Question

What is the Macaulay duration in years of a 3% coupon bond with 2 years to maturity and a face value of $100? Assume the bond is trading at a yield of 8%, and that the next coupon payment is to be made exactly 6 months from today.

Round your answer to 3 decimal places. For example if your answer is 5.5175, then please write down 5.518.

Answer 1

Period	Cash Flow from Bond	Discounting factor = 1/(1+R)^N	PV of the cash flows = Cash flow x Df	Weighted cash flow = Period x Cash flow	Present value of weighted cash flow = Weighted Cash flow x Df
N	CF	Df = 1/(1+8%/2)^N	PV = CF x Df	WCF = CF x N	WPV = WCF x Df
1.00	1.5000	0.9615	1.4423	1.5000	1.4423
2.00	1.5000	0.9246	1.3868	3.0000	2.7737
3.00	1.5000	0.8890	1.3335	4.5000	4.0005
4.00	101.5000	0.8548	86.7626	406.0000	347.0505
		Total = P = Price =	90.9253	Total = Weighted Price = WP	355.2670
Period	Cash Flow from Bond	Discounting factor = 1/(1+R)^N	PV of the cash flows = Cash flow x Df	Weighted cash flow = Period x Cash flow	Present value of weighted cash flow = Weighted Cash flow x Df
N	CF	Df = 1/(1+8%/2)^N	PV = CF x Df	WCF = CF x N	WPV = WCF x Df
1.00	1.5000	0.9615	1.4423	1.5000	1.4423
2.00	1.5000	0.9246	1.3868	3.0000	2.7737
3.00	1.5000	0.8890	1.3335	4.5000	4.0005
4.00	101.5000	0.8548	86.7626	406.0000	347.0505
		Total = P = Price =	90.9253	Total = Weighted Price = WP	355.2670

Macaulay Duration = 0.5 x WP/P = 0.5 x 355.2670/90.9253 = 1.954 Years