1、Valuation and Rates of Return,10,1-2,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,1-3,

2、Valuation of Financial Assets,1-4,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 markets perceived level of risk associated with the individual security It is also competitive

3、ly 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,1-5,Valuation of Bonds,A bond provides an annuity stream of inter

4、est 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 pr

5、incipal,1-6,Valuation of Bonds (contd),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;

6、 t = Number corresponding to a period (running from 1 to n); n = Number of periods; Y = Yield to maturity (or required rate of return),1-7,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:,1-8,Present Value of Princ

7、ipal 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 prin

8、cipal 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 $1,000,1-9,Relationship Between Bond Prices and Yields,Bond prices are inversely related to bond yields (move in opposite directions) As interest rates in the econ

9、omy change, the price or value of a bond changes: if the required rate of return increases, the price of the bond will decrease if the required rate of return decreases, the price of the bond will increase,PPT 10-8,1-10,Bond price and required rate of return(yield to maturity),If the market rate is

10、higher than the coupon rate (the annual interest payment divided by the par value), the bond will sell at discount (below par value) If the market rate is equal to the coupon rate, the bond will sell at par value If the market rate is lower than the coupon rate, the bond will sell at premium ( above

11、 par value),1-11,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,1-12,Concept of Yield to Maturity,Real rate

12、 of return: Demanded by the investor against current use of the funds on a non-adjusted basis Inflation premium: Compensation towards the negative effect of inflation on the value of a dollar Risk free rate of return compensates for the use of funds and loss due to inflation Risk Premium: Towards sp

13、ecial risks of an investment,1-13,Risk Premium (contd),Business Risk: inability of the firm to retain its competitive position and stability and growth Financial risk: inability of the firm to meet its debt obligations as and when due Assuming the risk premium is 3%, an overall required rate of retu

14、rn of 10% can be computed;,1-14,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%;,1-15,Increase in Inflation Premium (contd),Present value of principal payment a

15、t 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,1-16,Decrease in Inflation Premium,Assuming that the inflation premium declines: Th

16、e required rate of return decrease to 8%, where the 20 year bond with a 10% interest rate would now sell for; Present value of interest payments,1-17,Decrease in Inflation Premium (contd),Present value of principal payment at maturity Total present value,1-18,Bond Price Table,1-19,Time to Maturity,I

17、nfluences the impact of a change in yield to maturity on valuation Longer the maturity, the greater the impact of changes in yield,1-20,Impact of Time to Maturity on Bond Prices,1-21,Determining Yield to Maturity from the Bond Price,The yield to maturity (Y), that will equate the interest payments (

18、 ) and the principal payments ( ) to the price of the bond ( ) Assuming that a 15 year bond pays $110 per year (11%) in interest and $1,000 after 15 years in principal repayment Choosing an initial percentage to try as a discount rate, we have:,1-22,1,300 1,200 1,100 1,000 900 800 700,Bond Price ($)

19、,30,25,15,Number of years to maturity,* The relationship in the graph is not symmetrical in nature.,10% bond, $1,000 par value,Assumes 12% yield to maturity,5,0,Assumes 8% yield to maturity,PPT 10-10,Relationship between time to maturity and bond price*,1-23,Compute the yield to maturity,Trial and e

20、rror process Interpolation method A less exact calculation of the yield to maturity Principal -Price of the bond Approximate Yield = Annual interest payment + Number of years to maturity to Maturity . 6 (Price of the bond) +.4( Principal payment),1-24,Semiannual Interest and Bond Prices,A 10% intere

21、st 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

22、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,1-25,Semiannual Interest and Bond Prices (contd),At a present value of a $50 annuity for the 40 periods, at discount

23、rate of 6%: Present value of interest payments Present value of principal payment at maturity Total present value,1-26,Valuation of Preferred Stock,Preferred stock: usually represents a perpetuity (something with no maturity date) has a fixed dividend payment is valued without any principal payment

24、since it has no ending life is considered a hybrid security owners have a higher priority of claim than common shareholders price is based upon PV of future dividends,PPT 10-12,1-27,Valuation of Preferred Stock,1-28,Determining the Rate of Return (Yield) from the Market Price,Assuming the annual pre

25、ferred 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:,1-29,Valuation of Common Stock,The value of common stock is the present value of a stream of future dividends Common stock di

26、vidends can vary, unlike preferred stock dividends There are 3 possible cases: No growth in dividends (valued like preferred stock) Constant growth in dividends Variable growth in dividends Required rate of return reflects the dividend yield on the stock and the expected growth rate in the dividend,

27、PPT 10-13,1-30,Valuation of Common Stock,General formula No growth in dividends Constant growth in dividends,1-31,Valuation of a Supernormal Growth Firm,PPT 10-18,1-32,Stock valuation under supernormal growth,1-33,Determining the Required Rate of Return from the Market Price,Determining the required

28、 rate of return, knowing the first years 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% $40,1-34,V

29、aluation Using the Price-Earnings Ratio,The Price-Earnings (P/E) ratio can also be used to value common stocks The P/E ratio is influenced by many factors: the earnings and sales growth of the firm the risk (or volatility in performance) the debt-equity structure the dividend policy the quality of m

30、anagement a number of other factors,PPT 10-14,1-35,High vs. Low P/Es,A stock with a high P/E ratio: indicates positive expectations for the future of the company means the stock is more expensive relative to earnings typically represents a successful and fast-growing company is called a growth stock

31、 A stock with a low P/E ratio: indicates negative expectations for the future of the company may suggest that the stock is a better value or buy is called a value stock,PPT 10-15,Cost of Capital,11,1-37,Chapter 11 - Outline,Cost of Capital Cost of Debt Cost of Preferred Stock Cost of Common Equity:

32、Common Stock Retained Earnings Optimum Capital Structure Marginal Cost of Capital The Security of Market Line Summary and Conclusions,PPT 11-2,1-38,Cost of Capital,The cost of capital represents the overall cost of future financing to the firm The cost of capital is normally the relevant discount ra

33、te to use in analyzing an investment It represents the minimal acceptable return from the investment If your cost of funds is 10%, you must earn at least 10% on your investments to break even! The cost of capital is a weighted average of the various sources of funds in the form of debt and equity WA

34、CC = Weighted Average Cost of Capital,PPT 11-3,1-39,Steps in measuring a firms cost of capital,1. Compute the cost of each source of capital. 2. Assign weights to each source. Conversion of historical cost of capital structure to market values may be required. 3. Compute the weighted average of the

35、component costs.,1-40,Cost of Capital Baker Corporation,1-41,Cost of Debt,Measured by interest rate, or yield, paid to bondholders Example: $1,000 bond paying $100 annual interest 10% yield Calculation is complex discount rate or premium from par value bonds To determine the cost of a new debt in th

36、e marketplace: The firm will compute the yield on its currently outstanding debt,1-42,Approximate Yield to Maturity (Y),Annual interest payment + Number of years to maturity 0.6 (Price of the bond) + 0.4 (Principal payment) Assuming: Y = $101. 50 + 20 .6 ($940) + .4 ($1,000) = $101.50 + 20 $564 + $4

37、00 Y = $101.50 + 3 = $104.50 = 10.84% $964 $964,Principal payment Price of the bond,$1,000 - $940,60,1-43,Tax and flotation cost consideration,Market-determined yields on various financial instruments will equal the cost of those instruments to the firm with adjustment tax and flotation cost conside

38、ration,1-44,Adjusting Yield for Tax Considerations,Yield to maturity indicates how much the firm has to pay on a before-tax basis Interest payment on a debt is a tax-deductible expense Due to this, the true cost is less than the stated cost,1-45,Adjusting Yield for Tax Considerations (contd),The aft

39、er-tax cost of debt is calculated as shown below: Assuming:,1-46,Yield of Preferred Stock,Preferred stock: has a fixed dividend (similar to debt) has no maturity date dividends are not tax deductible and are expected to be perpetual or infinite Yield of preferred stock = annual dividend price of sto

40、ck Yield of new preferred stock = annual dividend price-flotation costs Flotation costs: selling and distribution costs (such as sales commissions) for the new securities,PPT 11-6,1-47,Cost of Preferred Stock (contd),The cost of preferred stock is as follows: Where, = Cost of preferred stock; = Annu

41、al dividend on preferred stock; = Price of preferred stock; F = Floatation, or selling cost Assuming annual dividend as $10.50, preferred stock is $100, and flotation, or selling cost is $4. Effective cost is: = $10.50 = $10.50 = 10.94% $100 - $4 $96,1-48,Cost of Common Equity Valuation Approach,In

42、determining the cost of common stock, the firm must be sensitive to pricing and performance demands of current and future stockholders Dividend valuation model: Where, = Price of the stock today; = Dividend at the end of the year (or period); = Required rate of return; g = Constant growth rate in di

43、vidends Assuming = $2; = $40 and g = 7%, equals 12 percent = $2 + 7% = 5% + 7% = 12% $40,1-49,Alternate Calculation of the Required Return on Common Stock,Capital asset pricing model (CAPM) Where: = Required return on common stock; = Risk-free rate of return, usually the current rate on Treasury bil

44、l securities; = Beta coefficient (measures the historical volatility of an individual stocks return relative to a stock market index; = return in the market as measured by an approximate index Assuming = 5.5%, = 12%, = 1.0, would be: = 5.5% + 1.0 (12% - 5.5%) = 5.5% + 1.0 (6.5%) = 5.5% + 6.5% = 12%,

45、1-50,Cost of Retained Earnings,Sources of capital for common stock equity: Purchaser of the new shares external source Retained earnings internal source Represent the present and past earnings of the firm minus previously distributed dividends Belong to the current stockholders may be paid in the fo

46、rm of dividends or reinvested in the firm Reinvestments represent a source of equity capital supplied by the current stockholders An opportunity cost is involved,1-51,Cost of Retained Earnings (contd),The cost of retained earnings is equivalent to the rate of return on the firms common cost represen

47、ting the opportunity cost represents both the required rate of return on common stock, and the cost of equity in the form of retained earnings For ease of reference, = Cost of common equity in the form of retained earnings = Dividend at the end of the first year, $2 = Price of stock today, $40 g = C

48、onstant growth rate in dividends, 7% = $2 + 7% = 5% + 7% = 12% $40,1-52,Cost of New Common Stock,A slightly higher return than , representing the required rate of return of present stockholders, is expected Needed to cover the distribution costs of the new securities Common stock New common stock,1-

49、53,Cost of New Common Stock (contd),Assuming = $2, = $40, F (Flotation or selling costs) = $4 and g = 7%; = $2 + 7% $40 - $4 = $2 + 7% $36 = 5.6% + 7% = 12.6%,1-54,Overview of Common Stock Costs,1-55,Optimum Capital Structure,The optimum (best) situation is associated with the minimum overall cost o

50、f capital: Optimum capital structure means the lowest WACC Usually occurs with 40-70% debt in a firms capital structure WACC is also referred to as the required rate of return or the discount rate Based upon the market value rather than the book value of the firms debt and equity,PPT 11-8,1-56,Optim

51、al Capital Structure Weighting Costs (contd),Assessment of different plans (next slide): Firm is able to initially reduce weighted average cost of capital with debt financing Beyond Plan B, continued use of debt becomes unattractive and greatly increases costs of sources of financing,1-57,Optimal Ca

52、pital Structure Weighting Costs (contd),Cost (After-tax) Weights Weighted Cost Financial Plan A: Debt 6.5% 20% 1.3% Equity. 12.0 80 9.6 10.9% Financial Plan B: Debt 7.0% 40% 2.8% Equity. 12.5 60 7.5 10.3% Financial Plan C: Debt 9.0% 60% 5.4% Equity. 15.0 40 6.0 11.4%,1-58,Cost of Capital Curve,1-59,

53、Debt as a Percentage of Total Assets (2006),1-60,Capital acquisition and investment decision making,The discount rate used in evaluating capital projects should be the weighted average cost of capital. If the cost of capital is earned on all projects, the residual claimants of the earnings stream, t

54、he owners, will receive their required rate of return. If the overall return of the firm is less than the cost of capital, the owners will receive less than their desired rate of return because providers of debt capital must be paid. For most firms, the cost of capital is fairly constant within a re

55、asonable range of debt-equity mixes. Changes in money and capital market conditions (supply and demand for money), however, cause the cost of capital for all firms to vary upward and downward over time.,1-61,Cost of capital over time,Cost of capital (Ka),x,y,Debt-equity mix (percent),Kat,Kat + 1,Kat

56、 + 2,1-62,Investment Projects Available to the Baker Corporation,1-63,Cost of capital and investment projects for the Baker Corporation,1-64,The Marginal Cost of Capital,The market may demand a higher cost of capital for each amount of fund required if a large amount of financing is required Equity

57、(ownership) capital is represented by retained earnings Retained earnings cannot grow indefinitely as the firms capital needs to expand Retained earnings is limited to the amount of past and present earnings that can be redeployed into investments,1-65,The Marginal Cost of Capital (contd),Assumptions: 60% is the amount of equity capital a firm must maintain to keep a balance between fixed income securities and ownership interest Baker Corporation has $23.40 million of retained earning available for investment There is adequate retained earning to support the capital structure as