You see a fast growing company that is estimated to have dividend growth of 24%,

Question

You see a fast growing company that is estimated to have dividend growth of 24%, 18%, and 14% over each of the next three years (24% in year 1, 18% in year 2, 14% in year 3) The company paid a dividend of $2.78 per share over the past twelve months. Dividends are expected to grow at a constant rate of 3.0% per year beginning in year 4 to perpetuity The risk-free rate of return is 3% and the market risk premium (expected return on the S&P; 500 minus the risk-free rate of return) is 5.5%. The stock has a beta of 1.15 versus the S&P; 500. Calculate the intrinsic value of this stock using the two-stage dividend discount model. (6 points) SHOW ALL WORK

Explanation / Answer

Forecast dividends for the next four years given the growth rate and current dividend

D1 = D0 x (1 + g) = 2.78 x 1.24 = 3.45, D2 = 3.45 x 1.18 = 4.07, D3 = 4.07 x 1.14 = 4.64, D4 = 4.64 x 1.03 = 4.78

Using CAPM, Cost of equity, r = Rf + beta x MRP = 3% + 1.15 x 5.5% = 9.325%

Using DCF model, Stock Price in year 3, P3 = D4 / (r - g) = 4.78 / (9.325% - 3%) = $75.51

Intrinsic Value today, P0 = D1 / (1 + r) + D2 / (1 + r)^2 + (D3 + P3) / (1 + r)^3

=3.45 / 1.09325 + 4.07 / 1.09325^2 + (4.64 + 75.51) / 1.09325^3

= $67.90

Year Dividend 0 2.78 1 3.45 2 4.07 3 4.64 4 4.78

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