Value of stock =$100
Value of stock B=$83.33
Value of stock C = $104.51
Solution:
Stock A
A dividend of $10 a share forever is a perpetuity.
PV of a perpetuity = [tex]\frac{CF}{Ke}[/tex]
where CF is the cash-flow expected per compounding period = $10
ke=return on investment or market capitalization rate=0.1
Value of stock A = $100
Stock B
Given D1=$5, g = 4% forever- this stream of cash-flows can be valued using the constant growth model where
PV= [tex]\frac{D1}{Ke-g}[/tex]
where D1 is the dividend expected at the end of year 1 = $5
ke is the return on investment or market capitalization rate = 0.1
g is the growth rate = 0.04
Value of stock B= $83.33
Stock C
The stock dividends have two distinct growth periods, the 1st 6 years where g= 20% and after that, zero growth
Price of the stock C = [tex]\frac{D}{(1+Ke)^{1}} + \frac{D}{(1+Ke)^{2}}+ \frac{D}{(1+Ke)^{3}}+ \frac{D}{(1+Ke)^{4}}+ \frac{D}{(1+Ke)^{5}}+ \frac{D}{(1+Ke)^{6}}[/tex]
where P6= [tex]\frac{D7}{Ke}[/tex] = [tex]\frac{D6}{Ke}[/tex]
Price of the stock C = [tex]\frac{5}{(1+0.1)^{1}} + \frac{5(1.2)}{(1+0.1)^{2}}+ \frac{5(1.2)^{2} }{(1+0.1)^{3}}+ \frac{5(1.2)^{3}}{(1+0.1)^{4}}+ \frac{5(1.2)^{4}}{(1+0.1)^{5}}+ \frac{5(1.2)^{6}}{0.1*(1+0.1)^{6}}[/tex]
= $104.51
Stock C is more valuable as it has a higher present value of cash flows.
