8-1 July 21 Outline Bond and Stock Differences Common Stock Valuation

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July 21 Outline

• Bond and Stock Differences• Common Stock Valuation

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Bonds and Stocks: Similarities• Both provide long-term

funding for the organization

• Both are future funds that an investor must consider

• Both have future periodic payments

• Both can be purchased in a marketplace at a price “today”

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Bonds and Stocks: Differences• From the firm’s perspective: a

bond is a long-term debt and stock is equity

• From the firm’s perspective: a bond gets paid off at the maturity date; stock continues indefinitely.

• We will discuss the mix of bonds (debt) and stock (equity) in a future chapter entitled capital structure

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Bonds and Stocks: Differences

• A bond has coupon payments and a lump-sum payment; stock has dividend payments forever

• Coupon payments are fixed; stock dividends change or “grow” over time

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A visual representation of a bond with a coupon payment (C) and a maturity value (M)

1 2 3 4 5

$C1 $C2 $C3 $C4 $C5

$M

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A visual representation of a share of common stock with dividends (D) forever1 2 3 4 5

$D1 $D2 $D3 $D4 $D5 $D∞

∞

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Comparison Valuations

1 2 3Bond

C CCM

P0

0

1 2 3Common Stock

D1 D2 D3 D∞P0

0

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Notice these differences:• The “C’s” are constant and equal• The bond ends (year 5 here)• There is a lump sum at the end

1 2 3 4 5

$C1 $C2 $C3 $C4 $C5

$M

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Notice these differences:• The dividends are typically

different• The stock never ends• There is no lump sum

1 2 3 4 5

$D1 $D2 $D3 $D4 $D5 $D∞

∞

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Cash Flows for Stockholders

If you buy a share of stock, you can receive cash in two ways:

1. The company pays dividends

2. You sell your shares, either to another investor in the market or back to the company

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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?

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Visually this would look like:

1

D1 = $2

P1 = $14

R = 20%

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Compute the Present Value

1

D1 = $2

P1 = $14

R = 20%

$1.67

$11.67

PV =$13.34

1 year = N

20% = Discount rate

$2 = Payment (PMT)

$14 = FV

PV = ?

-13.34

1st

2nd

TI BA II Plus

8-148-14

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Two Period Example

Now, what if you decide to hold the stock for two years? In addition to the dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year. Now how much would you be willing to pay?

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Visually this would look like:

2

D1 = $2

P2 = $14.70

R = 20% 1

D2 = $ 2.10

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Compute the Present Value

2

D1 = $2

P2 = $14.70

R = 20% 1

D2 = $ 2.10$1.67$1.46

$ 10.21

$ 13.34 = P0

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What is the Observed Pattern?

We value a share of stock by bring back all expected future dividends into present value terms; since the corporation does not have a finite life, we must consider all such dividends, even those in the distant future.

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So how do you compute the future

dividends?Three scenarios:

1. A constant dividend (zero growth)

2. The dividends change by a constant growth rate

3. We have some unusual growth periods and then level off to a constant growth rate

So how do you compute the future dividends?We start with the general pricing formula for an annuity with constant growth:

where D1 is next period’s dividend, R is the discount rate, g is the (constant) growth rate, and R > g. Note that as n grows arbitrarily large (goes toward ), then

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0 1

1 (1 ) (1 ),

n ng RP D

R g

10 .

DP

R g

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1. Constant Dividend – Zero Growth• The firm will pay a

constant dividend forever

• This is like preferred stock

• Since g = 0, this implies that

1 10 .

D DP

g RR

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2. Constant Growth Rate of Dividends

Dividends are expected to grow at a constant percent per period; i.e., D2 = D1(1+g), D3 = D1(1+g)2, …, Dn+1 = D1(1+g)n, and so forth. Then we end up with the constant growth formula, AKA the “Gordon” model:

10 .

DP

R g

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Dividend Growth Model (DGM) Assumptions

In order to use the Gordon constant growth model, the following three requirements must be met:

1.The growth of all future dividends must be constant,

2.The growth rate must be smaller than the discount rate ( g < R), and

3.The growth rate must not be equal to the discount rate (g ≠ R)

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DGM – Example 1

Suppose Big D, Inc., just paid a dividend (D0) of $0.50 per share. 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?

