Question 3 (25 points) Bay-area Engineering and Associates (BEA), has decided to issue a perpetual bond. The bond has a face value of $1,000 and makes 10% annual coupon payments. The current discount rate on the bond is 8%. There is a 35% probability that the discount rate on the bond one year from today will increase to 10%, and a 65% probability that it will decline to 5%. a) What is the current price of the bond, if the bond is non-callable? (6%) b) (i) If BEA decides instead to make the bond callable in one year with a call price at $1,400 per bond, when (if ever) should the company choose to exercise the call option? Explain.(4%) (ii) Will the callable bond have a higher or lower current price compared to the non-callable bond in part (a)? (2%) c) What is current price of the callable bond? (6%) d) What is the current value of the call provision to BEA? (7%)