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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 Assistants Ruchit Agarwal Manish Bhargava Odelia D’Mello David Wu
[email protected] [email protected] [email protected] [email protected]
For 01/27/08: Familiarize yourself with the 10-K for Cracker Barrel (CBRL). We will be applying all the tools we learn in class to CBRL. You can download the 10-K from the SEC Edgar website (http://www.sec.gov/edgar.shtml). Answer questions on handout regarding the Company’s industry, strategy, and accounting policies. Lecture 2
Page 1 of 12
Valuation Economic theory teaches that the value of any resources equals the present value of the payoffs expected from the resource, discounted at a rate compensating for the inherent risk & delayed consumption of the payoffs. The first financial model for common equity (and the basis for all models used today) is the dividend-discounting model:
∞ Dividends t + j Equity Valuet = Et ∑ j j =1 (1 + re )
Lecture 2
Page 2 of 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 repurchase of equity). Then, using the dividend-discounting model, we get the following (see last page of notes for a derivation): Residual Income is simply earnings less a charge for the use of capital
Equity Valuet = BVEt +
Et ( NI t + 1 - re BVEt ) Et ( NI t + 2 - re BVEt +1 ) + + ... (1 + re ) (1 + re ) 2
Thus, the residual income valuation model is very straightforward in theory. It simply states that the value of an investment is equal to the amount invested, plus the present value of all future abnormal earnings or residual income.
Lecture 2
Page 3 of 12
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:
Equity Valuet = BVEt +
Et [ ( ROEt +1 - re ) BVEt ] Et [ ( ROEt + 2 - re )( BVEt +1 ) ] + + ... (1 + re ) (1 + re ) 2
Thus, equity value is simply the book value of equity plus the present value of future abnormal returns on equity, weighted by the BVE outstanding at the time. Why focus on earnings and book values?
But, is the focus on accounting numbers justified?
Lecture 2
Page 4 of 12
Nichols and Wahlen (2004): How do accounting numbers relate to stock returns? Figure 1 The Three Links Relating Earnings to Stock Returns Link 1 Current Period Earnings
Link 1 assumes that current period earnings numbers provide information that equity shareholders can use to form expectations for future earnings.
Expected Future Earnings
Test: How do earnings numbers relate to share prices?
Link 2
Link 3 Current Share Price
Link 3 assumes that share prices reflect the present value of all expected future dividends.
Link 2 assumes that current and expected future profitability determines the firm’s expected future dividendpaying capacity.
Expected Future Dividends
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 change between those dates. Thus, it is important to isolate the new information in earnings when examining the association between earnings and returns.
To make sure the changes in price reflect revised expectations of payoffs and not just differences in risk, we subtract returns on a portfolio of firms with comparable size.
Lecture 2
Page 5 of 12
Testing the three links: The relation between earnings changes and stock returns Compare earnings this year (t) to earnings last year (t-1). If the change is positive, put the firm in one portfolio; if the change is negative, put the firm in another portfolio. Do the same thing for operating cash flows. The average abnormal returns of the portfolios are graphically depicted below.
Testing the three links,
continued: Sign and magnitude of earnings changes
Lecture 2
Page 6 of 12
Instead of forming portfolios on just the sign of the change, group firms into 10 portfolios based on the magnitude of earnings (scaled by assets to allow cross-sectional comparability).
Testing link 1: Earnings
persistence and stock returns If new earnings will persist, then the new earnings should have a greater effect on price.
Lecture 2
Page 7 of 12
Another test of the three links: Does accounting provide new information to market participants? Rank all firms based on the magnitude of their quarterly earnings surprise using analyst forecasts 5 days before the announcement as an expectation.
Lecture 2
Page 8 of 12
Is the market
completely efficient with respect to accounting information? Rank all firms based on the magnitude of their quarterly earnings surprise using analyst forecasts 60 days before the announcement as an expectation. Take a long position in the 10% of firms with the greatest unexpected earnings, and an offsetting short position in the 10% of firms with the lowest unexpected earnings. Hold these stocks for either 60 (trading) days.
