o Case 11 Gilbert Enterprises Stock valuation An Important Question-What's a Small Business Really Worth? Summary and Review of Formulas

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1 An Important Question-What's a Small Business Really Worth? The value of a small, privately held business takes on importance when the business is put up for sale, is part of a divorce settlement, or is being valued for estate purposes at the time of the owner's death. The same basic principles that establish valuation for Fortune 500 companies apply to small businesses as well. However, there are important added considerations. One factor is that private businesses often lack liquidity. Unlike a firm trading in the public securities market, there is no ready market for a local clothing goods store, a bowling alley, or even a doctor's clinic. Therefore, after the standard value has been determined, it is usually reduced for lack of liquidity. Although circumstances vary, the normal reduction is in the 30 percent range. Thus, a business that is valued at $100,000 on the basis of earnings or cash flow may be assigned a value of $70,000 for estate valuation purposes. There are other factors that are important to small business valuation as well. For example, how important was a key person to the operation of a business? If the founder of the business was critical to its functioning, the firm may have little or no value in his or her absence. For example, a bridal consulting shop or a barber shop may have minimal value upon the death of the owner. On the other hand, a furniture company with established brand names or a small TV station with programming under contract may retain most of its value. Another consideration that is important i valuing a small business is the nature of the company's earnings. They are often lower thar they would be in a publicly traded compan1 Why? First of all, the owners of manysmal businesses intermingle personal expenses wit business expenses. Thus, family cars, healt insurance, travel, and so on, may be chargee as business expenses when, in fact, they hav" a personal element to them. While the IRS tries to restrict such practices, there are fine lines i-. distinguishing between personal and business uses. As a general rule, small, private businessee try to report earnings as low as possible to mini mize taxes. Contrast this with public companies that report earnings quarterly with the inten: of showing ever-growing profitability. For thi reason, in valuing a small, privately held company, analysts often rework stated earnings ir an attempt to demonstrate earning power that is based on income less necessary expenditures The restated earnings are usually higher. After these and many other factors are taker. into consideration, the average small, private company normally sells at 5 to 10 times average adjusted earnings for the previous three years. It is also important to identify recent sale prices of comparable companies, and business brokers may be able to supply such informatio When establishing final value, many people often look to their CPA or a business consultal to determine the true worth of a firm. pays no current dividends, at some point in the future, stockholders will be rewarded with cash dividends. We then take the present value of their deferred dividends. A second approach to valuing a firm that pays no cash dividend is to take the present value of earnings per share for a number of periods and add that to the present value of a future anticipated stock price. The discount rate applied to future earnings is generally higher than the discount rate applied to future dividends. Summary and Review of Formulas o Case 11 Gilbert Enterprises Stock valuation 302 The primary emphasis in this chapter is on valuation of financial assets: bonds, preferred stock, and common stock. Regardless of the security being analyzed, valuation is normally based on the concept of detemtining the present value of future cash flows. Thus we draw on many of the time-value-of-money techniques developed in Chapter 9. Inherent in the valuation process is a determination of the rate of return that investors demand. When we have computed this value, we have also identified what it will cost the corporation to raise new capital. Let's specifically review the valuation techniques associated with bonds, preferred stock, and common stock.

Chapter 10 Valuation and Rates of Return 303 Bonds The price, or current value, of a bond is equal to the present value of interest payments (It) over the life of the bond plus the present value of

2 Chapter 10 Valuation and Rates of Return 303 Bonds The price, or current value, of a bond is equal to the present value of interest payments (It) over the life of the bond plus the present value of the principal payment Pn) at maturity. The discount rate used in the analytical process is the yield to maturity (Y). The yield to maturity (required rate of return) is determined in the marketplace by such factors as the real rate of return, an inflation premium, and a risk premium. The equation for bond valuation was presented as Formula Ph =~. \ = 1 It _.. + ~ (10-1) The actual terms in the equation are solved by the use of present value tables. We say the present value of interest payments is: PYA = A X PVIFA (Appendix D) The present value of the principal payment at maturity is: PV = FV X PV IF (Appendix B) We add these two values together to determine the price of the bond. We use both annual or semiannual analysis. The value of the bond will be strongly influenced by the relationship of the yield to maturity in the market to the interest rate on the bond and also the length of time to maturity. If you know the price of the bond, the size of the interest payments, and the maturity of the bond, you can solve for the yield to maturity through a trial and error approach (discussed in the chapter and expanded in Appendix loa), by an approximation approach as presented in Formula 10-2, or by using financially oriented calculators (in Appendix lob at the end of the chapter) or appropriate computer software. -~ Preferred Stock In determining the value of preferred stock, we are taking the present value of an infinite stream of level dividend payments. This would be a tedious process if the mathematical calculations could not be compressed into a simple formula. The appropriate equation is Formula PI' Dp = K p (10-1-) According to Formula 10-4, to find the preferred stock price (PI') we take the constant annual dividend payment (D p ) and divide this value by the rate of return that preferred stockholders are demanding (K p )' If, on the other hand, we know the price of the preferred stock and the constant annual dividend payment, we can solve for the required rate of return on preferred stock as: K p = Dp PI' (10-5)

304 Part 4 The Capital Budgeting Process Common Stock The value of common stock is also based on the concept of the present value of an expected stream of future dividends.

