HighTech Company is expected to retain all of its earnings for the next two years but start to pay dividends 3 years from today. The first dividend is expected to be $3. Assume that the dividends will grow rapidly at a rate of 10% per year during years 4 to 7. For each year after that it grows at a constant rate of 5%. Assume a discount rate of 12%.
What is the constant growth starting from year 8?
What is the stock price today given this constant growth rate?
Retention ratio = 100%; b = 1
D3 = 3
Short-term high growth rate, gS = 10% and gL = 5% (long-term)
a) Price
Using H-DDM formula,
V3 = [ D3 * (1+gL) / (r-gL) ] + [ D3 * H * (gS-gL) / (r-gL)]
where the values given are as:
Substituting values, P3 = [ 3 * ( 1+0.05)/(0.12 - 0.05) ] + [ 3 * 2 * (0.10 - 0.05)/(0.12 - 0.05)]
Price = $35.08
b) Given:
Retention ratio,b = $4/$8 = 0.50; ROE = 15%; g = b * ROE = 0.50 * 0.15 = 0.075 (constant growth rate from year 8)
Price:
D3 = 3
Short-term high growth rate, gS = 10% and gL = 7.5% (long-term)
a) Price
Using H-DDM formula,
V3 = [ D3 * (1+gL) / (r-gL) ] + [ D3 * H * (gS-gL) / (r-gL)]
where the values given are as:
Substituting values, P3 = [ 3 *( 1+0.075)/(0.12 - 0.075) ] + [ 3 * 2 * (0.10 - 0.075)/(0.12 - 0.075)]
growth rate = 7.5%
Price = $53.38
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