Big Ideas Inc. paid a dividend of $5.00 per share on its common stock yesterday.

Question

Big Ideas Inc. paid a dividend of $5.00 per share on its common stock yesterday. Dividends are expected to grow at a constant rate of 10% for the next 2 years at which point the dividends will begin to grow at a constant rate indefinitely. If the stock is selling for $50 today and the required return is 15%, what is the expected annual dividend growth rate after year two?

Please be specific and give me step by step how to (on a financial calculator if possible) or on an Excel sheet. I get lost on the constant rate indefinitely.
I am a not good with this and so please explain like I was two.

Explanation / Answer

According to the given information, D0 (Dividend in year-0) = $5.00 D1 = D0 (1+g) {where g is the growth rate; D1 is the Dividend in year-1}      = $5.00 (1 + 0.10)      = $5.5 D2 = D1 (1+g) {D2 is the dividend in year-2}       = $5.5 (1 + 0.1)       = $6.05 P0 = $50 (P0 is the current price of the stock) Required return (R) = 15% CAlculating the stock price in the year-2: P2 = D2 (1+g) / (R - g) But we don't know the growth rate after year-2. Computing the value of growth rate using the formula for current price : P0 = [D1 / (1+R)^1] + [D2 / (1+R)^2] + [P2 / (1+R)^2] $50 = [$5.5 / (1+0.15)] + [$6.05 / (1+0.15)^2] + [$6.05(1+g) / (0.15 -g)] / (1+0.15)^2 $50 = $4.783 + $4.575 + [$6.05(1+g) / (0.15 -g)] / 1.3225 $50 = $9.358 + [$6.05(1+g) / (0.15 -g)] / 1.3225 ($50 - $9.358) = [$6.05(1+g) / (0.15 -g)] / 1.3225 40.642 = [$6.05(1+g) / (0.15 - g) ] / 1.3225 If the 1.3225 comes to left hand side, then it is multiplied with $40.642 $53.75 = $6.05 (1+g) / (0.15-g) If (0.15- g) is multiplied with $53.75 $53.75 (0.15 - g) = $6.05 (1+g) $8.0625 - $53.75g = $6.05 + $6.05g The $53.75g will go to the right side and taking "g" common we get $2.0125 = ($53.75 + $6.05 )g g = $2.0125 / $59.8    = 3.365% Therefore, the constant growth rate after 2 years indefinitely is 3.365%         According to the given information, D0 (Dividend in year-0) = $5.00 D1 = D0 (1+g) {where g is the growth rate; D1 is the Dividend in year-1}      = $5.00 (1 + 0.10)      = $5.5 D2 = D1 (1+g) {D2 is the dividend in year-2}       = $5.5 (1 + 0.1)       = $6.05 P0 = $50 (P0 is the current price of the stock) Required return (R) = 15% CAlculating the stock price in the year-2: P2 = D2 (1+g) / (R - g) But we don't know the growth rate after year-2. Computing the value of growth rate using the formula for current price : P0 = [D1 / (1+R)^1] + [D2 / (1+R)^2] + [P2 / (1+R)^2] $50 = [$5.5 / (1+0.15)] + [$6.05 / (1+0.15)^2] + [$6.05(1+g) / (0.15 -g)] / (1+0.15)^2 $50 = $4.783 + $4.575 + [$6.05(1+g) / (0.15 -g)] / 1.3225 $50 = $9.358 + [$6.05(1+g) / (0.15 -g)] / 1.3225 ($50 - $9.358) = [$6.05(1+g) / (0.15 -g)] / 1.3225 40.642 = [$6.05(1+g) / (0.15 - g) ] / 1.3225 If the 1.3225 comes to left hand side, then it is multiplied with $40.642 $53.75 = $6.05 (1+g) / (0.15-g) If (0.15- g) is multiplied with $53.75 $53.75 (0.15 - g) = $6.05 (1+g) $8.0625 - $53.75g = $6.05 + $6.05g The $53.75g will go to the right side and taking "g" common we get $2.0125 = ($53.75 + $6.05 )g g = $2.0125 / $59.8    = 3.365% Therefore, the constant growth rate after 2 years indefinitely is 3.365%        

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