3 304 Part 4 The Capital Budgeting Process Common Stock The value of common stock is also based on the concept of the present value of an expected stream of future dividends. Unlike preferred stock, the dividends are not necessarily level. The firm and shareholders may experience: 1. No growth in dividends. 2. Constant growth in dividends. 3. Variable or supernormal growth in dividends. It is the second circumstance that receives most of the attention in the financial literature. If a firm has constant growth (g) in dividends (D) and the required rate of return (I(,,) exceeds the growth rate, Formula 10-9 can be utilized. P D_ 1 _ o-k,,-g (l0-9) In using Formula 10-9, all we need to know is the value of the dividend at the end of the first year, the required rate of return, and the discount rate. Most of our valuation calculations with common stock utilize Formula If we need to know the required rate of return (I(,,) for common stock, Formula can be employed. D K e = _pi + g n (l0--io) The first term represents the dividend yield on the stock and the second term the growth rate. Together they provide the total return demanded by the investor. List of Terms required rate of return 283 financial risk 286 yield to maturity 285 perpetuity 293 rea] rate of return 285 dividend valuation model 295 inflation premium 285 dividend yield 299 risk-l'ree rate of return 285 price~earnings ratio 299 risk premium 286 supernormal growth 300 business risk 286 Discussion Questions 1. How is valuation of any financial asset related to future cash flows? 2. Why might investors demand a lower rate of return for an investment in ExxonMobil as compared to United Airlines? 3. What are the three factors that influence the required rate of return by investors? 4. If inflationary expectations increase, what is likely to happen to yield to maturity on bonds in the marketplace? What is also likely to happen to the price of bonds?

Chapter 10 Valuation and Rates of Return 305 5. Why is the remaining time to maturity an important factor in evaluating the impact of a change in yield to maturity on bond prices? 6.

4 Chapter 10 Valuation and Rates of Return Why is the remaining time to maturity an important factor in evaluating the impact of a change in yield to maturity on bond prices? 6. What are the three adjustments that have to be made in going from annual to semiannual bond analysis? 7. Why is a change in required yield for preferred stock likely to have a greater impact on price than a change in required yield for bonds? 8. What type of dividend pattern for common stock is similar to the dividend payment for preferred stock? 9. What two conditions must be met to go from Formula 10-8 to Formula 10-9 in using the dividend valuation model? P=~ ( 10-9) U K.,-g 10. What two components make up the required rate of return on common stock? 11. What factors might influence a firm's price-earnings ratio? 12. How is the supernormal growth pattern likely to vary from the normal, constant growth pattern? 13. What approaches can be taken in valuing a firm's stock when there is no cash dividend payment? 1. The Titan Corp. issued a $1,000 par value bond paying 8 percent interest with 15 years to maturity. Assume the current yield to maturity on such bonds is 10 percent. What i~ the price of the bond? Do annual analysis. 2. Host Corp. will pay a $2.40 dividend (D]) in the next 12 months. The required rate of return (Ke) is 13 percent and the constant growth rate (g) is 5 percent. a. Compute the stock price (Po). b. If Ke goes up to 15 percent, and all else remains the same, what will be the stock price (Po)? c. Now assume in the next year, D 1 = $2.70, Ke = 12 percent, and g is equal to 6 percent. What is the price of the stock? Solutions 1. Present Value of Interest Payments PYA = A X PYIFA (n = 15, i = 10%) Appendix D PYA = $80 X = $ Present Value of Principal Payment at Maturity PY = FV X PY IF (n = 15, i = 10%) Appendix B PY = $1,000 X.239 = $239 Total Present Value (Bond Price) Practice Problems and SoluUons Bond vallie Common stock value Present value of interest payments. $ Present value of principal payment at maturity Bond price,. $847.48

5 Part 4 The Capital Budgeting Process 2. p-~ (10-9) o-k.,-g $2.40 $2.40 a. Po = 0.13 _ 0.05 = 0.08 = $30.00 $2.40 $2.40 b. Po = 0.15 _ 0.05 = 0.10 = $24.00 $2.70 $2.70 c. Po = 0.12 _ 0.06 = 0.06 = $45.00 fllti' ~ All problems are available in Homework Manager. Please see the preface for more information. (For the first 18 bond problems, assume interest payments are on an annual basis.) 1. The Lone Star Company has $1,000 par value bonds outstanding at 9 percent interest. The bonds will mature in 20 years. Compute the current price of the bonds if the present yield to maturity is: a. 6 percent. b. 8 percent. c. 12 percent. 2. Applied Software has $1,000 par value bonds outstanding at 12 percent interest. The bonds will mature in 25 years. Compute the current price of the bonds if ( the present yield to maturity is: a. 11 percent. b. 13 percent. c. 16 percent. aluc 3. Barry's Steroids Company has $1,000 par value bonds outstanding at 12 percent interest. The bonds will mature in 50 years. Compute the current price of the bonds if the percent yield to maturity is: a. 4 percent. b. 14 percent. Bond value 4. Referring back to Problem 3, part b, what percent of the total bond value does the repayment of principal represent? 5. Essex Biochemical Co. has a $1,000 par value bond outstanding that pays 10 percent annual interest. The current yield to maturity on such bonds in the market is 7 percent. Compute the price of the bonds for these maturity dates: a. 30 years. b. 15 years. c. 1 year. 6. The Hartford Telephone Company has a $1,000 par value bond outstanding that pays 11 percent annual interest. The current yield to maturity on such bonds in the market is 14 percent. Compute the price of the bonds for these maturity dates:

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Score: 8.5, Chapter 3 Row Name 50} ~-k~. A <?c.. 80

Math 70 - Test #2A - Spring 09 Score: 8.5, Chapter 3 Row Name 50} ~-k~. A