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
[pic]
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
[pic]
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:
[pic]
• 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:
[pic]
• M= # of years growing at g1
[pic]
[pic]
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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
[pic]
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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