Chapter 7 Quick Quiz

1. Chapter 7 Quick Quiz 1. Under what conditions will the coupon rate, current yield, and yield to maturity be the same? 2. What does it mean when someone says a bond is selling “at par”? At “a discount”? At “a premium”? 3. What is a “transparent” market?

2. Chapter 7 Quick Quiz 4. What is the “Fisher Effect”? 5. What is meant by the “term structure” of interest rates? How is the term structure of interest rates related to the yield curve?

3. Chapter 7 Quick Quiz 1. Under what conditions will the coupon rate, current yield, and yield to maturity be the same? A bond’s coupon rate, current yield, and yield-to-maturity be the same if and only if the bond is selling at par. 2. What does it mean when someone says a bond is selling “at par”? At “a discount”? At “a premium”? A par bond is selling for its face value (typically $1000 for corporate bonds); the price of a discount bond is less than par, and the price of a premium bond is greater than par. 3. What is a “transparent” market? A market is transparent if it is possible to easily observe its prices and trading volumes.

4. Chapter 7 Quick Quiz 4. What is the “Fisher Effect”? The Fisher Effect is the name for the relationship between nominal returns, real returns, and inflation 5. What is meant by the “term structure” of interest rates? How is the term structure of interest rates related to the yield curve? The term structure of interest rates is the relationship between nominal interest rates on default-free, pure discount securities and time to maturity. The yield curve is the graph of the term structure existing at a point in time (the snapshot of term structure relation between maturities at a point in time)

5. BA 180.02 Corporate Finance September 25, 2002

6. Today’s Agenda • Stock Valuation • Debt (i.e. bonds) vs. Equity (i.e. stock) • Features of Stocks • Stock Markets • Valuation of Stocks Under Certain Dividend Streams

7. Debt Not an ownership interest Creditors do not have voting rights Interest is considered is considered as a cost of doing business and is tax deductible Creditors have legal recourse if interest or principal payments are missed Excess debt can lead to financial distress and bankruptcy Equity Ownership interest Common stockholders vote for the board of directors and other issues Dividends are not considered as a cost of doing business and are not tax deductible Dividends are not a liability of the firm and stockholders have no legal recourse if dividends are not paid An all equity firm cannot go bankrupt (but of course can go out of business if shareholders decide to, do not confuse this with bankruptcy!) Differences Between Debt and Equity

8. Features of Common and Preferred Stock • Features of Common Stock • Residual claimants • Limited Liability • Voting Rights • Eligible for dividends, but no guarantee • Features of Preferred Stock • Preference over common stock - dividends, liquidation • Dividend arrearages • Stated liquidating value

9. The Stock Markets • Primary vs. secondary markets • New York Stock Exchange (NYSE) Operations Exchange members Commission brokers Specialists Floor brokers Floor traders Stated/liquidating value • Nasdaq Operations Dealers vs. brokers Multiple market makers

10. Introduction to Stock Valuation • By now you have seen that the value of an asset depends on the magnitude, timing, and risk of the cash flows. • Equity securities have the feature that the cash flows are uncertain. • We will also need to account for risk more carefully. • Remember that we are interested in cash flows, not accounting earnings.

11. Valuation Approach • To determine the value of a stock we need to know something about the cash flows. • Let’s start by assuming we will hold the stock for one year. • If we pay P0 today and get a dividend D1 when we sell for P1 we have: • It seems that both the future stock price and the dividend matter.

12. Valuation Approach (cont’d) • Now step forward to time 1 • Substitute into the Time 0 price • Repeating this substitution,

13. Basic Valuation Equation • We can say the value of a stock is the present value of all future dividends. • There are two reasons why this statement is not very helpful. • We don’t know what the future dividends will be. • We don’t know what discount rate to use in the present value calculations.

14. Special Cases in Stock Valuation • There are certain dividend patterns that make the application of our valuation formula easier • Constant Dividends (perpetuity) • Constant Growth in Dividends (growing perpetuity) • Supernormal Dividend Growth • We have already done the first case in the section on Discounted Cash Flows. • The second case is only a slight modification from the first • For the third case we split the problem into pieces and use the tools we have already learned.

15. Constant Dividends • This is simply a perpetuity: • This is based on getting the first dividend payment in one year.

16. Constant Dividend Growth • Now we have a perpetuity with a constant growth rate: • This is the present value of a growing perpetuity • Remember this only works if r > g • Note: The formula only requires a constant growth after D1; we don’t need the growth rate between D0 and D1 • This is the ‘dividend growth model’ or the ‘Gordon growth model’

17. Constant Dividend Growth (how to derive)

18. Constant Dividend Growth (how to derive - cont’d) • More Generally,

19. An Example – Common Stock Valuation The per share annual dividend on a common stock is expected to be $3.00 one year from today. Stock holders require a 12% rate of return. Find the fair value of the stock for each of the following cases: • dividends are constant every year forever • dividends are growing at a constant rate of 5% per year forever • dividends will grow at 25% for 3 years and then at 5% per year forever (remind me later!!!)

