Question #158636

Expert's answer

Determine the projected dividend for the coming year:

In order to calculate the projected dividend in the year for the stock having differential growth, the dividend in the year 3 should be divided with the number of time of the future value of interest factor. It should be noted that the stock price, dividend growth rates and the required return are given. Hence, calculate the dividend in the year 3 as below:

"D_3 = Dividend \\; in \\; the \\; year \\;0 (1+g)^{number \\; of \\; years} \\\\\n\n= D_0(1.30)^3"

It is given that the growth rate for the year 4 is 18%. Hence, the dividends for the year 4 are calculated as under:

"D_4 = D_0(1.30)^3(1.18)"

From the given information, it is evident that the stock will be constant after the 4th dividend. Hence, calculate the price of the stock in the year 4. It is calculated by dividing the dividend in year 5 with the difference between the required rate of return and growth calculated as below:

"P_4 = \\frac{D_0(1+g_1)^3(1+g_2)(1+g_3)}{R-g_3} \\\\\n\n=\\frac{D_0(1.30)^3(1.18)(1.08)}{0.11-0.08} \\\\\n\n= 93.33D_0"

Hence, the price of stock in year 4 will be 93.33D_{0}.

From the above calculation, it is clear that the stock price in year 4 is 93.33 times of the dividend paid today. Hence, the price of today should be determined. The price of the stock today is the present value of the dividends in the next four years and the value of stock in the year 4 calculated as below:

"P_0 = \\frac{D_0(1.30)}{1.11}+ \\frac{D_0(1.30)^2}{1.11^2}+ \\frac{D_0(1.30)^3}{1.11^3}+\\frac{(1.30)^3(1.18)}{1.11^4}+\\frac{93.33D_0}{1.11^4}"

Now determine the value of today stock by combining the last two terms. Use the following calculation to determine the present value of stock:

"P_0=D_0(\\frac{1.30}{1.11} + \\frac{1.30^2}{1.11^2} + \\frac{1.30^3}{1.11^3} + \\frac{(1.30^3(1.18)+93.33)}{1.11^4}) \\\\\n\n= 65.00"

Hence, the price of stock today is 65.00.

Substitute the current stock price in the above equation to determine the current dividend as below:

"65=74.43D_0 \\\\\n\nD_0 = \\frac{65.00}{74.43} \\\\\n\n= 0.87"

Hence, the current dividend is 0.87.

Finally, determine the dividend for the next year by applying the growth rate on the current dividend as below:

"D_1 = Current \\; dividend \\times (1+Growth) \\\\\n\n= 0.87 \\times 1.30 \\\\\n\n= 1.14"

Hence, the dividend in the next year is 1.14.

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