Question

Which of the following stocks is most likely to be priced highest? Assume that all stocks pay $3 dividend per share per year and are the same in all other aspects.

a)A stock whose annual dividend is expected to grow by 12% for the first two years and then 4% thereafter, with the discount rate of 12%.

b)A stock whose annual dividend is expected to not grow, with the discount rate of 12%.

c)A stock whose annual dividend is expected to grow by 4% per year forever, with the discount rate of 12%.

Answer 1

Given that,

Current dividend D0 = $3

a). annual dividend is expected to grow by 12% for the first two years and then 4% thereafter

=> D1 = 3*1.12 = $3.36

D2 = 3.36*1.12 = $3.76

g = 4%

Discount rate r = 12%

So, stock price at year 2 using constant dividend growth model is

P2 = D2*(1+g)/(r - g) = 3.76*1.04/(0.12-0.04) = $48.92

So, current share price is sum of PV of future dividends and P2 discounted at r

=> P0 = D1/(1+r) + D2/(1+r)^2 + P2/(1+r)^2 = 3.36/1.12 + 3.76/1.12^2 + 48.92/1.12^2 = $45

So, current stock price in option a is $45

b). when annual dividend is expected to not grow, with the discount rate r = 12%

Stock price today using perpetuity is

P0 = annual dividends/discount rate = 3/0.12 = $25

So, current stock price in option b is $25

c). When annual dividend is expected to grow by 4% per year forever

g = 4%

Discount rate r = 12%

So, current stock price using constant dividend growth model is

P0 = D0*(1+g)/(r - g) = 3*1.04/(0.12-0.04) = $39

So, current stock price in option c is $25

So, option a is priced highest.