Question

Question 20 Not yet answered Points out of 2.5 P Flag question What is the Macaulay duration of a five year 2000 par value bond with 8% annual coupons and an effective rate of interest equal to 7%? Select one: A. 4.0 B. 4.1 C. 4.2 D. 4.3 ○ E. 4.5

Answer 1

The Macaulay Duration (or simply Duration) of a Bond is effectively the average time period (in years) in which the true cost or intrinsic value of the bond gets recovered by its cash flows.

First, we calculate the Intrinsic Value of bond from the given information, which is done as follows:

1) Coupon amount (par value * annual coupon rate) = 2000 * 8% = 160

2) Intrinsic Value = 160 * PVIFA (7%, 5 years) + 2000 * PVIF (7%, 5th year) = 160 * 4.10 + 2000 * 0.713 = 2082

$\therefore$  Intrinsic Value of the bond is 2082.

Now we calculate the macaulay duration, which involves the following steps:

Step 1 - Multiply the Present Value of each Cash Flow with the time period (t) in which it is received (cash flow * pvif * t)

Step 2 - Add up all the results obtained in step 1 for each time period

Step 3 - Divide the amount obtained in step 2 by the bond's Intrinsic Value. The resultant value is the Duration.

Given below is the complete calculation:

Time Period (a)	Cash Flows (b)	PVIF @ 7% (c)	Amount = (a) * (b) * (c)
1	160	0.9346	149.536
2	160	0.8734	279.488
3	160	0.8163	391.824
4	160	0.7629	488.256
5	2160 (=2000+160)	0.7130	7700.400

Total Sum of the 'Amount' column = 9009.504

$\therefore$ Macaulay Duration = 9009.504 / 2082 = 4.327 years which is approximately equal to 4.3 years

Hence the correct option is D - 4.3