Suppose that the assets of a firm are now priced at $100mil and are driven by a

Question

Suppose that the assets of a firm are now priced at $100mil and are driven by a two-state binomial model and that the risk-free rate of interest is zero. Furthermore the firm has currently just one outstanding share. The asset return in the up-node at the end of one period is 20% while in the down-node (at the end of the one period) is 0%. The firm has a zero coupon convertible bond with one period to maturity as well and with a face value of 100mil.The bond is convertible into 11 shares of common stock at the maturity of the bond at the option of the bondholder. What should be the value of the convertible bond? What should be the value of the equity of the firm? What will happen if the risk free rate is 1% instead of 0%?

Explanation / Answer

Value of Convertiable Bond :

Coversion Value = Conversion Ratio * Share Price

11 * 100 = 1100

Conversion is at option of bond holder.

Zero Coupun convertiable Bond, So Interest = 0

Year to Maturity = 1

Face Value = 100 mil

Required Return = 20%

Value of Bond = CV or MV whichever is higher * PVIFA (20% , 1 year)

= 1100 * 0.8333

= 916.67

b. Value of Equity of firm

Value of equity = 916.67 mil

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