DrakeDRAKE UNIVERSITY

MBA

Stock ValuationA Discounted Cash Flow Approach

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Fin 200Common Stock

Provides Ownership in the firm, owners have the right to:

Share proportionally in dividends paidVote on stockholder mattersShare proportionally in assets remaining after all liabilities are paid in event of liquidation.

Dividends are declared by management

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Fin 200Preferred Stock

Claim prior to common

Fixed dividend schedule

Missing payment does not constitute default

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Fin 200

The Market for Common Stocks

Secondary Market TransactionsOutstanding shares are traded between investors, transactions do not raise money for the firm

Sale of additional sharesIf the firm decides to increase the number of shares outstanding it sells them in the primary market, raising money for the firm

Initial Public OfferingThe initial sale of shares in a firm that was previously privately held.

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Fin 200A General Valuation Model

The basic components of the valuation are:

An estimate of the future cash flow stream from owning the assetThe required rate of return for each period based upon the riskiness of the asset

The value is then found by discounting each cash flow by its respective discount rate and then summing the PV’s (Basically the PV of an Uneven Cash Flow Stream)

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Fin 200The Formal Model

The value of the asset should then be equal to:

nnj

nt

tj

t2

2j

2

1j

1

)r(1

CF

)r(1

CF

)r(1

CF

r1

CFV

n

1tt

tj

t

)r(1

CFV

How do we apply the model to find the value of a stock?

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Fin 200All Stocks

Regardless of type of stock, the return from owning the stock is usually earned in one of two ways:Dividends

Dividends are declared by management and paid on a per share basis to the share holder

Capital GainsCapital Gains represent the change in the price of the stock

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Fin 200

General Valuation Model Stocks

Assuming that the firms pays dividends, the future expected cash flows received from owning the stock are the dividends that the firm is expected to pay.

What about the capital gains?

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Fin 200Basic Stock Valuation

The firm is a legal entity that continues forever, we are assuming that dividends continue forever (t = infinity)Valuation would then be the PV of the dividends, Dt, from t = 0 to t = infinity.

The Dividends are discounted at the required rate of return for the investor , rs

)r(1

D

)r(1

D

)r(1

DVP̂

s2

s

2

s

1stock0

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Fin 200

What about the future price?

Let = the stock price in one yearThere are two future cash flows Dividend one and the future price.

0 1

1P̂

11 DP̂

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Fin 200Valuation

The valuation would then be:

What is equal to?

)r(1

P̂DP̂V

s

110stock

1P̂

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Fin 200Valuation

The value of the stock at time 1 must equal the PV of the cash flows that come after it. The PV of D2, D3, etc. at time t=1

)r(1

D

)r(1

D

)r(1

DP̂

s2

s

3

s

21

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Fin 200Valuation

Substitute for in our equation:1P̂

)r(1

P̂DP̂V

s

110stock

)r(1

)r(1

D

)r(1

D

)r(1

DD

P̂Vs

s2

s

3

s

21

0stock

)r(1

D

)r(1

D

)r(1

DP̂

s2

s

3

s

21

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Fin 200

Which leaves our original equation

)r(1

)r(1

D

)r(1

D

)r(1

DD

P̂Vs

s2

s

3

s

21

0stock

)r(1

D

)r(1

D

)r(1

DP̂Value

s2

s

2

s

10Stock

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Fin 200Dividends

The key to valuing the stock then becomes your assumption about whether dividends change over time.If they do change you need to decide how to estimate possible future changes in dividends.This can in part be determined by the type of stock (common or preferred).

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Fin 200Pref Stock Valuation

Often it is assumed that the dividends are constant for a preferred stock. If there is no maturity date the valuation is the same as a perpetuity:

)r(1

D

)r(1

D

)r(1

DP̂Value

ps2

ps

2

ps

10Stock Pref

DDD 21

ps0Stock Pref r

DP̂Value

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Fin 200Dividends

For common stock the dividend is usually not expected to remain the same amount forever. Constant dividends formally were often a goal of management, but they represent a decline in real income.

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Fin 200

Constant Growth in Dividends

One possible assumption is that dividends grow at a constant rate.In this case

D1=D0(1+g) D2=D1(1+g) =D0(1+g)2 D3=D2(1+g) =D0(1+g)3

etc… Use this in the basic formula in the

valuation formula from before.

