Question

Find the duration of a 6% coupon bond making semiannually coupon payments if it has three years until maturity and has a yield to maturity of 6%. What is the duration if the yield to maturity is 10%? Note: The face value of the bond is $100. (Do not round intermediate calculations. Round your answers to 4 decimal places.) Duration 6% YTM years 10% YTM years

Answer 1

A В C E F G Weight based on present value Present Value Cashflow PVF @3% Time*Weight Time (Cashflow PVF) 2 3 0.9709 2.912621359 0.0291 0.0291 0.9426 0.0566 2 3 2.827787727 0.0283 5 2.745424978 3 3 0.9151 0.0275 0.0824 6 0.1066 4 3 0.8885 2.665461144 0.0267 7 5 3 0.8626 2.587826353 0.0259 0.1294 86.26087844 8 6 103 0.8375 0.8626 5.1757 Total 5.5797 10 Duration of semiannual bond = Sum of (time* weight) 2 11 = 5.5797 2 12 =2.7899 years 13 14 15 b) Present Value Weight based (Cashflow PVF) on present value Cashflow PVF @5% Time*Weight Time 16 17 0.0318 1 3 0.9524 2.8571 0.0318 18 2 3 0.9070 2.7211 0.0303 0.0606 19 0.0288 3 3 0.8638 2.5915 0.0865 20 2.4681 4 3 0.8227 0.0275 0.1099 21 5 3 0.7835 2.3506 0.0262 0.1308 6 103 0.7462 76.8602 0.8554 5.1326 23 TOTAL 89.8486 TOTAL 5.5522 Duration of semiannual bond 5.5522 2 2.7761 years 24 I LO LO LC LO LO

EXCEL FORMULA:

A В C E F G Weight based on present value -E3/100 -E4/100 =E5/100 -E6/100 =E7/100 -E8/100 Present Value Time*Weight Cashflow PVF @3% Time (Cashflow PVF) 2 = 100*6% / 2 -100*6%/2 -100*6%/2 = 100*6% /2 = 100*6% / 2 =1/ (1+3%)^B3 =1/(1+3% )^B4 -1/ (1+3% )^B5 =1/(1+3% )^B6 -1/ (1+3% )^B7 - 1/ (1+3% )^B8 -C3*D3 -C4*D4 =F3*B3 =F4*B4 1 4 2 -C5*D5 -C6*D6 =F5*B5 3 6 F6*B6 4 -C7*D7 =F7*B7 7 6 -100+3 -C8*D8 8 SUM(G3:G8) Total 10 Duration of semiannual bond Sum of (time* weight)/ 2 = 5.5797/2 11 12 13 2.7899 14 15 b) Present ValueWeight based (Cashflow PVF) on present Time*Weight Cashflow PVF @5% Time 16 value =1/(1+5%)^B17 - 1/ (1+5% )^B18 =1/(1+5% )^B19 =1/(1+5% )^B20 -1/ (1+5% )^B21 =1/(1+5% )^B22 -100*6% / 2 -100*6%/2 -100*6%/2 -100*6%/2 = 100*6% / 2 -C17*D17 -C18*D18 -C19*D19 =E17/E23 =E18/E23 =E19/E23 =E20/E23 -E21/E23 -E22/E23 =F17*B17 17 1 18 F18*B18 2 19 F19*B19 3 -F20*B20 -F21*B21 -C20*D20 -C21*D21 -C22*D22 20 4 21 =F22 B22 -100+3 22 23 =SUM(G17:G22 ТОTAL -SUM(E17:E22) TOTAL 24 Duration of semiannual bond= 5.5522 / 2 2.7761 years Ln LO