Question $2$: Bond Valuation $(45$ points$)$

Evergreen Inc. has issued a semi$-$annual coupon bond. The bond has a $$1000$ face value, a

$10\%$ coupon rate, and matures in $8$ years. The current annual yield$-$to$-$maturity for all bonds

of the company is $7\%($note: this is APR$).$

a$)$ What is the semi$-$annual coupon amount?

b$)$ What is the price of this bond?

c$)$ What is the current yield of this bond?

Suppose Evergreen believes that its current share price is undervalued and considers

buying back shares. To do this, Evergreen decides to issue a zero$-$coupon bond that matures

in $5$ years and use the proceeds to buy back shares. The firm decides to buy back $10,000$

shares for now. The current stock price of Evergreen is $$30,$ and assume the buyback

decision does not change the stock price. Assume the effective annual rate $($EAR$)$ that can

be used to discount this new zero$-$coupon bond is $7\mathrm{.}12\%($same as that of the existing bonds$).$

d$)$ What is the total face value of the zero$-$coupon bond that Evergreen needs to issue?