2 3 2 1 1 1 2 Etc etc etc FIN 300 Stocks Pt 1 32 1 2 1 1 Constant Price

2 3 2 1 1 1 2 etc etc etc fin 300 stocks pt 1 32 1 2

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𝑃𝑃 2 = 𝐷𝐷𝐷𝐷𝐷𝐷 3 𝑅𝑅 − 𝐸𝐸 = 𝐷𝐷𝐷𝐷𝐷𝐷 2 1 + 𝐸𝐸 𝑅𝑅 − 𝐸𝐸 = 𝐷𝐷𝐷𝐷𝐷𝐷 1 1 + 𝐸𝐸 2 𝑅𝑅 − 𝐸𝐸 Etc., etc., etc. FIN 300 - Stocks Pt. 1 32 𝑃𝑃 1 = 𝐷𝐷𝐷𝐷𝐷𝐷 2 𝑅𝑅 − 𝐸𝐸 = 𝐷𝐷𝐷𝐷𝐷𝐷 1 1 + 𝐸𝐸 𝑅𝑅 − 𝐸𝐸
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Constant Price & Dividend Growth Go back to this: Note that: Therefore: FIN 300 - Stocks Pt. 1 33 𝑃𝑃 1 = 𝐷𝐷𝐷𝐷𝐷𝐷 2 𝑅𝑅 − 𝐸𝐸 = 𝐷𝐷𝐷𝐷𝐷𝐷 1 1 + 𝐸𝐸 𝑅𝑅 − 𝐸𝐸 𝑃𝑃 0 = 𝐷𝐷𝐷𝐷𝐷𝐷 1 𝑅𝑅 − 𝐸𝐸 𝑃𝑃 1 = 𝑃𝑃 0 1 + 𝐸𝐸 Important! – This means that the price grows at the same constant rate g
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Constant Growth When the dividend grows at a constant, perpetual rate “g” The price of the stock also grows from year to year at the same growth rate As seen before, the year-over-year growth rate of the stock is the capital gains yield (or, return) So, (in the constant growth model) the “g” also just happens to be the capital gains yield (or, return) The dividend grows at rate g forever; therefore, the price grows at the same constant, perpetual rate FIN 300 - Stocks Pt. 1 34
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Total Return and Constant Growth We know from earlier that Total Return (R) = Dividend Yield + Capital Gains Yield We now know that in the constant growth model Capital Gains Yield (or, return) = g So, R – g = R – capital gains yd. = dividend yd. FIN 300 - Stocks Pt. 1 35 BTW, since R & g stay the same, the div. yd. is constant, as well!
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Constant Growth & Returns/Yields Just to summarize – Important to know! If the dividend grows at a constant rate “g” forever The price grows at the same constant rate “g” forever The rate of price growth is also known as the capital gains yield (or, return) So, the same “g” is also the capital gains yield (or, return) (Total) Return (“R”) is the sum of the capital gains yield “g” and the dividend yield FIN 300 - Stocks Pt. 1 36
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Re-Write Constant Growth Formula FIN 300 - Stocks Pt. 1 37 𝑃𝑃 0 = 𝐷𝐷𝐷𝐷𝐷𝐷 1 𝑅𝑅 − 𝐸𝐸 𝑅𝑅 − 𝐸𝐸 = 𝐷𝐷𝐷𝐷𝐷𝐷 1 𝑃𝑃 0 𝑅𝑅 = 𝐷𝐷𝐷𝐷𝐷𝐷 1 𝑃𝑃 0 + 𝐸𝐸 Multiply both sides by (R-g) and divide both sides by P 0 R = Total Return (or, discount rate for the stock investor) Dividend Yield = End Div./Begin Price g = capital gains yield (also, dividend growth)
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More Examples w/Constant Growth Example 1 - Given: A share of stock sells for $100 today Shareholders require a 20% return on the stock The share pays a $2 dividend at the end of the year Also, the dividends are expected to grow at a constant perpetual rate forever What should the stock sell for in 1 year?
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