Semiannual Compounding A non-zero coupon bond adjusted for semiannual compounding. (1+k/2)1(1+k2)+….+12+Mv /2/2 1+k丿2)2*n 312 MV #7(1+ka12)(1+k/2)2n 1/2(PVIFAK /22*n)+ MV(PVIFK-/22*n) 4-16
4-16 (1 + kd /2 ) 2 * n (1 + kd /2 ) 1 Semiannual Compounding A non-zero coupon bond adjusted for semiannual compounding. V = + + ... + I / 2 I / 2 + MV = 2*n t=1 (1 + kd /2 ) t I / 2 = I/2 (PVIFAkd /2 , 2*n) + MV (PVIFkd /2 , 2*n) (1 + kd /2 ) 2 * + n MV I / 2 (1 + kd /2 ) 2
Semiannual Coupon Bond Example Bond c has a $1,000 face value and provides an 8% semiannual coupon for 15 years. The appropriate discount rate is 10%(annual rate What is the value of the coupon bond? V=$40(PVFA5%,30)+$100(PVF5%,3 =$40(15373)+$100(231) [Table M [Table 1 =$61492+$23100 =$84592 4-17
4-17 V = $40 (PVIFA5%, 30) + $1,000 (PVIF5%, 30) = $40 (15.373) + $1,000 (.231) [Table IV] [Table II] = $614.92 + $231.00 = $845.92 Semiannual Coupon Bond Example Bond C has a $1,000 face value and provides an 8% semiannual coupon for 15 years. The appropriate discount rate is 10% (annual rate). What is the value of the coupon bond?
Preferred Stock valuation Preferred Stock is a type of stock that promises a(usually ) fixed dividend but at the discretion of the board of directors Preferred Stock has preference over common stock in the payment of dividends and claims on assets 4-18
4-18 Preferred Stock is a type of stock that promises a (usually) fixed dividend, but at the discretion of the board of directors. Preferred Stock has preference over common stock in the payment of dividends and claims on assets. Preferred Stock Valuation
Preferred Stock valuation Div DiV DiVp 1+k)2 ■■ (1+kp) ∞Div ∑ 七1(1+k) or DivP(PVIFA K This reduces to a perpetuity VE DiVo/k 4-19
4-19 Preferred Stock Valuation This reduces to a perpetuity! (1 + kP) 1 (1 + kP) 2 (1 + kP) V = + + ... + DivP DivP DivP = t=1 (1 + kP) t DivP or DivP (PVIFA kP , ) V = DivP / kP
Preferred Stock EXample Stock PS has an 8%, $100 par value issue outstanding. The appropriate discount rate is 10%. What is the value of the preferred stock? Divp=$100(8%)=$8.00 =10% =Divp/kp=$8.00/10% =$80 4-20
4-20 Preferred Stock Example DivP = $100 ( 8% ) = $8.00. kP = 10%. V = DivP / kP = $8.00 / 10% = $80 Stock PS has an 8%, $100 par value issue outstanding. The appropriate discount rate is 10%. What is the value of the preferred stock?