Question

5 pts A new tech stock is expected to pay a dividend of $1.00 per share next year (D1). Dividends will grow rapidly at 20% per year through Year 9 (D9 will be $4.30 per share). After that, dividends will grow at modest pace of $0.10 per year, forever (D10 is $4.40, etc.). If investors require a return of 15.20 percent, what shou ld the price of this stock be today? Answer in "XX.XX" format, with no additional punctuation. For example, if your answer is $45.45, enter "45.45".

Answer 1

Answer:-

Given

Dividend (D1) = $ 1
Growth of dividends = 20% per year till year 9
D2 = $ 1 x (1+0.2) =$ 1.2
D3 = $ 1.2 x 1.2 = $ 1.44
D4 = $ 1.44 x 1.2 = $ 1.73
D5 = $ 1.73 x 1.2 = $ 2.08
D6 = $ 2.08 x 1.2 = $ 2.49
D7 = $ 2.49 x 1.2 = $ 2.99
D8 = $ 2.99 x 1.2 = $ 3.59
D9 = $ 3.59 x 1.2 = $ 4.30
D10 = $ 4.30 + $ 0.10 = $ 4.40

Growth in perpetuity can be considered at 2% ( Long term growth rate) since the dividend is seen growing at $ 0.10 per year

Computing the PV of dividend cash flows at the discount rate of 15.20% = 0.152 and long term growth rate = 2% = 0.02

V0 = $ 1 + 1.2 / (1.152) + 1.44 / 1.152²  + .............. + $ 4.30 / (1.152)⁸ + $ 4.40 x (1+0.02) / (1.152)⁹ x ( 0.152 - 0.02)
Vo = $ 10.67 + $ 4.40 x (1+0.02) / (1.152)⁹ x ( 0.152 - 0.02)
Vo = $ 10.67 + $ 4.49 / 0.472
Vo = $ 10.67 + $ 9.51
Vo = $ 20.18

Therefore the price of the stock today = $ 20.18