Suppose Ford Motor Company sold a issue of bonds with a 10 years maturity, a $1000 par value, a 10 percent coupon rate, and semiannual interest payments.

a) Two years after the bonds were issued, the going rate of interest on bond such as these fell to 6 percent. At what price would the bond sell?

b) Suppose that, 2 years after the initial offering, the interest rate has fallen to 12 percent. At what price would the bond sell?

c) Suppose the condition in part a) existed that is, interest rates fell to 6 percent, 2 years after the issue date, suppose further that the interest rate remained at 6% for the next 8 years. What would happen to the price of the Ford Motor Company bonds over time?

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a) When interest rates fall, the value of a bond with a fixed coupon rate increases because the bond's coupon payments become relatively more attractive than newly issued bonds with lower coupon rates. Using the formula for the present value of a bond, we can calculate the price of the bond after two years with a 6% interest rate:

n = 20 (10 years x 2 semiannual periods per year) r = 3% (6% / 2) C = $50 ($1000 par value x 10% coupon rate / 2) FV = $1000

PV = C x (1 - (1 + r)^-n) / r + FV / (1 + r)^n = $50 x (1 - (1 + 0.03)^-20) / 0.03 + $1000 / (1 + 0.03)^20 = $1,154.14

Therefore, the bond would sell for $1,154.14.

b) Conversely, when interest rates rise, the value of a bond with a fixed coupon rate decreases because the bond's coupon payments become relatively less attractive than newly issued bonds with higher coupon rates. Using the same formula, we can calculate the price of the bond after two years with a 12% interest rate:

n = 20 r = 6% C = $50 FV = $1000

PV = C x (1 - (1 + r)^-n) / r + FV / (1 + r)^n = $50 x (1 - (1 + 0.06)^-20) / 0.06 + $1000 / (1 + 0.06)^20 = $826.18

Therefore, the bond would sell for $826.18.

c) If interest rates remained at 6% for the next 8 years, the bond would continue to sell for $1,154.14 because the coupon rate is fixed at 10%. However, if interest rates fluctuated during the remaining 8 years, the bond's price would be affected. For example, if interest rates rose to 8%, the bond's price would fall because the coupon rate of 10% would become less attractive than newly issued bonds with higher coupon rates. Conversely, if interest rates fell to 4%, the bond's price would rise because the coupon rate of 10% would become more attractive than newly issued bonds with lower coupon rates. The bond's price would continue to fluctuate based on changes in interest rates and the attractiveness of its fixed coupon rate relative to newly issued bonds.