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Stock Valuation
Chapter 9.1,9.2
Outline
• Investing in stocks– Capital gains, dividend yield, return
• The Constant Dividend Growth Model• The Dividend and Growth Tradeoff• The DGM with Changing Growth rates• Further problems
Investing in Stocks
A One-Year Investor
There are two potential sources of cash flows form owning a stock:• The firm might pay out cash to shareholders in the form
of dividends• The investor can generate cash flows by selling shares at
some future date
The investor pays the current price P0 and at the end of the year expects to receive dividend Div1 and to sell the stock at P1
Equity Cost of Capital
Both potential sources of cash flows form owning a stock are risky• Dividends change overtime• Stock prices fluctuate considerably
Equity investors demand compensation for this higher risk and require a risk-premium as reflected in the:
Equity cost of capital rE
Capital Gains and Dividend Yield
The expected one-period total return on investment in a stock is the sum of the expected capital gain yield and dividend yield
Dividend Yield Capital Gain Rate
Total return on the stock
Stock Prices and Returns
Dividend Yield for stocks in the Dow Jones Industrial Average (2013)
5.33%
3.5% 1.79%
3.03%
2.18%
2.31%
Dividend Yield for stocks in the Dow Jones Industrial Average (2013)
Dividend Yield for stocks in the Nasdaq 100 (2013)
A Two Year Investment
Suppose that the investor wishes to hold the stock for two years
Setting the stock price equal to the present value of future cash flows implies
Dividend Discount Model
Suppose that the investor wishes to hold the stock for n years
Dividend Discount Model
In Efficient Markets
The Constant Dividend Growth Model
Estimating Future Expected Dividend
The simplest approach is to assume that Dividends grow over time with a constant growth rate, g, forever
Constant Dividend Growth Model
Stock Valuation: Constant Dividend Growth
Market Information
Constant Dividend Growth: Application GE
Historical Dividends
Dividends per-share (Dec 2000 – Sept 2013)
Historical Stock Price
Stock price appreciation (from $48.8 to $24.22): -50%
Average annual dividend growth (2000-2013): 6.854%
Implied rate of return on equity for growth 6.854%
The Dividend and Growth Tradeoff (within the Constant Dividend Growth model)
Dividends and Growth
The stock price increases with the level of dividends and the growth rate
What determines the level of growth?
Can management increase the share price by changing its dividend policy?
A Simple Model of Growth
Dividends are paid out of earnings according to the dividend payout rate
Cash flows that are not paid out as dividends are retained
Retention Rate = 1- Dividend payout rate
Dividends and Investment
The firm can pay a higher current dividend by increasing its payout rate
How would a higher payout rate affect future dividends?
Earnings year n Earnings year n+1
Div n New Investment n
Div n+1 New Investment n+1
Calculating Earnings Growth Rate
Cutting Dividends for Profitable Growth
Cutting Dividends for Profitable Growth
Cutting Dividends for Profitable Growth
Second Example
Comparing the two alternatives
Stocks in Nasdaq 100 that have zero dividends
The DGM with changing Growth Rates
Changing Growth Rates
Often firms’ growth rates change overtime:
Young firms tend to retain a high fraction of earnings in order to take advantage of investment opportunities and as a result have high earnings growth rates
As firms mature, their growth slows to rates more typical of established companies. At that point, their earnings exceed their investment needs and they begin to pay dividends
DDM with Constant Long-Term Growth
When growth rates only stabilize at a constant level “g” after period “N+1” ends we value according to:
Where the future price PN is
Varying Growth Rate
Varying Growth Rate
Varying Growth Rate
Further Problems
Acap CorporationQuestion 3 (2nd Edition)Suppose Acap Corporation will pay a dividend of $2.80 per share at the end of this year and $3 per share next year. You expect Acap’s stock price to be $52 in two years. If Acap’s equity cost of capital is 10%:
a. What price would you be willing to pay for a share of Acap stock today, if you planned to hold the stock for two years?
b. Suppose instead you plan to hold the stock for one year. What price would you expect to be able to sell a share of Acap stock for in one year?
c. Given your answer in part (b), what price would you be willing to pay for a share of Acap stock today, if you planned to hold the stock for one year? How does this compare to your answer in part (a)?
Acap CorporationBuy and hold for two years
Price one year from now
Price one year from now
Colgate-PalmoliveQuestion 12 (2nd Edition):Colgate-Palmolive Company has just paid an annual dividend of $0.96. Analysts are predicting an 11% per year growth rate in earnings over the next five years. After then, Colgate’s earnings are expected to grow at the current industry average of 5.2% per year.
If Colgate’s equity cost of capital is 8.5% per year and its dividend payout ratio remains constant, what price does the dividend-discount model predict Colgate Stock should sell for?
Colgate-PalmoliveExpected price time 5
Current Price