Question

Sia Dance Studios has an annual cash dividend policy that raises the dividend each year by 3​%. Last​ year's dividend, Div 0Div0​, was $8 per share. The company will be in business for 40 years with no liquidating dividend. What is the price of this stock if

 a. an investor wants a return of 9​%?

b. an investor wants a return of 10​%?

c.  an investor wants a return of 13​%?

d.  an investor wants a return of 15​%?

e.  an investor wants a return of 18​%?

round to the nearest cent

Answer 1

Growth rate = 3%

Last dividend = 8

Next year dividend = 8*(1+3%)= 8.24

No of years (n)=` 40

Present value of growing annuity formula will be applicable to calculate value of growing dividends

a. required return (i)= 9%

(Next Dividend*(1-((1+g)^n/(1+i)^n))/(i-g)

(8.24*(1-((1+3%)^40/(1+9%)^40)))/(9%-3%)

123.0705255

Stock price is $123.07

b. required return (i)= 10%

(Next Dividend*(1-((1+g)^n/(1+i)^n))/(i-g)

(8.24*(1-((1+3%)^40/(1+10%)^40)))/(10%-3%)

109.2300885

Stock price is $109.23

c. required return (i)= 13%

(Next Dividend*(1-((1+g)^n/(1+i)^n))/(i-g)

(8.24*(1-((1+3%)^40/(1+13%)^40)))/(13%-3%)

80.37568329

Stock price is $80.38

d. required return (i)= 15%

(Next Dividend*(1-((1+g)^n/(1+i)^n))/(i-g)

(8.24*(1-((1+3%)^40/(1+15%)^40)))/(15%-3%)

67.83044515

Stock price is $67.83

e. required return (i)= 18%

(Next Dividend*(1-((1+g)^n/(1+i)^n))/(i-g)

(8.24*(1-((1+3%)^40/(1+18%)^40)))/(18%-3%)

54.69452766

Stock price is $54.69