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Equity Valuation

CHAPTER 12

Exam 2

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Fundamental analysis

Identify stocks that are mispriced relative to true value Compare the actual market price and the true price estimated

from various models using publicly available information The true price estimated from models is the intrinsic value

(IV) Market price (MP): consensus value of all potential trades

(buyers and sellers) Trading signal

IV > MP: underpriced, buy IV < MP: overpriced, sell IV = MP: fairly priced, hold

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• If estimated E(r) > Required Return, the stock is undervalued.

• If estimated E(r) < required return, the stock is overvalued

• required return is from a pricing model, e.g. CAPM:

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Determine underpriced/overpriced stocks (calculate alpha)

Determine underpriced/overpriced stocks (calculate alpha) example: stock ABC, the current price Po = 48, expected price

in 1 year E(P1) = 52, expected dividend in 1 year E(D1) = 4 rf = 6, RPm = 5, beta = 1.2 Is this stock overpriced or underpriced? Step 1: calculate the estimated expected return

estimated E(R) = (52+4-48)/48 = 16.7% Step 2: calculate required return from CAPM

required E(R) = 6 + 1.2(5) = 12 Step 3: calculate alpha

alpha = 16.7 – 12 = 4.7 > 0 stock is undervalued

•V0 (intrinsic value) > P0 (market price) buy (undervalued)

•V0 (intrinsic value) < P0 (market price) sell or sell short (overvalued)

•In market equilibrium, V0 = P0 (fairly priced)

•k is required return

Intrinsic value --The present value of a firm’s expected future net cash flows discounted by the required rate of return.

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Determine underpriced/overpriced stocks (calculate intrinsic value)

Determine underpriced/overpriced stocks (calculate intrinsic value) Previous example

Vo = 50 > Po = 48, the current market price is undervalued compared with the intrinsic value

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Estimate intrinsic value

Dividend discount model (DDM) P/E ratios approach

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Dividend discount model (infinite horizon):the intrinsic value is the present value of all futures dividends discounted by the required return

Dividend discount model (DDM)

Dividend discount model (DDM)

No growth model: The same amount of dividend every year (perpetuity)

Example: a preferred stock, D = 5, required return k = 15%. What is the value of this stock Vo = 5/.15 = 33.33

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Dividend discount model (DDM): constant growth rate

Constant growth model: dividend grows at a constant rate g

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Dividend discount model (DDM): constant growth rate

Example 1: stock ABC, next year dividend = 3, required return k = 15%, constant growth rate = 8%. What is the value of the stock

Example 2: stock ABC, just paid dividend = 0.50, required return k = 15%, constant growth rate = 2%. What is the value of the stock

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• If expected dividend D1 increases, then V0 increases.

• If k decreases, then V0 increases.

• If g increases, then V0 increases.

• Price grows at the same rate as dividend

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Implications of constant growth DDM

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Implications of constant growth DDM

Required return k:

In equilibrium, the intrinsic value = market price i.e. Vo = Po, therefore,

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DividendYield

CapitalGains Yield

Estimate growth rate g

Company A: 2 scenarios No investment opportunities: the expected return of all projects in the

company < required return k. In this case, the company would choose to pay 100% of the earning as dividends and let the stockholders invest in the market by themselves

Has investment opportunities: if the company has investment opportunity, expected return of projects is higher than required return k, then the company would choose low dividend payout policy, (a smaller fraction of earning goes to dividend) say

40% dividend (dividend payout ratio) 60% retained earning to be used for reinvestment (plow-back ratio or

earning retention ratio)

Dividend Payout Ratio and Plowback Ratio

Dividend Payout Ratio: Percentage of earnings paid out as dividends

Plowback (or Earning Retention) Ratio:

Fraction of earnings retained and reinvested in the firm

Estimate growth rate g

Company A, total asset 100 mil, all equity financed. ROE = 15%.

Total earning = 15% (100) = 15 mil If 60% of earning is reinvested, new additional capital is

60%(15) = 9 mil Old capital = 100, new capital = 9, total capital = 109 Growth rate g is the growth rate in value of capital (stock)

g = (109-100)/100 = 9%

g b ROE

Where:

ROE = Return on Equityb = Plowback Ratio (or Earning Retention Ratio) Example: g = 15% (0.6) = 9%

Plowback Ratio and GrowthPlowback Ratio and Growth

Partitioning value

Example, Company A, expected earning E1=5

No growth: pay all earnings as dividend, D = 5 With growth: ROE = 15%, b = 0.6 so g = ? No growth: P*0= E1/k = D/k = 40

with growth: P0 = D1/(k-g) = 5(.4)/(0.15-0.125) = 57.14

Why the price with growth is higher than the price with no growth?

Price (with growth) = P*0 (no growth) + PVGO (present value of growth opportunities)

PVGO is reward to growth opportunities 57.14 = 40 + 17.14

Partitioning Value: Growth and No Growth Components

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PVGO = Present Value of Growth Opportunities

E1 = Earnings Per Share for period 1

Example: Takeover Target has a dividend payout ratio of 60% and an ROE of 20%. If it expects earnings to be $ 5 per share, the appropriate capitalization rate is 15%? What is the intrinsic value, what is PVGO, what is NGVo?

