Theory of Stock Valuation

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Theory of Stock Valuation

• Same theory as bond valuation
• Find PV of future cash flows
• Use investors required rate of return as the
  discount rate in finding PV

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Cash Flows from Owning Stock

• Dividends
• Capital gain (loss) from selling at a higher
  (lower) price than you paid for the stock

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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

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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 investors required rate of return

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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?

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Using Financial Calculator
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

• 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 lt 10
• Pay less than 40.63 ? Return gt 10

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BUTfuture stock cash flows are not known with
certainty

• Future dividends arent known with certainty
• Dividends may be estimated, but it will only be
  an estimate
• Future selling price isnt known with certainty
• How to overcome these problems?

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Future Selling Price

• Can prove mathematically that it doesnt matter
  that we dont know what we can sell a stock for
  in the future
• Need to use mathematical formula for finding PV
  to prove this point

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Mathematical Formula for Finding PV

• PV FV x (1i)-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)

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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.

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• 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.

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• 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.

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Constant Dividend (No Growth)

• P0 Dp/Kp
• P0 Intrinsic value Price today
• Dp Preferred Dividend (fixed amount, doesnt
  change)
• Kp Required rate of return on P/S
• Preferred stock is an example where the dividend
  is constant

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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

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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

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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

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What if a company isnt paying dividends?

• Just because a company is not currently paying
  dividends doesnt 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.

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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?

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• 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

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Valuing Non-public Corporations

• Twitter article

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• Estimate total revenue
• users 250 M by 2013
• Revenue per user 2 by 2013
• 250 M 2 500 M total rev by 2013

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• Borrow ratios from comparable firm
• Googles profit margin .27 and Googles PE 20
• .27 500 M 135 M profit
• 135 20 2.7 B total value (as measured by
  price shares)

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• 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 Twitter