Question

Nonconstant Growth Stocks

Assume today is December 31, 2017. Imagine Works Inc. just paid a dividend of $1.20 per share at the end of 2017. The dividend is expected to grow at 15% per year for 3 years, after which time it is expected to grow at a constant rate of 5% annually. The company's cost of equity (r_s) 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.
$_____ per share

Answer 1

Price of stock = PV of dividends

Price of stock = Dividend / ( rate - growth )

The above formula is used in the assumption that there is only one rate and it increases in perpetuity. Since this case has variable rates, the formula has to be altered to include all the growth rates.

Step 1

Calculate the dividend for each period, formula to be used the Time Value Money formula where

Future value = Present value * ( 1+ growth rate )

example - the dividend currently (year 0) is 1.2 and is increased by 15% so dividend for year 1is 1.2 * ( 1+ 0.15) = 1.38 . SImiliarily the dividend for year 2 and year 3 is calculated.

Year 4 grows, the dividend will be 2.0988075, but since we need to know the value of dividend for years beyond ( perpetuity), growing at a rate of 5%, we will use the Time value Money formula, where

PV = FV / ( r - g) , where FV = 2.0988075 , r = .095 ( 9.5%) , g = 0.05 (5%)

Thus, the dividend amount for all dividend from year 4 to perpetuity is 46.6401667

Step 2

Once the dividends have been found for the respective years, they need to be discounted to the present year to calculate the price for the stock, using the Present Value Formula where,

Present Value = Future Value / ( 1 + r) ^ n , r= equity return (9.5%) and n = year

Future value is the dividend for the period

Thus, all the dividends will be discounted to the present year

Step 3

The last dividend will be discounted to 3 years and not 4 years, because the Future Value of year is the value at the beginning of the year and thus will only be discounted to 3 years just as the dividend at year 3

Step 4

The price (value) of stock will be the addition of all the dividend PV's, thus the stock price today will be 39.498 $ ( ANSWER)