4.1 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Chapter 4 The Valuation of Long-Term Securities

4.2 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. After studying Chapter 4, you should be able to: 1. Distinguish among the various terms used to express value. 2. Value bonds, preferred stocks, and common stocks. 3. Calculate the rates of return (or yields) of different types of long-term securities. 4. List and explain a number of observations regarding the behavior of bond prices.

4.3 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. The Valuation of Long-Term Securities Distinctions Among Valuation Concepts Bond Valuation Preferred Stock Valuation Common Stock Valuation Rates of Return (or Yields) Distinctions Among Valuation Concepts Bond Valuation Preferred Stock Valuation Common Stock Valuation Rates of Return (or Yields)

4.4 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Price,Value,and Worth u Price u Price:What you pay for something u Value u Value:The theoretical maximum price you could pay for something u Worth u Worth:The maximum amount you are willing to pay for a purchase

4.5 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Liquidation Value Liquidation value Liquidation value represents the amount of money that could be realized if an asset or group of assets is sold separately from its operating organization.

4.6 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Going-Concern Value Going-concern value Going-concern value represents the amount a firm could be sold for as a continuing operating business.

4.7 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Book and Firm Value (2) a firm value: total assets minus liabilities and preferred stock as listed on the balance sheet. Book value Book value represents either: (1) an asset value: the accounting value of an asset – the asset’s cost minus its accumulated depreciation; Book value Book value represents either: (1) an asset value: the accounting value of an asset – the asset’s cost minus its accumulated depreciation;

4.8 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Market and Intrinsic Value Intrinsic value Intrinsic value represents the price a security “ought to have” based on all factors bearing on valuation. Market value Market value represents the market price at which an asset trades.

4.9 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. What is Intrinsic Value? intrinsic value economic value. u The intrinsic value of a security is its economic value. u In efficient markets, the current market price of a security should fluctuate closely around its intrinsic value.

4.10 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Importance of Valuation It is used to determine a security’s intrinsic value. It helps to determine the security worth. This value is the present value of the cash-flow stream provided to the investor. It is used to determine a security’s intrinsic value. It helps to determine the security worth. This value is the present value of the cash-flow stream provided to the investor.

4.11 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Important Bond Terms bond face value par value (principal) A bond has face value or it is called par value (principal). It is the amount that will be repaid when the bond matures. bond A bond is a debt instrument issued by a corporation, banks municipality or government.

4.12 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Important Bond Terms u Maturity value (MV) u Maturity value (MV) [or face value] of a bond is the stated value. In the case of a US bond, the face value is usually $1,000. u Maturity time (MT) u Maturity time (MT) is the time when the company is obligated to pay the bondholder the face V.

4.13 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Important Bond Terms This is the annual interest rate that will be paid by the issuer of the bond to the owner of the bond. coupon rate The bond’s coupon rate is the stated rate of interest on the bond in %. This rate is typically fixed for the life of the bond.

4.14 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Important Bond Terms discount rate (capitalization) u The discount rate (capitalization) is the interest rate used in determining the present value of series of future cash flows.

4.15 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Different Types of Bonds u 1) Bonds have infinite life (Perpetual Bonds). u 2) Bonds have finite maturity. u A) Nonzero Coupon Bonds u B) Zero - Coupon Bonds

4.16 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 1) Perpetual Bonds perpetual bond 1) A perpetual bond is a bond that never matures. It has an infinite life. perpetual bond 1) A perpetual bond is a bond that never matures. It has an infinite life. (1 + k d ) 1 (1 + k d ) 2  (1 + k d )  V = III =   t=1 (1 + k d ) t I  or I (PVIFA k d,  ) Ik d V = I / k d [Reduced Form]

4.17 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Meaning of symbol u V u V = Present Intrensic Value u I u I = Periodic Interest Payment In Value Not %; or it is the actual amount paid by the issuer kd kd = Required Rate of Return or Discount Rate per Period

4.18 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Perpetual Bonds Formula u

4.19 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Perpetual Bond Example perpetual bond Bond P has a $1,000 face value and provides an 8% annual coupon. The appropriate discount rate is 10%. What is the value of the perpetual bond? perpetual bond Bond P has a $1,000 face value and provides an 8% annual coupon. The appropriate discount rate is 10%. What is the value of the perpetual bond? I$80 I = $1,000 ( 8%) = $80. k d 10% k d = 10%. VIk d V = I / k d [Reduced Form] $8010% $800 = $80 / 10% = $800. Maximum payment I$80 I = $1,000 ( 8%) = $80. k d 10% k d = 10%. VIk d V = I / k d [Reduced Form] $8010% $800 = $80 / 10% = $800. Maximum payment

4.20 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Another Example u Suppose you could buy a bond that pay SR 50 a year forever. Required rate of return for this bond is 12%, what is the PV of this bond? u V = I/kd = 50/0.12 = SR

4.21 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Comment on the example u This is the maximum amount that should be paid for this bond. u If the market price is more than this value never buy it.

