Problem: $12\mathrm{.}8$

Solution $12\mathrm{.}8$

St$.$ John Medical, a surgical equipment manufacturer, has been hit hard by increased

competition. Analysts predict that earnings and dividends will decline at a rate of $5$

percent annually into the foreseeable future. If the firm's last dividend $($D$)$ was $$2\mathrm{.}00$

and the investors' required rate of return is $15$ percent, what will be the company's stock

price in three years?

Last Dividend $$2\mathrm{.}00$

Expected Growth Rate $-5\%$

Required Rate of Return $15\%$

As indicated in Problem $12\mathrm{.}4.$a$,$ the constant growth model applies to negative growth as well as positive growth. In fact, the starting numbers are the same:

Step$1$: E$($P$0)=$ D$0*[1+$E$($g$)]=2\mathrm{.}00*1+5\%$ $$1\mathrm{.}90$ $$9\mathrm{.}50$

R$($Re$)-$ E$($g$)15\%--5\%20\%$

Step $2$: $$8\mathrm{.}15$