$5.$ Bailey$$s Pet Supply, Inc. has straight nonconvertible bond that currently yield $8\mathrm{.}75\%.$ Bailey's stock sells for $$25$ per share, has an expected constant growth rate of $5\mathrm{.}9\%,$ and has a dividend yield of $5\%.$ Bailey plans on issuing convertible bonds that will have a $$1,000$ par value, a coupon rate of $7\mathrm{.}85\%,$ a $20-$year maturity, and a conversion ratio of $35.$ Coupon payments will be made annually. The bonds will be noncallable for $5$ years, after which they will be callable at a price of $$1,080$; this call price would decline by $$5$ per year in Year $6$ and each year thereafter. For simplicity, assume that the bonds may be called or converted only at the end of a year, immediately after the coupon and dividend payments. Management will call the bonds when the bonds$$ conversion value exceeds $25\%$ of the bonds$$ par value $($not their call price$).$

a$)$ For each year, calculate: $(1)$ the anticipated stock price; $(2)$ the anticipated conversion value; $(3)$ the anticipated straight$-$bond price; and $(4)$ the cash flow to the investor assuming conversion occurs. At what year do you expect the bonds will be forced into conversion with a call? What is the bond$$s value in conversion when it is converted at this time? What is the cash flow to the bondholder when it is converted at this time?

b$)$ What is the expected rate of return on the proposed convertible issue?