Partitioning Value: Growth and No Growth Components

Partitioning Value: Example ROE = 20% d = 60% b = 40%

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

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

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Partitioning Value: ExamplePartitioning Value: Example

VVoo = value with growth = value with growth

NGVNGVoo = no growth component value = no growth component value

PVGO = Present Value of Growth OpportunitiesPVGO = Present Value of Growth Opportunities

Shifting growth rate model (multistage growth model)

In constant growth DDM, g is constant over time In practice, there are some periods g is high (when more

investment opportunities), some periods g is low (when less investment opportunities)

Shifting growth rate model (multistage growth model)

Shifting growth rate model (multistage growth model)

Changing growth rates:

temporary high(or low) growth

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Shifting growth rate model (multistage growth model)

Example: Whitewater Rapids Company is expected to have dividends grow at a rate of 20% for the next three years. In three years, the dividends will settle down to a more sustainable growth rate of 5% which is expected to last “forever.” If Whitewater just paid a dividend of $2.00 and its level of risk requires a discount rate of 15%, what is the intrinsic value of Whitewater stock?

Shifting growth rate model (multistage growth model) Compute the dividends until growth levels off

D1 = 2(1.2) = $2.40

D2 = 2.4(1.2) = $2.88

D3 = 2.88(1.2) = $3.46

Find the expected future price at the year growth leves off P3 = D3(1+g) / (k – g) = 3.46(1.05) / (.15 - .05) = 36.3

Find the intrinsic value which is the present value of the all expected future cash flows V0 = 2.4 / (1.15) + (2.88) / (1.15)2 + (3.46) / (1.15)3

+ (36.3) / (1.15)3 = 30.40

Price-Earning (P/E) Ratios

Ratio of Stock price to its earnings per share Useful for firm valuation:

in practice Forecasts of E Forecasts of P/E

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Price-Earning (P/E) Ratios and growth

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P/E Ratio with Constant Growth

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Price-Earning (P/E) Ratio

Plowback ratio (b) (k = 12%)0 0.25 0.50 0.75

A. Growth rate gROE10 0 2.5 5 7.512 0 3 6 914 0 3.5 7 10.5B. P/E ratioROE10 8.33 7.89 7.14 5.5612 8.33 8.33 8.33 8.3314 8.33 8.82 10.00 16.67

Some comments with P/E Ratios

High plowback ratio (b) High Growth Rate (g) (g = ROE*b)

BUT

High g (if due to high b) High P/E ratio

higher b higher P/E only when ROE > k

P/E ratio and Risk

Holding everything equal:

High risk (k), Low P/E.

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P/E ratios in practice

P/E ratio proxies for expected growth in dividends or earnings. If the stock is correctly priced, the rule of thumb is

P/E ≈ g or PEG ≈ 1 PEG > 1 then overpriced PEG < 1 then underpriced PEG: no theoretical explanation but works very well

Peter Lynch, the famous portfolio manager, said in this book One Up on Wall Street

The P/E ratio of any company that is fairly priced will equal its growth rate. I am talking here about growth rate of earnings.... If the P/E ratio of Coca-Cola is 15, you’d expect the company to be growing at 15% per year, etc. But if the P/E ratio is less than the growth rate, you may have found yourself a bargain.

Pitfalls in P/E AnalysisPitfalls in P/E Analysis

• Earnings are based on accounting data

Current price and current earnings

Future expected earnings is more appropriate

• In P/E formula, E is an expected trend

• In financial pages, E is the actual past period's earnings• Different accounting methods will give different earnings

Other Valuation Ratios & Approaches

Price-to-book: price per share/book value per shareHow aggressively the market values the firm

Price-to-cash flow: price per share/cash flow per share Price-to-sales: price per share/sales per share

Some start-up firms do not have earnings so sale is more appropriate. Be creative: depending on particular situation to design your own ratio

16. J anet Ludlow’s firm requires all its analysts to use a two-stage DDM and the CAPM to value stocks. Using these measures, Ludlow has valued QuickBrush Company at $63 per share. She now must value SmileWhite Corporation.

a. Calculate the required rate of return for SmileWhite using the information in the following table:

(K)

b. Ludlow estimates the following EPS and dividend growth rates for SmileWhite:

(K)

Estimate the intrinsic value of SmileWhite using the table above, and the two-stage DDM. Dividends per share in 2007 were $1.72.

c. Recommend QuickBrush or SmileWhite stock for purchase by comparing each company’s intrinsic value with its current market price.

d. Describe one strength of the two-stage DDM in comparison with the constant growth DDM. Describe one weakness inherent in all DDMs.

SummarySummary

• Valuation approaches:-Balance sheet values (P/E ratio)-Present value of expected future dividends

• DDM states that the price of a share of stock is equal to the present value of all future dividends discounted at the appropriate required rate of return

• Constant growth model DDM:

• P/E ratio is an indication of the firm's future growth opportunities

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