Question

An Apple annual coupon bond has a coupon rate of 5.1% face value of $1000, and 4 years to maturity. If its yield to maturity is 5.1%, what is its Macaulay duration? answer in years, rounded to three decimal places

Answer 1

Macaulay Duration = 3.718 Years

Explanation

Macaulay Bond duration is nothing but the weighted average of time where weights are taken from present value of cash flow generated by the bonds.

t	CF	DF	PV	W	t * W
1	51	0.951475	48.52521	0.048525	0.048525
2	51	0.905304	46.17052	0.046171	0.092341
3	51	0.861374	43.93008	0.04393	0.13179
4	1051	0.819576	861.3742	0.861374	3.445497
			1000		3.718153

t = Years on time line.

CF = Cash flow. As we know during the 3 years only cash flow is the coupon amount = 1000 * 5.10 % = 51

But in the year - 4 ........ we get the face value paid back = 1000 + 51 = 1051

Discounting factors are computed as ....... 1/1.051 = 0.951475 and there after continue to press " = " to get remaining years DF values.

PV = CF * DF

W = weights are obtained as PV / 1000

t * W is the product of first column ( t) with ( W)

Total of ( t * W ) .........gives the bond duration.