Dividend Discount Models

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1 Data Code Go to User: SUNYSB Password: STONYBROOK11794 Download software for WorldwatchInsight and Marketlink and corresponding manuals Login using your personal login name and password

2 Valuation of a Firm Cash Flow Analysis can be used to value public traded companies Simple in concept complex in How to define cash flow dividends, net earnings, free cash flow Determining the future value of cash flows Incorporating uncertainty bankruptcy, credit downgrades, business fluctuations. Can be addressed by discounting rate.

3 Dividend Discount Models The value of a company, V, is the sum of its dividends, discounted by a factor r Let rbe the discount rate and D k be the dividend in year k, k 1, 2, If all dividend payments are known: V D1 1+ r D2 (1+ r) D3 (1+ r)

4 Dividend Discount Models Assume dividends grow at a constant rate g: Constant Growth Dividend Model V 2 k 1 D1 D1(1+ g) D1(1+ g) (1+ g) D k ( 1+ r) (1+ r) (1+ r) k 1 (1+ r) We can find a closed form for V ifr > g V D r g 1

5 Dividend Discount Models Discounted Growth Formula: Consider a dividend stream that grows at a rate of gper period. Assign r > gas the discount rate per period. Then the present value of the stream, starting one period from the present, with the dividend D 1, is V (1+ g) D r g Where D is the current dividend

6 17:35 New York Currency: USD EARNINGS FUNDAMENTALS IBM Cash Flow Close 1/2/9 $ Dividend $2.1 per share per year IBM s dividend growth rate ~ 1% per year Past 12 month earnings $9.7 per share Shares Outstanding: 1,31,884, Market Cap: $161,2,7, Earnings Growth Rate: 1.5% IBM began paying dividends in 1913

7 Valuing IBM IBM just paid a dividend of $2. per share, or $2,621,768,. Earnings are projected to grow at 1.5% for the foreseeable future and dividends have also grown at a similar rate historically. Using a discount rate of 15%, what is the value of IBM according to the dividend discount model? The dividend model values IBM at $64,378,969,778 or $49 per share.

8 Other Valuation Methods Dividends are only one way of determining the value of a company Some companies do not pay dividends Discounted value of the net earnings stream Cash flow stream of maximum present value that can be taken out and distributed to the owners (free cash flow) cash generated through operations

9 Mean-Variance Portfolio Theory Typical investments have uncertain returns Single Period Investing: Money invested at the initial time and payoff attained at period end, e.g. zero coupon bond Ways of treating investment uncertainty: Mean-Variance Analysis, Utility Function Analysis, Arbitrage or Comparison Analysis Mean-Variance uses Probability Theory Leads to CAPM

10 Asset Return When Buying Asset: Investment instrument that may be bought and sold If you buy an asset at time t for amount X and sell it at time t 1 for X, the rate of return, r, for the asset is r X X 1 1 X X X 1

11 Example: Google Stock You buy Google at the closing price on 12/31/8 and sell it at the closing price on 9/3/9. What is your rate of return? 12/31/8 closing price: $ /3/9 closing price: $ r $ $37.65 $37.65 $ %

12 Asset Returning When Shorting Shorting: The act of selling an asset that you do not own Arrange to borrow the asset from someone who owns it and then sell it with the intent of buying it at a later date, presumably at a lower price, and repaying the lender. Only profitable if the asset declines in price Theoretically losses are unlimited risk of shorting higher than risk of going long

13 Examples of Shorting Speculation: Betting on an asset declining As a hedge: Remove undesirable exposures. A copper producer wants to lock in the price of copper that is being produced for the year; copper futures can be sold now, guaranteeing a price. Statistical arbitrage: Only way to neutralize unwanted factors in a portfolio

14 Assumptions for Shorting In reality, shorting has a cost, a borrow rate for theoretical work assume zero Borrow rate is usually tied to lending rates Stocks and bonds for shorting may be sourced by your broker Return computation is the same as for buying, but treat the initial outlay as negative r X 1 X X

15 Profits on Shorting Assume you shorted 1 share of Google instead of buying $37.65 and buy it back at $ Since the price of Google went up, lost $188.2 r $ $37.65 $ % $ 37.65*.6117 $188.2

Homework. Due Monday 11/2/2009 at beginning of class Chapter 6: 2 Additional Homework: Download data for

Homework. Due Monday 11/2/2009 at beginning of class Chapter 6: 2 Additional Homework: Download data for Data Code Go to http://stonybrook.datacodeinc.com User: SUNYSB Password: STONYBROOK11794 Download software for WorldwatchInsight and Marketlink and corresponding manuals Login using your personal login