$(15$ points $-$ Time Value of Money$)$ Today is Year $0$ and suppose a startup is considering the issuance of a

structured instrument to raise capital. In the first three years from now, this works like a coupon bond with

face value of $$100,$ paying $5\%$ coupon annually. After three years, this note can be redeemed for face value,

or converted to a dividend$-$paying common stock using the face value of the bond. It is expected that the

dividend would be $$7$ per share, paid annually. Suppose for now that the required rate of return for both

stocks and bonds are $7\%.$

$($a$)(3$ points$)$ Write down the single timeline that represents the cash flow of this instrument if the bond is

converted to stock.

$($b$)(6$ points$)$ Write down the equation that solves for the price of this structured instrument if the bond is

converted to stock. $($Caution: Watch out for the cash flow and discounting timing!$)$

$($c$)(6$ points$)$ At the conversion time, if the company performance declines and the expected dividend paid is

now only $$5$ per share $-$ would you decide to convert this bond to stock or redeem for the face value?

Why?