Assume today is December 31, 2017. Imagine Works Inc. just paid a dividend of $1
ID: 2792756 • Letter: A
Question
Assume today is December 31, 2017. Imagine Works Inc. just paid a dividend of $1.30 per share at the end of 2017. 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, 2017)? Round your answer to the nearest cent. Do not round intermediate calculations.
Explanation / Answer
D0 = 1.3
D1 = 1.3*1.12 = 1.46
D2 = 1.46*1.12 = 1.63
D3 = 1.63*1.12 = 1.83
D4 = 1.83*1.06 = 1.94
According to dividend-discount model,
P0 = D1/(R-G)
P0 = Current stock price
D1 - Dividend at t =1
R - Required rate
G - Growth rate
P3 = D4/(R-g) = 1.94/(0.095-0.06) = 55.314
To find P0 discount the future dividends and P3
P0 = 1.46/(1+0.095)^1 + 1.63/(1+0.095)^2 + 1.83/(1+0.095)^3 + 55.314/(1+0.095)^3 = 46.21
Current share price = $46.21