chapter 9 valuing stocks. copyright ©2014 pearson education, inc. all rights reserved.9-2 9.1 the...

Chapter 9

Valuing Stocks

Copyright ©2014 Pearson Education, Inc. All rights reserved. 9-2

9.1 The Dividend Discount Model

• A One-Year Investor– Potential Cash Flows

• Dividend• Sale of Stock

– Timeline for One-Year Investor

• Since the cash flows are risky, we must discount them at the equity cost of capital.

1 10

1

E

Div PP

r


Dividend Yields, Capital Gains, and Total Returns

• Dividend Yield

• Capital Gain– Capital Gain Rate

• Total Return– Dividend Yield + Capital Gain Rate

• The expected total return of the stock should equal the expected return of other investments available in the market with equivalent risk.

1 01 1 1

0 0 0

Dividend Yield Capital Gain Rate

1

E

P PDiv P Divr

P P P


Textbook Example 9.1


The Dividend-Discount Model Equation

• What is the price if we plan on holding the stock for N years?

– This is known as the Dividend Discount Model.

– The price of any stock is equal to the present value of the expected future dividends it will pay.

1 20 2

E E E E

1 (1 ) (1 ) (1 )

N NN N

Div PDiv DivP

r r r r

31 20 2 3

1E E E E

1 (1 ) (1 ) (1 )

n

nn

Div DivDiv DivP

r r r r


9.2 Applying the Discount-Dividend Model (cont'd)

• Constant Dividend Growth Model

– The value of the firm depends on the current dividend level, the cost of equity, and the growth rate.

1E

0

Div

r gP

gr

g1Div

gr

DivP

E

0

E

10



KS 7.50% Stock Price $59.00g 1.50% Expected return 5.500%D1 $2.36Stock Value $39.33

Earnings Growth RateTo Find Ks Dividends (TV) Dividends (Retention)RF First b (retention ratio)Km Last (D0) Dividend Payout RatioBeta N ROEKs 0.00% g (if not given) #DIV/0! g (if not given)

Dividend Yield published 2.36If D1 given enter here

Stock Valuation


Constant Growth

• The XYZ Corp recently paid a $3.00 dividend. Dividends are expected to grow at the historic growth rate of 7%. The required return for the company’s equity is 16%. What is the value of the stock?

• If the stock traded at $37, what would you do?


Dividends Versus Investment and Growth

• A Simple Model of Growth

– Dividend Payout Ratio

• The fraction of earnings paid as dividends each year

– Assuming the number of shares outstanding is constant, the firm can do two things to increase its dividend:

• Increase its earnings (net income)

• Increase its dividend payout rate

E

Earnings Dividend Payout Rate

Shares Outstanding

t

tt t

t

PS

Div


Dividends Versus Investment and Growth (cont'd)

• A Simple Model of Growth

Change in Earnings New Investment Return on New Investment

New Investment Earnings Retention Rate

Change in EarningsEarnings Growth Rate

Earnings

Retention Rate Return on New Investment

Retention Rate Return on New Investment g



•If the firm keeps its retention rate constant, then the growth rate in dividends will equal the growth rate of earnings.



• Profitable Growth– If a firm wants to increase its share price, should

it cut its dividend and invest more, or should it cut investment and increase its dividend?

– The answer will depend on the profitability of the firm’s investments.

– Cutting the firm’s dividend to increase investment will raise the stock price if, and only if, the new investments have a positive NPV.

– If and only if, there is information describing why they want to do this.


Textbook Example 9.3 (cont'd)


TAP – Dividend Discount Model

Yahoo Finance

RF 3.67% DIV

Km 12% 2012 1.28

Beta .93 2011 1.28

Div Yield 2.5 2010 1.16

ROE 5.07 2009 1.00

DIV payout

58% 2008 .84


KS 10.00%g 6.50%D1 $1.36Stock Value $38.95

To Find KsRF 3.67%Km 12.00%Beta 0.93Ks 11.42%

Dividend Yield 2.50%Capital Gains 6.50%Ks 9.00%

Stock Price $53.20Expected return 9.062%

Earnings Growth RateDividends (TV) Dividends (Retention)First $0.84 b (retention ratio) 42.00%Last (D0) $1.28 Dividend Payout Ratio 58.00%N 4 ROE 5.07%g (if not given) 11.10% g (if not given) 2.13%


Changing Growth Rates

• We cannot use the constant dividend growth model to value a stock if the growth rate is not constant.

– For example, young firms often have very high initial earnings growth rates. During this period of high growth, these firms often retain 100% of their earnings to exploit profitable investment opportunities. As they mature, their growth slows. At some point, their earnings exceed their investment needs and they begin to pay dividends.


Differential Growth (Variable)

• Due to an innovative production process the company will be able to pay dividends at an above normal rate of 12% for the next 4 years. After that the growth will return to the industry standard of 9%. The most recent dividend was 4.25 and the required return for the company’s equity is 20%. What is the value?

Super-Normal stock valuation

Current Dividend $4.25 Future DividendPV of DividendNormal Growth Rate 9.00% 1 $3.967Supernormal Growth Rate 12.00% 2 $3.702Supernormal Growth Period 4.0 3 $3.455Required Return 20.00% 4 $3.225Current Stock Price 5 $0.000

6 $0.0007 $0.000

15 $0.000$14.349$31.957

Value of the Stock $46.307


Limitations of the Dividend-Discount Model

• There is a tremendous amount of uncertainty associated with forecasting a firm’s dividend growth rate and future dividends.

• Small changes in the assumed dividend growth rate can lead to large changes in the estimated stock price.


9.3 Total Payout and Free Cash Flow Valuation Models

• Share Repurchases and the Total Payout Model

– Share Repurchase• When the firm uses excess cash to buy back its own

stock

– Implications for the Dividend-Discount Model• The more cash the firm uses to repurchase shares, the

less it has available to pay dividends.

• By repurchasing, the firm decreases the number of shares outstanding, which increases its earnings per and dividends per share.


9.3 Total Payout and Free Cash Flow Valuation Models (cont'd)

• Share Repurchases and the Total Payout Model

– Total Payout Model

• Values all of the firm’s equity, rather than a single share. You discount total dividends and share repurchases and use the growth rate of earnings (rather than earnings per share) when forecasting the growth of the firm’s total payouts.

00

(Future Total Dividends and Repurchases)

Shares OutstandingPV

PV


TAP – Total Payout Model

Yahoo Finance

Shares repurchased

0

WACC 8.83

Number of shares 182.6

Dividends Paid 231.04

Est (EPS) growth 3.10Total Payout Model

Get the WACC from thatswacc.com/

231.040

8.83%182.6

3.10%

22.77Value of Stock

Dividends paid outStock RepurchasesWACC# sharesGrowth of Earnings


The Discounted Free Cash Flow Model

• Discounted Free Cash Flow Model

– Determines the value of the firm to all investors, including both equity and debt holders

– The enterprise value can be interpreted as the net cost of acquiring the firm’s equity, taking its cash, paying off all debt, and owning the unlevered business.

Enterprise Value Market Value of Equity Debt Cash


The Discounted Free Cash Flow Model (cont'd)

• Valuing the Enterprise

– Free Cash Flow• Cash flow available to pay both debt holders and

equity holders

– Discounted Free Cash Flow Model

Unlevered Net Income

Free Cash Flow (1 ) Depreciation

Capital Expenditures Increases in Net Working Capital

cEBIT

0 (Future Free Cash Flow of Firm)V PV

0 0 00

0

Cash Debt

Shares Outstanding

V

P



• Implementing the Model

– Often, the terminal value is estimated by assuming a constant long-run growth rate gFCF for free cash flows beyond year N, so that:

1 20 2

wacc wacc wacc wacc

1 (1 ) (1 ) (1 )

N NN N

FCF VFCF FCFV

r r r r

1

wacc wacc

1

( )

N FCF

N NFCF FCF

FCF gV FCF

r g r g


Stock Valuation Models

• The free cash flow valuation model estimates the value of the entire company and uses the cost of capital as the discount rate.

• to estimate the value of equity:

cashVVV DsF

cashVVV DFs


Free Cash Flow Model

• The firm has estimated the growth of FCF to be 7% over the foreseeable future. The most recent FCF was $700,000. The firms WACC = 13%.– What is the firms value?

• The firm has 1,000,000 in cash and market value of debt at 7,500,000. The firm has 100,000 shares.– What is the value of equity? Per share?

333,483,12

06.

000,749

07.13.

07.1*000,700VF

333,983,5

000,000,1000,500,7333,483,12

-

cashVVV DFS


Free Cash Flow Valuation

WACC 13.00% Market Value of Debt 7,500,000.00$ g 7.00% Cash Available 1,000,000.00$ FCF1 $749,000 Market Value of Common $5,983,333Value of Corp $12,483,333

Number of Shares 100,000 Free CF Value per share 59.83$ FirstLast (FCF0) $700,000Ng (if not given) #DIV/0!

If FCF1 given enter here


TAP FCF Model

Free Cash Flow Valuation

Yahoo Finance

Cash 624 FCF (ratios)

Total debt

8245 2012 1839

# shares 187.1 2011 792

Growth of FCF

3.7% 2010 -74

Estimate next years FCF

1000 2009 714

WACC 8.83%g 3.70%FCF1 $1,000Value of Corp $19,493

Free CFFirstLast (FCF0) $1,839Ng (if not given) #DIV/0!

If FCF1 given enter here $1,000.00

Market Value of Debt 8,245.00$ Cash Available 624.00$ Market Value of Common $11,872

Number of Shares 187 Value per share 63.49$



• Connection to Capital Budgeting

– The firm’s free cash flow is equal to the sum of the free cash flows from the firm’s current and future investments, so we can interpret the firm’s enterprise value as the total NPV that the firm will earn from continuing its existing projects and initiating new ones.

• The NPV of any individual project represents its contribution to the firm’s enterprise value.

• To maximize the firm’s share price, we should accept projects that have a positive NPV.


Figure 9.1 A Comparison of Discounted Cash Flow Models of Stock Valuation


9.4 Valuation Based on Comparable Firms

• Method of Comparables (Comps)

– Estimate the value of the firm based on the value of other, comparable firms or investments that we expect will generate very similar cash flows in the future.


Valuation Multiples

• Valuation Multiple– A ratio of firm’s value to some measure of the

firm’s scale or cash flow

• The Price-Earnings Ratio– P/E Ratio

• Share price divided by earnings per share



PE Multiplier

Company PE 21.300Estimated EPS $1.380

Value of Stock $29.394

Multiplier models


TAP – PE Multiplier Model

Yahoo Finance

PE (industry) 37.49

PE (forward) 12.41

EPS1 3.98

Mutlipler Model

Estimated PE 3.98Estimated EPS $12.410

Estimated Value $49.392

Estimated PE 3.98Estimated EPS $37.490

Estimated Value $149.210


Valuation Multiples (cont'd)

• Enterprise Value Multiples

– This valuation multiple is higher for firms with high growth rates and low capital requirements (so that free cash flow is high in proportion to EBITDA).

0 1 1

1

/

wacc FCF

V FCF EBITDA

EBITDA r g


Enterprise Value Multipliers

Company EV Multiplier (EBITDA) 7.400EBITDA $30.700Debt $125.000Cash# of shares 5.400Value of Stock $18.922


TAP – EBITDA Value MultiplierYahoo Finance

EV Multiplier 17.54

EBITDA 765

Debt 4650

Cash 511.1

# shares 182.61

Enterprise Value Multipliers

Company EV Multiplier (EBITDA) 17.400EBITDA $765.000Debt $4,650.000Cash $511.100# of shares 182.610Value of Stock $50.228



• Other Multiples– Multiple of sales– Price to book value of equity per share– Enterprise value per subscriber

• Used in cable TV industry



• Price to Sales

Yahoo Finance

Price to sales 2.41

Estimated Sales 4310

# shares 182.61

Price to Sales

Company P / S 2.410Estimated Sales $4,310.000# of shares 182.610Est sales / share 23.602$



Limitations of Multiples

• When valuing a firm using multiples, there is no clear guidance about how to adjust for differences in expected future growth rates, risk, or differences in accounting policies.

• Comparables only provide information regarding the value of a firm relative to other firms in the comparison set. – Using multiples will not help us determine if an

entire industry is overvalued,


Comparison with Discounted Cash Flow Methods

• Discounted cash flows methods have the advantage that they can incorporate specific information about the firm’s cost of capital or future growth.

– The discounted cash flow methods have the potential to be more accurate than the use of a valuation multiple.


Growth Opportunities (not in text)

• Growth opportunities are opportunities to invest in positive NPV projects.

• The value of a firm can be conceptualized as the sum of the value of a firm that pays out 100% of its earnings as dividends plus the net present value of the growth opportunities.– Value as a cash cow– Value of investment opportunities

NPVGOR

EPSP


The NPVGO Model: Example

Consider a firm that has EPS of $5 at the end of the first year, a dividend-payout ratio of 30%, a discount rate of 16%, and a return on retained earnings of 20%.

• The dividend at year one will be $5 × .30 = $1.50 per share.

• The retention ratio is .70 ( = 1 -.30), implying a growth rate in dividends of 14% = .70 × 20%.

From the dividend growth model, the price of a share is:

7 5$1 4.1 6.

5 0.1$

gR

D ivP 1

0


The NPVGO Model: Example

First, we must calculate the value of the firm as a cash cow.

Second, we must calculate the value of the growth opportunities. (3.50 = 5.00 – 1.50) = retained earn per share. g = retention calculation

Finally,

2 5.3 1$1 6.

5$

R

E P SP 0

75.43$14.16.

875$.

gR16.

20.50.350.3

P0

7 5$7 5.4 32 5.3 1P 0


TAP - NPVGO Model

What does a negative NPVGO value mean?What would a negative stock value imply?

NPVGO Model

EPS1 $3.98

Value as Cash Cow $39.800NPVGO -$0.851Stock Value $38.949


Retention Rate and Firm Value

• An increase in the retention rate will:– Reduce the dividend paid to shareholders– Increase the firm’s growth rate

• These have offsetting influences on stock price

• Which one dominates?– If ROE>R, then increased retention increases firm

value since reinvested capital earns more than the cost of capital.


Dividends-and-Earnings Approach (not in text)

• Very similar to variable-growth DVM

• Uses present value to value stock

• Assumes stock value is capitalized value of its annual dividends and future sale price

• Works well with companies who pay little or no dividends

Present value ofa share of stock

Present value offuture dividends

Present value of

the price of the stockat date of sale


TAP – Earnings Dividend Model

Current EPS $2.440EPS Growth Rate 4.000% Historical DataRequired Return 11.417% EPS DPS Dividend PayoutEst Dividend Payout 35.000% 2008 $2.090 $0.760 36.364%

2009 $3.880 $0.920 23.711%Risk Free Rate 3.670% 2010 $3.780 $1.080 28.571%Beta 0.93 2011 $3.630 $1.240 34.160%Km 12.000% 2012 $2.440 $1.280 52.459%Required Return (ks) 11.417% Average Dividend Payout 35.053%

Historical EPS Growth 3.947%

Year Est EPS Est Div Payout Estimated Dividends PV of Dividend1 2013 $2.538 35.000% $0.888 $0.8882 2014 $2.639 35.000% $0.924 $0.9243 2015 $2.745 35.000% $0.961 $0.9614 2016 $2.854 35.000% $0.999 $0.9995 2017 $2.969 35.000% $1.039 $1.039

PV of Estimated Div $4.811

EPS PE Ratio Price PV of Price$2.969 12.41 $36.841 $21.457



Stock Valuation Techniques: The Final Word

• No single technique provides a final answer regarding a stock’s true value. All approaches require assumptions or forecasts that are too uncertain to provide a definitive assessment of the firm’s value.

– Most real-world practitioners use a combination of these approaches and gain confidence if the results are consistent across a variety of methods.


Comparison of models

Current Price 43.43

Dividend Discount 43.52

Total Payout 54.35

FCF 63.49

PE (company) 43.53

PE (industry) 59.07

Enterprise multiplier 44

Price to sales multiplier 45.61

NPVGO -19.85

Earnings – Dividend 26.27


9.5 Information, Competition, and Stock Prices

• Information in Stock Prices

– Our valuation model links the firm’s future cash flows, its cost of capital, and its share price. Given accurate information about any two of these variables, a valuation model allows us to make inferences about the third variable.


Figure 9.3 The Valuation Triad


9.5 Information, Competition, and Stock Prices (cont'd)

• Information in Stock Prices

– For a publicly traded firm, its current stock price should already provide very accurate information, aggregated from a multitude of investors, regarding the true value of its shares.

• Based on its current stock price, a valuation model will tell us something about the firm’s future cash flows or cost of capital.


Competition and Efficient Markets

• Efficient Markets Hypothesis

– Implies that securities will be fairly priced, based on their future cash flows, given all information that is available to investors.


Competition and Efficient Markets (cont'd)

• Public, Easily Interpretable Information

– If the impact of information that is available to all investors (news reports, financials statements, etc.) on the firm’s future cash flows can be readily ascertained, then all investors can determine the effect of this information on the firm’s value.

• In this situation, we expect the stock price to react nearly instantaneously to such news.



• Private or Difficult-to-Interpret Information

– Private information will be held by a relatively small number of investors. These investors may be able to profit by trading on their information.

• In this case, the efficient markets hypothesis will not hold in the strict sense. However, as these informed traders begin to trade, they will tend to move prices, so over time prices will begin to reflect their information as well.



• Private or Difficult-to-Interpret Information

– If the profit opportunities from having private information are large, others will devote the resources needed to acquire it.

• In the long run, we should expect that the degree of “inefficiency” in the market will be limited by the costs of obtaining the private information.


Figure 9.4 Possible Stock Price Paths


Lessons for Investors and Corporate Managers

• Consequences for Investors

– If stocks are fairly priced, then investors who buy stocks can expect to receive future cash flows that fairly compensate them for the risk of their investment.

• In such cases the average investor can invest with confidence, even if he is not fully informed.


Lessons for Investors and Corporate Managers (cont'd)

• Implications for Corporate Managers

– Focus on NPV and free cash flow

– Avoid accounting illusions

– Use financial transactions to support investment


The Efficient Markets Hypothesis

Versus No Arbitrage• The efficient markets hypothesis states that

securities with equivalent risk should have the same expected return.

• An arbitrage opportunity is a situation in which two securities with identical cash flows have different prices.

chapter 9 valuing stocks. copyright ©2014 pearson education, inc. all rights reserved.9-2 9.1 the...

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