$(30$ points$)$ AGE Corp retained $5,000,000$ of its earnings in $2022,$ which was $20,000,000.$

The company maintains a stable payout ratio. The outstanding number of shares of the

company is $5,000,000$ and currently trading at $31\mathrm{.}5.$ The present value of growth

opportunities is estimated to be $3\mathrm{.}5$ per share. If the investors require a $15\%$ return for

buying$/$holding the AGE Corp stock,

a$.$ What is the expected growth rate for the company?

b$.$ What is the return AGE Corp. earns on its invested capital?

c$.$ How would the market react to a decline in ROIC to $10\%?$ What is the new growth rate

and PVGO for the company?

d$.$ If the managers want to maintain the original growth rate, what is the required change in

the payout policy?

e$.$ How would the stockholders react to the new payout policy of the company? Why?