Lecture 2
Page 9 of 12
Nichols and Wahlen (2004): Summary and Takeaways Accounting earnings capture many of the same events affecting firm value that are reflected in price.
The accrual accounting process starts with cash flows and adds information about transactions and events during the year to arrive at a more useful measure of firm performance (earnings).
The information in accounting earnings is credible, despite concerns of earnings management.
In some cases, the accounting system provides new information to the capital markets.
Evidence strongly suggests that stock prices are not fully efficient with respect to accounting information.
Lecture 2
Page 10 of 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 are omitted for simplicity):
Value0 = =
NI 1 - ( BVE1 - BVE0 ) NI 2 - ( BVE2 - BVE1 ) + + ... (1 + re ) (1 + re ) 2 NI 1 - BVE1 + BVE0 NI 2 - BVE2 + BVE1 + + ... (1 + re ) (1 + re ) 2 Add and subtract reBVE0 (sum=0). We can then rearrange to express value as a function of beginning BVE and future residual income.
Lecture 2
=
NI 1 − re BVE0 - BVE1 + BVE0 + re BVE0 NI 2 − re BVE1 - BVE2 + BVE1 + re BVE1 + + ... (1 + re ) (1 + re ) 2
=
NI 1 − re BVE0 - BVE1 + (1 + re ) BVE0 NI 2 − re BVE1 - BVE2 + (1 + re ) BVE1 + + ... (1 + re ) (1 + re ) 2
= BVE0 +
NI 1 − re BVE0 BVE1 BVE1 NI 2 − re BVE1 BVE2 BVE2 − + + − + + ... (1 + re ) (1 + re ) (1 + re ) (1 + re ) 2 (1 + re ) 2 (1 + re ) 2
= BVE0 +
NI 1 − re BVE0 NI 2 − re BVE1 + + ... (1 + re ) (1 + re ) 2
Page 11 of 12
This works as long as
. But thanks to our steady state assumption, BVET −1 =0 T → ∞ (1 + r )T e lim
BVE grows at g in perpetuity, and g < (1+re).
Lecture 2
Page 12 of 12
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 Assistants Ruchit Agarwal Manish Bhargava Odelia D’Mello David Wu
[email protected] [email protected] [email protected] [email protected]
For 01/27/08: Familiarize yourself with the 10-K for Cracker Barrel (CBRL). We will be applying all the tools we learn in class to CBRL. You can download the 10-K from the SEC Edgar website (http://www.sec.gov/edgar.shtml). Answer questions on handout regarding the Company’s industry, strategy, and accounting policies. Lecture 2
Page 1 of 12
Valuation Economic theory teaches that the value of any resources equals the present value of the payoffs expected from the resource, discounted at a rate compensating for the inherent risk & delayed consumption of the payoffs. The first financial model for common equity (and the basis for all models used today) is the dividend-discounting model:
∞ Dividends t + j Equity Valuet = Et ∑ j j =1 (1 + re )
Lecture 2
Page 2 of 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 repurchase of equity). Then, using the dividend-discounting model, we get the following (see last page of notes for a derivation): Residual Income is simply earnings less a charge for the use of capital
Equity Valuet = BVEt +
Et ( NI t + 1 - re BVEt ) Et ( NI t + 2 - re BVEt +1 ) + + ... (1 + re ) (1 + re ) 2
Thus, the residual income valuation model is very straightforward in theory. It simply states that the value of an investment is equal to the amount invested, plus the present value of all future abnormal earnings or residual income.
Lecture 2
Page 3 of 12
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:
Equity Valuet = BVEt +
Et [ ( ROEt +1 - re ) BVEt ] Et [ ( ROEt + 2 - re )( BVEt +1 ) ] + + ... (1 + re ) (1 + re ) 2
Thus, equity value is simply the book value of equity plus the present value of future abnormal returns on equity, weighted by the BVE outstanding at the time. Why focus on earnings and book values?
But, is the focus on accounting numbers justified?
Lecture 2
Page 4 of 12
Nichols and Wahlen (2004): How do accounting numbers relate to stock returns? Figure 1 The Three Links Relating Earnings to Stock Returns Link 1 Current Period Earnings
Link 1 assumes that current period earnings numbers provide information that equity shareholders can use to form expectations for future earnings.
