$($ Investment Management $)($ Finance$)$

The stock of Project Fairy is currently selling for $24$ per share. Earnings per share in the coming

year are expected to be $2\mathrm{.}50.$ The company has a policy of paying out $60\%$ of its earnings each

year in dividends. The rest is retained and invested in projects that earn a $20\%$ internal rate of

return per year. This situation is expected to continue indefinitely.

a$.$ Assuming the current market price of the stock reflects its intrinsic value as computed

using the constant$-$growth DDM $($dividend discount model$),$ what rate of return do

Project Fairy's investors require?

b$.$ By how much does Project Fairy's stock price change if all its earnings are paid as

dividends and nothing is reinvested?

c$.$ If the company were to increase its dividend payout ratio from $60\%$ to $70\%,$ what would

happen to its stock price?