Question $2(20$ points$)$

ABC is an established company operating in a rapidly growing market. Its earnings per share this

year $($at time $1)$ are expected to be $$2\mathrm{.}70.$ These earnings are currently growing at $12\%$ per year.

After this year, this growth rate of earnings is expected to continue for four more years $($years $2,$

$3,4,$ and $5).$ To support the earnings growth, the firm will retain much of its earnings. At time $1$

and time $2,$ the firm expects to payout $20\%$ of its earnings as dividends. Then, beginning at time

$3,$ the payout ratio will increase to $35\%$ of earnings and remain at this level through time $5.$

Beginning at time $6,$ it is expected that the payout ratio of the company will be $70\%.$ This payout

ratio is expected to remain constant forever. The time $6$ earnings are expected to be $5\mathrm{.}3\%$ higher

than the earnings at time $5.$ ABC expects this $5\mathrm{.}3\%$ growth rate of earnings to continue forever.

Given its risk, the required rate of return for this company is $13\mathrm{.}2\%$ p$.$a$.$

a$.$ What is the current value of a share of ABC stock? Express final answer to the nearest penny.

b$.$ What fraction of the current value of ABC can be attributed to the present value of growth

opportunities? Express final answer to $4$ digits after the decimal.