# Introduction to Finance: Class 4

## Stock Valuation

*What is stock valuation?*

There are many ways to determine the value or worth of a stock (refamiliarize yourself with what a stock is).

Each stock is different, and each industry sector has unique properties that may require varying valuation approaches…Stock is sometimes referred to as shares, securities or equity.

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Key Concepts:

- What is Common Stock?
- Common Stock Valuation
- Dividends
- Required Returns
- Current Value of a Stock

## What is Common Stock?

- A share of stock represents an ownership stake in the firm

- More reading here

- An investor who buys a share of stock has two basic rights:

- Control Rights
- Voting right: elect representatives (directors) who hire management to run the firm

- Cash Flow Rights
- Right to share proportionally in dividends paid
- Dividends are discretionary payments by corporation to shareholders in the form of cash or stock

- Equity Financing
- Differences between Debt & Equity Financing (REVIEW)
- Debt
- Not an ownership interest
- Creditors do not have voting rights
- Interest is considered a cost of doing business and is tax deductible
- Creditors have legal recourse if interest or principal payments are missed
- Excess debt can lead to financial distress and bankruptcy

- Equity
- Ownership interest
- Common stockholders vote for the board of directors and other issues
- Dividends are not considered a cost of doing business and are not tax deductible
- Dividends are not a liability of the firm, and stockholders have no legal recourse if dividends are not paid
- An all equity firm can not go bankrupt merely due to debt since it has no debt

- Debt

- Differences between Debt & Equity Financing (REVIEW)

## Common Stock Valuation

- More difficult than bond valuation since:
- Cash flows are not known
- Stocks have an infinite life
- Don’t know what rate of return market requires

- If you buy share of stock, you receive cash in two ways
- The company pays dividends
- You sell your shares either to another investor in the market or back to the company

- As with bonds, the price of the stock is the present value of these expected cash flows

**One-Period Example**

- Suppose you are thinking of purchasing the stock of Moore Oil, Inc. You expect it to pay a $2 dividend in one year, and you believe that you can sell the stock for $14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay?
- Compute the PV of the expected cash flows
- Price = (14 + 2) / (1.2) = $13.33

**Two-Period Example**

- Now, what if you decide to hold the stock for two years? In addition to the $2 dividend in one year, you expect a dividend of $2.10 and a stock price of $14.70 both at the end of year 2. Now how much would you be willing to pay?
- PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)^2 = 13.33

**Three-Period Example**

- Finally, what if you decide to hold the stock for three periods? In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 and a stock price of $15.435 both at the end of year 3. Now how much would you be willing to pay?
- PV = 2 / 1.2 + 2.10 / (1.2)^2 + (2.205 + 15.435) / (1.2)^3 = 13.33

**Developing the Stock Valuation Model**

- You could continue to push back when you sell the stock

- You would find that the price of the stock is really just the present value:

- So, how can we estimate all future dividend payments?

## Dividends

### Estimating Dividends: Special Cases

- Constant dividend (zero growth)
- The firm will pay a constant dividend forever

- Constant dividend growth
- The firm will increase the dividend by a constant percent every period

- Supernormal growth
- Dividend growth is not consistent initially, but settles down to constant growth eventually

**Constant Dividend**

- If dividends are expected to be constant (Dt=D) at regular intervals forever, then value stock as a perpetuity
- P0 = D / R

- Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price?
- Quarterly required return = 10% / 4 = 2.5%
- P0 = .50 / .025 = $20

**Constant Dividend Growth Model**

**Dividend Growth Model: Example**

- Suppose Joe’s Place, Inc. just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for?
- P0 = D1 / (R – g)

- D1 = D0 x (1+g)
- D1 = 0.50 x (1+ 0.02) = 0.51

- P0 = 0.51 / (.15 – .02)
- P0= $3.92

**Dividend Growth Model Assumptions**

- Stock grows at constant rate (g constant)
- Product market the firm operates in “settles down” to a steady state
- Firms manage dividend policy to foster constant growth

- Required return exceeds growth rate (R > g)
- Geometric series assumes “r” < 1 (or (1+g)/(1+R) < 1)
- In long run, relation must hold
- In short run, R may be less than g (supernormal growth problem)

**Nonconstant Dividend Growth**

- In short run, supernormal growth rate may exceed required return (g > R)
- In long run, dividend policy reverts to:

- No future dividends
- All future dividends are constant
- All future dividends grow at a constant rate

**Nonconstant Dividend Growth: Example**

- Suppose a firm expects to increase dividends by 20% in one year and by 15% in two years. After that, dividends will increase at a rate of 5% per year indefinitely. If last year’s dividend was $1 and the required return is 20%, what is the price of the stock?
- Compute the dividends until growth levels off
- D1 = 1(1.2) = $1.20
- D2 = 1.20(1.15) = $1.38
- D3 = 1.38(1.05) = $1.449

- Compute the dividends until growth levels off

- Find the expected future price of dividends starting in Year 3
- P2 = D3 / (R – g) = $1.449 / (.2 – .05) = $9.66

- Find the present value of the expected future cash flows
- P0 = $1.20 / (1.2) + ($1.38 + 9.66) / (1.2)2 = $8.67

**Stocks that Don’t Pay Dividends**

- Many firms do not pay dividends: Apple, Google, Amazon
- Are the shares of these firms worthless?
- No – instead of paying dividends, they plowback cash flow into internal projects

- For a stock that currently pays no dividend, market value derives from
- Hope of future dividends, and/or
- Expectation of a liquidating dividend

- Our valuation models only say that dividends cannot be zero in all periods

## Required Returns

- Rearrange and solve for R

- Total return has two parts
- Dividend yield (D1/P0) – return from dividend next period
- Capital gain yield (g) – rate at which value of investment grows

**Required Return: Example**

- A firm’s stock is selling for $10.50. It just paid a $1 dividend and dividends are expected to grow at 5% per year.

- What is the required return?
- R = D1/P0 + g
- R = [$1 x (1.05)/$10.50] + .05 = 15%

- What is the dividend yield?
- Dividend yield = D1/P0
- Dividend yield = $1.05 / $10.50 = 10%

- What is the capital gains yield?
- Capital gain yield = g = 5%

Other methods to consider…. here.

## Current Value of a Stock

- We covered special cases that allow us to value stocks
- As with bonds, numerous factors influence price of stock
- Large fluctuations in value of stocks (even over short periods)

- Current value of stock determined by the market
- Constantly changing as new information arrives and investors reassess firm’s future cash flows and risks

- Easiest way to find current value is the Internet

## Wrap-Up

- Stock represents ownership stake in the firm
- Stock price is the present value of all expected future dividends
- Required return is sum of dividend yield and capital gain

## For more classes:

## Education Series

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