Stock and Its Valuation

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Stock and Its Valuation. The application of the present value concept. Today’s agenda. Review what we have learned in the last lecture Stock and its valuation Some terminology about a stock Value a stock Simple dividend discount model Dividend growth model.

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### Stock and Its Valuation

The application of the present value concept

FIN 351: lecture 4

Today’s agenda
• Review what we have learned in the last lecture
• Stock and its valuation
• Some terminology about a stock
• Value a stock
• Simple dividend discount model
• Dividend growth model
What have we learned in the last lecture
• Bond?
• How to value a bond?
• Yield to maturity and spot rates?
• Term structure of interest rates and yield curve?
Some questions
• A bond that pays annual coupon is issued with a coupon rate of 4%, maturity of 30 years, and a yield to maturity of 7%, what will be the rate of return if you buy it now and hold it for one year and the yield to maturity in the next year will be 8%?
What is a stock?
• A (common) stock is a financial claim that has the following properties:
• A right to receive dividends after creditors have been paid
• A right to vote at the annual meeting
• A limited liability security
• Dividends are periodic cash flows to share holders
Stocks & Stock Market

Primary Market - Place where the sale of new stock first occurs.

Secondary market - market in which already issued securities are traded by investors.

P/E ratio - Price per share divided by earnings per share.

Dividend yield- Dividends per share divided by the stock price

Values of stocks

Book Value of a stock- the value according to the balance sheet in the accounting.

Market Value of a stock – the value according to the traded stock prices in the market.

Stock valuation
• When you want to invest in a stock, you are very interested in whether the stock is under-priced or over-priced. To find out, you need to value the stock
• Two simple approaches to price a stock
• Simple dividend discount model
• Dividend growth model
• We will apply these two approaches to real stocks, for example, IBM
Simple dividend discount model: valuing IBM
• We will first use the dividend discount model to value the International Business Machine.
• What does the company do?
• http://finance.yahoo.com/
• Symbol “IBM”
• We see price is recently \$180
• hit “detailed”
• we see the company is paying \$3 dividend per share (we will do an annualized problem for simplicity, here we assume that all the earnings are paid out as dividends)
Valuing IBM (continue)
• Let’s suppose IBM is going to continue paying \$3 dividend per share, forever
• We are planning to buy the stock and hold it forever
• Of course, we must be able to draw the cash flow diagram

\$3

\$3

\$3

\$3

\$3

\$3

PV

???

Yr2

Yr3

Yr4

Yr5

Time=infinity

Yr1

Valuing IBM (continue)
• How much is IBM worth?
• Suppose the required rate of return by the investor is 10%.
• The present value of future dividend cash flows should equal the price of IBM.
Valuing IBM (3)
• Clearly, the price calculated using this simple model is below the current market price
• Why?
• we have undervalued the stock
• the market has overvalued the stock
• Let’s be humble and assume the former
• where did we go wrong?
Valuing IBM (4)
• Sensitivity of our answer to discount rate:
• Clearly, this is still not the answer

Price

Discount rate

\$42.9

7%

\$37.5

8%

\$33.3

9%

11%

\$27.27

Valuing IBM (5)
• What if the dividend is not constant ?
• Suppose the dividend were to grow at 4% per year:
• the next dividend will be \$3
• in two years we will receive \$3.12
• and so on …
• Can we derive the formula for a growing perpetuity?
• define g ≡ 4% the growth rate
• define C ≡ 3 the dividend received in year one
Dividend growth model
• When dividends grow at a rate of g=4%, the cash flow diagram looks like as follows:

\$3*(1.04)∞

\$3.0

\$3.12

\$3.24

\$3.37

PV

???

Yr2

Yr3

Yr4

Yr5

Time=infinity

Yr1

Dividend growth model (2)
• Based on the diagram, we have the math equation:
Dividend growth (continue)
• To calculate the PV of dividend flows with a growth, we can have some math exercise as follows:

because

Dividend growth (continue)
• How to calculate dividend perpetuity with a growth:
Dividend growth model (5)
• Do you think that this formula makes sense ?
• When g increases, what will happen to the stock price?
• When r increases, what will happen to the stock price?
• When g =0, what happens?
• When g>r, what will happen to the stock price?
• In order to use the formula, r must be greater than g.
Back to the valuation of IBM
• Sensitivity of our answer to growth rate of dividends
• Next year’s dividend is still \$3.0
• Discount rate is constant at 10%
• Certainly, we are close,
• but g=5% is reasonable?

Stock price

Growth rate

\$33.3

1%

\$37.5

2%

\$50.0

3%

\$60.0

4%

\$75.0

5%

Discount rate

Stock price

6%

7%

8%

9%

10%

11%

12%

60

50

43

38

33

30

27

1%

2%

75

60

50

43

38

33

30

Dividend

Growth rate

3%

100

75

60

50

43

33

38

4%

150

100

75

60

50

38

43

5%

300

150

100

75

60

50

43

67

5.5%

600

200

120

86

55

46

Another way of looking at stock valuation
• Suppose stock A pays dividend of \$3 every year, with a discount rate of 10%. What is the stock price now in the following three cases
• (a) hold it for ever
• (b) hold for five years
• (c) hold it for twenty years
Another example
• Suppose stock A pays dividend of \$3 next year, with a constant dividend growth rate of 5% and a discount rate of 10%. What is the stock price now in the following three cases
• (a) hold it for ever
• (b) hold for one year
• (c) hold it for two years
More on the dividend discount model
• So far, we have used the dividend cash flows to calculate the stock price.
• In the real world, can we apply this formula to figure out the stock prices for all the stocks? How?
How to decide on the growth rate
• If a firm chooses to pay a lower dividend, and reinvest the funds, the stock price may increase because future dividends may be higher.

Payout Ratio - Fraction of earnings paid out as dividends

Plowback Ratio - Fraction of earnings retained by the firm.

More on the dividend growth

Growth can be calculated by the return on equity times the plowback ratio

Let g= the dividend growth rate

g = return on equity X plowback ratio

Example

Our company forecasts to pay a \$5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plow back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision?

Solution

Our company forecasts to pay a \$5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plow back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision?

No Growth

With Growth

Solution

Our company forecasts to pay a \$5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plow back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision?

With Growth

No Growth

The present value of growth opportunities

If the company did not plowback some earnings, the stock price would remain at \$41.67. With the plowback, the price rose to \$75.00.

The difference between these two numbers (75.00-41.67=33.33) is called the Present Value of Growth Opportunities (PVGO).

PVGO again

Present Value of Growth Opportunities (PVGO) - Net present value of a firm’s future investments.

Valuing Common Stocks

Expected rate of return- The percentage yield that an investor forecasts from a specific investment over a set period of time. Sometimes called the holding period return (HPR).

Expected return

Expected Return– the ratio of the profit over the initial cost

Here, P1 is the expected price in period 1, P0 is the current price and Div1 is the expected dividend payment in period 1.

An example

Example: A stock pays dividend of \$3 every year. The current stock price is \$100. The expected price is \$110 for the next year. If you hold the stock this year, what is the expected rate of return?

My solution
• The expected return is 13/100=13%
• P0=\$100
• P1=\$110
• Div=\$3
Another example

Imagine Corporation has just paid a dividend of \$0.40 per share. The dividends are expected to grow at 30% per year for the next two years and at 5% per year thereafter. If the required rate of return in the stock is 15%, calculate the current stock price.

Solution