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Business Valuation. Chapter 12. Nov 26, 2012. Learning Objectives. Understand the importance of business valuation. Understand the importance of stock and bond valuation. Learn to compute the value and yield to maturity of bonds.

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1. Business Valuation Chapter 12 Nov 26, 2012

2. Learning Objectives • Understand the importance of business valuation. • Understand the importance of stock and bond valuation. • Learn to compute the value and yield to maturity of bonds. • Learn to compute the value and expected yield on preferred stock and common stock. • Learn to compute the value of a complete business.

3. Importance of Business Valuation • If the basic goal of the firm is to maximize the value of the firm, then it is important to be able to measure that value • When a firm contemplates raising money, it needs to know the value of it’s securities so it knows how much (shares/bonds) to issue. • If you want to invest in a company, it’s important to know if the company is over valued or under valued

4. General Valuation Model • To develop a general model for valuing a business, we consider three factors that affect future earnings: • Size of cash flows (Axiom 3) • Timing of cash flows (Axiom 2) • Risk of receiving cash flows (Axiom 1)

5. Total Value of a Business Model The present value of a firm is equal to: • Present value of current liabilities • + present value of long term debt • + present value of preferred stock • + present value of stockholder’s equity • = Total present value of the Business • (Note: the present value of the current liabilities is basically the same as their book value)

6. Bond Valuation Model • Bond Valuation is an application of time value model introduced in chapter 8. • The value of the bond is the present value of the cash flows the investor expects to receive. • What are the cash flows from a bond investment?

7. Bond Valuation Model • 3 Types of Cash Flows • Amount paid to buy the bond (PV) • Coupon interest payments made to the bondholders (PMT) • Repayment of Par value at end of Bond’s life (FV). Other Factors in Bond valuation: • Bond’s time to maturity (N) • Discount rate (I/Y)

8. Bond Valuation Model • Calculator: • n = time until maturity • I/Y = k = discount rate/cost of capital • PV = value of the bond (Vb) • PMT = coupon interest paid (\$ Int) • FV = par value at maturity

9. IBM 63/8 13 6.6 228 965/8 -1/8 IBM Bond Wall Street Journal Information: Cur Net Bonds Yld Vol Close Chg AMR 6¼24 cv 6 91¼ -1½ ATT 8.35s25 8.3 110 102¾ +¼ IBM 63/8 05 6.6 228 965/8 -1/8 Kroger 9s19 8.8 74 1017/8 -¼ Link to Bondtrac Financial Information

10. Cur Net Bonds Yld Vol Close Chg AMR 6¼24 cv 6 91¼ -1½ ATT 8.35s25 8.3 110 102¾ +¼ IBM 63/8 05 6.6 228 965/8 -1/8 Kroger 9s19 8.8 74 1017/8 -¼ IBM 63/8 13 6.6 228 965/8 -1/8 IBM Bond Wall Street Journal Information: Suppose IBM makes annual coupon payments. The person who buys the bond at the beginning of 2009 for \$966.25 will receive 5 annual coupon payments of \$63.75 each and a \$1,000 principal payment in 5 years (at the end of 2013). Assume t0 is the beginning of 2009.

11. 2009 2010 2011 2012 2013 0 1 2 3 4 5 63.75 63.75 63.75 63.75 63.75 1000.00 IBM Bond Timeline: Compute the Value for the IBM Bond given that you require an 8% return on your investment.

12. \$63.75 Annuity for 5 years \$1000 Lump Sum in 5 years 2009 2010 2011 2012 2013 N I/YR PV PMT FV 0 1 2 3 4 5 63.75 63.75 63.75 63.75 63.75 1000.00 IBM Bond Timeline: –935.12 Bond is selling for \$966.25. Would you buy it? 5 8 ? 63.75 1,000

13. If an investor purchases a 6.375% annual coupon bond today for \$966.25 and holds it until maturity (5 years), what is the expected annual rate of return ? 2009 2010 2011 2012 2013 0 1 2 3 4 5 63.75 63.75 63.75 63.75 63.75 -966.25 1000.00 ?? + ?? 966.25 Yield to Maturity (IRR) VB = 63.75(PVIFA5, x%) + 1000(PVIF5,x%) Mathematically, solve by trial and error.

14. -966.25 2009 2010 2011 2012 2013 N I/YR PV PMT FV 0 1 2 3 4 5 63.75 63.75 63.75 63.75 63.75 1000.00 Yield to Maturity 7.203% Calculator Solution: 5 ? -966.25 63.75 1,000

15. -966.25 2009 2010 2011 2012 2013 0 1 2 3 4 5 63.75 63.75 63.75 63.75 63.75 1000.00 Yield to Maturity • If YTM (7.203%) > Coupon Rate (6.375%), bond Sells at a DISCOUNT • If YTM < Coupon Rate bond Sells at a PREMIUM

16. 2009 2010 2011 2012 2013 0 1 2 3 4 5 45.00 1000.00 45 45 45 45 45 45 45 45 45 Most Bonds Pay Interest Semi-Annually: e.g. semiannual coupon bond with 5 years to maturity, 9% annual coupon rate. K = 10% Instead of 5 annual payments of \$90, the bondholderreceives 10 semiannual payments of \$45.