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Fin 200

Constant Growth in Dividends

)r(1

D

)r(1

D

)r(1

DP̂

s2

s

2

s

10

3s

30

2s

20

s

00

)r(1

g)(1D

)r(1

g)(1D

)r(1

g)(1DP̂

3

s

3

2s

2

s00

)r(1

g)(1

)r(1

g)(1

)r(1

g)(1DP̂

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Fin 200Constant Growth continued

1tt

s

t

00)r(1

g)(1DP̂

)r(1

g)(1

)r(1

g)(1

)r(1

g)(1DP̂

s2

s

2

s00

gr

g)(1

)r(1

g)(1

s1tt

s

t

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Fin 200Constant Growth

gr

g)(1

)r(1

g)(1

s1tt

s

t

1tt

s

t

00)r(1

g)(1DP̂

gr

D

gr

g)(1DP̂V

s

1

s00Stock

Substitute

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Fin 200Practice Problem

How much would you be willing to pay for a share of stock in Bulldog Industries given the following information? Assume that Bulldog just paid $1.00 dividend and that the dividend is expected to grow at 5% each year forever and that the appropriate discount rate for the risk associated with the firm is 10%.

 

gr

g)(1DP̂

s

00

21$

05.10.

)05.1(0.1$

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Fin 200Total Return

The total return earned by the shareholder has two components:

t

1t

Price

Dividend YieldDividend

t

t1t

P

PPYieldGainsCapital

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Fin 200Practice Problem Part 2

Find the the dividend and capital gains yield in the previous problem.

05.21

1.05YieldDividend

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Fin 200Practice Problem Part 2

t

t1t

P

PPYieldGainsCapital

05.22P̂05.10.

)05.1(05.1gr

g)(1D1t

s

1)(t

05.21

21-22.05YieldGainsCapital

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Fin 200Rates of Return

The total return for owning the stock is then the sum of the capital gains yield and the dividend yield.In the previous example, we estimated the future value of the stock at time t+1.Therefore the total return found by adding the capital gains yield to the divided yield would be the expected rate of return, sk̂

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Fin 200Rates of Return

IF you calculated the return after you observed the price at time t+1 then you would have found the actual or realized rate of return ( ). In this case your values for price are not the expected value, but the actual observed value.

sr

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Fin 200Note:

For a constant growth stock. Given the observed price of the stock and assuming it is equal to value, you can solve for the expected total return by rearranging the constant growth equation.

gr

D

gr

g)(1DPP̂

s

1

s

000

1s Dg)-P(r

0

1s P

Dg)-(r

gP

Dr̂r

0

1ss

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Fin 200

gP

Dr̂

0

1s

GainsYield Capital

Expected

Yield Dividend

Expected

Return of Rate

Expected

In the case of constant growth,The expected capital gains yield is equal to the expected growth rate

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Fin 200Non Constant Growth

Assume that the firm grows at a fast rate for a short period of time then starts constant growthValue would equal the PV of each of the early dividends plus the PV of the constant growth portion

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Fin 200

To find the value of this stock,

1. Discount the dividend received during each period of the supernormal growth period.

2. Find the value of the stock in year m assuming constant growth, the horizon value (use equation above)

3. Discount the PV of the stock in year m (found in 2)) back to the current year.

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Fin 200

Non Constant Growth Valuation

Assume non constant growth is for two periods

2

s

2

s

10Stock

)r(1

D

)r(1

DP̂V

2s

2

)r(1

gsr

D

The PV of the firstTwo dividends

The PV of theConstant Growth

From t = 2 to infinity

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Fin 200Practice Problem-Data

Assume that the average firm in your company’s industry is expected to grow at a constant rate of 7%. Your company is about a risky as the average firm in the industry, and investors are requiring a 15% return for investing in firms in the industry. Your firm has just introduced a new product which it expects to increase earnings each of the next two years. The expectation is that dividends will grow at 40% next year and 20% the year after that then return to the 7% constant growth rate of the industry. The last dividend paid by the firm was $0.75.

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Fin 200Practice Problem-questions

a) What is the current price of the stock?b) What is the capital gains yield and divined

yield if the stock was held for the first year?c) What is the capital gains yield and dividend

yield if the stock was bought following the third dividend and held until it paid the fourth dividend?

d) Explain your answers in b) and c) (Did the capital gains yield and dividend yield change over time? and if so how? Will you expect it to change after year four? why or why not?)