Question

You expect a share of stock to pay dividends of $1.00, $1.25, and $1.50 for each of the next 3 years. After that, the dividends will grow at the sustainable growth rate until infinity. a. Calculate the sustainable growth rate assuming the company generates a rate of return of 20% on its equity and maintain a plowback ratio of 0.3. b. Assuming investors expect a 12% rate of return on the stock, what is the price of the stock today?

Answer 1

a.

g = ROE x b

g = Constant growth rate

ROE = Return on equity = 20 %

b = Plow back ratio = 0.3

g = 0.20 x 0.3 = 0.06 or 6 %

Sustainable growth rate is 6 %

b.

D₁ = $ 1, D₂ = $ 1.25, D₃= $ 1.50

D₄ = D₃ x (1+ g) = $ 1.50 x (1+0.06) = $ 1.50 x 1.06 = $ 1.59

Price of stock in year 3, P₃ = D₄/ (k – g)

k = Required rate of return = 0.12

g = Dividend growth rate = 0.06

P₃ = $ 1.59/ (0.12 – 0.06) = $ 1.59/0.06 = $ 26.50

Current stock price, P₀ = D₁/(1+r) + D₂/(1+r)² + D₃/(1+r)³ + P₃/(1+r)³

                                 = $ 1/ (1+0.12) + $ 1.25/ (1+0.12)² + $ 1.5/ (1+0.12)³ + $ 26.5/ (1+0.12)³

                                 = $ 1/ (1.12) + $ 1.25/ (1.12)² + $ 1.5/ (1.12)³+ $ 26.5/ (1.12)³

                                 = $ 1/ 1.12 + $ 1.25/ 1.2544 + $ 1.5/ 1.404928 + $ 26.5/ 1.404928

          = $ 0.892857142857143 + $ 0.996492346938775+ $ 1.06767037172012+ $ 18.8621765670554

                                 = $ 21.8191964285714 or $ 21.82

Price of the stock today is $ 21.82