4.22 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Nonzero Coupon Bonds onzero Coupon Bond 1) A Nonzero Coupon Bond is a coupon paying bond with a finite life (MV). (1 + k d ) 1 (1 + k d ) 2 n (1 + k d ) n V = II + MVI =  n t=1 (1 + k d ) t I nn V = I (PVIFA k d, n ) + MV (PVIF k d, n ) n (1 + k d ) n + MV

4.23 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Bond C has a $1,000 face value and provides an 8% annual coupon for 30 years. The appropriate discount rate is 10%. What is the value of the coupon bond? Coupon Bond Example V or PV V or PV= $80 (PVIFA 10%, 30 ) + $1,000 (PVIF 10%, 30 ) = $80 (9.427 ) + $1,000 (.057 ) [Table IV] [Table II] $ = $ $57.00 = $ V or PV V or PV= $80 (PVIFA 10%, 30 ) + $1,000 (PVIF 10%, 30 ) = $80 (9.427 ) + $1,000 (.057 ) [Table IV] [Table II] $ = $ $57.00 = $

4.24 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Comments on the Example u The interest payments have a present value of $754.16, where the principal payment at maturity has a present value of $57. This bond PV is $ u So, no one should pay more than this price to buy this bond.

4.25 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Another Example u

4.26 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Important Note u In this case, the present value of the bond is in excess of its $1,000 par value because the required rate of return is less than the coupon rate. Investors are willing to pay a premium to buy this bond.

4.27 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Important Note u When the required rate of return is greater than the coupon rate, the bond PV will be less than its par value. Investors would buy this bond only if it is sold at a discount from par value.

4.28 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Semiannual Compounding k d 2 (1) Divide k d by 2 n2 (2) Multiply n by 2 I2 (3) Divide I by 2 k d 2 (1) Divide k d by 2 n2 (2) Multiply n by 2 I2 (3) Divide I by 2 Most bonds in the US pay interest twice a year (1/2 of the annual coupon). Adjustments needed: Most bonds in the US pay interest twice a year (1/2 of the annual coupon). Adjustments needed:

4.29 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 2 2 n (1 + k d /2 ) 2 * n 2 (1 + k d /2 ) 1 Semiannual Compounding non-zero coupon bond A non-zero coupon bond adjusted for semi-annual compounding. V = I / 2 2 I / 2 + MV =  2n2*n2n2*n t=1 2 (1 + k d /2 ) t 2 I / n 2 2n = I/2 (PVIFA k d /2, 2*n ) + MV (PVIF k d /2, 2*n ) 2 2 n (1 + k d /2 ) 2 * n + MV 2 I / 2 2 (1 + k d /2 ) 2

4.30 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. V V= $40 (PVIFA 5%, 30 ) + $1,000 (PVIF 5%, 30 ) = $40 ( ) + $1,000 (.231 ) [Table IV] [Table II] $ = $ $ = $ V V= $40 (PVIFA 5%, 30 ) + $1,000 (PVIF 5%, 30 ) = $40 ( ) + $1,000 (.231 ) [Table IV] [Table II] $ = $ $ = $ Semiannual Coupon Bond Example Bond C has a $1,000 face value and provides an 8% semi-annual coupon for 15 years. The appropriate discount rate is 10% (annual rate). What is the value of the coupon bond?

4.31 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Zero-Coupon Bonds ero-Coupon Bond 2) A Zero-Coupon Bond is a bond that pays no interest but sells at a deep discount from its face value; it provides compensation to investors in the form of price appreciation. n (1 + k d ) n V = MV n = MV (PVIF k d, n )

4.32 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. V $57.00 V= $1,000 (PVIF 10%, 30 ) = $1,000 (0.057 ) = $57.00 Zero-Coupon Bond Example Bond Z has a $1,000 face value and a 30 year life. The appropriate discount rate is 10%. What is the value of the zero-coupon bond?

