Question

Question 1

Wonderland Corp. will pay a dividend of $3.5 next year. The company plans tomaintain a constant growth rate of 5 percent a year forever. Investors’ required rate ofreturn is 12 percent.

Robinson Corp. will pay the following dividends over the next four years: $20, $18, $15 and $3. Afterwards the company pledges to maintain a constant 5 percent growthrate in dividends, forever. Investors’ required rate of return is 12 percent.

Required:

1. (a) How much will you pay for these two stocks?

2. (b) If both companies change its policy to maintain a constant growth rate of 4 percent, what is the percentage change of these two stocks?

3. (c) What does this tell you about the relationship and stock price sensitivity between the dividend growth and the stock price of these two stocks? [within 100 words]

Answer 1

a]

value of Wonderland stock = next year dividend / (required return - growth rate)

value of Wonderland stock = $3.5 / (12% - 5%)

value of Wonderland stock = $50

value of Robinson stock = present value of next 4 years dividend + present value of terminal value at end of 4 years

Terminal value at end of 4 years = Year 4 dividend * (1 + growth rate after 4 years) / (required return - growth rate after 4 years)

Present value = future value / (1 + required return)number of years

The value of stock today = $73.39

b]

value of Wonderland stock = next year dividend / (required return - growth rate)

value of Wonderland stock = $3.5 / (12% - 4%)

value of Wonderland stock = $43.75

% change = ($43.75 - $50) / $50

% change = -12.50%

value of Robinson stock = present value of next 4 years dividend + present value of terminal value at end of 4 years

Terminal value at end of 4 years = Year 4 dividend * (1 + growth rate after 4 years) / (required return - growth rate after 4 years)

Present value = future value / (1 + required return)number of years

The value of stock today = $69.58

% change = ($69.58 - $73.39) / $73.39

% change = -5.20%

c]

This tells us that higher the dividend growth, higher the stock value. The stock price of Wonderland stock is more sensitive to changes in the growth rate.