FI 3300 – Chapter 9 Valuation of Stocks and Bonds

1. FI 3300 – Chapter 9Valuation of Stocks and Bonds Instructor: Ryan Williams

2. Learning Objectives • Value a bond given its coupon rate, par value, yield-to-maturity, time to maturity and payment frequency. • Given all but one of the factors of a bond’s value, find the remaining factor. • Value a stock using the dividend discount model under assumptions of constant growth and non-constant growth. • Given all but one of the factors of a stock’s value, find the remaining factor.

3. Remember – different words for the same thing • Cost of capital (from firm’s point of view) = required rate of return (from investor’s point of view) = interest rate in problems. • Cost of debt = investor’s required rate of return on debt • Cost of equity = investor’s required rate of return on equity.

4. What is a financial security? • It’s a contract between the provider of funds and the user of funds. • The contract specifies the: • amount of money that has been provided • terms & conditions of how the user is going to repay the provider • Provider: you (ordinary investor), the bank, venture capitalist, etc. • User: entrepreneur or firm with good business idea/product but no (or not enough) money to execute the idea.

5. TVM and valuing financial securities • To an investor who owns a financial security (a stock or a bond), the security is a stream of future expected cash flows. • The value of any security is the Present Value of all the future expected cash flows from owning the security, discounted at the appropriate discount rate (required rate of return). • When we learn to value stocks and bonds later, we are just applying TVM concepts we already know.

6. Common financial securities

7. Types of debt securities • Fixed-coupon bonds • Zero-coupon bonds • Consols (Perpetual bonds) • Variable-rate bonds • Income bonds • Convertible bonds • Callable bonds

8. Fixed coupon bonds • Firm pays a fixed amount (‘coupon’) to the investor every period until bond matures. • At maturity, firm pays face value of the bond to investor. • Face value also called par value. Most common face value is $1000. • Period: can be year, half-year (6 months), quarter (3 months).

9. How to read a bond General Motors 30 year bond Par Value = $1000 Interest paid Semi-annual Interest Rate = 8%.

10. Zero coupon and consul bonds Zero-coupon bond • Zero coupon rate, no coupon paid during bond’s life. • Bond holder receives one payment at maturity, the face value. Consol bond • Pays a fixed coupon every period forever. • Has no maturity.

11. Other types of bonds • Variable-rate bond: Coupon rate is not fixed, but is tied to a specific interest rate. • Income bond: pays the coupon only when borrower’s earnings are high enough. • Convertible bond: allows holder to convert it to another security, usually issuer’s common stock. • Callable bond: issuer has the right to buy back the bond (before maturity) at a predetermined price.

12. Equity securities • Equity security means common stock. • Common stock holders have control privileges, i.e., have a say in firm’s operating decisions. • Exercise control privileges by voting on matters of importance facing the firm. Voting takes place during shareholder meetings. • Board of directors: Elected by shareholders to make sure management acts in the best interests of shareholders. • Common stock holders can expect two types of cash flows: • Dividends • Money received from selling shares

13. Preferred Stock • Owners of preferred stock are paid after payment to debt holders, but before payment to equity holders. • No maturity. • Has stated par value and stated dividend. • Firm can omit paying preferred stock dividend without going into default. • Usually non-voting.

14. Stock/Bond payoffs • Pretend a firm only exists for one year, and debt has face value of $600,000. The distribution of funds is as follows:

15. Securities Markets • Securities markets: markets for the trading of financial securities. • Primary market: • Markets in which companies raise money by selling securities to investors. • Every security sells only once in the primary market. • Initial public offering market: firms become publicly owned by issuing (selling) shares to investors for the first time. • Secondary market: • Markets in which already issued securities trade. • Trading is primarily among investors. Issuers are usually not involved.

16. Securities Markets • Money market: markets for trading of debt securities with less than one-year maturity. • Capital markets: market for trading of intermediate-term and long-term debt and common stock. • Spot markets: securities are bought and sold for ‘on-the-spot’ delivery. • Futures markets: trading takes place now, but full payment and delivery of the asset takes place in the future, e.g., 6 months or 1-year.

