Part ii #$3.$ Valuation of stocks

Question $16[5$ marks$]$

Today is Dec. $31,2070,$ and Houston Tea Party, Inc. $($HTP$)$ has just paid an annual dividend of $$10$ per share. The company$$s dividend in one year from today will increase by $4\%$ and is expected to grow at the same rate each year thereafter. That is$,$ the firm is expected to pay a dividend of $$10\mathrm{.}4$ at the end of $2071$ and its annual dividend will increase by $4\%$ each year. The market requires a $12\%$ return on the investments similar to HTP$$s equity shares. Find the price of the firm$$s stock.

$($Lecture notes pp$\mathrm{.}62-63)$

Answer $($show the steps$/$calculation toward your results$)$:

Question $17[5$ marks$]$

Consider the Houston Tea Party $($HTP$)$ stock described in Question $16$ with the following changes:

Suppose you were considering buying shares of HTP on Dec. $29,2070,$ when the firm was about to pay an annual dividend of $$10.$ All other assumptions remain unchanged. What would you have paid for when you bought shares of HTP on Dec. $29,2070?($Lecture notes p$\mathrm{.}63)$

Answer $($show the steps$/$calculation toward your results$)$:

$$

Question $18[5$ marks, plus bonus $5$ marks for the complete and correct answer$]$

Open AEye Ltd$.$ is a software developer specialized in AI$-$assisted medical imaging and diagnostic devices and is in its early growth phase. Today is Dec. $31,1990,$ and the firm$$s earnings are expected to grow at a rate of $10\%$ for the next $10$ years until the end of $2000.$ From $2001$ on$,$ Open AEye$$s growth will be at a rate of $5\%$ per year forever. Assume that all earnings are distributed through dividends at the end of each year, and the firm has just paid an annual dividend of $$4$ per share for $1990.$ What will be the price of Open AEye stock if investors require a $15\%$ return?

$($Lecture notes pp$\mathrm{.}64-65)$

Answer $($show the steps$/$calculation toward your results$)$: