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10 Valuation and Rates of Return Chapter McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline • Valuation of assets, based on the present value of future cash flows. • The required rate of return in valuing an asset is based on the risk involved. • Bond valuation and its determination. • Stock valuation and its determination. • Price-earnings ratio. 10-2 Valuation of Financial Assets • Helps in evaluating financial commitment a firm needs to make to: – Stockholders and bondholders. – Attract investment. • Cost of corporate financing (capital) is used in analyzing the feasibility of an investment on an ensuing project. 10-3 Valuation of Financial Assets 10-4 Valuation Concepts • Valuation of a financial asset is based on determining the present value of future cash flows. – Required rate of return (the discount rate) • Depends on the market’s perceived level of risk associated with the individual security. • It is also competitively determined among companies seeking financial capital. • Implying that investors are willing to accept low return for low risk and vice versa. • Efficient use of capital in the past results in a lower required rate of return for investors. 10-5 Valuation of Bonds • A bond provides an annuity stream of interest payments and a principal payment at maturity. – Cash flows are discounted at Y (yield to maturity). – Value of Y is determined in the bond market. – The price of the bond is: • Equal to the present value of regular interest payments. • Discounted by the yield to maturity added to the present value of the principal. 10-6 Valuation of Bonds (cont’d) • Assuming interest payments ( ) = $100; principal payments at maturity ( ) = $1,000; yield to maturity (Y) = 10% and total number of periods (n) = 20. Thus, the price of binds ( ); • Where: • = Price of the bond; = Interest payments; = Principal payment at maturity; t = Number corresponding to a period (running from 1 to n); n = Number of periods; Y = Yield to maturity (or required rate of return) 10-7 Present Value of Interest Payments • To determine the present value of a $100 annuity for 20 years, with a discount rate of 10%. – We have: 10-8 Present Value of Principal Payment (Par Value) at Maturity • Principal payment at maturity is used interchangeably with par value or face value of the bond. • Discounting $1,000 back to the present at 10%, we have: • The current price of the bond, based on the present value of interest payments and the present value of the principal payment at maturity: • Here, the price of the bond is essentially the same as its par, or stated value to be received at maturity of $1,000. 10-9 Concept of Yield to Maturity • The yield to maturity or the discount rate is the required rate of return required by bondholders. • Three factors influence the required rate of return: – Required real rate of return. – Inflation premium. – Risk premium. 10-10 The Real Rate of Return • Demanded by the investor against current use of the funds on a non-adjusted basis. – The financial ‘rent’ the investors charges for the usage of their funds for a given period. • Usually about 2 to 3%. 10-11 Inflation Premium • Compensation towards the negative effect of inflation on the value of a dollar. – Premium added to the real rate of return: • Ensures that the investor will not ‘pay’ the borrower to use his or her funds. • The risk-free rate of return can be determined. 10-12 Risk Premium • Towards special risks of an investment. – Business risk: inability of the firm to retain its: • Competitive position. • Maintain stability and growth. – Financial risk: inability of the firm to meet its: • Debt obligations as and when due. • Is relative to the type of investments. 10-13 Risk Premium (cont’d) • Assuming the risk premium is 3%, an overall required rate of return of 10% can be computed; 10-14 Increase in Inflation Premium • Assume this goes up from 4 to 6%, with everything else being constant. – Present value of interest payments: $100 annuity for 20 years at a discount rate of 12%; 10-15 Increase in Inflation Premium (cont’d) – Present value of principal payment at maturity: Present value of $1,000 after 20 years at a discount rate of 12%; – Total present value: Assuming that increase inflation increases required rate of return and decreases the bond price by $150 approximately. 10-16 Decrease in Inflation Premium • Assuming that the inflation premium declines: – The required rate of return (yield to maturity) decrease to 8%, where the 20 year bond with a 10% interest rate would now sell for; – Present value of interest payments 10-17 Decrease in Inflation Premium (cont’d) – Present value of principal payment at maturity – Total present value 10-18 Bond Price Table 10-19 Time to Maturity • Influences the impact of a change in yield to maturity on valuation. • Longer the maturity, the greater the impact of changes in yield. 10-20 Impact of Time to Maturity on Bond Prices 10-21 Determining Yield to Maturity from the Bond Price • The yield to maturity (Y), that will equate the interest payments ( ) and the principal payments ( ) to the price of the bond ( ). – Assuming that a 15 year bond pays $110 per year (11%) in interest and $1,000 after 15 years in principal repayment. – Choosing an initial percentage to try as a discount rate, we have: 10-22 Relationship Between Time to Maturity and Bond Price 10-23 Example - 13% Discount Rate • Present value of interest payments: • Present value of principal payment at maturity • Total present value 10-24 Example – 12% Discount Rate • Present value of interest payments • Present value of principal payment at maturity • Total present value 10-25 Formula for Bond Yield • Weighted average is used to get the average investment over 15 year holding period. 10-26 Semiannual Interest and Bond Prices • A 10% interest rate may be paid as $50 twice a year in the case of semiannual payments. • To make the conversion: – Divide the annual interest rate by two. – Multiply the number of years by two. – Divide the annual yield to maturity by two. • Assuming a 10%, $1,000 par value bond has a maturity of 20 years, the annual yield at 12%: – 10%/2 = 5% semiannual interest rate; hence 5% X $1,000 = %50 semiannual interest. – 20 X 2 = 40 periods to maturity – 12%/2 = 6% yield to maturity, expressed on a semiannual basis. 10-27 Semiannual Interest and Bond Prices (cont’d) • At a present value of a $50 annuity for the 40 periods, at discount rate of 6%: – Present value of interest payments – Present value of principal payment at maturity – Total present value 10-28 Valuation and Preferred Stock • Preferred stock represents a perpetuity, having no maturity date. – It has a fixed dividend payment. – It has no binding contractual obligation of interest on debt. – Being a hybrid security, it does not have: • The ownership privilege of a common stock. • The legal provisions that could be enforced on debt. 10-29 Perpetuity of a Preferred Stock • Where, • = the price of the preferred stock; = the annual dividend for the preferred stock (constant); = required rate of return (discount rate) applied to preferred stock dividends. • A more usable formula is: • Assuming, the annual dividend is $10, and the stockholder requires a 10% rate of return, the price of the preferred stock would be: 10-30 Perpetuity of a Preferred Stock (cont’d) • If the rate of return required by security holders change, the value of the preferred stock also changes. • The longer the period of an investment, the greater the impact of a change in the require rate of return. • With perpetual security, the impact is at a maximum. • Assuming that the required rate of return has increased to 12%. The value of the preferred stock would be: • If it were reduced to 8%, the value of the preferred stock would be: 10-31 Determining the Rate of Return (Yield) from the Market Price • Assuming the annual preferred dividend ( ) is $10 and the price of the preferred stock ( ) is $100, the required rate of return (yield): • A higher market price provides quite a decline in the yield: 10-32 Valuation of Common Stock • Interpreted by the shareholder as the present value of an expected stream of future dividends. • The ultimate value of any holding lies with: – The distribution of earnings in the form of dividend payments. • The earnings must be translated into cash flow for the stockholder. 10-33 Dividend Valuation Model • Where, • = Price of stock today; • D = Dividend for each year; • = the required rate of return for common stock (discount rate). • This formula, with modifications is generally applied to three different situations: – No growth in dividends. – Constant growth in dividends. – Variable growth in dividends. 10-34 No Growth in Dividends • The common stock pays a constant dividend as in the case of a preferred stock. • This is not a very popular option. • Where, • = Price of the common stock; = Current annual common stock dividend (constant); = Required rate of return for common stock. • Assuming = $1,86 and = 12%, the price of the stock would be: 10-35 Constant Growth in Dividends • The general valuation process is shown: • Where, • = Price of common stock today; • = Dividend in year 1, ; • = Dividend in year 2, , and so on; • g = Constant growth rate in dividends; • = Required rate of return for common stock (discount rate). 10-36 Constant Growth in Dividends (cont’d) • Assuming: – – – – – = Last 12 month’s dividend (assume $1.87); = First year, $2.00 (growth rate, 7%); = Second year, $2.14 (growth rate, 7%); = Third year, $2.29 (growth rate, 7%) etc; = Required rate of return (discount rate), 12%. 10-37 Constant Growth Dividend Valuation Model • Where: • • • • g = Price of the stock today; = Dividend at the end of the first year; = Required rate of return (discount rate); = Constant growth rate in dividends. • Based on the current example; computed as: = $2.00; = .12; g = .07. is 10-38 Stock Valuation Based on Future Stock Value • Assumption: To know the present value of an investment. – Stock is held on for three years and then sold. – Adding the present value of three years of dividends, and the present value of the stock price after three years gives the present value of the benefits. – The appropriate formula to be used is: 10-39 Determining the Required Rate of Return from the Market Price • Determining the required rate of return, knowing the first year’s dividend, the stock price, and the growth rate (g): • Assuming; = Required rate of return (to be solved); • = Dividend at the end of the first year, $2.00; • = Price of the stock today, $40; • g = Constant growth rate 7%, we have: = $2.00 + 7% = 5% + 7% = 12% $40 10-40 Determining the Required Rate of Return from Market Price (cont’d) • The stockholder is receiving a current dividend plus anticipated growth in the future. – If the dividend yield is low, the growth rate must be high to provide the necessary return. – If the dividend rate is low, a high dividend yield will be expected. – The first term represent the dividend yield the stockholder will receive. – The second represents the anticipated growth in dividends, earnings, and stock price. 10-41 Price-Earnings Ratio Concept and Valuation • A multiplier applied to current earnings to determine the value of a share of stock in the market. • Influenced by: – Earnings and sales growth of a firm. – Risk (or volatility in performance). – The debt-equity structure of the firm. – The dividend policy. – The quality of management. 10-42 Variable Growth in Dividends – Supernormal Growth • Present value of dividends during the exceptional growth is observed. – Present value of the normal, constant dividends that follow the supernatural growth period: • Is used to determine the price of the stock at the end of the supernatural growth period. – Discounting this price to the present and adding it to the present supernormal value: • Gives us the current price of the stock. 10-43 Variable Growth in Dividends – No Dividends • Approach 1: though no dividend is paid currently – The stockholders will be paid a cash dividend at a later date. • The present value of their deferred payments may be used. • Approach 2: – Take the present value of earnings per share for a number of periods. – Add that to the present value of the future anticipated stock price. 10-44 Stock Valuation under Supernormal Growth Analysis 10-45