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