1. FI 3300 - Corporate Finance Zinat Alam 1 FI3300 Corporation Finance – Chapter 9 Bond and Stock Valuation

2. FI 3300 - Corporate Finance Zinat Alam 2 Learning objectives Describe the concepts underlying the cost of capital. Compute the price of a consol and a preferred stock. Compute the price of a zero-coupon bond. Compute the price of a fixed-coupon bond. Know the pricing properties of a fixed-coupon bond. Compute the price of common stock under various assumptions about dividend growth.

3. FI 3300 - Corporate Finance Zinat Alam 3 Cost of capital 1  Cost of capital How much the firm is willing to pay to get funds from investors In other words, it is the cost to the firm for acquiring money from investors Usually expressed as a percentage

4. FI 3300 - Corporate Finance Zinat Alam 4 Cost of capital 2 An investor will provide funds to the firm only if she earns her required rate of return If investor provides funds to the firm (i.e., a financial security was bought and sold), the following must be true: Investor earns her required rate of return from the transaction Firm pays just its cost of capital for the funds Thus investor’s required rate of return = firm’s cost of capital

5. FI 3300 - Corporate Finance Zinat Alam 5 Cost of capital 3 Capital can be provided either by issuing debt (e.g., bonds) or equity (common stock).  If debt is issued, Investor’s required rate of return on debt security = firm’s cost of debt  If equity is issued, Investor’s required rate of return on equity security = firm’s cost of equity

6. FI 3300 - Corporate Finance Zinat Alam 6 Blast from the past: last lecture  Required rate of return on debt security is also known as: Cost of debt Yield-to-maturity (YTM for short) Discount rate  Required rate of return on equity security is also known as: Cost of equity Discount rate

7. FI 3300 - Corporate Finance Zinat Alam 7 Bond Valuation Consols, Preferred stock Zero-coupon bonds Fixed-coupon bonds

8. FI 3300 - Corporate Finance Zinat Alam 8 Consols 1 Pays a fixed coupon every period forever. Has no maturity. Investor who buys a consol is buying the perpetuity of the fixed coupon. So, use PV formula of a perpetuity to find the present value/price of the consol Price of consol =

9. FI 3300 - Corporate Finance Zinat Alam 9 Consols 2  Remember earlier that cost of capital = investor’s required rate of return. So, we can re-arrange the equation to find the firm’s cost of consol capital.  Cost of consol capital  We can apply the same ideas to value preferred stocks. This is because the cash flows from a preferred stock is also a perpetuity!

10. FI 3300 - Corporate Finance Zinat Alam 10 Preferred stock Pays a fixed dividend forever. Price of preferred stock is simply the present value of a perpetuity. Required rate of return on preferred stock. Preferred stock dividend Required rate of return on preferred stock/ cost of capital for preferred stock Price of preferred stock

11. FI 3300 - Corporate Finance Zinat Alam 11 Consol problem 1  Problem 9.2ABC 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? Verify that cost of debt = 0.0952 or 9.52% Use cost of debt from above to find price of consol. Verify that price of consol = 90/0.0952 = 945.38

12. FI 3300 - Corporate Finance Zinat Alam 12 Consol problem 2  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)?  No. of consols = 100 million/ consol price = 105,778  Problem 9.4If ABC wanted to issue it’s consols at par, that is, at a price of $1,000, what coupon must it pay?  Use coupon = price x required rate of return  Verify that coupon = $95.20 per year

13. FI 3300 - Corporate Finance Zinat Alam 13 Zero-coupon bond (ZCB) 1 Call this ZCB for short. Zero coupon rate, no coupon paid during bond’s life. Bond holder receives one payment at maturity, the face value (usually $1000). Price of a ZCB, P ZCB F = face value of the bond cost of ZCB debt capital (in decimals) N = number of years to maturity

14. FI 3300 - Corporate Finance Zinat Alam 14 Zero-coupon bond (ZCB) 2 As long as interest rates are positive, the price of a ZCB must be less than its face value. Why? With positive interest rates, the present value of the face value (i.e., the price) has to be less than the face value.

15. FI 3300 - Corporate Finance Zinat Alam 15 ZCB Problems 1) Find the price of a ZCB with 20 years to maturity, par value of $1000 and a required rate of return of 15% p.a. N=20, I/Y=15, FV=1000, PMT=0. Price = $61.10 2) XYZ Corp.’s ZCB 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). PV=-354, FV=1000, N=16, PMT=0. Required rate of return/ Cost of debt =6.71% p.a. These problems are just basic TVM problems where you receive one lump sum in the future.

16. FI 3300 - Corporate Finance Zinat Alam 16 Fixed-coupon bond (FCB) 1 Call this FCB for short. 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, half-year (6 months), quarter (3 months).

17. FI 3300 - Corporate Finance Zinat Alam 17 Fixed-coupon bond (FCB) 2 FCB gives you a stream of fixed payments plus a lump sum payment (face value) at maturity. This cash flow stream is just an annuity plus a lump sum at maturity. Therefore, we calculate the price of a FCB by finding the PV of the annuity and lump sum. We use the financial calculator to compute the price of the FCB.