17. 2009 2010 2011 2012 2013 0 1 2 3 4 5 45.00 1000.00 45 45 45 45 45 45 45 45 45 N I/YR PV PMT FV Calculator Solution: –961.38 10 5 ? 45 1,000

18. Interest Rate Risk • Bond Prices fluctuate over Time • As interest rates in the economy change, required rates on bonds will also change resulting in changing market prices. Interest Rates VB

19. Bond Prices fluctuate over Time • As interest rates in the economy change, required rates on bonds will also change resulting in changing market prices. Interest Rates VB VB Interest Rates Interest Rate Risk

20. 52 Weeks Yld Vol Net Hi Lo Stock Sym Div % PE 100s Hi Lo Close Chg s 42½ 29 QuakerOats OAT 1.14 3.3 24 5067 35 34¼ 34¼ -¾ s 36¼ 25 RJR Nabisco RN .08p ... 12 6263 29¾ 285/8 287/8 -¾ 237/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235/8 23¾ ... 7¼ 5½ RJR Nab pfC .60 9.4 ... 2248 6½ 6¼ 63/8-1/8 0 1 2 3  P0=23.75 D1=2.31 D2=2.31 D3=2.31 D=2.31 237/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235/8 23¾ ... Valuing Preferred Stock P0 = Value of Preferred Stock = PV of ALL dividends discounted at investor’s Required Rate of Return

21. 52 Weeks Yld Vol Net Hi Lo Stock Sym Div % PE 100s Hi Lo Close Chg s 42½ 29 QuakerOats OAT 1.14 3.3 24 5067 35 34¼ 34¼ -¾ s 36¼ 25 RJR Nabisco RN .08p ... 12 6263 29¾ 285/8 287/8 -¾ 237/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235/8 23¾ ... 7¼ 5½ RJR Nab pfC .60 9.4 ... 2248 6½ 6¼ 63/8-1/8 0 1 2 3  2.31 (1+ kp) 2.31 (1+ kp )2 2.31 (1+ kp )3 P0=23.75 D1=2.31 D2=2.31 D3=2.31 D=2.31 P0 = + + +···  237/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235/8 23¾ ... Dp kp 2.31 .10 = \$23.10 = P0 = Valuing Preferred Stock Buy?

22. Yield (K) on Preferred Stock • The rate of return (K) an investor would earn if they pay the current market price (MP) and receive the promised dividends (Div) • If MP = Div / K, then solving for K, we get • K = Div / MP • If Div is \$2.31 and MP is \$23.75, then • K = YTM = \$2.31/\$23.75 = 9.73%

23. P0 D1 D2 D3 D D1 (1+ ks ) D2 (1+ ks )2 D3 (1+ ks )3 P0 = + + +··· 0 1 2 3  Valuing Individual Shares of Common Stock P0 = PV of ALL expected dividends discounted at investor’s Required Rate of Return Not like Preferred Stock since D0 = D1 = D2 = D3 = DN , therefore the cash flows are no longer an annuity.

24. P0 D1 D2 D3 D D1 (1+ ks ) D2 (1+ ks )2 D3 (1+ ks )3 P0 = + + +··· 0 1 2 3  Valuing Individual Shares of Common Stock P0 = PV of ALL expected dividends discounted at investor’s Required Rate of Return Investors do not know the values of D1, D2, .... , DN. The future dividends must be estimated. Link to Quote.com

25. Assume that dividends grow at a constant rate (g). D1=D0 (1+g) D2=D0 (1+g)2 D3=D0 (1+g)3 D=D0 (1+g) D0 D0 (1+ g)3 (1+ ks )3 D0 (1+ g) (1+ ks ) D0 (1+ g)2 (1+ ks )2  P0 = + + + ··· + D0(1+g) ks – g D1 ks – g P0 = = 0 1 2 3  Constant Growth Dividend Model Reduces to: Requires ks > g

26. D0(1+g) ks – g D1 ks – g P0 = = 1.14(1+.07) .11– .07 P0 = = \$30.50 Constant Growth Dividend Model What is the value of a share of common stock if the most recently paid dividend (D0) was \$1.14 per share and dividends are expected to grow at a rate of 7%? Assume that you require a rate of return of 11% on this investment.

27. D0(1+g) P0 ks = + g Yield, or Total Return on Common Stock What is the yield on stock when D0 = .08, g=.20, and current price (P0) = \$28.875 Link to Financial Web Link to Yahoo Finance

28. D0(1+g) P0 ks = + g .08(1+.2) 28.875 ks = + .20 Yield, or Total Return on Common Stock What is the yield on stock when D0 = .08, g=.20, and current price (P0) = 28.875 = .0033 + 0.20 = 20.33%

29. Total Market Value of a Business Market value of a business: • Present value of current liabilities • + present value of long term debt • + present value of preferred stock • + present value of stockholder’s equity • = Total value of Business Assets • (Note: the present value of the current liabilities is basically the same as their book value)

30. The P/E Valuation Model • You can use the Price/Earnings ratio to value a share of stock if you can determine the P/E ratio of the Industry • Stock Price = Industry P/E ratio x EPS • EPS is earnings per share of the firm • If projected EPS is \$2 and industry P/E is 15, • The Stock price = \$2 x 15 = \$30 • Stock price x shares outstanding = firm value • If 10M shares, then x \$30 = \$300,000,000

31. Other Valuation Methods • Angel investor investments (uses what investors are willing to pay for stock during development stage) • Present value of discounted future cash flows from operations (depends on predictability of future cash flows) • Rule of thumb – 10 times future earnings (assumes 10% desired rate of return)

32. Market Capitalization • Market Cap = Shares Outstanding x market price per share • Current Market price = \$25 per share • Shares Outstanding = 100,000,000 • Then market cap = \$2.5 billion

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