4.33 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Note on the example u The investor should not pay more than this value ($57) now to redeem it 30 years later for $1,000. The rate of return is 10% as it is stated here.

4.34 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Preferred Stock Preferred Stock is a type of stock that promises a (usually) fixed dividend, but at the discretion of the board of directors. Preferred Stock Valuation Preferred Stock has preference over common stock in the payment of dividends and claims on assets.

4.35 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Preferred Stock Valuation u

4.36 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Preferred Stock Valuation perpetuity This reduces to a perpetuity! (1 + k P ) 1 (1 + k P ) 2  (1 + k P )  V V = Div P =   t=1 (1 + k P ) t Div P  or Div P (PVIFA k P,  ) V V = Div P / k P

4.37 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Preferred Stock Example Div P $8.00 k P 10% VDiv P k P $8.0010% $80 Div P = $100 ( 8% ) = $8.00. k P = 10%. V = Div P / k P = $8.00 / 10% = $80 preferred stock Stock PS has an 8%, $100 par value issue outstanding. The appropriate discount rate is 10%. What is the value of the preferred stock?

4.38 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Example: Xerox preferred that pays $4.125 dividend per year. Suppose our required rate of return on Xerox preferred is 9.5% V p = = $43.42

4.39 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Expected Rate of Return on Preferred Just adjust the valuation model: = D p p k V = D p k Po

4.40 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Example If we know the preferred stock price is $40, and the preferred dividend is $4.125, the expected return is: = D Po p k = =.1031

4.41 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Common Stock Valuation Pro rata share of future earnings after all other obligations of the firm (if any remain). may Dividends may be paid out of the pro rata share of earnings. Pro rata share of future earnings after all other obligations of the firm (if any remain). may Dividends may be paid out of the pro rata share of earnings. Common stock Common stock represents the ultimate ownership (and risk) position in the corporation.

4.42 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Common Stock Valuation (1) Future dividends (2) Future sale of the common stock shares (1) Future dividends (2) Future sale of the common stock shares common stock What cash flows will a shareholder receive when owning shares of common stock?

4.43 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Common Stock Valuation u It is the expectation of future dividends and a future selling price that gives value to the stock. u Cash dividends are all that stockholders, as a whole, receive from the issuing company.

4.44 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Dividend Discount Model u Dividend discount models are designed to compute the intrinsic value of the common stock under specific assumptions: u 1) The expected growth pattern of future dividend. u 2) The appropriate discount rate.

4.45 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Dividend Valuation Model Basic dividend valuation model accounts for the PV of all future dividends. (1 + k e ) 1 (1 + k e ) 2  (1 + k e )  V = Div 1  Div  Div 2 =   t=1 (1 + k e ) t Div t Div t :Cash Dividend at time t k e : Equity investor’s required return Div t :Cash Dividend at time t k e : Equity investor’s required return

4.46 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Adjusted Dividend Valuation Model The basic dividend valuation model adjusted for the future stock sale. (1 + k e ) 1 (1 + k e ) 2 n (1 + k e ) n V = Div 1 nn Div n + Price n Div 2 n n:The year in which the firm’s shares are expected to be sold. n n Price n :The expected share price in year n. n n:The year in which the firm’s shares are expected to be sold. n n Price n :The expected share price in year n.

4.47 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Dividend Growth Pattern Assumptions The dividend valuation model requires the forecast of all future dividends. The following dividend growth rate assumptions simplify the valuation process. Constant Growth No Growth Growth Phases The dividend valuation model requires the forecast of all future dividends. The following dividend growth rate assumptions simplify the valuation process. Constant Growth No Growth Growth Phases

4.48 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Constant Growth Model constant growth model The constant growth model assumes that dividends will grow forever at the rate g. (1 + k e ) 1 (1 + k e ) 2 (1 + k e )  V = D 0 (1+g)D 0 (1+g)  = (k e - g) D1D1 D 1 :Dividend paid at time 1. g : The constant growth rate. k e : Investor’s required return. D 1 :Dividend paid at time 1. g : The constant growth rate. k e : Investor’s required return. D 0 (1+g) 2

4.49 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Constant Growth Model Example common stock Stock CG has an expected dividend growth rate of 8%. Each share of stock just received an annual $3.24 dividend. The appropriate discount rate is 15%. What is the value of the common stock? D 1 $3.24$3.50 D 1 = $3.24 ( ) = $3.50 V CG D 1 k e $ $50 V CG = D 1 / ( k e - g ) = $3.50 / ( ) = $50 common stock Stock CG has an expected dividend growth rate of 8%. Each share of stock just received an annual $3.24 dividend. The appropriate discount rate is 15%. What is the value of the common stock? D 1 $3.24$3.50 D 1 = $3.24 ( ) = $3.50 V CG D 1 k e $ $50 V CG = D 1 / ( k e - g ) = $3.50 / ( ) = $50

