Example 6.1 Find present values based on the payment period How many coupon payments are there? What is the semiannual coupon payment? What is the semiannual yield? ·B=$70[1-1/(1.08)14]/.08+$1,000/(1.08)14=$917.56 .Or PMT=70;N=14;IY=8;FV=1,000;CPT PV=-917.56
10 Example 6.1 n Find present values based on the payment period q How many coupon payments are there? q What is the semiannual coupon payment? q What is the semiannual yield? § B = $70[1 – 1/(1.08)14] / .08 + $1,000 / (1.08)14 = $917.56 § Or PMT = 70; N = 14; I/Y = 8; FV = 1,000; CPT PV = -917.56
Interest Rate Risk Change in price due to changes in interest rates Interest rates up,bond price down! Long-term bonds have more interest rate risk than short-term bonds More-distant cash flows are more adversely affected by an increase in interest rates Lower coupon rate bonds have more interest rate risk than higher coupon rate bonds More of the bond's value is deferred to maturity (thus,for a longer time)if the coupons are small 11
11 Interest Rate Risk n Change in price due to changes in interest rates q Interest rates up, bond price down! q Long-term bonds have more interest rate risk than short-term bonds n More-distant cash flows are more adversely affected by an increase in interest rates q Lower coupon rate bonds have more interest rate risk than higher coupon rate bonds n More of the bond’s value is deferred to maturity (thus, for a longer time) if the coupons are small
Figure 6.2 Bond value ($ 2,000 $1,768.62 30-year bond 1,500 $1,047.62 1-year bond 1,000 $916.67 500 $502.11 Interest 5 10 15 20 rate (% Value of a Bond with a 10 Percent Coupon Rate for Different Interest Rates and Maturities Time to Maturity Interest Rate 1 Year 30 Years 5% $1,047.62 $1,768.62 1 1,000.00 1,000.00 15 956.52 671.70 20 916.67 502.11 12
12 Figure 6.2
Computing YTM Yield to maturity is the rate implied by the current bond price Finding the YTM requires trial and error if you do not have a financial calculator,and is similar to the process for finding r with an annuity If you have a financial calculator,enter N,PV, PMT and FV,remembering the sign convention(PMT and FV need to have the same sign;PV the opposite sign) 13
13 Computing YTM n Yield to maturity is the rate implied by the current bond price n Finding the YTM requires trial and error if you do not have a financial calculator, and is similar to the process for finding r with an annuity n If you have a financial calculator, enter N, PV, PMT and FV, remembering the sign convention (PMT and FV need to have the same sign; PV the opposite sign)