20. Stock Price Sensitivity to Dividend Growth ‘g’ Stock price ($) 50 45 D1 = $1 Required return, R = 12% 40 35 30 25 20 15 10 5 Dividend growth rate, g 0 8% 10% 2% 6% 4%

21. Stock Price Sensitivity to Required Return ‘r’ Stock price ($) 100 90 80 D1 = $1 Dividend growth rate, g, = 5% 70 60 50 40 30 20 Required return, R 10 8% 14% 6% 10%

22. Non-constant Dividend Growth • For some companies it may be more realistic to assume that dividends will have a particular pattern for some time. • For example: an internet company may not pay any dividends for the first 7 years of activity, or • a company may be in a high growth market for the first 3 years and then in a medium/low growth market as the industry matures • For such cases of non-constant growth we will assume that the transition period will eventually end and then their would be constant (or zero) growth.

23. Supernormal Growth • A case in point is of ‘supernormal’ growth’ over some finite length in time. If the expected dividend growth rate is higher than the discount rate (g > r), our perpetuity formula does not work. • This kind of growth is not sustainable but may occur for some period of time. • We break the problem into pieces, value them separately, then add them together. • Value the “normal” growth period (g < r) with existing formulas. • Value the supernormal period (g > r) by simply calculating the present value of each cash flow and adding them up.

24. Components of the Required Return • r = Dividend Yield + Capital Gains Yield • r = D1 / P0 + g • The Capital Gains yield is the same as the growth rate in dividends for the steady growth case. • Example: We see a stock selling for $40 per share, the next dividend is $2 per share. You think the dividend will grow by approx. 10% per year indefinitely. What return does the stock offer you, if you are correct?

25. The Discount Rate • We have recognized that the riskiness of the cash flows affects the value of an asset. • The discount rate is what makes this adjustment. • Riskier cash flows require a higher return. • Risky cash flows are worth less than safe ones. • Where do we get the discount rate? • Capital Asset Pricing Model (CAPM) or other model • Historical or Peer Group

26. A Warning • Determination of the discount rate is far from perfect. • Be aware that the answer to any present value analysis is highly sensitive to the discount rate. • In the case of stocks, the cash flows themselves are also very difficult to forecast accurately. • DO NOT OVER-EMPHASIZE THE ANSWER YOU GET FROM A STOCK VALUATION MODEL. IF IT IS DIFFERENT THAN THE MARKET PRICE, YOUR ASSUMPTIONS ARE PROBABLY NOT GOOD.

27. Zero Dividend Firms • If a firm is not currently paying dividends, does this mean the stock is valueless? • NO! Just because a firm is not paying dividends now does not mean it will never pay dividends in the future • If you knew a stock would never pay dividends (or some other form of distribution) it would be worthless • Why would a firm not pay dividends? • Investing the cash in profitable opportunities • This will make future dividends even larger

28. Example 1: Constant Dividends • Coca Cola pays dividends of $0.56 per share. Using a 15% discount rate, what is the value of a share? D1 = D2 = … = D∞ = 0.56 = D r = 0.15 P0 = D/r = 0.56/0.15 = $3.73

29. Example 2: Constant Dividend Growth • Historically, Coca Cola has annual dividend growth of 13%. What is the value of a share with a $0.56 dividend now (D0), assuming a constant future growth equal to the historic average? The required rate is 15%. D0 = $0.56 g = 0.13 r = 0.15 P0 = D1/(r-g) = D0 x (1+g)/(r-g) = 0.56x(1.13)/(0.15- 0.13) = $31.64

30. Example 3: Supernormal Growth • Coca Cola had 18% dividend growth over the last 5 years. Assume this growth continues for the next 5 years, then reverts to 13% growth. How much is the stock worth? Do=$0.56 • Note that the discount rate is 15% (Before solving let’s call 0.18 as g1 and 0.13 as g2)

31. Example 4: Stable Growth • A mature company paid a $2.10 dividend this year and you expect the future dividends to grow 4% annually. What is the value of the stock if the discount rate is 10%? D0 = $2.10 g = 4% r = 10% P0 = D1/(r-g)=D0 x(1+g)/(r-g) = 2.10x(1.04)/(0.10-0.04) = $36.4

32. Example 5: Technology Company • Suppose a tech company will pay no dividends for the next five years. It will then start paying a $1 dividend which will increase 15% annually for the next five years before it reaches it perpetual growth rate of 10%. How much is a share worth at a 15% discount rate? P0 $ 12.1

33. Example 6: Finding the Dividend • A stock is trading for $75 per share on the basis of 6% dividend growth and a 15% discount rate. What must the current (time zero) dividend be on the stock? So D0 turns out to be 75x0.09/1.06 ≈ $6.368

34. Example 7: Finding the Dividend • A stock has a required rate of return of 10%. The stock's dividend yield is 6%. What is the dividend the firm is expected to pay in one year if the current stock price is $40? What was its current dividend? (assume constantly growing dividends) Dividend yield=D1 / P0 0.06=D1 / 40 D1 is $2.4. To find the current dividend, first have to get g, g=r-D1/P0=0.1-0.06=0.04 and then using D0=D1/(1+g) D0=2.4/1.04 ≈ $2.3077

35. Example 8: Negative Growth • A company in a declining industry currently pays a $5 dividend. Because the industry prospects are poor, you expect growth to decline by 10% annually. With a 10% discount rate, what is the value of a share? Here notice that g is negative so r-g=0.2 D1=D0 x (1+g)=5 x 0.9= $4.5 P0=D1/(r-g)=4.5/0.2=$22.5

36. Example 9: Finding the Discount Rate • What is the discount rate if a stock trades for $25, current dividends are $2/share, and expected dividend growth is 10%? P0=D1/(r-g) 25=2x1.1/(r-0.1) r =2.2/25 + 0.1 = 0.188=18.8%