4.50 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Zero Growth Model zero growth model The zero growth model assumes that dividends will grow forever at the rate g = 0. (1 + k e ) 1 (1 + k e ) 2 (1 + k e )  V ZG = D1D1 DD = keke D1D1 D 1 :Dividend paid at time 1. k e : Investor’s required return. D 1 :Dividend paid at time 1. k e : Investor’s required return. D2D2

4.51 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Zero Growth Model Example common stock Stock ZG has an expected growth rate of 0%. Each share of stock just received an annual $3.24 dividend per share. The appropriate discount rate is 15%. What is the value of the common stock? D 1 $3.24$3.24 D 1 = $3.24 ( ) = $3.24 V ZG D 1 k e $ $21.60 V ZG = D 1 / ( k e - 0 ) = $3.24 / ( ) = $21.60 D 1 $3.24$3.24 D 1 = $3.24 ( ) = $3.24 V ZG D 1 k e $ $21.60 V ZG = D 1 / ( k e - 0 ) = $3.24 / ( ) = $21.60

4.52 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. growth phases model The growth phases model assumes that dividends for each share will grow at two or more different growth rates. (1 + k e ) t V =  t=1 n  t=n+1  + D 0 (1 + g 1 ) t D n (1 + g 2 ) t Growth Phases Model

4.53 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. D 0 (1 + g 1 ) t D n+1 Growth Phases Model growth phases model Note that the second phase of the growth phases model assumes that dividends will grow at a constant rate g 2. We can rewrite the formula as: (1 + k e ) t ( k e – g 2 ) V =  t=1 n + 1 (1 + k e ) n

4.54 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Growth Phases Model Example Stock GP has an expected growth rate of 16% for the first 3 years and 8% thereafter. Each share of stock just received an annual $3.24 dividend per share. The appropriate discount rate is 15%. What is the value of the common stock under this scenario?

4.55 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Growth Phases Model Example Stock GP has two phases of growth. The first, 16%, starts at time t=0 for 3 years and is followed by 8% thereafter starting at time t=3. We should view the time line as two separate time lines in the valuation.  D 1 D 2 D 3 D 4 D 5 D 6 Growth of 16% for 3 years Growth of 8% to infinity!

4.56 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Growth Phases Model Example Note that we can value Phase #2 using the Constant Growth Model  D 1 D 2 D 3 D 4 D 5 D Growth Phase #1 plus the infinitely long Phase #2

4.57 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Growth Phases Model Example Note that we can now replace all dividends from year 4 to infinity with the value at time t=3, V 3 ! Simpler!!  V 3 = D 4 D 5 D D4k-g D4k-g We can use this model because dividends grow at a constant 8% rate beginning at the end of Year 3.

4.58 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Growth Phases Model Example Now we only need to find the first four dividends to calculate the necessary cash flows D 1 D 2 D 3 V New Time Line D4k-g D4k-g Where V 3 =

4.59 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Growth Phases Model Example Determine the annual dividends. D 0 = $3.24 (this has been paid already) D 1 $3.76 D 1 = D 0 (1 + g 1 ) 1 = $3.24(1.16) 1 =$3.76 D 2 $4.36 D 2 = D 0 (1 + g 1 ) 2 = $3.24(1.16) 2 =$4.36 D 3 $5.06 D 3 = D 0 (1 + g 1 ) 3 = $3.24(1.16) 3 =$5.06 D 4 $5.46 D 4 = D 3 (1 + g 2 ) 1 = $5.06(1.08) 1 =$5.46 Determine the annual dividends. D 0 = $3.24 (this has been paid already) D 1 $3.76 D 1 = D 0 (1 + g 1 ) 1 = $3.24(1.16) 1 =$3.76 D 2 $4.36 D 2 = D 0 (1 + g 1 ) 2 = $3.24(1.16) 2 =$4.36 D 3 $5.06 D 3 = D 0 (1 + g 1 ) 3 = $3.24(1.16) 3 =$5.06 D 4 $5.46 D 4 = D 3 (1 + g 2 ) 1 = $5.06(1.08) 1 =$5.46

