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### Valuation

Curriculum designed for use with the Iowa Electronic Markets

by

Roger Ignatius

Thomas A. Rietz

Valuation: Lecture Outline

- Principles of Valuation
- Discounted Dividend Models
- Constant Dividend Model
- Constant Growth Model

- Discounted Cash flow Model
- Market Multiple Models
- P/E versus Past and Peers
- P/S versus Past and Peers
- P/CF versus Past and Peers

- Summary

Principles of Valuation

- Book Value
- Depreciated value of assets minus outstanding liabilities

- Liquidation Value
- Amount that would be raised if all assets were sold independently

- Market Value (P)
- Value according to market price of outstanding stock

- Intrinsic Value (V)
- NPV of future cash flows (discounted at investors’ required rate of return)

Intrinsic Valuation Procedure

- Asset Characteristics
- Size of Future Cash flows
- Time of Future Cash flows
- Risk of Future Cash flows

- Investor Characteristics
- Assessment of Cash flow Riskiness
- Risk Preferences

Investors’ Required Rate of Return (k)

Where Does the Discount Rate (k) Come From?

- CAPM: k = rf + bxRP
- Beta (b) is estimated using historical data and is available from many sources
- The risk free rate (rf) is the current Treasury rate
- Typically the 3-mo rate, but other are sometimes used

- The risk premium (RP) is a historical average relative to the rf used

Example: Estimating k for Wal-Mart (WMT) on 4/27/01

- Inputs
- Three month Treasury rate: 3.75%
- Historical average RP (1926-1996): 8.74%
- Beta for Dell (from MoneyCentral): 0.9

- Computing k:
- CAPM: k = 0.0375 + 0.9x0.0874 = 11.62%

Discounted Dividend Models

- Dividends will be
- Forecast directly
- Assumed to be constant
- Assumed to grow at a constant rate or
- Some combination of the above

- Stock pricing relationship:

Constant Dividend (Zero Growth Model) Model

- If Dt is constant, then it is an ordinary perpetuity:

- Stock pricing relationship:

Example: Wal-Mart (4/27/01)

- The price of Wal-Mart was actually $52.83
- Can you explain the difference?

- The current (annual) dividend is: $0.28
- According to the constant dividend (zero growth) model:

Why do a firm’s dividends grow?

- Because earnings grow. Why?
- Because of reinvested funds
- Used to expand or to undertake new projects
- Used in positive NPV projects

- Leads to
- Earnings growth
- Investments growth and
- Dividend growth

Constant Growth Model

- If Dt grows at a constant rate, g, then it is a growth perpetuity:

- Stock pricing relationship:

How do You Estimate Growth (g)?

- NOTE: Must have g<k in the long run!

- Historical average
- Average analyst forecast
- Sustainable growth
- g = (1-Payout Ratio)xROE

- Required return versus dividend yield:

Estimating g for Wal-Mart (4/27/01)

- What should it be?
- 1st 3 are too high b/c long run must have g<k
- Guess: 11%?

- 5 year historical average: 19.72%
- Average 5-year analyst forecast: 14.4%
- Sustainable growth
- g = (1-0.17)x0.22 = 18.26%

- Required return versus dividend yield:

Example: Wal-Mart (4/27/01)

- The price of Wal-Mart was actually $52.83
- Notes:
- Must have g<k in long run
- As gk, the price increases without bound

- Current (annual) dividend is: $0.28
- If we use estimated growth of 11%:

Summary of Dividend Discount Models

- Represents the value of dividends received by shareholders
- Requires
- A discount rate (k)
- Dividends (D)
- Steady or zero growth (g, with g<k)

- Trouble valuing
- Companies with D=0
- Fast growing companies with g>k

Discounted Cash Flow Model

- Shareholders receive or “own”:
- Dividends
- Re-invested earnings
- The effects of re-invested earnings are captured in dividend growth if a firm pays dividends and growth can be estimated

- An alternative valuation comes from valuing cash flows available to stockholders directly
- Useful for companies that pay no dividends

What Constitutes Cash flows?

- There is some debate over exactly what constitutes cash flows
- The GAAP cash flow statement:
- CF = NI + depreciation – preferred stock dividends
- This should represent CFs that are either
- Paid out in common stock dividends or
- Re-invested

What Discount Rate Should be used?

- It depends on the definition of CFs
- If CFs are defined as those available to all investors, WACC should be used
- If CFs are defined as those available to common stockholders, k from CAPM should be used

- We will use the latter

Example: Estimating k for K-Mart (K) on 4/27/01

- Inputs
- Three month Treasury rate: 3.75%
- Historical average RP (1926-1996): 8.74%
- Beta for K-Mart (from MoneyCentral): 1

- Computing k:
- CAPM: k = 0.0375 + 1x0.0874 = 12.49%

How do You Estimate Growth (g)?

