Question

What is the duration of a 10-year bond, selling for $877.11, with an 8% annual coupon? a. 7.62 b.7.33 c.7.04 d. 6.95

Answer 1

Par Value of Bond = $1,000

Annual Coupon Rate = 8%

Hence, coupon amount = $80

Let us depict the yearly cash flows given by this bond :-

А B в C D Years Cash Flow Hoc vouw 1080

Bond is currently trading at $877.11.

Let us use "Goal Seek" function to find out the discount rate for arriving at the current price of bond

Using Goal seek we find that discount rate =10%

Attaching the calculations:-

А в C D Discount Rate 10% Years 0.68 Cova un AwN Cash Flow PV Factor PV of Cash Flows 800.91 72.73 0.83 66.12 0.75 60.11 54.64 0.62 49.67 80 0.56 45.16 0.51 41.05 80 0.47 37.32 80 0.42 33.93 1080 0.39 416.39 Sum 877.11

A B Discount Rate 0.1 80 2 80 Years Cash Flow PV Factor =1/(1+$D$2) B5 =1/(1+$D$2) B6 =1/(1+$D$2)^B7 =1/(1+$D$2)^B8 =1/(1+$D$2)^B9 =1/(1+$D$2)^B10 7 80 =1/(1+$D$2)^B11 =1/(1+$D$2)^B12 9 80 =1/(1+$D$2)^B13 10 =1080 =1/(1+$D$2)^B14 Sum PV of Cash Flows =C5*D5 =C6*D6 =C7*D7 =C8*D8 =C9*D9 =C10*D10 =C11*011 =C12*D12 =C13*D13 =C14*D14 =SUM(E5:E14) 80

Now, let us calculate the Present Value of Weighted Cash Flow, by multiplying the "PV of Cash Flows" column with Years column.

Attaching the calculations:-

A B C D E Discount Rate 10% Years Cash Flow PV Factor PV of Cash Flows PV of Weighted Cash Flow 800.91 72.73 72.73 80 0.83 66.12 132.23 0.75 60.11 180.32 0.68 54.64 218.56 0.62 49.67 248.37 80 0.56 45.16 270.95 0.51 41.05 287.37 0.47 37.32 298.56 80 0.42 33.93 305.35 1080 0.39 416.39 4163.87 Sum 877.11 6178.31

A B _c C Discount Rate 0.1 80 Years Cash Flow PV Factor 80 =1/(1+$D$2)^B5 =1/(1+$D$2)^B6 =1/(1+$D$2)^B7 =1/(1+$D$2)^B8 =1/(1+$D$2)^B9 =1/(1+$D$2)^B10 =1/(1+$D$2)^B11 =1/(1+$D$2)^B12 9 =1/(1+$D$2)^B13 10 =1080 =1/(1+$D$2) B14 Sum PV of Cash Flows PV of Weighted Cash Flow =C5*D5 =E5*B5 =C6*D6 =E6*B6 =C7*D7 =E7*B7 =C8*D8 =E8*B8 =C9*D9 =E9*B9 =C10*D10 =E10*B10 =C11*011 =E11*B11 =C12*D12 =E12*B12 =C13*D13 =E13*B13 =C14*D14 =E14*B14 =SUM(E5:E14) =SUM(F5:F14) 80 00

To arrive at the Duration we have to divide the sum of "PV of Weighted Cash Flow" by the current market price.

Hence, Duration = (6,178.31 / 877.11) = 7.04 years

Answer is Option C