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### Chapter 18

Models of Equity Valuation

- Basic Types of Models
- Balance Sheet Models
- Dividend Discount Models
- Price/Earning Ratios

- Estimating Growth Rates and Opportunities

Intrinsic Value and Market Price

- Intrinsic Value
- Self assigned Value
- Variety of models are used for estimation

- Market Price
- Consensus value of all potential traders

- Trading Signal
- IV > MP Buy
- IV < MP Sell or Short Sell
- IV = MP Hold or Fairly Priced

No Growth Model

Stocks that have earnings and dividends that are expected to remain constant.

Preferred Stock

Constant Growth Model

g = constant perpetual growth rate

Constant Growth Model: Example

E1 = $5.00 b = 40% k = 15%

(1-b) = 60% D1 = $3.00 g = 8%

V0 = 3.00 / (.15 - .08) = $42.86

Estimating Dividend Growth Rates

g = growth rate in dividends

ROE = Return on Equity for the firm

b = plowback or retention percentage rate

(1- dividend payout percentage rate)

Specified Holding Period Model

PN = the expected sales price for the stock at time N

N = the specified number of years the stock is expected to be held

Growth & No Growth Components of Value

PVGO = Present Value of Growth Opportunities

E1 = Earnings Per Share for period 1

Partitioning Value: Example

ROE = 20% d = 60% b = 40%

E1 = $5.00 D1 = $3.00 k = 15%

g = .20 x .40 = .08 or 8%

Vo = value with growth

NGVo = no growth component value

PVGO = Present Value of Growth Opportunities

Price Earnings Ratios

- P/E Ratios are a function of two factors
- Required Rates of Return (k)
- Expected growth in Dividends

- Uses
- Relative valuation
- Extensive Use in industry

P/E Ratio: No Expected Growth

- E1 - expected earnings for next year
- E1 is equal to D1 under no growth

- k - required rate of return

Numerical Example: No Growth

E0 = $2.50 g = 0 k = 12.5%

P0 = D/k = $2.50/.125 = $20.00

PE = 1/k = 1/.125 = 8

Numerical Example with Growth

b = 60% ROE = 15% (1-b) = 40%

E1 = $2.50 (1 + (.6)(.15)) = $2.73

D1 = $2.73 (1-.6) = $1.09

k = 12.5% g = 9%

P0 = 1.09/(.125-.09) = $31.14

PE = 31.14/2.73 = 11.4

PE = (1 - .60) / (.125 - .09) = 11.4

Pitfalls in P/E Analysis

- Use of accounting earnings
- Historical costs
- May not reflect economic earnings

- Reported earnings fluctuate around the business cycle.

Other Valuation Ratios

- Price-to-Book
- Price-to-Cash Flow
- Price-to-Sales

Inflation and Equity Valuation

- Inflation has an impact on equity valuations.
- Historical costs underestimate economic costs.
- Empirical research shows that inflation has an adverse effect on equity values.
- Research shows that real rates of return are lower with high rates of inflation.

Lower Equity Values with Inflation

- Shocks cause expectation of lower earnings by market participants.
- Returns are viewed as being riskier with higher rates of inflation.
- Real dividends are lower because of taxes.

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