Assume today is December 31, 2013. Imagine Works Inc. just paid a dividend of $1
ID: 2787659 • Letter: A
Question
Assume today is December 31, 2013. Imagine Works Inc. just paid a dividend of $1.25 per share at the end of 2013. The dividend is expected to grow at 12% per year for 3 years, after which time it is expected to grow at a constant rate of 6% annually. The company's cost of equity (rs) is 9.5%. Using the dividend growth model (allowing for nonconstant growth), what should be the price of the company's stock today (December 31, 2013)? Round your answer to the nearest cent. Do not round intermediate calculations.
Explanation / Answer
Last dividend = $1.25
Growth rate for 3 years = 12%
Dividend at the end of year 1 = D1 = $1.25*1.12 = $1.40
D2 = $1.25*1.122 = $1.568
D3 = $1.25*1.123 = $1.7562
Growth rate after 3 years = 6%
D4 = $1.7562 * 1.06 = $1.8615
Stock at the end of year 3 = D4/(Cost of equity-Growth rate) = $1.8615/(0.095-0.06) = $53.1866
Present value of year 3 stock price = $53.1866/1.0953 = $40.51
Present value of dividend for fiirst 3 years = $1.40/1.095 + $1.568/1.0952 + $1.7562/1.0953 = $3.92
Stock price today = $40.51 + $3.92 = $44.43