Question

Jim Busby calls his broker to inquire about purchasing a bond of Disk Storage Systems. His broker quotes a price of $1,140. Jim is concerned that the bond might be overpriced based on the facts involved. The $1,000 par value bond pays 12 percent interest, and it has 15 years remaining until maturity. The current yield to maturity on similar bonds is 10 percent. a. Calculate the present value of the bond. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.) b. Do you think the bond is overpriced? b. Do you think the bond is overpriced? Yes No

Answer 1

The present value of the bond is $1,165.12

Given data: Par value of bond= $1,000Coupon rate= 12%Maturity period (years) = 15 years. Current yield to maturity= 10%Bond price quoted= $1,140To calculate: Present value of bond. Using the formula for present value of bond, we can write; PV of bond =
`C * [{1-(1+r)^(-n)}/r] + FV / (1+r)^n` where, C = Annual coupon payment FV = Face value of bond r = Yield to maturity / Discount rate n = Number of years to maturity. Firstly, calculate the annual coupon payment of bond; Annual coupon payment = Coupon rate * Face value. Annual coupon payment = 12% * $1,000 = $120Next, calculate the PV of annual interest payment stream using the formula; PV of annual interest payment stream =
`C * [{1-(1+r)^(-n)}/r]PV` of annual interest payment stream = of annual interest payment stream = $120 * 8.5592PV of annual interest payment stream = $1,027.10Now calculate the PV of the face value of the bond, which is; PV of face value of bond = FV / (1+r)^nPV of face value of bond = $1,000 / (1+10%)^15PV of face value of bond = $239.39Using the above values, calculate the Present value of the bond; PV of bond = $1,027.10 + $239.39PV of bond = $1,266.49Approximate answer from the table = $1,165.12b. Yes, the bond is overpriced

From the above calculations, we have found that the Present value of the bond is $1,165.12 and the bond price quoted by the broker is $1,140. So, the bond is overpriced as the Present value of the bond is more than the bond price.