Question

A stock expects to pay a dividend of $3.72 per share next year. The dividend is expected to grow at 25 percent per year for three years followed by a constant dividend growth rate of 4 percent per year in perpetuity. What is the expected stock price per share 5 years from today, if the required return is 12 percent?

Answer 1

The price of a stock is the sum of present value of all its expected future dividends. The stock price in the given case can be calculated as the sum of present values of dividends in the first four years, plus the present value of the perpetual dividends that grow at a constant growth rate of 4%. The calculations are as shown below: C D E F G H I J K 1 Growth rate for first three years 2 Terminal growth rate 3 Required return B 25% 4% 12% 5 Year 6 Dividend 7 Present value Sum of present value of 8 dividends till year 4 1 $3.72 $3.32 2 $4.65 $3.71 3 $5.81 $4.14 4 $7.27 $4.62 $15.78 $94.45 Calculated using the formula to calculate the present value of a growing perpetuity Terminal value at the end of 11 year 4 Present value of the terminal 12 value $60.03 13 14 Total value of the stock $75.81 The formula implementation in excel is as shown below: А 1 Growth rate for first three years 2 Terminal growth rate 3 Required return 25% 4% 12% 5 Year 6 Dividend 7 Present value Sum of present value of 8 dividends till year 4 $3.72 =B6*(1+$B$1) =C6*(1+$B$1) =B6/(1+$B$3)BS =C6/(1+$B$3)“CS =D6/(1+$B$3) "D5 =SUM(B7:17) =D6*(1+$B$1) =E6/(1+$B$3)^E5 =E6*(1+B2)/($B$3-B2) Calculated using the formula to calculate the present value of a growing perpetuity Terminal value at the end of 11 year 4 Present value of the terminal 12 value =B11/(1+B3)“ES 14 Total value of the stock =B12+B8 Therefore, the price of the given stock is $75.81

Answer 2

What is the expected stock price per share 5 years from today, if the required return is 12 percent?
P5=D6/(r-g)=3.72*1.25^3*1.04*1.04/(12%-4%)=98.23125

Answer 3

Dividend in 5 years = dividend next year*(1+high growth period rate)^3*(1+low growth period rate)

=3.72*(1+0.25)^3*(1+0.04) = 7.56

Price = recent dividend* (1 + growth rate )/(cost of equity - growth rate)

Price = 7.56 * (1+0.04) / (0.12 - 0.04)

Price = 98.28