Question

Suppose a two-year bond with annual 10% coupon rate is trading at par. The bonds face value is $1,000. What is the Macaulays duration? Please show formula.

Answer 1

The Macaulays duration is calculated as below:

Period (A)	Cash Flow (B)	Present Value Discount Factor (C)	A*B*C
1	100 (1,000*10%)	0.9091 [1/(1+10%)^1]	90.91
2	1,100 (1,000*10% + 1,000)	0.8264 [1/(1+10%)^2]	1,818.18
Present Value of Cash Flows, Weighed by Time to Receipt			1,909.09

Macaulays Duration = Present Value of Cash Flows, Weighed by Time to Receipt/Bond's Current Market Value = 1,909.09/1,000 = 1.91 (answer)

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Notes:

1) As the bond is trading at par, the face value of bonds and current market value of bonds will be the same at $1,000. The bond's yield to maturity will be same as coupon rate as the bond is trading at par.

2) The formula can be derived as follows:

Macaulays Duration = [(Cash Flow Year 1*Period*Present Value Discount Factor Year 1) + (Cash Flow Year 2*Period*Present Value Discount Factor Year 2)]/Current Market Value of Bonds