Question

As discussed in Chapter 11, the value of a share of stock is determined by calculating the present value of all future dividends. These calculations assume a discount rate that is the required rate of return for the investor. The dividends paid may be either constant, increasing at a constant growth rate, or increasing at a rate that changes over time. Please answer each of the following questions and show all of your work.

a. Assume ABC stock pays a constant dividend of $2 per share per year and the investor has an 8 percent required rate of return. What is the value of a share of ABC stock?

b. Now assume DEF stock has a $2 dividend with a 6 percent growth rate. What is the value of DEF stock?

c. What is the value of DEF stock if the Board of Directors increases the dividend to $3 per share? Assume all other variables remain constant.

d. What is the value of DEF stock if the investor’s required rate of return drops to 7 percent (assume dividend is still at $2)?

Answer 1

Option A

Constant Dividend = $2

Required rate of return = 8%

Present value of perpetual dividend = Dividend / Required rate of return

Present value of perpetual dividend = 2/8%

Present value of perpetual dividend = 25

Option B

Dividend = $2

Dividend growth = 6%

Required rate of return = 8%

As per DDM

Share price = Dividend *(1+growth rate)/(Required rate of return - Growth)

Share price = (2*(1+6%)) / (8%-6%)

Share price 106

Option C

Dividend = $3

Dividend growth = 6%

Required rate of return = 8%

As per DDM

Share price = Dividend *(1+growth rate)/(Required rate of return - Growth)

Share price = 3 / (8%-6%)

Share price 150

Option D

Dividend = $2

Dividend growth = 6%

Required rate of return = 7%

As per DDM

Share price = Dividend *(1+growth rate)/(Required rate of return - Growth)

Share price = (2*(1+6%)) / (7%-6%)

Share price = 212