Value of a Financial Asset Pr Zoubida SAMLAL

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

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 belowinvestment 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. $I 0 $I 1 $I $I+$M 2 . . . n

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. $65 0 1 $65 2 $65 … $65 +$1000 28

Bond Valuation n Vb = S t=1 $It (1 + kb)t $M + (1 + kb)n Vb = $It (PVIFA kb, n) + $M (PVIF kb, n)

Valuation of Long-Term 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. 1, 000 $70, 000 70, 000 . . . 0 1 2 3 4 9 10 LO 8 Solve present value problems related to deferred annuities and bonds.

Valuation of Long-Term Bonds Present Value $70, 000 70, 000 1, 070, 000 . . . 0 1 2 3 4 9 10 BE 6 -15 Arcadian Inc. issues $1, 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? LO 8 Solve present value problems related to deferred annuities and bonds.

Valuation of Long-Term Bonds Table A-4 $70, 000 x Interest Payment 6. 71008 Factor = PV of Interest $469, 706 Present Value LO 8 Solve present value problems related to deferred annuities and bonds.

Valuation of Long-Term Bonds PV of Principal Table A-2 $1, 000 x . 46319 Principal Payment Factor = $463, 190 Present Value LO 8 Solve present value problems related to deferred annuities and bonds.

Valuation of Long-Term Bonds BE 6 -15 Arcadian Inc. issues $1, 000 of 7% bonds due in 10 years with interest payable at year-end. Present value of Interest $469, 706 Present value of Principal 463, 190 Bond current market value $932, 896 LO 8 Solve present value problems related to deferred annuities and bonds.

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?

120 0 1 120 2 120 3 . . . 1000 120 20 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 ) + 1000 (PVIF. 12, 20)

Bond Example Mathematical Solution: PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) PV = 120 (PVIFA. 12, 20 ) + 1000 (PVIF. 12, 20) PV = PMT 1 1 - (1 + i)n i + FV / (1 + i)n

• 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, 170. 27 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 ) + 1000 (PVIF. 10, 20 )

Bond Example Mathematical Solution: PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) PV = 120 (PVIFA. 10, 20 ) + 1000 (PVIF. 10, 20 ) PV = PMT 1 1 - (1 + i)n i + FV / (1 + i)n

Bond Example Mathematical Solution: PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) PV = 120 (PVIFA. 10, 20 ) + 1000 (PVIF. 10, 20 ) PV = PMT 1 1 - (1 + i)n i PV = 120 1 - 1 (1. 10 )20. 10 + FV / (1 + i)n + 1000/ (1. 10) 20 =$1, 170. 27

• 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 = -$867. 54 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 ) + 1000 (PVIF. 14, 20 ) PV = PMT PV = 120 1 1 - (1 + i)n i 1 1 - (1. 14 )20. 14 + FV / (1 + i)n + 1000/ (1. 14) 20 = $867. 54

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 0 $1000 10

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

PV = -508 FV = 1000 0 Mathematical Solution: PV = FV (PVIF i, n ) 508 = 1000 (PVIF i, 10 ). 508 = (PVIF i, 10 ) [use PVIF table] PV = FV /(1 + i) 10 508 = 1000 /(1 + i)10 1. 9685 = (1 + i)10 i = 7% 10