Common Stock Valuation



Common Stock Valuation

Chapter 10

Fundamental Analysis Approaches

Present value approach

1 Capitalization of expected income

2 Intrinsic value based on the discounted value of the expected stream of cash flows

Multiple of earnings (P/E) approach

• Stock worth some multiple of its future earnings

Present Value Approach (Capitalization of Income)

Intrinsic value of a security is

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Ke = appropriate discount rate

In using model, to estimate the intrinsic value of the security must:

2 Discount rate (Capitalization Rate, Required Rate of Return)

1 Required rate of return: minimum expected rate to induce purchase given the level of risk

2 The opportunity cost of dollars used for investment

3 Expected cash flows and timing of cash flows

1 Stream of dividends or other cash payouts over the life of the investment

2 Dividends paid out of earnings and received by investors

1 Earnings important in valuing stocks

3 Retained earnings enhance future earnings and ultimately dividends

1 If use dividends in PV analysis, don’t use retained earnings in the model

• Retained earnings imply growth and future dividends

• Compared computed price to actual price

Dividend Discount Model

Current value of a share of stock is the discounted value of all future dividends

Problems:

1 Need infinite stream of dividends

1 Dividends received 40-50 years in the future are worth very little in present value with the discount rate is sufficiently high (12%, 14%, 16%)

2 Dividend stream is uncertain

• Dividends not guaranteed

• Declared by Board of Directors

1 Must estimate future dividends

3 Dividends may be expected to grow over time

• Must model expected growth rate of dividends and the growth rate need not be constant

Dividend Discount Model-Zero Growth

Assume no growth in dividends

Fixed dollar amount of dividends reduces the security to a perpetuity

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Kp = appropriate discount rate

Similar to preferred stock because dividend remains unchanged

Dividend Discount Model-Constant Growth-Gordon Model

Assumes a constant growth in dividends

Dividends expected to grow at a constant rate, g, over time

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where

• g: growth rate

• ke: required return

3 Ke > g

4 D1 is the expected dividend at end of the first period

5 D1 =D0 (1+g)

Implications of constant growth

1 Stock prices grow at the same rate as the dividends (g)

1 Problem: what if higher growth in price than dividends or visa versa

2 Stock total returns grow at the required rate of return

1 Growth rate in price plus growth rate in dividends equals k, the required rate of return

3 A lower required return or a higher expected growth in dividends raises prices

Reasons for Different Values of Same Stock

• Each investor may use their individual k

• Each investor has their own estimate of g

Dividend Discount Model-Multiple Growth

Multiple growth rates: two or more expected growth rates in dividends

1 Ultimately, growth rate must equal that of the economy as a whole

1 The company/industry is maturing and when it reaches maturity –grows at the rate of the economy

2 Assume growth at a rapid rate for n periods followed by steady growth

Multiple growth rates approach:

1 First present value covers the period of super-normal (or sub-normal) growth

2 Second present value covers the period of stable growth

1 Expected price uses constant-growth model as of the end of super- (sub-) normal period (time period m)

2 Value at m must be discounted to time period zero

Two Period Growth Model:

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• m = length of time firm grows at g1

• g2 < k

• g1: growth rate for period 1

• g2 : growth rate for period 2

• ke: required return

• Example: required rate of return =18% Current dividend is 2.00 dividends are expected to grow at 12% for first 6 years then at 6%

• Present value of First 6-Years' Dividends:

| | | | |

|Year |Dividend |P.V. Interest Factor |Present Value |

|t |Dt |PVIF18.t = 1/(1 + .18)t |Dt x PVIF18.t |

| | | | |

|1 |$ 2.240 |.874 |$ 1.897 |

| | | | |

|2 |2.509 |.718 |1.801 |

| | | | |

|3 |2.810 |.609 |1.711 |

| | | | |

|4 |3.147 |.516 |1.624 |

| | | | |

|5 |3.525 |.437 |1.540 |

| | | | |

|6 |3.948 |.370 |1.461 |

| | |

|PV (First 6-Years' Dividends |$10.034 |

• Value of Stock at End of Year 6:

• P6 = D7/(Ke - g2) where g2 = .06

• D7 = D6(1 + g2) = 3.948(1 + .06) = $4.185

• P6 = 4.185/(.18 - .06) = $34.875

• Present Value of P6

• PV(P6) = P6/(1 + ke)6 = $34.875/(1 + .18)6 = $34.875 x .370 = $12.904

• Value of Common Stock (Po)

• Po = PV(First 6-Year's Dividends) + PV(P6) = 10.034 + 12.904 = 22.94

• Example using the two period growth formulae:

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• M= # of years growing at g1

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What About Capital Gains?

Is the dividend discount model only capable of handling dividends?

1 Capital gains are also important

Price received in future reflects expectations of dividends from that point forward

1 Discounting dividends or a combination of dividends and price produces same results

No Dividend Model

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Intrinsic Value Implications

“Fair” value based on the capitalization of income process

1 The objective of fundamental analysis

If intrinsic value >( ................
................

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