Different Types of Bonds A non-zero coupon bond is a coupon paying bond with a finite life 1+k)1(*∥2+…人+MV (1+k) MV ∑ (1+k)(1+k) I(PVIFAK.)+ MV(PVIF K-n) 4-11
4-11 Different Types of Bonds A non-zero coupon bond is a coupon paying bond with a finite life. (1 + kd ) 1 (1 + kd ) 2 (1 + kd ) V = + + ... + n I I I + MV = n t=1 (1 + kd ) t I = I (PVIFA kd , n ) + MV (PVIF kd , n ) (1 + kd ) + n MV
Coupon Bond Example 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? =$80(PVFA10%,30)+$1,000(PVF0%,30 =$80(9427)+$1,000057) [ TableMM[Table的 =$75416+$57.00 =$811.16. 4-12
4-12 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? V = $80 (PVIFA10%, 30) + $1,000 (PVIF10%, 30) = $80 (9.427) + $1,000 (.057) [Table IV] [Table II] = $754.16 + $57.00 = $811.16. Coupon Bond Example
Different Types of Bonds 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 MV(PVIFK,n) (1+k)2 d 4-13
4-13 Different Types of Bonds 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. (1 + kd ) n V = MV = MV (PVIFkd , n)
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? V=$1,000(PⅦF10%,30) =$1,000(057) =$5700 4-14
4-14 V = $1,000 (PVIF10%, 30) = $1,000 (.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?
Semiannual Compounding Most bonds in the U.S. pay interest twice a year (1 2 of the annual coupon) Adjustments needed (1)Divide ka by 2 (2)Multiply n by 2 (3)Divide I by 2 4-15
4-15 Semiannual Compounding (1) Divide kd by 2 (2) Multiply n by 2 (3) Divide I by 2 Most bonds in the U.S. pay interest twice a year (1/2 of the annual coupon). Adjustments needed: