new lecture 2 spring 09

8/14/2019 New Lecture 2 Spring 09

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Spring 2009 NBA 5060

Lecture 2 Basic Valuation and the Role of Accounting Numbers

1. Basic valuation theory

2. The relation between earnings and returns

3. Additional Notes: Deriving the Residual Income Model

Teaching AssistantsRuchit Agarwal [email protected] Bhargava [email protected] DMello [email protected] Wu [email protected]

For 01/27/08:

Familiarize yourself with the 10-K for Cracker Barrel (CBRL). We will be applying allthe tools we learn in class to CBRL. You can download the 10-K from the SEC Edgarwebsite (http://www.sec.gov/edgar.shtml).

Answer questions on handout regarding the Companys industry, strategy, andaccounting policies.

Lecture 2 Page 1 of 12
http://www.sec.gov/edgar.shtmlhttp://www.sec.gov/edgar.shtmlhttp://www.sec.gov/edgar.shtmlhttp://www.sec.gov/edgar.shtml


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Valuation

Economic theory teaches that the value of any resources equals thepresent value of the payoffs expected from the resource, discounted at arate compensating for the inherent risk & delayed consumption of thepayoffs.

The first financial model for common equity (and the basis for all modelsused today) is the dividend-discounting model:

+=

=

+1 )1(j

je

jtttr

DividendsEValueEquity



3/12

Residual Income Valuation

The basic assumption is the clean surplus relation. Essentially, we need:

BVEt= BVEt-1 + Net Incomet Dividendst

Where dividends include net capital transactions (issuance less repurchaseof equity).

Then, using the dividend-discounting model, we get the following (see lastpage of notes for a derivation):

( ) ( )...

)1()1( 21 +

++

++= +++

e

te2tt

e

te1tttt

r

BVEr-NIE

r

BVEr-NIEBVEValueEquity

Thus, the residual income valuation model is very straightforward in theory.

It simply states that the value of an investment is equal to the amountinvested, plus the present value of all future abnormal earnings or residualincome.


Residual Income is simply

earnings less a charge forthe use of capital


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The Residual Income Model reformulated in terms of ROEs:

Define ROE as to be earnings divided by beginning total equity. That is,

ROEt= NIt / BVEt-1

Then, substitute NIt+1 = ROEt+1*BVEt into the above equation to get:

( )[ ] ( )( )[ ]

)1()1( 211 +

++

++= +++

e

te2tt

e

tetttt

r

BVEr-ROEE

r

BVEr-ROEEBVEValueEquity

Thus, equity value is simply the book value of equity plus the present valueof future abnormal returns on equity, weighted by the BVE outstanding atthe time.

Why focus on earnings and book values?

But, is the focus on accounting numbers justified?



5/12

Nichols and Wahlen (2004): How do accounting numbers relate tostock returns?

Figure 1The Three Links Relating Earnings to Stock Returns

Current Period Earnings

Link 1

Link 1 assumes that currentperiod earnings numbers

provide information that equityshareholders can use to form

expectations for future earnings.

Expected FutureEarnings

Test:How do earnings

numbers relate toshare prices?

Link 2

Link 2 assumesthat current andexpected future

profitabilitydetermines thefirms expectedfuture dividend-paying capacity.

Current Share Price

Link 3

Link 3 assumes that shareprices reflect the present valueof all expected future dividends.

Expected FutureDividends

Remember, price depends on the information known to the market at time t.If information changes from period t to period t+1, price should changebetween those dates.

Thus, it is important to isolate the new information in earnings whenexamining the association between earnings and returns.

To make sure the changes in price reflect revised expectations of payoffsand not just differences in risk, we subtract returns on a portfolio of firmswith comparable size.



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Testing the three links: The relation between earnings changes andstock returns

Compare earnings this year (t) to earnings last year (t-1). If the change ispositive, put the firm in one portfolio; if the change is negative, put the firmin another portfolio. Do the same thing for operating cash flows.

The average abnormal returns of the portfolios are graphically depictedbelow.

Testingthe threelinks,

continued: Sign and magnitude of earnings changes



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Instead of forming portfolios on just the sign of the change, group firms into10 portfolios based on the magnitude of earnings (scaled by assets to allowcross-sectional comparability).

Testinglink 1:Earnings

persistence and stock returns

If new earnings will persist, then the new earnings should have a greatereffect on price.



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Is themarket

completely efficient with respect to accounting information?

Rank all firms based on the magnitude of their quarterly earnings surpriseusing analyst forecasts 60 days before the announcement as anexpectation.

Take a long position in the 10% of firms with the greatest unexpectedearnings, and an offsetting short position in the 10% of firms with the lowest

unexpected earnings. Hold these stocks for either 60 (trading) days.



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Nichols and Wahlen (2004): Summary and Takeaways

Accounting earnings capture many of the same events affecting firm valuethat are reflected in price.

The accrual accounting process starts with cash flows and addsinformation about transactions and events during the year to arrive at amore useful measure of firm performance (earnings).

The information in accounting earnings is credible, despite concerns ofearnings management.

In some cases, the accounting system provides new information to thecapital markets.

Evidence strongly suggests that stock prices are not fully efficient withrespect to accounting information.



11/12

Additional Notes: Deriving the Residual Income Model from the DDM

Recall that we can define dividends as follows:

Dividends1 = Net Income1 Change in Common Equity1 = NI1 (BVE1 BVE0)

Thus, we can express the value of the equity as follows (expectation operators areomitted for simplicity):

( ) ( )

...)1()1(

...)1()1()1()1()1()1(

...)1(

)1()1(

)1(

...)1()1(

...

)1()1(

...)1()1(

2 100

222

100

21100

2

111000

2

10

2

10

++

++

+=

++

++

+

+

++

+

+

+=

++

++++

++=

++

+++

+

++=

+

+

++

+

+=

++

++

=

e

e2

e

e1

e

2

e

2

e

e2

e

1

e

1

e

e1

e

e2e2

e

e1e1

e

e2e2

e

e1e1

e

22

e

11

e

22

e

11

0

r

BVErNI

r

BVErNIBVE

r

VEB

r

VEB

r

BVErNI

r

VEB

r

VEB

r

BVErNIBVE

rBVErVEB-BVErNI

rBVErVEB-BVErNI

r

BVErBVEVEB-BVErNI

r

BVErBVEVEB-BVErNI

r

BVEVEB-NI

r

BVEVEB-NI

r

BVE-VEB-NI

r

BVE-VEB-NIValue


Add and subtract reBVE0 (sum=0). We can thenrearrange to express value as a function ofbeginning BVE and future residual income.


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This works as long as

0)1(

lim 1 =+

T

e

T

T r

BVE

. But thanks to our steady state assumption,

BVEgrows at gin perpetuity, and g< (1+re).


new lecture 2 spring 09

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