18. FI 3300 - Corporate Finance Zinat Alam 18 Fixed-coupon bond (FCB) 2 Price of the FCB, P FCB Number of periods to maturity Fixed periodic coupon Face value Cost of debt capital

19. FI 3300 - Corporate Finance Zinat Alam 19 Find FCB price 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.  PMT = 25. Why? FV=1000, PMT =25, I/Y=5, N=40. CPT, then PV. PV = -571.02. Thus, price = $571.02 < par value

20. FI 3300 - Corporate Finance Zinat Alam 20 Useful property 1 Go back to the bond in the last problem.  Suppose annual coupon rate = 10%.  Verify that price = $1000 = par value  Suppose annual coupon rate = 12%  Verify that price = $1,171.59 > par value. It turns out that the following property is true.

21. FI 3300 - Corporate Finance Zinat Alam 21 Useful property 2 Coupon rate < discount ratePrice < face valueBond is selling at a discount Coupon rate = discount ratePrice = face valueBond is selling at par Coupon rate > discount ratePrice > face valueBond is selling at a premium Note: discount rate = cost of debt = required rate of return = yield to maturity

22. FI 3300 - Corporate Finance Zinat Alam 22 Apply what we learnt  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

23. FI 3300 - Corporate Finance Zinat Alam 23 Try one more  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.

24. FI 3300 - Corporate Finance Zinat Alam 24 Find YTM, Coupon rate 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)? Verify that YTM = 11.80% 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)? Verify that annual coupon rate = 6.69% What happens if bond pays coupon annually? Quarterly?

25. FI 3300 - Corporate Finance Zinat Alam 25 Long FCB question 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 nominal 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. Verify that annual coupon rate = 7.01%

26. FI 3300 - Corporate Finance Zinat Alam 26 Common stock For common stock, the future cash flows are:  Dividends  Selling price These cash flows are highly uncertain.  To find the value of common stock, we make assumptions about how dividends evolve in the future. We look at 3 set of assumptions: Constant dividend stream Dividends grow at constant rate (constant dividend growth model) Non-constant dividend growth

27. FI 3300 - Corporate Finance Zinat Alam 27 Constant dividend stream  Same amount of dividend is paid for ever.  Cash flow stream resembles a perpetuity.  Thus, we value the common stock in the same way as we value the preferred stock.  Common stock price, P e  Cost of equity capital, r e Common stock dividend Cost of equity capital or required rate of return on equity

28. FI 3300 - Corporate Finance Zinat Alam 28 Dividends grow at constant rate 1 Assume that dividends grow at a constant rate, g, per period forever. Given this assumption, the price of common stock equals D 0 = Dividend that the firm just paid Dividend growth rate Required rate of return on equity Don’t panic. D 1 = D 0 (1 + g)

29. FI 3300 - Corporate Finance Zinat Alam 29 Dividends grow at constant rate 2 Useful properties. All other things unchanged, If D 0 increases (decreases), P e increases (decreases). If g increases (decreases), P e increases (decreases). If r e increases (decreases), P e decreases (increases).

30. FI 3300 - Corporate Finance Zinat Alam 30 Dividends grow at constant rate 2 By rearranging the above equation, we can find the required rate of return on equity For the constant growth model to work, r e > g. Dividend yield Capital gains yield Required rate of return on equity

31. FI 3300 - Corporate Finance Zinat Alam 31 Constant growth problems 1  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)? In this question D 1 is already given to you. Verify that Price = $37.5

32. FI 3300 - Corporate Finance Zinat Alam 32 Constant growth problems 2  Johnson Foods Inc. just paid a dividend of $10 (i.e., D 0 = 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) Straightforward application of price formula. Verify that price = $94.55

33. FI 3300 - Corporate Finance Zinat Alam 33 Constant growth problems 3  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., D 0 = 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)? Use r e = (D 1 /P) + g. Verify that r e = 14.55%

34. FI 3300 - Corporate Finance Zinat Alam 34 Constant growth problems 4  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)? use r e = (D 1 /P) + g Verify that g = 7.5%

35. FI 3300 - Corporate Finance Zinat Alam 35 Non-constant dividend growth 1 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.

36. FI 3300 - Corporate Finance Zinat Alam 36 Non-constant dividend growth 2 Consider ABC Co.’s dividend stream: Discount rate is 15%. T = 0 $2.00$3.00$3.50 Dividends grow at 5% forever T =1T = 2T = 3T = 4

37. FI 3300 - Corporate Finance Zinat Alam 37 What to do? Use constant growth formula to find stock price at the end of year 3. Call this stock price P 3. Add P 3 to dividend received at t=3. This sum is the cash flow for t=3. Find PV of this cash flow. Find PV of dividends at t=1, t=2. Current stock price = sum of 2 and 3.

38. FI 3300 - Corporate Finance Zinat Alam 38 Apply the method to find ABC’s stock price P 3 = (3.5 x (1.05))/(0.15 – 0.05) = 36.75 Find cash flow at t=3  36.75 + 3.50 = 40.25 Current stock price, P 0

39. FI 3300 - Corporate Finance Zinat Alam 39 Another type of non-constant growth problem Malcolm Manufacturing, Inc. just paid a $2.00 annual dividend (that is, D 0 = 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

40. FI 3300 - Corporate Finance Zinat Alam 40 Summary Find the price/ present value of debt and equity securities Consols, preferred stock are valued using the same techniques. Fixed-coupon bonds are valued as an annuity plus a lump sum (face value at maturity) Common stocks are valued under 3 different assumptions about dividends Constant dividends Dividends grow at constant rate Dividends grow at different rates