Question

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What is the Macaulay's duration of a bond witha par value of $10,000 that has a coupon rate of 6.5 percent annually and a final maturity of two years? Assume that the required rate of return is 4 percent compounded semiannually. 4. a. 1.949 years b. 1.910 years 1.876 years d. 1.713 years I C.

Answer 1

Macaulay duraiton is calculated by weightage average term to maturity of a cash flow to the bond.

Mac duration = PV of cash flows / price today

For our question, Par value = $10,000 . Annual coupon rate = 6.5%

So every 6 months, the bond will pay $325

cash flows =:

0.5 year = 325

1 year= 325

1.5 years = 325

2 years = 10325

discount rate is compounded semiannually, so 6 months rate = 2%

Finding PV of cash flows:

0.5 year = 325 /1.02 = 318.627

1 year= 325 /1.02^2= 312.3798

1.5 years = 325 /1.02^3=306.254

2 years = 10325/1.02^4=9538.70

Total= 0.5*318.627+1*312.3798+1.5*306.254+2*9538.7= 20008.47

current bond price = 9538.70+306.254+312.3798+318.627= 10475.96

Mac duration = Total/ current bond price = 1.910 years

option b