8-1 July 21 Outline Bond and Stock Differences Common Stock Valuation

8-2 Bonds and Stocks: Similarities Both provide long-term funding for the organization Both are future funds that an investor must consider Both have future periodic payments Both can be purchased in a marketplace at a price “today”

8-3 Bonds and Stocks: Differences From the firm’s perspective: a bond is a long-term debt and stock is equity From the firm’s perspective: a bond gets paid off at the maturity date; stock continues indefinitely. We will discuss the mix of bonds (debt) and stock (equity) in a future chapter entitled capital structure

8-4 Bonds and Stocks: Differences A bond has coupon payments and a lump-sum payment; stock has dividend payments forever Coupon payments are fixed; stock dividends change or “grow” over time

8-5 A visual representation of a bond with a coupon payment (C) and a maturity value (M) $C 1 $C 2 $C 3 $C 4 $C 5 $M

8-6 A visual representation of a share of common stock with dividends (D) forever $D 1 $D 2 $D 3 $D 4 $D 5 $D ∞ ∞

8-7 Comparison Valuations 123 Bond CCC M P0P Common Stock D1D1 D2D2 D3D3 D∞D∞ P0P0 0

8-8 Notice these differences: The “C’s” are constant and equal The bond ends (year 5 here) There is a lump sum at the end $C 1 $C 2 $C 3 $C 4 $C 5 $M

8-9 Notice these differences: The dividends are typically different The stock never ends There is no lump sum $D 1 $D 2 $D 3 $D 4 $D 5 $D ∞ ∞

8-10 Cash Flows for Stockholders If you buy a share of stock, you can receive cash in two ways: 1.The company pays dividends 2. You sell your shares, either to another investor in the market or back to the company

8-11 One-Period Example Suppose you are thinking of purchasing the stock of Moore Oil, Inc. You expect it to pay a $2 dividend in one year, and you believe that you can sell the stock for $14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay?

8-12 Visually this would look like: 1 D 1 = $2 P 1 = $14 R = 20%

8-13 Compute the Present Value 1 D 1 = $2 P 1 = $14 R = 20% $1.67 $11.67 PV =$13.34

1 year = N 20% = Discount rate $2 = Payment (PMT) $14 = FV PV = ? st 2nd TI BA II Plus 8-14

8-15 Two Period Example Now, what if you decide to hold the stock for two years? In addition to the dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year. Now how much would you be willing to pay?

8-16 Visually this would look like: 2 D 1 = $2 P 2 = $14.70 R = 20% 1 D 2 = $ 2.10

8-17 Compute the Present Value 2 D 1 = $2 P 2 = $14.70 R = 20% 1 D 2 = $ 2.10$1.67 $1.46 $ $ = P 0

8-18 What is the Observed Pattern? We value a share of stock by bring back all expected future dividends into present value terms; since the corporation does not have a finite life, we must consider all such dividends, even those in the distant future.

8-19 So how do you compute the future dividends? Three scenarios: 1.A constant dividend (zero growth) 2.The dividends change by a constant growth rate 3.We have some unusual growth periods and then level off to a constant growth rate

So how do you compute the future dividends? We start with the general pricing formula for an annuity with constant growth: where D 1 is next period’s dividend, R is the discount rate, g is the (constant) growth rate, and R > g. Note that as n grows arbitrarily large (goes toward ), then 8-20

Constant Dividend – Zero Growth The firm will pay a constant dividend forever This is like preferred stock Since g = 0, this implies that

Constant Growth Rate of Dividends Dividends are expected to grow at a constant percent per period; i.e., D 2 = D 1 (1+g), D 3 = D 1 (1+g) 2, …, D n+1 = D 1 (1+g) n, and so forth. Then we end up with the constant growth formula, AKA the “Gordon” model:

8-23 Dividend Growth Model (DGM) Assumptions In order to use the Gordon constant growth model, the following three requirements must be met: 1.The growth of all future dividends must be constant, 2.The growth rate must be smaller than the discount rate ( g < R), and 3.The growth rate must not be equal to the discount rate (g ≠ R)

8-24 DGM – Example 1 Suppose Big D, Inc., just paid a dividend (D 0 ) of $0.50 per share. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for?

8-25 DGM – Example 1 Solution P 0 =.50 ( ) P 0 = = $3.92

8-26 DGM – Example 2 Suppose Moore Oil Inc., is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price?

8-27 DGM – Example 2 Solution P 0 = P 0 = = $13.34

Unusual Growth; Then Constant Growth Just draw the time line with the unusual growth rates identified and determine if/when you can use the Dividend Growth Model. Deal with the unusual growth dividends separately.

8-29 Non-constant Growth Problem Statement Suppose a firm is expected to increase dividends by 20% in one year and by 15% for two years. After that, dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock?

8-30 Non-constant Growth Problem Statement Draw the time line and compute each dividend using the corresponding growth rate: g = 20%g = 15% g = 5% D 0 = $ ∞ D1D1 D2D2 D3D3

8-31 Non-constant Growth Problem Statement Draw the time line and compute each dividend using the corresponding growth rate: g = 20%g = 15% g = 5% D 0 = $ ∞ D1D1 D2D2 D3D3 D 1 = ($1.00) (1 + 20%) = $1.00 x 1.20 = $1.20 =1.20

8-32 Non-constant Growth Problem Statement Draw the time line and compute each dividend using the corresponding growth rate: g = 20%g = 15% g = 5% D 0 = $ ∞ D1D1 D2D2 D3D3 D 2 = ($1.20) (1 + 15%) = $1.20 x 1.15 = $1.38 =1.38

8-33 Non-constant Growth Problem Statement Draw the time line and compute each dividend using the corresponding growth rate: g = 20%g = 15% g = 5% D 0 = $ ∞ D1D1 D2D2 D3D3 D 3 = ($1.38) (1 + 15%) = $1.38 x 1.15 = $1.59 =1.59

8-34 Non-constant Growth Problem Statement Now we can use the DGM starting with the period of the constant growth rate at our time frame of year 3: g = 20%g = 15% g = 5% D 0 = $ ∞ D1D1 D2D2 D3D3 P 3 = D 3 (1 + g) / (R – g) P 3 = 1.59 (1.05)/ ( ) = $11.13 R = 20%

8-35 Non-constant Growth Problem Statement We now have all of the dividends accounted for and we can compute the present value for a share of common stock: g = 20%g = 15% g = 5% D 0 = $ ∞ D1D1 D2D2 D3D3 R = 20% P 3 = 11.13

8-36 Non-constant Growth Problem Statement g = 20%g = 15% g = 5% D 0 = $ ∞ D1D1 D2D2 D3D3 R = 20% P 3 = $9.32

8-37 Stock Price Sensitivity to Dividend Growth, g D 1 = $2; R = 20% Growth Rate Stock Price

Stock Price Sensitivity to Required Return, R D 1 = $2; g = 5% Growth Rate Stock Price 8-38

8-39 Using the DGM to Find R Start with the DGM and then algebraically rearrange the equation to solve for R:

8-40 Finding the Required Return - Example Suppose a firm’s stock is selling for $ It just paid a $1 dividend, and dividends are expected to grow at 5% per year. What is the required return? R = [1(1.05)/10.50] +.05 = 15% What is the dividend yield? 1(1.05) / = 10% What is the capital gains yield? g =5%

8-41 Valuation Using Multiples We can use the PE ratio and/or the price-sales ratio: P t = Benchmark PE ratio X EPS t P t = Benchmark price-sales ratio X Sales per share t

8-42 Stock Valuation Summary