cost, which equates to ($1080 - $964) / $964 = 12%. This reflects the total return on the investment, including both interest payments and the gain from purchasing the bond below its face value.
When market interest rates rise, the price of existing bonds will generally fall to yield a comparable rate to new issues, thus causing previously issued bonds with lower interest rates to sell for less than their face value. The reverse happens when interest rates fall; bonds with higher coupon rates compared to the market become more valuable, selling for more than face value to reflect the better yield.