Expected Future Earnings
Test: How do earnings numbers relate to share prices?
Link 2
Link 3 Current Share Price
Link 3 assumes that share prices reflect the present value of all expected future dividends.
Link 2 assumes that current and expected future profitability determines the firm’s expected future dividendpaying capacity.
Expected Future Dividends
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 change between those dates. Thus, it is important to isolate the new information in earnings when examining the association between earnings and returns.
To make sure the changes in price reflect revised expectations of payoffs and not just differences in risk, we subtract returns on a portfolio of firms with comparable size.
Lecture 2
Page 5 of 12
Testing the three links: The relation between earnings changes and stock returns Compare earnings this year (t) to earnings last year (t-1). If the change is positive, put the firm in one portfolio; if the change is negative, put the firm in another portfolio. Do the same thing for operating cash flows. The average abnormal returns of the portfolios are graphically depicted below.
Testing the three links,
continued: Sign and magnitude of earnings changes
Lecture 2
Page 6 of 12
Instead of forming portfolios on just the sign of the change, group firms into 10 portfolios based on the magnitude of earnings (scaled by assets to allow cross-sectional comparability).
Testing link 1: Earnings
persistence and stock returns If new earnings will persist, then the new earnings should have a greater effect on price.
Lecture 2
Page 7 of 12
Another test of the three links: Does accounting provide new information to market participants? Rank all firms based on the magnitude of their quarterly earnings surprise using analyst forecasts 5 days before the announcement as an expectation.
Lecture 2
Page 8 of 12
Is the market
completely efficient with respect to accounting information? Rank all firms based on the magnitude of their quarterly earnings surprise using analyst forecasts 60 days before the announcement as an expectation. Take a long position in the 10% of firms with the greatest unexpected earnings, and an offsetting short position in the 10% of firms with the lowest unexpected earnings. Hold these stocks for either 60 (trading) days.
Lecture 2
Page 9 of 12
Nichols and Wahlen (2004): Summary and Takeaways Accounting earnings capture many of the same events affecting firm value that are reflected in price.
The accrual accounting process starts with cash flows and adds information about transactions and events during the year to arrive at a more useful measure of firm performance (earnings).
The information in accounting earnings is credible, despite concerns of earnings management.
In some cases, the accounting system provides new information to the capital markets.
Evidence strongly suggests that stock prices are not fully efficient with respect to accounting information.
Lecture 2
Page 10 of 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 are omitted for simplicity):
Value0 = =
NI 1 - ( BVE1 - BVE0 ) NI 2 - ( BVE2 - BVE1 ) + + ... (1 + re ) (1 + re ) 2 NI 1 - BVE1 + BVE0 NI 2 - BVE2 + BVE1 + + ... (1 + re ) (1 + re ) 2 Add and subtract reBVE0 (sum=0). We can then rearrange to express value as a function of beginning BVE and future residual income.
Lecture 2
=
NI 1 − re BVE0 - BVE1 + BVE0 + re BVE0 NI 2 − re BVE1 - BVE2 + BVE1 + re BVE1 + + ... (1 + re ) (1 + re ) 2
=
NI 1 − re BVE0 - BVE1 + (1 + re ) BVE0 NI 2 − re BVE1 - BVE2 + (1 + re ) BVE1 + + ... (1 + re ) (1 + re ) 2
= BVE0 +
NI 1 − re BVE0 BVE1 BVE1 NI 2 − re BVE1 BVE2 BVE2 − + + − + + ... (1 + re ) (1 + re ) (1 + re ) (1 + re ) 2 (1 + re ) 2 (1 + re ) 2
= BVE0 +
NI 1 − re BVE0 NI 2 − re BVE1 + + ... (1 + re ) (1 + re ) 2
Page 11 of 12
This works as long as
. But thanks to our steady state assumption, BVET −1 =0 T → ∞ (1 + r )T e lim
BVE grows at g in perpetuity, and g < (1+re).
Lecture 2
Page 12 of 12
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