17. Console is just a perpetuity! Price of consol =

18. All debt securities have similar form • Will list a “par value” and a coupon rate. • Par value is NOT Present Value, and • Coupon rate is NOT the cost of debt/required rate of return

19. Consol problem • Problem 9.2 ABC Corp. wants to issue perpetual debt in order to raise capital. It plans to pay a coupon of $90 per year on each bond with face value $1,000. Consols of a comparable firm with a coupon of $100 per year are selling at $1,050. What is the cost of debt capital for ABC? What will be the price at which it will issue its consols?

20. Consol problem • Problem 9.3 If ABC (from the problem above) wanted to raise $100 million dollars in debt, how many such consols would it have to issue (to nearest whole number)?

21. Consol problem • Problem 9.4 If ABC wanted to issue it’s consols at par, that is, at a price of $1,000, what coupon must it pay?

22. Zero coupon bond • Zero coupon rate, no coupon paid during bond’s life. • Bond holder receives one payment at maturity, the face value (usually $1000). • Most common example are government bonds • How does investor get a return?

23. Zero coupon bond - 2 • This is just a lump sum problem! • You have a Future Value (par value) • Present Value (today’s price or market price) • Rate

24. Example problems – zero coupon bonds • Find the price of a zero coupon bond with 20 years to maturity, par value of $1000 and a required rate of return of 15% p.a. • XYZ Corp.’s zero coupon bond has a market price of $ 354. The bond has 16 years to maturity and its face value is $1000. What is the cost of debt for the ZCB (i.e., the required rate of return).

25. Fixed-coupon bonds • Firm pays a fixed amount (‘coupon’) to the investor every period until bond matures. • At maturity, firm pays face value of the bond to investor. • Face value also called par value. Unless otherwise stated, always assume face value to be $1000. • Period: can be year, semi-annual (6 months), quarter (3 months). Most common are semi-annual.

26. This is just a lump-sum + annuity! • PV is today’s price or market price • FV is the par value lump sum • PMT is the period coupon payments.

27. Example problem - FCB • A $1,000 par value bond has coupon rate of 5% and the coupon is paid semi-annually. The bond matures in 20 years and has a required rate of return of 10%. Compute the current price of this bond.

28. Useful relationships

29. Useful relationship example • A 10-year annual coupon bond was issued four years ago at par. Since then the bond’s yield to maturity (YTM) has decreased from 9% to 7%. Which of the following statements is true about the current market price of the bond? • The bond is selling at a discount • The bond is selling at par • The bond is selling at a premium • The bond is selling at book value • Insufficient information

30. Example - 2 • One year ago Pell Inc. sold 20-year, $1,000 par value, annual coupon bonds at a price of $931.54 per bond. At that time the market rate (i.e., yield to maturity) was 9 percent. Today the market rate is 9.5 percent; therefore the bonds are currently selling: • at a discount. • at a premium. • at par. • above the market price. • not enough information.

31. Other types of FCB problems • Finding yield-to-maturity. THIS IS IDENTICAL TO SOLVING FOR R. • Finding coupon rate

32. Other FCB problems • 1)A $1,000 par value bond sells for $863.05. It matures in 20 years, has a 10 percent coupon rate, and pays interest semi-annually. What is the bond’s yield to maturity on a per annum basis (to 2 decimal places)? • 2) ABC Inc. just issued a twenty-year semi-annual coupon bond at a price of $787.39. The face value of the bond is $1,000, and the market interest rate is 9%. What is the annual coupon rate (in percent, to 2 decimal places)?

33. Two part FCB problem • HMV Inc. needs to raise funds for an expansion project. The company can choose to issue either zero-coupon bonds or semi-annual coupon bonds. In either case the bonds would have the SAME required rate of return, a 20-year maturity and a par value of $1,000. If the company issues the zero-coupon bonds, they would sell for $153.81. If it issues the semi-annual coupon bonds, they would sell for $756.32. What annual coupon rate is Camden Inc. planning to offer on the coupon bonds? State your answer in percentage terms, rounded to 2 decimal places.

