Value of a Financial Asset Pr. Zoubida SAMLAL

Value Book value: value of an asset as shown on a firm’s balance sheet; historical cost. Liquidation value: amount that could be received if an asset were sold individually. Market value: observed value of an asset in the marketplace; determined by supply and demand. Intrinsic value: economic or fair value of an asset; the present value of the asset’s expected future cash flows.

Security Valuation In general, the intrinsic value of an asset = the present value of the stream of expected cash flows discounted at an appropriate required rate of return. Can the intrinsic value of an asset differ from its market value?

Valuation C t = cash flow to be received at time t. k = the investor’s required rate of return. V = the intrinsic value of the asset. V = t = 1 n $C t (1 + k) t

Valuation and Characteristics of Bonds

Characteristics of Bonds  Bonds pay fixed coupon (interest) payments at fixed intervals (usually every six months) and pay the par value at maturity.

Types of Bonds Debentures - unsecured bonds. Subordinated debentures - unsecured “junior” debt. Mortgage bonds - secured bonds Zeros - bonds that pay only par value at maturity; no coupons. Junk bonds - speculative or below- investment grade bonds; rated BB and below. High-yield bonds.

Bond Valuation Discount the bond’s cash flows at the investor’s required rate of return.

Bond Valuation Discount the bond’s cash flows at the investor’s required rate of return. – The coupon payment stream (an annuity).

Bond Valuation Discount the bond’s cash flows at the investor’s required rate of return. – The coupon payment stream (an annuity). – The par value payment (a single sum).

Characteristics of Bonds  Bonds pay fixed coupon (interest) payments at fixed intervals (usually every six months) and pay the par value at maturity n $I $I $I $I $I $I+$M

Example: AT&T 6 ½ 32 Par value = $1,000 Coupon = 6.5% or par value per year, or $65 per year ($32.50 every six months). Maturity = 28 years (matures in 2032). Issued by AT&T.

Example: AT&T 6 ½ 32 Par value = $1,000 Coupon = 6.5% or par value per year, or $65 per year ($32.50 every six months). Maturity = 28 years (matures in 2032). Issued by AT&T … 28 $65 $65 $65 $65 $65 $65 +$1000

Bond Valuation V b = $I t (PVIFA k b, n ) + $M (PVIF k b, n ) $I t $M (1 + k b ) t (1 + k b ) n V b = + n t = 1 

LO 8 Solve present value problems related to deferred annuities and bonds. Two Cash Flows: Periodic interest payments (annuity). Principal paid at maturity (single-sum). Bonds current market value is the combined present values of the both cash flows. Valuation of Long-Term Bonds ,000 $70, ,000 1,000,000

BE6-15 Arcadian Inc. issues $1,000,000 of 7% bonds due in 10 years with interest payable at year-end. The current market rate of interest for bonds is 8%. What amount will Arcadian receive when it issues the bonds? 01 Present Value ,000 $70, ,000 Valuation of Long-Term Bonds 1,070,000 LO 8 Solve present value problems related to deferred annuities and bonds.

Table A-4 LO 8 Solve present value problems related to deferred annuities and bonds. $70,000 x = $469,706 Interest PaymentFactorPresent Value PV of Interest Valuation of Long-Term Bonds

Table A-2 LO 8 Solve present value problems related to deferred annuities and bonds. $1,000,000 x = $463,190 Principal PaymentFactorPresent Value PV of Principal Valuation of Long-Term Bonds

BE6-15 Arcadian Inc. issues $1,000,000 of 7% bonds due in 10 years with interest payable at year-end. Valuation of Long-Term Bonds LO 8 Solve present value problems related to deferred annuities and bonds. Present value of Interest $469,706 Present value of Principal 463,190 Bond current market value $932,896

Bond Example Suppose our firm decides to issue 20-year bonds with a par value of $1,000 and annual coupon payments. The return on other corporate bonds of similar risk is currently 12%, so we decide to offer a 12% coupon interest rate. What would be a fair price for these bonds?

P/YR = 1 N = 20 I%YR = 12 FV = 1,000 PMT = 120 Solve PV = -$1,000 Note: If the coupon rate = discount rate, the bond will sell for par value.

Bond Example Mathematical Solution: PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) PV = 120 (PVIFA.12, 20 ) (PVIF.12, 20 )

Bond Example Mathematical Solution: PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) PV = 120 (PVIFA.12, 20 ) (PVIF.12, 20 ) 1 PV = PMT 1 - (1 + i) n + FV / (1 + i) n i

Suppose interest rates fall immediately after we issue the bonds. The required return on bonds of similar risk drops to 10%. What would happen to the bond’s intrinsic value?

P/YR = 1 Mode = end N = 20 I%YR = 10 PMT = 120 FV = 1000 Solve PV = -$1,170.27

P/YR = 1 Mode = end N = 20 I%YR = 10 PMT = 120 FV = 1000 Solve PV = -$1, Note: If the coupon rate > discount rate, the bond will sell for a premium.

Bond Example Mathematical Solution: PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) PV = 120 (PVIFA.10, 20 ) (PVIF.10, 20 )

Bond Example Mathematical Solution: PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) PV = 120 (PVIFA.10, 20 ) (PVIF.10, 20 ) 1 PV = PMT 1 - (1 + i) n + FV / (1 + i) n i

Bond Example Mathematical Solution: PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) PV = 120 (PVIFA.10, 20 ) (PVIF.10, 20 ) 1 PV = PMT 1 - (1 + i) n + FV / (1 + i) n i PV = (1.10 ) / (1.10) 20 =$1,

Suppose interest rates rise immediately after we issue the bonds. The required return on bonds of similar risk rises to 14%. What would happen to the bond’s intrinsic value?

P/YR = 1 Mode = end N = 20 I%YR = 14 PMT = 120 FV = 1000 Solve PV = -$867.54

P/YR = 1 Mode = end N = 20 I%YR = 14 PMT = 120 FV = 1000 Solve PV = -$ Note: If the coupon rate < discount rate, the bond will sell for a discount.

Bond Example Mathematical Solution: PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) PV = 120 (PVIFA.14, 20 ) (PVIF.14, 20 ) 1 PV = PMT 1 - (1 + i) n + FV / (1 + i) n i 1 PV = (1.14 ) / (1.14) 20 = $

Zero Coupon Bonds No coupon interest payments. The bond holder’s return is determined entirely by the price discount.

Zero Example Suppose you pay $508 for a zero coupon bond that has 10 years left to maturity. What is your yield to maturity?

Zero Example Suppose you pay $508 for a zero coupon bond that has 10 years left to maturity. What is your yield to maturity? $508 $1000

Zero Example P/YR = 1 Mode = End N = 10 PV = -508 FV = 1000 Solve: I%YR = 7%

Mathematical Solution: PV = FV (PVIF i, n ) 508 = 1000 (PVIF i, 10 ).508 = (PVIF i, 10 ) [use PVIF table] PV = FV /(1 + i) = 1000 /(1 + i) = (1 + i) 10 i = 7% 0 10 PV = -508 FV = 1000