To raise fund to finance the establishment of surgical mask production lines, MKTV Mall Company Limited's chief financial officer, Wing Cheng (Wing), suggested issuing perpetual bonds with coupon rate of 8.1% and a face value of $1,000 each Coupon is paid annually.

The current market interest rate is 8%. Wing estimates a 0.7 probability that it will fall to 6%., and a 0.3 probability that next year's interest rate will increase to 10%.

Required:

(a) If MKTV Mall adopts Wing's suggestion, evaluate the current market value of the perpetual bond given the probabilities of interest rate change.

(b)The chairperson, Andy Siu (Andy), makes additional suggestion of adding a call provision into the bond contract and make them callable in one year. He suggests the call premium is equal to twice the annual coupon. Andy also wants to make the bonds could be issued at par (i.e. $1,000).

Determine what the new coupon rate of the callable bonds should be to achieve what Andy wants. (Assume that the bonds will be called if the interest rates fall.)

(c) Andy wonders if his idea of call provision could create any value. Calculate the value of the call provision for the callable bond proposed in part (b)