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
K c
= investor’s required rate of return

Example 1
 D
1
= $1.00
 D
2
= $1.25
 D
3
= $1.50
 P
3
= $50
 If you require a 10% rate of return, what is the most you will pay for this stock?

Using Financial Calculator
P/Y C/Y N I/Y PV PMT FV
1
1
1
1
1
1
1
1
3
3
1
2
10
10
10
10
-.9090
0
-1.033
0
-1.127
0
-37.57
0
1.00
1.25
1.50
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 < 10%
Pay less than $40.63 → Return > 10%

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
 P
0
= $40.63 (same answer as we got using a financial calculator)

Theoretical Determination of
Future Selling Price
 The future selling price (P n
) 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)
P
0
= D p
/K p
 P
0
= Intrinsic value = Price today
 D p
= Preferred Dividend (fixed amount, doesn’t change)
 K p
= 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?
 P
0
= $1.25/.12 = $10.42

Dividends Growing at a Constant
Growth Rate
P
0
= D
1
/(K c
- g)
 P
0
= Intrinsic value = Price today
 D
1
= Dividend expected 1 year from now
 D
1
= Last dividend paid x (1 + g)
 K c
= 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?
 P
0
= ($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?

 P
4
= D
5
/K c
-g



P
4
= $5/(.12-.08) = $125
P
0
= P
4
(1 + K c
) -4
P
0
= $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
Twitter