Question

Find the Macaulay's Duration of the following bond using a table of cash flows, present values, etc. TTM = 4 years, Coupon rate = 6%, Par Value = $1,000, YTM = 8%, coupon is paid semiannually.

Answer 1

Macaulay Duration of the given bond =3.59875575 Years.

Detailed calculation as follows:

1 E (All amounts in $) 2 Face Value 1000 3 Coupon rate 6% Semiannual interest= B2*B3/F5 = 4 Term (No. of years) 5 Frequency Semi annual No. of times a year (k) 6 Annual Interest Rate(YTM) 8% Semiannual discount rate (o)= B6/2 = 30 0.04 7 1 5 30 8 Cash Flow Period (i) 2 4 8 Total 9 Interest 30 30 30 30 30 30 30 30 10 Redemption 1000 11 Total cash flow (CF) 30 30 30 30 30 30 1030 12 Present value Formula CF/(1+r)^i CF/(1+r)^i CF/(1+r)^i CF/(1+r)^i CF/(1+r)^i CF/(1+r)^i CF/(1+r)^i CF/(1+r)^i. Cell reference B11/(1+F6)^B8 C11/(1+F6)^CE D11/(1+F6)^DE E11/(1+F6)^EE F11/(1+F6)^F8 G11/(1+F6)^G8 G11/(1+F6)^H8 G11/(1+F6)^18 value 28.84615385 27.73668639 26.66989076 25.644125724.6578132 23.70943577 22.7975344 752.6109112 932.672551 17 Proportion of PV 18 Cell ref B15/J15 C 15/J15 D15/J15 E15/J15 F15/J15 G15/115 H15/115 115/J15 Value 0.03092849 0.029738933 0.028595128 0.02749532 0.026437803 0.025420964 0.024443235 0.806940131 19 20 0.10998126 0.132189015 0.152525787 0.171102645 6.455521052 7.1975115 21 Time* proprtion of PV 22 Macaulay Duration (Years) 0.03092849 0.059477866 =L21/F5= 0.085785383 3.59875575