10/20/20151 HFT 4464 Chapter 7 Common Stock. 7-2 Chapter 7 Introduction This chapter introduces...

04/20/2304/20/23 11

HFT 4464HFT 4464Chapter 7Chapter 7

Common StockCommon Stock

7-2

Chapter 7 Introduction

This chapter introduces common stocks including unique features that differentiate common stock from other securities and basic common stock valuation models.

7-3

Organization of Chapter 7

Common stock as a residual ownership claim on a corporation

The difficulty in estimating the value of common stock relative to bonds and preferred stock.

Common stock features Basic common stock valuation Relationship between investor required rate of

return, earnings and dividend growth, and common stock value

7-4

Common Stock as Residual Ownership

Common stock is quite different than bonds and preferred stock:

Return is dependent upon success of firm Provides a residual claim on firm’s assets Ownership rights to cash flows remaining

after all other claims are paid Not a contractual obligation and no stated

maturity

7-5

Difficulty of Estimating Common Stock Value

The value of a security is the sum of the present values of its future expected cash flows. Common stock is difficult to value because future cash flows are uncertain.

Future common stock dividends are difficult to forecast accurately.

The future common stock selling price is difficult to forecast.

7-6

Common Stock Features

The defining features of common stock include:

A residual claim on assets and cash flow

Variable return

Voting rights

No set maturity

7-7

Common Stock Features

A corporation’s board of directors controls the firm.

Members are elected by stockholders.

Has the power to hire, fire, and set compensation for corporate executives

Determines corporate policy and strategy

Makes major corporate decisions

7-8

Common Stock Financing—Pros and Cons

Pros

It has lower risk than debt or preferred stock financing due to the lack of a fixed dividend.

Fewer restrictions than debt financing; a debt contract generally includes many restrictions on future corporate actions.

Expansion of a firm’s equity generally increases a firm’s debt capacity.

7-9

Common Stock Financing—Pros and Cons

Cons

The costs of issuing common stock are generally much higher than the costs of issuing debt and preferred stock.

Common stock is a riskier investment than bonds or preferred stock. Investors require a higher rate of return which translates into a higher cost of raising funds with common stock.

7-10

Valuing Common Stock

The value of common stock is the sum of the present values of its future expected cash flows. We will cover 4 basic models for valuing common stock:

General valuation model Zero-growth model Constant-growth model Multiple growth rates ending in constant growth

model

7-11


First we will introduce the concept of growth of a company’s earnings.

Earnings belong to the common stockholders:

They are paid back to the stockholders as dividends or

Invested back into the company and called additions to retained earnings.

7-12


When earnings are retained and invested into profitable projects, the company’s earnings grow. The pace of growth depends upon:

The amount of earnings retained

The returns earned on the projects

7-13


A firm’s earnings growth rate can be computed as follows:

Growth = retention ratio x ROE

Growth = earnings growth rate

Retention ratio = 1 – dividend payout ratio

ROE = Return on Stockholders Equity

7-14


For example, what is a firm’s earnings growth rate if it pays 40% of earnings as dividends and earns a 20% return on stockholders equity?

Growth = retention ratio x ROE

Growth = (1 – 40%) x 20% = 60% x 20% = 12%

7-15

General Dividend Valuation Model

The value of common stock is the PV of the expected dividends to be received plus the PV of the expected price the stock is sold for in the future:

For simplicity we will assume a firm pays out dividends just once a year.

ne

nn

e

n2

e

2

e

10

k1

P

k1

d.....

k1

d

k1

dP

7-16

General Dividend Valuation Model

Suppose an investor expects a common stock’s dividends to be $1.00, $1.05, and $1.10 at the end of each of the next 3 years and expects to sell the stock for $15 in 3 years. If the investor requires a 15% rate of return, what is the stock’s value today?

25.12$

15%1

$15.00

15%1

$1.10

15%1

$1.05

15%1

$1.00P 3320

7-17

Zero-Growth Dividend Valuation Model

If a company’s dividends are not growing, but the company is paying out a constant dividend every year, this is similar to investing in preferred stock. The value of the common stock would be the PV of a perpetuity.

e0 k

dP

7-18


Suppose a company expects earnings of $5 per share and because they do not expect to grow, all earnings are paid out as dividends. Thus all future dividends are expected to be $5.00 per share. If investors require a 10% rate of return, the stock’s value today is:

00.50$10%

$5.00P0

7-19


Treating zero-growth common stock as a perpetuity seems to imply an investor will hold the stock forever! What if the investor just plans to hold the stock for 2 years and then sell it?

What would the stock’s selling price be in 2 years?

00.50$10%

$5.00P2

7-20


This investor expects to receive a $5 dividend for each of 2 years and then sell the stock for $50 in 2 years. The value of the stock today is:

The investor’s holding period does not affect the stock’s value!

00.50$

10%1

$50.00

10%1

$5.00

10%1

$5.00P 220

7-21

Constant-Growth Dividend Valuation Model

A company with a constant dividend payout ratio and constant return on equity will have a constant growth rate.

For example, what is the growth rate for a company earning 12% on equity and a 40% dividend payout ratio?

