Question

Assume we have 2 stocks: stock A with $4 earnings per share (at the end of the year) distributes all earnings as dividend and make no reinvestment. stock B with $4 eanrings per share (at the end of the year) distributes 50% as dividend and return of reinvestment is 30%. Assume expected return for stock A and stock B are both 20%. Please calculate price of stock A and price of stock B, and what is the price difference?

Multiple Choice

a.)Price of stock A $10, Price of stock B $40, difference is $30.

b.)Price of stock A $20, Price of stock B $80, difference is $60.

c.)Price of stock A $10, Price of stock B $80, difference is $70.

d.)Price of stock A $20, Price of stock B $40, difference is $20.

Answer 1

Given about stock A,

earning E1 = $4

Reinvestment rate RR = 0%

So, growth rate of the firm = ROE*RR = 0

Required return rs = 20%

So, Price of the stock is calculated using Perpetuity formula

Price = E*(1 - RR)/rs = 4/0.20 = $20

Price of stock A = $20

Given about stock B,

earning E1 = $4

Reinvestment rate RR = 50%

ROE = 30%

So, growth rate of the firm = ROE*RR = 0.3*0.5 = 15%

Required return rs = 20%

So, Price of the stock is calculated using Constant growth formula

Price = E*(1 - RR)/(rs-g) = 4*(1-0.5)/(0.20-0.15) = $40

So price of stock B is $40

So, difference in price = 40-20 = $20

Option D is correct.