A Ford Motor Co. coupon bond has a coupon rate of 4%, a face value of $1,000 and

Question

A Ford Motor Co. coupon bond has a coupon rate of 4%, a face value of $1,000 and pays annual coupons. The bond will mature in 4 years. The bond's yield-to-maturity is 5.3%. What is this bond's Macaulay Duration (MacD)?

(Hint: Not covered in the eText. Check out your class notes and the TopHat note titled "Bond risk and duration".

Step 1: Find the coupon amounts and draw the cashflow timeline.

Step 2: Compute the bond's price discounting each cashflow one by one from Step 1 at the bond's yield-to-maturity.

Step 3: Multiply each cashflow's present value from Step 2 with that cash flow's duration. For example, the coupon to be paid in 2 years has a duration of 2.

Step 4: Add up the terms from Step 3 and divide the sum by the bond's price from Step2. This is the bond's MacD).

Explanation / Answer

Coupons=4%*1000=40

Step 2: Price=(40/1.053+40/1.053^2+40/1.053^3+1040/1.053^4)=954.2221

Step 3: (1*40/1.053+2*40/1.053^2+3*40/1.053^3+4*1040/1.053^4)=3596.52

Step 4: Macaulay Duration=3596.52/954.2221=3.769

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