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DGM – Example 1 Solution

P0 = .50 ( 1 + .02) .15 - .02

g-R

D

g-R

g)1(DP 10

0

P0 = .51 .13

= $3.92

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DGM – Example 2

Suppose Moore Oil Inc., is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price?

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DGM – Example 2 Solution

P0 = 2.00 .20 - .05

g-R

D

g-R

g)1(DP 10

0

P0 = 2.00 .15

= $13.34

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3. Unusual Growth;Then Constant

Growth

Just draw the time line with the unusual growth rates identified and determine if/when you can use the Dividend Growth Model.

Deal with the unusual growth dividends separately.

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Non-constant Growth Problem Statement

Suppose a firm is expected to increase dividends by 20% in one year and by 15% for two years. After that, dividends will increase at a rate of 5% per year indefinitely.

If the last dividend was $1 and the required return is 20%, what is the price of the stock?

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Draw the time line and compute each dividend using the corresponding growth rate:

g = 20% g = 15% g = 15% g = 5% D 0 =

$1.00

1 2 3 4

∞D1 D2 D3

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g = 20% g = 15% g = 15% g = 5% D 0 =

$1.00

1 2 3 4

∞D1 D2 D3

D1 = ($1.00) (1 + 20%) = $1.00 x 1.20 = $1.20

=1.20

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g = 20% g = 15% g = 15% g = 5% D 0 =

$1.00

1 2 3 4

∞D1 D2 D3

D2 = ($1.20) (1 + 15%) = $1.20 x 1.15 = $1.38

=1.38

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Non-constant Growth Problem StatementDraw the time line and compute each dividend using the corresponding growth rate:

g = 20% g = 15% g = 15% g = 5% D 0 =

$1.00

1 2 3 4

∞D1 D2 D3

D3 = ($1.38) (1 + 15%) = $1.38 x 1.15 = $1.59

=1.59

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Non-constant Growth Problem StatementNow we can use the DGM starting with the period of the constant growth rate at our time frame of year 3:

g = 20% g = 15% g = 15% g = 5% D 0 =

$1.00

1 2 3 4

∞D1 D2 D3

P3 = D3 (1 + g) / (R – g)P3 = 1.59 (1.05)/ (.20 - .05) = $11.13

R = 20%

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We now have all of the dividends accounted for and we can compute the present value for a share of common stock:

g = 20% g = 15% g = 15% g = 5% D 0 =

$1.00

1 2 3 4

∞D1 D2 D3

R = 20%

1.20 1.38 1.59P3 = 11.13

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g = 20% g = 15% g = 15% g = 5% D 0 =

$1.00

1 2 3 4

∞D1 D2 D3

R = 20%

1.20 1.38 1.59

P3 = 11.13$9.32

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Stock Price Sensitivity to

Dividend Growth, gD1 = $2; R = 20%

0

50

100

150

200

250

0 0.05 0.1 0.15 0.2

Growth Rate

Stoc

k P

rice

Stock Price Sensitivity to

Required Return, RD1 = $2; g = 5%

0

50

100

150

200

250

0 0.05 0.1 0.15 0.2 0.25 0.3

Growth Rate

Sto

ck P

rice

8-38

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Using the DGM to Find R

gP

D g

P

g)1(D R

g-R

D

g - R

g)1(DP

0

1

0

0

100

Start with the DGM and then algebraically rearrange the equation to solve for R:

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Finding the Required Return - Example

Suppose 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 = [1(1.05)/10.50] + .05 = 15%What is the dividend yield?

1(1.05) / 10.50 = 10%What is the capital gains

yield?

g =5%

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Valuation Using Multiples

We can use the PE ratio and/or the price-sales ratio:

Pt = Benchmark PE ratio X EPSt

Pt = Benchmark price-sales ratio X Sales per sharet

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Stock Valuation Summary

Documents

8-1 July 21 Outline Bond and Stock Differences Common Stock Valuation