Question

A company is a fast growing technology company. The firm projects a rapid growth of 40 percent for the next two years and then a growth rate of 20 percent for the following two years. After that, the firm expects a constant-growth rate of 12 percent. The firm expects to pay its first dividend of $1.25 a year from now. If your required rate of return on such stocks is 20 percent, what is the current price of the stock? $21.70 is the answer. I am looking for how to solve this without excel.

Answer 1

As per Constant Growth Model,

Current Stock Price = PV(Dividends) + PV(Horizon Value)

D₁ = $1.25

D₂ = 1.40(1.25) = $1.75

D₃ = 1.20(1.75) = $2.10

D₄ = 1.20(2.10) = $2.52

Horizon Value at Year 4 = D_i(1 + g)/(r - g)

Horizon Value at Year 4 = 2.52(1.12)/(0.20 - 0.12)

Horizon Value at Year 4 = $35.28

Current Stock Price = 1.25/(1.20) + 1.75/(1.20)² + 2.10/(1.20)³ + (2.52+35.28)/(1.20)⁴

Current Stock Price = 1.04 + 1.22 + 1.22 + 18.21

Current Stock Price = $21.70

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