4.60 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Growth Phases Model Example Now we need to find the present value of the cash flows Actual Values –0.08 Where $78 =

4.61 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Growth Phases Model Example We determine the PV of cash flows. D 1 D 1 $3.76 $3.27 PV(D 1 ) = D 1 (PVIF 15%, 1 ) = $3.76 (0.870) = $3.27 D 2 D 2 $4.36 $3.30 PV(D 2 ) = D 2 (PVIF 15%, 2 ) = $4.36 (0.756) = $3.30 D 3 D 3 $5.06 $3.33 PV(D 3 ) = D 3 (PVIF 15%, 3 ) = $5.06 (0.658) = $3.33 P 3 $5.46 P 3 = $5.46 / ( ) = $78 [CG Model] P 3 P 3 $78 $51.32 PV(P 3 ) = P 3 (PVIF 15%, 3 ) = $78 (0.658) = $51.32 We determine the PV of cash flows. D 1 D 1 $3.76 $3.27 PV(D 1 ) = D 1 (PVIF 15%, 1 ) = $3.76 (0.870) = $3.27 D 2 D 2 $4.36 $3.30 PV(D 2 ) = D 2 (PVIF 15%, 2 ) = $4.36 (0.756) = $3.30 D 3 D 3 $5.06 $3.33 PV(D 3 ) = D 3 (PVIF 15%, 3 ) = $5.06 (0.658) = $3.33 P 3 $5.46 P 3 = $5.46 / ( ) = $78 [CG Model] P 3 P 3 $78 $51.32 PV(P 3 ) = P 3 (PVIF 15%, 3 ) = $78 (0.658) = $51.32

4.62 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. D 0 ( ) t D4D4 Growth Phases Model Example intrinsic value Finally, we calculate the intrinsic value by summing all of cash flow present values. ( ) t ( 0.15–0.08 ) V =  t= ( ) n V = $ $ $ $51.32 V = $61.22

4.63 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Rates of Return(or Yields) u Rates of return is the profit on a securities or capital investment, usually expressed as an annual percentage rate. u Return is usually called yield.

4.64 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Yield to Maturity(YTM) on Bonds u

4.65 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Calculating Rates of Return (or Yields) cash flows 1. Determine the expected cash flows. market price (P 0 ) 2. Replace the intrinsic value (V) with the market price (P 0 ). market required rate of return discounted cash flows market price 3. Solve for the market required rate of return that equates the discounted cash flows to the market price. cash flows 1. Determine the expected cash flows. market price (P 0 ) 2. Replace the intrinsic value (V) with the market price (P 0 ). market required rate of return discounted cash flows market price 3. Solve for the market required rate of return that equates the discounted cash flows to the market price. Steps to calculate the rate of return (or Yield).

4.66 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Determining Bond YTM Determine the Yield-to-Maturity (YTM) for the annual coupon paying bond with a finite life. P 0 =  n t=1 (1 + k d ) t I nn = I (PVIFA k d, n ) + MV (PVIF k d, n ) n (1 + k d ) n + MV k d = YTM

4.67 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Determining the YTM $1,250 Julie Miller want to determine the YTM for an issue of outstanding bonds at Basket Wonders (BW). BW has an issue of 10% annual coupon bonds with 15 years left to maturity. The bonds have a par value of $1,000 and a current market value of $1,250. What is the YTM? $1,250 Julie Miller want to determine the YTM for an issue of outstanding bonds at Basket Wonders (BW). BW has an issue of 10% annual coupon bonds with 15 years left to maturity. The bonds have a par value of $1,000 and a current market value of $1,250. What is the YTM?

4.68 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. YTM Solution (Try 9%) $1,250 $1,250 = $100(PVIFA 9%,15 ) + $1,000(PVIF 9%, 15 ) $1,250 $1,250 = $100(8.061) + $1,000(0.275) $1,250 $1,250 = $ $ $1, [Rate is too high!] =$1, [Rate is too high!]

4.69 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. YTM Solution (Try 7%) $1,250 $1,250 = $100(PVIFA 7%,15 ) + $1,000(PVIF 7%, 15 ) $1,250 $1,250 = $100(9.108) + $1,000(0.362) $1,250 $1,250 = $ $ $1, = $1, [Rate is too low!] [Rate is too low!]

