Question

Leggio Corporation issued 20-year, 7% annual coupon bonds at their par value of $1,000 one year ago. Today, the market interest rate on these bonds has dropped to 6%. What is the new price of the bonds, given that they now have 19 years to maturity

Answer 1

To find the new price of the bonds, we can use the present value of a bond formula to calculate the price when the market interest rate is 6%. The present value of a bond formula is:

Price = (C * (1 - (1 + r)^-t) / r) + (F * (1 + r)^-t)

Where C = annual coupon payment, r = market interest rate, t = years to maturity, and F = face value.

In this case, the annual coupon payment is $1,000 * 7% = $70. With the market interest rate at 6%, r = 0.06. The bond now has 19 years to maturity, so t = 19. The face value is $1,000.

Price = ($70 * (1 - (1 + 0.06)^-19) / 0.06) + ($1,000 * (1 + 0.06)^-19)

First, calculate (1 + r)^-t:
(1 + 0.06)^-19 = 0.311804

Next, calculate the present value of the coupon payments:
($70 * (1 - 0.311804) / 0.06) = $70 * (0.688196 / 0.06) = $798.56

Now, calculate the present value of the face value:
($1,000 * 0.311804) = $311.80

Finally, add the present values to find the new price:
Price = $798.56 + $311.80 = $1,110.36

The new price of the bonds is $1,110.36.