Theory of Stock Valuation

Same theory as bond valuation Find PV of future cash flows Use investor’s required rate of return as

the discount rate in finding PV

Cash Flows from Owning Stock

Dividends Capital gain (loss) from selling at a

higher (lower) price than you paid for the stock

Difficulties in Valuing Stock

1) Future cash flows not known 2) Stock has no maturity - infinite life of

corporation 3) No way to easily observe the rate of

return that the market requires

Stock Valuation Symbols

D = dividend Subscript tells when dividend is expected to

be paid/received P = price Subscript tells when price is expected to be

paid/received

Kc = investor’s required rate of return

Example 1

D1 = $1.00

D2 = $1.25

D3 = $1.50

P3 = $50 If you require a 10% rate of return, what

is the most you will pay for this stock?

Using Financial Calculator

Sum PVs to get -40.63$40.63 is max price you are willing to pay for

this stock if you require a 10% rate of return.Pay more than $40.63 → Return < 10%Pay less than $40.63 → Return > 10%

P/Y C/Y N I/Y PV PMT FV

1 1 1 10 -.9090 0 1.00

1 1 2 10 -1.033 0 1.25

1 1 3 10 -1.127 0 1.50

1 1 3 10 -37.57 0 50.00

BUT…future stock cash flows are not known with certainty Future dividends aren’t known with

certainty Dividends may be estimated, but it will

only be an estimate Future selling price isn’t known with

certainty How to overcome these problems?

Future Selling Price

Can prove mathematically that it doesn’t matter that we don’t know what we can sell a stock for in the future

Need to use mathematical formula for finding PV to prove this point

Mathematical Formula for Finding PV

PV = FV x (1+i)-n

PV = 1.00(1.10)-1 + 1.25(1.10)-2 + 1.50(1.10)-3 + 50(1.10)-3

P0 = $40.63 (same answer as we got using a financial calculator)

Theoretical Determination of Future Selling Price The future selling price (Pn) is based on what

the next investor will pay for the stock. The next investor is valuing the stock based

on the present value of his/her expected future dividends and future selling price.

The next investor follows the same process, etc., etc., etc.

Since stock never matures, the actual determination of the next selling price can be put off indefinitely.

If the actual determination of the future selling price is pushed far enough out into the future, its present value will eventually approach zero.

With PV of future selling price dropping off to zero, value of stock becomes the PV of its dividend stream.

The question now becomes, how can you find the PV of an unending stream of dividends?

Can do it if you make assumptions about how dividends grow from year to year.

Constant Dividend (No Growth)

P0 = Dp/Kp

P0 = Intrinsic value = Price today

Dp = Preferred Dividend (fixed amount, doesn’t change)

Kp = Required rate of return on P/S Preferred stock is an example where

the dividend is constant

Example 2

If you require a 12% rate of return, what is the maximum price you will pay for a share of preferred stock that pays a $1.25 annual dividend?

P0 = $1.25/.12 = $10.42

Dividends Growing at a Constant Growth Rate

P0 = D1/(Kc - g)

P0 = Intrinsic value = Price today

D1 = Dividend expected 1 year from now

D1 = Last dividend paid x (1 + g)

Kc = Required rate of return g = Constant annual dividend growth rate

Example 3

How much would you pay for a share of common stock if the last dividend paid was $2.00 per share, dividends are expected to grow at a constant annual rate of 5%, and you require a 10% rate of return?

P0 = ($2 x 1.05)/(.10 - .05) = $42

What if a company isn’t paying dividends? Just because a company is not

currently paying dividends doesn’t mean that they never plan to.

Estimate when first dividend will be paid and at what rate dividends will grow.

Find price for year prior to first dividend. Discount future price back to present.

Example 4

You estimate that a company that is not currently paying dividends will pay a $5 dividend per share at the end of 5 years and that dividends will grow at a constant annual rate of 8% thereafter. If you require a 12% rate of return, what is the maximum price you will pay for the stock today?

P4 = D5/Kc-g

P4 = $5/(.12-.08) = $125

P0 = P4(1 + Kc)-4

P0 = $125(1+.12)-4 = $79.44 maximum price you are willing to pay today

Valuing Non-public Corporations

Twitter article

Estimate total revenue # users = 250 M by 2013 Revenue per user = $2 by 2013 250 M * $2 = $500 M total rev by 2013

Borrow ratios from comparable firm Google’s profit margin = .27 and

Google’s PE = 20 .27 * $500 M = $135 M profit $135 * 20 = $2.7 B total value (as

measured by price * # shares)

Discount future value back to present Use 20% as appropriate rate for small,

risky, high growth company N = 4; I/Y = 20; PMT = 0; FV = $2.7B PV = $1.3 Billion estimated value for

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