4.70 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 0.07$1, IRR$1,250 $ $1, = 0.09 – 0.07, 23= , 192= X $ $192 YTM Solution (Interpolate) $23 X =

4.71 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 0.07$1, IRR$1,250 $ $1,081 X $ $192 YTM Solution (Interpolate) $23 X =

4.72 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 0.07$1273 YTM$ YTM$1250 $ $1081 ($23)(0.02) $192 YTM Solution (Interpolate) $23 X X = X = YTM7.24% YTM = = or 7.24%

4.73 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 73 YIELD TO MATURITY u CALCULATING YIELD TO MATURITY EXAMPLE u Imagine three risk-free returns based on three Treasury bonds: Bond A,Bare pure discount types; mature in one year

4.74 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 74 Bond Ccoupon pays $50/year; matures in two years

4.75 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 75 YIELD TO MATURITY Bond Market Prices: Bond A$ Bond B$ Bond C$ WHAT IS THE YIELD-TO- MATURITY OF THE THREE BONDS?

4.76 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 76 YIELD TO MATURITY u YIELD-TO-MATURITY (YTM) u Definition: the single interest rate* that would enable investor to obtain all payments promised by the security. u very similar to the internal rate of return (IRR) measure * with interest compounded at some specified interval

4.77 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 77 YIELD TO MATURITY u CALCULATING YTM: u BOND A u Solving for r A (1 + r A ) x $ = $1000 r A = 7%

4.78 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 78 YIELD TO MATURITY u CALCULATING YTM: u BOND B u Solving for r B (1 + r B ) x $ = $1000 r B = 8%

4.79 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 79 YIELD TO MATURITY u CALCULATING YTM: u BOND C u Solving for r C (1 + r C )+{[(1+ r C )x$946.93]-$50 = $1000 r C = 7.975%

4.80 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 80 SPOT RATE u DEFINITION: Measured at a given point in time as the YTM on a pure discount security

4.81 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 81 SPOT RATE u SPOT RATE EQUATION: where P t = the current market price of a pure discount bond maturing in t years; M t = the maturity value s t = the spot rate

4.82 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 82 DISCOUNT FACTORS u EQUATION: Let d t = the discount factor

4.83 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 83 DISCOUNT FACTORS u EVALUATING A RISK FREE BOND: u EQUATION where c t = the promised cash payments n = the number of payments

4.84 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 84 FORWARD RATE u DEFINITION: the interest rate today that will be paid on money to be u borrowed at some specific future date and u to be repaid at a specific more distant future date

4.85 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 85 FORWARD RATE u EXAMPLE OF A FORWARD RATE Let us assume that $1 paid in one year at a spot rate of 7% has

4.86 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 86 FORWARD RATE u EXAMPLE OF A FORWARD RATE Let us assume that $1 paid in two years at a spot rate of 7% has a

4.87 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 87 FORWARD RATE f 1,2 is the forward rate from year 1 to year 2

4.88 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 88 FORWARD RATE u To show the link between the spot rate in year 1 and the spot rate in year 2 and the forward rate from year 1 to year 2

4.89 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 89 FORWARD RATE such that or

4.90 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 90 FORWARD RATE u More generally for the link between years t-1 and t: u or

4.91 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 91 FORWARD RATES AND DISCOUNT FACTORS u ASSUMPTION: u given a set of spot rates, it is possible to determine a market discount function u equation

4.92 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 92 YIELD CURVES u DEFINITION: a graph that shows the YTM for Treasury securities of various terms (maturities) on a particular date

4.93 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 93 YIELD CURVES u TREASURY SECURITIES PRICES u priced in accord with the existing set of spot rates and u associated discount factors

4.94 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 94 YIELD CURVES u SPOT RATES FOR TREASURIES u One year is less than two year; u Two year is less than three- year, etc.

4.95 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 95 YIELD CURVES u YIELD CURVES AND TERM STRUCTURE u yield curve provides an estimate of u the current TERM STRUCTURE OF INTEREST RATES u yields change daily as YTM changes

4.96 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 96 TERM STRUCTURE THEORIES u THE FOUR THEORIES 1.THE UNBIASED EXPECTATION THEORY 2. THE LIQUIDITY PREFERENCE THEORY 3. MARKET SEGMENTATION THEORY 4. PREFERRED HABITAT THEORY

4.97 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 97 TERM STRUCTURE THEORIES u THEORY 1: UNBIASED EXPECTATIONS u Basic Theory: the forward rate represents the average opinion of the expected future spot rate for the period in question u in other words, the forward rate is an unbiased estimate of the future spot rate.

