$(25$ points$)$ Apple earned $$15\mathrm{.}83$ per share this year and its proper Beta is $1\mathrm{.}27.$ Analyst

expects that the risk free rate, the market return, the earnings growth rate, and the payout ratio

of dividend would change in the following way;

Years $1-56-1011-1516-2021-$

Growth Rate of Earnings $12\mathrm{.}45\%10\mathrm{.}55\%8\mathrm{.}95\%8\mathrm{.}25\%4\mathrm{.}45\%$

Payout Ratio $50\%59\%63\%72\%75\%$

Risk Free Rate $1\mathrm{.}02\%1\mathrm{.}53\%2\mathrm{.}25\%2\mathrm{.}05\%1\mathrm{.}45\%$

Market Return $8\mathrm{.}23\%9\mathrm{.}55\%9\mathrm{.}95\%10\mathrm{.}58\%11\mathrm{.}95\%$

Using the information, answer following questions.

a$.$ By using CAPM, calculate five different expected cost of capital. What is the cost of

capital at time $12.$

b$.$ List growth rates and calculate expected earnings each year. What is the expected

earnings at time $15.$

c$.$ Write payout ratios on the given column and calculate future dividends. What is the

dividend at time $45.$

d$.$ List the cost of capital and calculate PV factor for each year. PV factor at time t is

given by:

What is the PV factor at time $10.$

e$.$ Using other two provided columns $($PV of dividend and Cumulative PV$),$ find the

expected value of Apple today.