Growth = (1 – 40%) x 12% = 60% x 12% = 7.2%

7-22


If we expect this company to have earnings of $5 per share in the coming year and the 7.2% growth rate is constant, we can compute the common stock value to an investor requiring a 10% return with the following constant growth model:

gk

dP

e

10

7-23


The company’s dividend in the coming year must be $2.00 per share:

d1 = $5.00 x 40% = $2.00

And thus the value of the stock is:

43.71$2.8%

$2.00

7.2%-10.0%

$2.00P0

7-24


Why is the value in this example higher than for the zero-growth example? Both examples assume earnings of $5 per share and a 10% rate of return.

The 7.2% growth rate makes the stock in the constant-growth example worth more!

7-25


Notice in the constant-growth example we made no assumptions about the investor’s holding period.

As we illustrated in the zero-growth valuation model, how long the investor plans to hold the stock should not affect the stock’s value today!

7-26


The constant-growth model provides good estimates of common stock value when a company’s future growth is expected to be stable.

The constant-growth model provides less accurate estimates when growth is difficult to estimate or large systematic differences year to year are expected in growth.

7-27

Valuing Stock with Multiple Growth Rates

Now we will consider how to estimate the value of common stock when several different growth rates are expected and the growth rates can be forecast with some degree of accuracy.

What if a company expects to pay a $2.15 dividend in a year and expects growth of 15% through the end of year 2? After year 2 growth is expected to decrease to 7.2% and stabilize at 7.2%.

7-28


We can picture the growth rates and cash flows as follows:

0 g = 15% 1 g = 15% 2 g = 7.2% |________|________|________________________ – $2.15 $2.47

What is the value of this stock to an investor requiring a 10% rate of return?

7-29


Remember, an investor’s holding period does not affect the value of common stock value.

Thus, in our example, we can use any holding period and it should not change the value of the stock!

To make the computation as easy as possible we will assume a 2-year holding period. The investor expects to receive 2 dividends (d1 and d2) and the selling price of the common stock in 2 years (P2).

7-30


If we can estimate the common stock selling price in 2 years, then we can use the general dividend valuation model to compute the stock value as follows:

3n

221

010%1

P

10%1

d

10%1

dP

7-31


Notice the growth rate in this example is constant at 7.2% annually after 2 years. This allows us to adapt the constant-growth model to estimate the price in 2 years.

The original constant-growth model is:

gk

dP

e

10

7-32


The constant-growth model can be viewed more generally as:

Adapting this to our example, we can estimate the stock’s price at the end of 2 years:

gk

dP

e

1nn

gk

dP

e

32

7-33


Estimate d3 by growing d2 at the 7.2% growth rate.

d3 = $2.47 x (1 + 7.2%) = $2.65

Use this along with the 7.2% growth rate after year 2 to estimate the price in 2 years:

64.94$2.8%

$2.65

%2.710%

$2.65P2

7-34


Now use the selling price in year 2 ($94.64) along with the expected dividends in the first 2 years ($2.15 and $2.47) to estimate the value of the stock today:

21.82$

10%1

$94.64

10%1

$2.47

10%1

$2.15P 320

7-35


Holding Period Assumption

We assumed a 2-year holding period in our computations. Assuming any other holding period would not have changed the answer. It would just change the computations and made the estimation of the stock’s value an even more difficult process!

7-36


Simplest Computation and Holding Period

When a stock is expected to have multiple growth rates, the easiest computation of the stock’s value is obtained by assuming a holding period exactly long enough to reach the point at which the growth rate becomes constant.

7-37

Value, Rate of Return, and Growth

What happens to a common stock’s value if the investor’s required rate of return increases but the future expected cash flows remain constant?

With the same expected future cash flows, the only way an investor can receive a higher rate of return is to pay less for the stock! Thus, higher rates of return cause stock values to decline!

7-38


Let’s use the constant-growth example to illustrate this inverse relation between rates of return and common stock value. Previously we assumed a $2 dividend in 1 year, a 7.2% growth rate, and a 10% rate of return, and obtained a value of $71.43 as follows:

43.71$2.8%

$2.00

7.2%-10.0%

$2.00P0

7-39


What if the general level of interest rates rises and as a result investors now require a 12% return on this common stock?

The stock value declines to $41.67. This same relationship would hold for any of the common stock valuation models we have presented in this chapter.

67.41$4.8%

$2.00

7.2%-12.0%

$2.00P0

7-40


What happens to a common stock’s value if the earnings and dividends growth rate increases but the rate of return remains the same?

With a higher growth rate dividends are now expected to be greater. Of course with the same rate of return, the value of the common stock will increase to investors!

7-41


Let’s use the constant-growth example to illustrate this direct relation between dividends and earnings growth and common stock value. Using the same beginning assumptions as before:

43.71$2.8%

$2.00

7.2%-10.0%

$2.00P0

7-42


What if the earnings and dividends growth rate rises from 7.2% to 8.0% and, as a result, future dividends are expected to be higher than before?

The stock value increases to $100.00. This same relationship would hold for any of the common stock valuation models we have presented in this chapter.

00.100$2.0%

$2.00

8.0%-10.0%

$2.00P0

7-43

Summary of Chapter 7 Topics

Common stock as a residual ownership claim

Features of common stock

Pros and cons of common stock financing

7-44

Summary of Chapter 7 Topics

Valuing common stock — 4 models introduced:

General valuation model Zero-growth model Constant-growth model Multiple growth rates ending in constant growth

model

Relationship between common stock value, rates of return, and earnings and dividend growth rates

7-45

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