4.98 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 98 TERM STRUCTURE THEORY: Unbiased Expectations u THEORY 1: UNBIASED EXPECTATIONS u A Set of Rising Spot Rates u the market believes spot rates will rise in the future u the expected future spot rate equals the forward rate u in equilibrium es 1,2 = f 1,2 where es 1,2 = the expected future spot f 1,2 = the forward rate

4.99 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 99 TERM STRUCTURE THEORY: Unbiased Expectations u THE THEORY STATES: u The longer the term, the higher the spot rate, and u If investors expect higher rates, u then the yield curve is upward sloping u and vice-versa

4.100 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 100 TERM STRUCTURE THEORY: Unbiased Expectations u CHANGING SPOT RATES AND INFLATION u Why do investors expect rates to rise or fall in the future? u spot rates = nominal rates u because we know that the nominal rate is the real rate plus the expected rate of inflation

4.101 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 101 TERM STRUCTURE THEORY: Unbiased Expectations u CHANGING SPOT RATES AND INFLATION u Why do investors expect rates to rise or fall in the future? u if either the spot or the nominal rate is expected to change in the future, the spot rate will change

4.102 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 102 TERM STRUCTURE THEORY: Unbiased Expectations u CHANGING SPOT RATES AND INFLATION u Why do investors expect rates to rise or fall in the future? u if either the spot or the nominal rate is expected to change in the future, the spot rate will change

4.103 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 103 TERM STRUCTURE THEORY: Unbiased Expectations u Current conditions influence the shape of the yield curve, such that u if deflation expected, the term structure and yield curve are downward sloping u if inflation expected, the term structure and yield curve are upward sloping

4.104 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 104 TERM STRUCTURE THEORY: Unbiased Expectations u PROBLEMS WITH THIS THEORY: u upward-sloping yield curves occur more frequently u the majority of the time, investors expect spot rates to rise u not realistic position

4.105 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 105 TERM STRUCTURE THEORY: Liquidity Preference u BASIC NOTION OF THE THEORY u investors primarily interested in purchasing short-term securities to reduce interest rate risk

4.106 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 106 TERM STRUCTURE THEORY: Liquidity Preference u BASIC NOTION OF THE THEORY u Price Risk u maturity strategy is more risky than a rollover strategy u to convince investors to buy longer-term securities, borrowers must pay a risk premium to the investor

4.107 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 107 TERM STRUCTURE THEORY: Liquidity Preference u BASIC NOTION OF THE THEORY u Liquidity Premium u DEFINITION: the difference between the forward rate and the expected future rate

4.108 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 108 TERM STRUCTURE THEORY: Liquidity Preference u BASIC NOTION OF THE THEORY u Liquidity Premium Equation L = es 1,2 - f 1,2 where L is the liquidity premium

4.109 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 109 TERM STRUCTURE THEORY: Liquidity Preference u How does this theory explain the shape of the yield curve? u rollover strategy u at the end of 2 years $1 has an expected value of $1 x (1 + s 1 ) (1 + es 1,2 )

4.110 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 110 TERM STRUCTURE THEORY: Liquidity Preference u How does this theory explain the shape of the yield curve? u whereas a maturity strategy holds that $1 x (1 + s 2 ) 2 u which implies with a maturity strategy, you must have a higher rate of return

4.111 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 111 TERM STRUCTURE THEORY: Liquidity Preference u How does this theory explain the shape of the yield curve? u Key Idea to the theory: The Inequality holds $1(1+s 1 )(1 +es 1,2 )<$1(1 + s 2 ) 2

4.112 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 112 TERM STRUCTURE THEORY: Liquidity Preference u SHAPES OF THE YIELD CURVE: u a downward-sloping curve u means the market believes interest rates are going to decline

4.113 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 113 TERM STRUCTURE THEORY: Liquidity Preference u SHAPES OF THE YIELD CURVE: u a flat yield curve means the market expects interest rates to decline

4.114 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 114 TERM STRUCTURE THEORY: Liquidity Preference u SHAPES OF THE YIELD CURVE: u an upward-sloping curve means rates are expected to increase

4.115 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 115 TERM STRUCTURE THEORY: Market Segmentation u BASIC NOTION OF THE THEORY u various investors and borrowers are restricted by law, preference or custom to certain securities

4.116 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 116 TERM STRUCTURE THEORY: Liquidity Preference u WHAT EXPLAINS THE SHAPE OF THE YIELD CURVE? u Upward-sloping curves mean that supply and demand intersect for short-term is at a lower rate than longer-term funds u cause: relatively greater demand for longer-term funds or a relative greater supply of shorter-term funds

