Assume $******$ that Lenny plc$\text{'}$s free cash$-$flows grow at $5\%$ per year forever. This growth is not affected by the firm's pay out policy. The first free cash flow per $***$ share in the next year $($year $1$ will be $$3.$ The discount rate is $15\%.$

Lenny plc $***$ is considering two potential pay out policies:

Policy A: Pay out all free cash flows as dividends. The first dividend will be paid in year $1.$

Required:

$($a$)$ What is the share $******$ price today?

$($b$)$ What will be the cum$-$dividend and ex$-$dividend prices in year $1$ and year $2?$

Policy B: Lenny plc uses year $1\text{'}$s free cash flow to repurchase shares. After the repurchase, the firm will pay out all $***$ future free cash flows as dividends starting from year $2.$

Required:

$($a$)$ What fraction of total shares can be repurchased in year $1?$

Hint: The fraction of shares is equivalent to the proportion of share price used to conduct the share repurchase.

$($b$)$ What is the dividend $******$ per share in year $2$ and year $3?$

Hint: The DPS for year $2$ would be proportionally higher than for year $1$ since the same cash sum $($FCF$)$ is now spread over less shares.

$($c$)$ What is the ex$-$dividend price and cum$-$dividend price in year $2?$