Ten years ago. Video Toys began manufacturing and selling coin-operated arcade g

Question

Ten years ago. Video Toys began manufacturing and selling coin-operated arcade games. Dividends are currently $ 1.50 per share, having grown at a 15 percent compound annual rate over the past 5 years. The growth rate is expected to be maintained, for the next three years after which dividends are expected to grow at half that rate for 3 years. Beyond that time, Video Toys dividends are expected to grow at 5 percent per year. What is the current value of a share of Video Toys common stock if your required rate of return is 18 percent.

Explanation / Answer

According to the given information: D0 = $1.50 D1 = $1.50 (1 + 0.15)       = $1.725 D2 = $1.725 (1 + 0.15)       = 1.984 D3 = $1.984 (1 + 0.15)      = $2.28 For the next three years, the dividends are expected to grow at half of the rate (7.5%) D4 = $2.28 (1 + 0.075)       = $2.45 D5 = $2.45 (1 + 0.075)       = $2.63 D6 = $2.63 (1 + 0.075)      = $2.83 After that dividends are expected to grow at 5% per year. After that dividends are expected to grow at 5% per year. D7 = $2.83 (1 + 0.05)       = $2.97 Required return = 18% The Dividends are expected to grow at a constant rate of 5% after year-6 so we can use the constant growth model to calculate the current price of the stock.Note that we are discounting the dividends at the required rate of return. P6 = D7 / (Ke - g)     = $2.97 / (0.18 - 0.05)     = $22.92 P0 = D1 / (1+Ke)^1 + D2 / (1+Ke)^2 + D3 / (1+Ke)^3 + D4 / (1+Ke)^4 + D5 / (1+Ke)^5 + D6 / (1+Ke)^6 + P6 / (1+Ke)^6      = $1.725 / 1.18 + $1.984 / 1.3924 + $2.28 / 1.643 + $2.45 / 1.94 + $2.63 / 2.29 + $2.83 / 2.7 + $22.92 / 2.7     = $1.462 + $1.425 + $1.3877 + $1.263 + $1.148 + $1.048 + $8.49     = $15.87 Therefore, the Current price of the stock is $15.87

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