Final answer:
Bond valuation is influenced by changes in market interest rates. When rates rise, a bond's price must fall to offer an attractive yield comparable to newer bonds at higher rates. The 8% bond's market price will decrease to stay competitive with new bonds offering 12% yields.
Step-by-step explanation:
A firm's bonds with an 8% semiannual coupon, 8 years until maturity, callable in 4 years at $1,041.83, and currently selling at a price of $1,082.33, invite an analysis of interest rates and bond valuation. With no risk attached, the bond would sell at face value ($1,000) and pay $80 per year until maturity.
However, if market interest rates rise to 12%, the bond's price must fall below face value to attract buyers, as newer bonds offer higher yields. Therefore, if a few years have passed and interest rates have risen, but our bond's interest rate remains at 8%, its market value will decrease to offer the same yield as the new bonds at 12%.
For example, if an investor purchased the bond with one year left to maturity at a reduced price of $964 and received the face value of $1,000 plus the last year's interest payment of $80, their yield would be ($1080 - $964)/$964 = 12%. This yield reflects total return from interest payments and capital gains. Clearly, the bond's pricing dynamically adjusts to the changing interest rate environment to remain competitive in the market.