Question

Sia Dance Studios has an annual cash dividend policy that raises the dividend each year by 5​%. Last​ year's dividend, Div0​, was $4 per share. The company will be in business for 60 years with no liquidating dividend. What is the price of this stock if

a.  an investor wants a return of 8​%?

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

c.  an investor wants a return of 12​%?

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

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

Answer 1

Price of stock is present value of cash flows that is dividend

Growth is 5%

First payment was 4

No of years is 60

Present value of growing annuity is

P.v = pmt/(r-g)(1-((1+g)/(1+r))^n)

Where pmt is first payment

r is required return

G is growth and n is no of years

When required return is 8%

= 4/(0.08-0.05)(1-(1.05/1.08)^60)

= 108.73

When required rate is 10%

Substituting 10% in place of 8% in above equation

= 75.09

At 12% is 55.95

At 15% is 39.82

At 18% is 30.74