- CFs will also grow
- Use methods similar to dividend growth, but
- Analysts forecasts are typically unavailable
- For many companies, dividend yield cannot be used b/c there is no dividend

- Often, earnings or sales growth are used
- Expenses and re-investment need to be relatively constant percentages of sales

- NOTE: Must have g<k in the long run!

Estimating g for K-Mart (4/27/01)

- 5 year sales growth: 2.35%
- Analysts’ 5 year earnings forecast: 10.3%
- Suppose, you believe K-Mart will not grow at all!

- From the historical income statement:

Example: K-Mart (4/27/01)

- The price of K-Mart was actually $9.82
- What must the market be expecting for K-Mart’s growth in the future?

- According to the last statements:
- CF = $1,216 million
- Shares = 486.5 million
CF/Share = $2.50

- If we use estimated growth of 0.0%:

Summary of Discounted Cash flow Models

- Represents the value of cash flows available to shareholders
- Requires
- A discount rate (k)
- A reasonable measure of cash flows
- IMPORTANT: How much depreciation MUST be replaced ? Model assumes zero.

- Steady or zero growth (g, with g<k)

- Trouble valuing
- Companies with CF<0
- Fast growing companies with g>k
- Companies with necessary replacement of depreciated assets

Market Multiples

- Valuations are derived by:
- Forecasting earnings, sales or cash flows
- Applying the company’s historical P/E, P/S or P/CF to forecast
- Applying industry average P/E, P/S or P/CF to current inputs

Why do P/E Ratios Make Sense?

- A company with a payout less than 1 will grow and be valued at:

- A company with a payout ratio of 1 will not grow and be valued at:

Logic of Market Multiple Models

- Sales, earnings and cash flow drive profits, growth and value
- P/S, P/E & P/CF ratios show the relationship between price and these value drivers
- Firms within an industry have similar sales, profit and cash flow patterns and similar required returns
- Therefore, a reasonable value for a firm is its sales, earnings or cash flows times the respective industry ratio

P/E Ratio Valuation

- If company “j” is “valued at industry ratios” relative to earnings:

- If company “j” is “valued at historical ratios” relative to earnings:

Example: Wal-Mart (4/27/01)

- Valued at historical P/E ratio:
- Analysts forecast next year’s earnings for WMT at $1.58
- WMT’s recent P/E was 37.7
- Then: P = $1.58x37.7 = $59.57

- Valued at industry average P/E ratio:
- This year, earnings for WMT were $1.40
- The industry average P/E was 36.0
- Then: P = $1.40x36.0 = $50.40

- The price of Wal-Mart was actually $52.83

P/S Ratio Valuation

- Using current sales, a company “j” is “valued at industry ratios” relative to sales:

- For companies w/o earnings, P/S is sometimes used
- If you have a sales forecast, company “j” is “valued at historical ratios” relative to sales:

Example: Amazon (4/27/01)

- For the year ending 12/00
- Sales = 2,762 million (income statement)
- Shares = 357.1 million (balance sheet)
Sales/Share = 2762/357.1 = 7.73

- Industry average P/S = 3.46
- So, using industry P/S Amazon should be priced at: 3.46x7.73 = $26.76
- The price of Amazon was actually $15.27

P/CF Ratio Valuation

- Using current cash flow, company “j” is “valued at industry ratios” relative to cash flows:

- For companies w/o dividends, P/CF is sometimes used
- If you have a cash flow forecast, company “j” is “valued at historical ratios” relative to cash flows:

Example: K-Mart (4/27/01)

- For the year ending 12/00
- CF = 1,216 million (discussed previously)
- Shares = 486.5 million (balance sheet)
CF/Share = 1216/486.51 = 2.50

- Industry average P/CF = 21.3
- Using industry P/CF K-Mart should be priced at: 21.3x2.50 = $53.24
- The price of K-Mart was actually $9.82
- Is K-Mart undervalued or in serious trouble?

Summary of Market Multiples Models

- Valuations using historical and industry ratios
- Provide useful benchmarks
- Useful when dividends and cash flows cannot be discounted directly
- Can be compared to current ratios as a measure of market sentiment

- Weaknesses
- Misleading for firms that are changing rapidly or do not resemble the industry

w/ dividends and constant expected (possibly zero) growth in dividends

Discounted Cash flow

w/o dividends and constant expected (possibly zero) growth in cash flows

P/E, P/S and P/CF ratios

Comparison with past or industry

Why several methods?

Each has strengths and weaknesses

Different methods useful in different situations

Each gives a different “take” on the value of the company’s stock

Provides a range of valuations instead of point estimates

Summary
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