4.117 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 117 TERM STRUCTURE THEORY: Preferred Habitat u BASIC NOTION OF THE THEORY: u Investors and borrowers have segments of the market in which they prefer to operate

4.118 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 118 TERM STRUCTURE THEORY: Preferred Habitat u When significant differences in yields exist between market segments, investors are willing to leave their desired maturity segment

4.119 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 119 TERM STRUCTURE THEORY: Preferred Habitat u Yield differences determined by the supply and demand conditions within the segment

4.120 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 120 TERM STRUCTURE THEORY: Preferred Habitat u This theory reflects both u expectations of future spot rates u expectations of a liquidity premium

4.121 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Determining Semiannual Coupon Bond YTM P 0 =  n2nn2n t=1 (1 + k d /2 ) t I / 2 nn = (I /2) (PVIFA k d /2, 2 n ) + MV(PVIF k d /2, 2 n ) + MV [ 1 + (k d / 2) 2 ] –1 = YTM Determine the Yield-to-Maturity (YTM) for the semiannual coupon paying bond with a finite life. n (1 + k d /2 ) 2 n

4.122 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Determining the Semiannual Coupon Bond YTM $950 Julie Miller want to determine the YTM for another issue of outstanding bonds. The firm has an issue of 8% semiannual coupon bonds with 20 years left to maturity. The bonds have a current market value of $950. What is the YTM? $950 Julie Miller want to determine the YTM for another issue of outstanding bonds. The firm has an issue of 8% semiannual coupon bonds with 20 years left to maturity. The bonds have a current market value of $950. What is the YTM?

4.123 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Determining Semiannual Coupon Bond YTM [ (1 + k d / 2) 2 ] –1 = YTM YTM=effective annual interest rate Determine the Yield-to-Maturity (YTM) for the semiannual coupon paying bond with a finite life. [ ( ) 2 ] –1 = or 8.71% Note: make sure you utilize the calculator answer in its DECIMAL form.

4.124 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Bond Price - Yield Relationship Discount Bond Discount Bond – The market required rate of return is more than the coupon rate, the price of the bond will be less than its face value (Par > P 0 ). Such a bond is said to be selling at a discount from face value.

4.125 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Bond Price - Yield Relationship u Premium Bond u Premium Bond – The market required rate of return is less than the stated coupon rate, the price of the bond will be more than its face value (P0 > Par). Such a bond is said to be selling at a premium over face value.

4.126 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Bond Price - Yield Relationship u Par Bond u Par Bond – The market required rate of return equals the stated coupon rate, the price will equal the face value (P0 = Par). Such a bond is said to be selling at par.

4.127 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Behavior of Bond Prices u If interest rates rise so that the market required rate of return increases, the bond price will fall. u If interest rates fall, the bond price will increase. In short, interest rates and bond prices move in opposite direction.

4.128 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Behavior of Bond Prices u The more bond price will change, the longer its maturity. u The more bond price will change, the lower the coupon rate. In short, bond price volatility is inversely related to coupon rate.

4.129 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Determining the Yield on Preferred Stock Determine the yield for preferred stock with an infinite life. P 0 = Div P / k P Solving for k P such that k P = Div P / P 0 Determine the yield for preferred stock with an infinite life. P 0 = Div P / k P Solving for k P such that k P = Div P / P 0

4.130 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Preferred Stock Yield Example k P = $10 / $100. k P 10% k P = 10%. k P = $10 / $100. k P 10% k P = 10%. Assume that the annual dividend on each share of preferred stock is $10. Each share of preferred stock is currently trading at $100. What is the yield on preferred stock?

4.131 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Determining the Yield on Common Stock Assume the constant growth model is appropriate. Determine the yield on the common stock. P 0 = D 1 / ( k e – g ) Solving for k e such that k e = ( D 1 / P 0 ) + g Assume the constant growth model is appropriate. Determine the yield on the common stock. P 0 = D 1 / ( k e – g ) Solving for k e such that k e = ( D 1 / P 0 ) + g

4.132 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Common Stock Yield Example k e = ( $3 / $30 ) + 5% k e 15% k e = 10% + 5% = 15% k e = ( $3 / $30 ) + 5% k e 15% k e = 10% + 5% = 15% Assume that the expected dividend (D 1 ) on each share of common stock is $3. Each share of common stock is currently trading at $30 and has an expected growth rate of 5%. What is the yield on common stock?