a$.$ ABC Company just paid its annual dividend of $$1\mathrm{.}22$ per share on its stock. The dividend payment is expected to grow at a constant rate of $5\%$ forever. If the current value of company ABC$$s shares is $$32$ per share, what is the required rate of return? $($Note: the value of dividend in this question is the dividend just paid, NOT the expected dividend for next year.$)$

b$.$

i$.$ Assume that AI stocks currently provide an expected rate of return of $18\%.$ AI Solutions, a large AI company will pay a year$-$end dividend of $$3$ per share at the end of this year. If the stock is selling at $$60$ per share, what does this stock price imply the market$$s expectation of AI Solutions$$ dividend growth rate, assuming the dividend growth rate will remain constant forever?

ii$.$ If the market revises its forecasts for AI Solutions$$ dividend growth rate to $8\%$ per year, what will be the price of AI Solutions stock?

iii. How will AI Solutions$$ price$-$earning ratio be affected with this revision on dividend growth rate?

c$.$ You are asked to use the adjusted DDM model to determine the value of company DEF. Currently, company DEF$$s earnings per share is $$0\mathrm{.}952,$ and its dividend per share is $$0\mathrm{.}286,$ which is paid based on a constant rate of $30\%$ of earnings per share. You anticipate that company DEF$$s earnings will grow at $32\%$ for two years and $13\%$ thereafter. Assume that the industry P$/$E ratio is $26.$ If investors$$ required rate of return is $14\%,$ calculate the present value of a share of company DEF.

d$.$ Assume that you are very confident that the stock market will perform well in the near future. Recently, one of your friends recommended a stock of a specific firm to you because the firm had performed very well in the past few years, the firm has a low beta $($i$.$e$.,$ a low degree of systematic risk$),$ and its beta is expected to remain low. You usually rely on beta as a measurement of a firm$$s systematic risk. If you are thinking about selecting a specific stock that will perform well in response to an expected runup in the stock market, should you seriously consider buying that stock? Why?