34. Stocks/equity • All of these are related to perpetuities

35. Preferred stock • You have a constant dividend (or cash flow) and assume it will go forever.

36. Common stock • With debt, cash flows can come from coupon payments + repayment of par. • With common stock, cash flows come from dividends or selling your stock. However, expected future dividends are the only thing that matters. Why? • Three different ways to make assumptions when we value: • Common dividend stream • Constant growth in dividends • Uneven growth (non-constant) in dividends

37. How do we price a stock? Constant Dividend <= dividend stock price=> <= required return on equity Comment – where does required return on equity come from?

38. How do we price a stock? Constant dividend growth • Assume that dividends grow at constant growth rate, g, to infinity: Don’t panic. D1 = D0(1 + g) D0 = Dividend that the firm just paid Required rate of return on equity Dividend growth rate

39. How do changes in these affect Stock Price?

40. Algebra – rearrange to solve for growth • Note that we can find rate by using this formula (if we have dividend, price, and growth). • If we don’t have this info – what do we use? Capital gains yield Required rate of return on equity Dividend yield

41. Example problem – constant growth • Jarrow Company will pay an annual dividend of $3 per share one year from today. The dividend is expected to grow at a constant rate of 7% permanently. The market requires 15% What is the current price of the stock (to 2 decimal places)?

42. Example problem 2 – constant growth • Johnson Foods Inc. just paid a dividend of $10 (i.e., D0 = 10.00). Its dividends are expected to grow at a 4% annual rate forever. If you require a 15% rate of return on investments of this risk level, what is Johnson Foods’s current stock price? (to 2 decimal places)

43. Example problem 3 – constant growth • The price of a stock in the market is $62. You know that the firm has just paid a dividend of $5 per share (i.e., D0 = 5). The dividend growth rate is expected to be 6 percent forever. What is the investors’ required rate of return for this stock (to 2 decimal places)?

44. Example problem 4 – constant growth • A firm is expected to pay a dividend of $5.00 on its stock next year. The price of this stock is $40 and the investor’s required rate of return is 20%. The firm’s dividends grow at a constant rate. What is this constant dividend growth rate (g)?

45. Example problem 5 • A stock’s expected growth rate is 4% and they just paid a dividend yesterday of $10 per share. This stock has a beta of 1.5, the risk free rate is 2% and the market premium is 7%. What is the price of this stock?

46. Non-constant growth • With this assumption, dividends grow at different rates for different periods of time. Eventually, dividends will grow at a constant rate forever. • Time line is very useful for valuing this type of stocks. • To value such stocks, also need the constant growth formula. • Best way to learn is through an example.

47. From book • in valuing the stock of ABC Corp. suppose that you forecast that dividends will be $2, $3, and $3.50 in the next three years, respectively. After that you expect dividends to grow at a rate of five percent per year forever. Let us suppose that the appropriate discount rate for ABC's stock is 15 percent. The projected future dividends are: D1 = $2.00, D2 = $3.00, D3 = $3.50, D4 = $3.50 x (1.05) = $3.675, and so on.

48. Non-constant dividend growth 2 • Consider ABC Co.’s dividend stream: • Discount rate is 15%. • WORK BACKWARDS!!!!! Dividends grow at 5% forever $2.00 $3.00 $3.50 T =1 T = 2 T = 3 T = 4 T = 0

49. Another example Malcolm Manufacturing, Inc. just paid a $2.00 annual dividend (that is, D0 = 2.00). Investors believe that the firm will grow at 10% annually for the next 2 years and 6% annually forever thereafter. Assuming a required return of 15%, what is the current price of the stock (to 2 decimal places)? Use timeline to ‘see’ the problem better. Verify that stock price = $25.29

50. Summary • Consol bonds • Zero coupon bonds • Fixed coupon bonds • Preferred Stock • Common stock – constant dividend • Common stock – constant growth • Common stock – non-constant growth