Two corporations A and B have exactly the same risk, and both have a current stock price of $100. Corporation A pays no dividend and will have a price of $120 one year from now. Corporation B pays dividends and will have a price of $113 one year from now after paying the dividend. The corporations pay no taxes and investors pay no taxes on capital gains, but pay a 30 percent income tax on dividends. What is the value of the dividend that investors expect corporation B to pay one year from today?
A)$7
B)$13
C)$10
D)$20

Question

Quizplus · Accepted Answer

Since both corporations have exactly the same risk, the investors would expect the same rate of return from both corporations. Let's assume that the rate of return is r. 
For Corporation A: 
Current Stock Price = $100 
Future Stock Price = $120 
Rate of return (r) = (120-100)/100 = 0.2 or 20%

For Corporation B: 
Current Stock Price = $100 
Future Stock Price after paying dividend = $113 
Let the dividend per share be x 
After paying the dividend, the price of the stock would be: 
(100-x) + (x*(1-0.3)) = 113 
Solving for x, we get x = $10 
So investors expect Corporation B to pay a dividend of $10 per share one year from today.

Two Corporations a and B Have Exactly the Same Risk