Question

New Business Ventures, Inc., has an outstanding perpetual bond with a coupon rate of 10 percent that can be called in one year. The bond makes annual coupon payments and has a par value of $1,000. The call premium is set at $135 over par value. There is a 60 percent chance that the interest rate in one year will be 12 percent, and a 40 percent chance that the interest rate will be 7 percent. If the current interest rate is 10 percent, what is the current market price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

First, it must be checked whether bond will be called when interest rate is 7%. That is, bond will be called if bond price calculated using 7% interest rate will be greater than call price of par value plus call premium. Price of a perpetual bond = Annual coupon payment / Market interest rate Annual coupon payment Market interest rate Price of a perpetual bond $100 ($1,000 x 10%] 7% $1,428.57 ($100 / 7%] Par value of the bond Add: Call premium agreed Call value of the bond $1,000 $135 $1,135 ($1000 + $135] As the price of a perpetual bond calculated at 7% market interest rate is higher than call value of the bond, this bond will be called at 7% market interest rate. Price of a bond = [(Chance % for 7% x (Call value + Annual coupon payment)) + (1-Chance %) x (Annual coupon payment / Other interest % + Annual coupon payment)] / (1+ Current interest %) Bond's current market price = [(40% x ($1,135 + $100)) + 60% x ($100/ 12% + $100)]/(1 + 10%) Bond's current market price = [(40% x $1,235) + 60% x ($833.33 + $100)] / 1.10 Bond's current market price = [$494.00 + 60% x $933.33] / 1.10 Bond's current market price = ($494.00 + $560.00] / 1.10 Bond's current market price = $1054.00 / 1.10 Bond's current market price = $958.18