An un$-$levered firm, Axe Company Ltd$.$ has an EBIT of $$500,000$ that it expects it will earn forever. The firm pays all of its earnings as dividends to shareholders $($i$.$e$.$ no growth$).$ The Axe Company Ltd$.$ has $100,000$ shares outstanding. When the firm was an un$-$levered firm, investors required a $12$ percent rate of return.

Now assume that the Axe Company Ltd$.$ issues $$400,000$ of debt with $7\mathrm{.}5\%$ coupon that maximized its value. The firm uses this debt to buy back shares. Assume that the firm has a tax rate of $40\%$ and equity investor will require a return of $12\mathrm{.}64\%$ at the new level of debt determined using CAPM.

a$.$ What is the market price of a share before any changes in the capital structure? $(2$ marks$)$

b$.$ Assuming that the firm uses the proceeds of the new debt to buy back shares, what should be the fair offer price to buy back the shares? $(7$ marks$)$

c$.$ How many shares firm can buy back $($assume that firm can buy fractional shares$)?(2$ marks$)$

d$.$ What is the market price of a share after the restructuring of the capital structure. Show your work to confirm that the new price is the approximately same as in the part c$.(4$ marks$)$