Equity Valuation

1

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

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Dividend discount model (DDM) P/E ratios approach

8-8

Suppose you are thinking of purchasing the stock of Moore Oil, Inc. and you expect it to pay a $2 dividend in one year and you believe that you can sell the stock for $14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay?◦ Compute the PV of the expected cash flows◦ Price = (14 + 2) / (1.2) = $13.33

8-9

Now what if you decide to hold the stock for two years? In addition to the dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year 2. Now how much would you be willing to pay?◦ PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)2 = 13.33

8-10

Finally, what if you decide to hold the stock for three years? In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 at the end of year 3 and the stock price is expected to be $15.435. Now how much would you be willing to pay?◦PV = 2 / 1.2 + 2.10 / (1.2)2 + (2.205 +

15.435) / (1.2)3 = 13.33

8-11

You could continue to push back when you would sell the stock

You would find that the price of the stock is really just the present value of all expected future dividends

So, how can we estimate all future dividend payments?

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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

8-13

Constant dividend◦The firm will pay a constant dividend forever◦This is like preferred stock◦The price is computed using the perpetuity

formula Constant dividend growth

◦The firm will increase the dividend by a constant percent every period

Supernormal growth◦Dividend growth is not consistent initially, but

settles down to constant growth eventually

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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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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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: Percentage of earnings paid out as dividends

Plowback (or Earning Retention) Ratio: Fraction of earnings retained and

reinvested in the firm

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%

Example, Company A, expected earning E1=5, k = 12.5% 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

PVGO = Present Value of Growth Opportunities

E1 = Earnings Per Share for period 1

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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?

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

Takeover Target is run by entrenched management that insists on reinvesting 60% of its earnings in projects that provide an ROE of 10% despite the fact that the firm’s required return k = 15%. The firm’s next year dividend = $2 per share, paid out of earnings of $5 per share. At what price should the firm sell? what is the present value of growth opportunities? Can we increase the firm’s value?

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)

Changing growth rates:

temporary high(or low) growth

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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?

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

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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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

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

Holding everything equal: High risk (k), Low P/E.

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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 StreetThe 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.

• 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

Price-to-book: price per share/book value per share◦ How 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

Discount the free cash flow for the firm Discount rate is the firm’s cost of

capital Components of free cash flow

◦After tax EBIT◦Depreciation◦Capital expenditures◦Increase in net working capital

In practice◦Values from these models may differ◦Analysts are always forced to make simplifying assumptions

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.

• 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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