What is the value of an Orion bond that has a 10 percent coupon, pays interest semiannually, and has 10 years to maturity, if the required rate of return is 12 percent?

Question

Quizplus · Accepted Answer

The value of the bond can be calculated using the present value of an annuity formula for the semiannual interest payments and the present value formula for the lump sum payment of the bond's face value at maturity. Given a 10% annual coupon rate on a $1,000 face value bond, the semiannual coupon payment is $50 (10% of $1,000 divided by 2). With a 12% annual required rate of return, the semiannual rate is 6% (12% divided by 2). The bond has 20 periods to maturity (10 years times 2). The present value of the annuity (coupon payments) is calculated as: PV = C * [1 - (1 + r)^-n] / r, where C is the coupon payment, r is the semiannual rate (as a decimal), and n is the total number of periods. The present value of the face value is calculated as: PV = F / (1 + r)^n, where F is the face value. Adding these two components gives the total value of the bond. Plugging in the numbers: PV of annuity = $50 * [1 - (1 + 0.06)^-20] / 0.06 ≈ $614.50, and PV of face value = $1,000 / (1 + 0.06)^20 ≈ $270.99. Adding these together gives approximately $885.49, which rounds to $885.50, making option B the correct answer.

What Is the Value of an Orion Bond That Has