$3.$ Firm A$$s common stock pays no dividends and sells for $$38.$ Firm B$$s

common stock pays a $$1\mathrm{.}50$ cash dividend and sells for $$29.$

Both firms have $$1000$ par convertible bonds with a $10-$year maturity and a

$9\%$ coupon. Firm A$$s bonds convert into $30$ shares of common stock, while

Firm B$$s convert into $38$ shares of common stock. Both firms$$ bonds are

currently selling for $$1,200.$

a$.$ What is the value of each bond in terms of stock?

b$.$ What is the premium paid over each bond's value as stock?

c$.$ What is each bond's income advantage over the stock into which the

bond can be converted?

d$.$ How long will it take for the income advantage to offset the premium

identified in part $($b$)?$

e$.$ If$,$ after five years, Firm A$\text{'}$s stock sells for $$48$ and the firm calls the bond,

what is the holding period return and the annual rate of return earned on an

investment in the stock or the bond?

f$.$ Why is the holding period return misleading?

g$.$ If the stock splits $2-1,$ what impact will that have on the price of the

convertible bond?

h$.$ If the convertible bond is held to maturity, what does the investor

receive? What is the annualized return?