Question

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5. Pleasantonia Corporation's bonds have a 25-year maturity, a \( 7.40 \% \) semiannual coupon, and a par value of \( \$ 1,000 \). The going interest rate \( (r d) \) is \( 6.40 \% \), based on semiannual compounding. What is the bond’s price?

Answer 1

We can use the formula for the present value of a bond to calculate its price:

Bond price = (Coupon payment / Discount rate) x [1 - 1 / (1 + Discount rate)^(Number of coupon payments)] + Par value / (1 + Discount rate)^(Number of coupon payments)

In this case, the coupon payment is $1,000 x 7.40% / 2 = $37, the discount rate is 6.40% / 2 = 3.20%, the number of coupon payments is 25 x 2 = 50, and the par value is $1,000.

Bond price = ($37 / 3.20%) x [1 - 1 / (1 + 3.20%)^50] + $1,000 / (1 + 3.20%)^50
Bond price = ($1,156.25) x (34.9829) + $268.44
Bond price = $40,464.06

Therefore, the bond's price is approximately $40,464.06.