Question

A 5-year, 6% annual-compounding bond priced to yield 8%.

a. Calculate the Macaulay duration of the bond.

b. Calculate the bond price.

c. Calculate the modified duration of the bond.

d. According the modified duration, what is the estimated bond price if the market yields decline to 7%?

e. Using financial calculator, calculate the actual bond price if rate does drop to 7%?

f. How does the actual bond price compare to the price predicted by the modified duration? Explain the reason for the difference.

g. Find the effective duration using 100 basis points change in interest rate.

Answer 1

a.

Face value		$1,000		Yield	8%
Coupon rate		6%
Term		5
Coupon No	1	2	3	4	5	Bond Price
Coupon amount	$60	$60	$60	$60	$60
Maturity value	0	0	0	0	$1,000
Total cash flow	$60	$60	$60	$60	$1,060
Present Value @ 8%	$55.56	$51.44	$47.63	$44.10	$721.42	$920.15
proportion	6.04%	5.59%	5.18%	4.79%	78.40%
Maculay duration	4.44

b. Bond price =$920.15

c. Modified duration = Maculay duration/(1+ yield/number of coupen per year) = 4.44/(1+0.08) = 4.11

d.

Face value		$1,000		Yield	7%
Coupon rate		6%
Term		5
Coupon No	1	2	3	4	5	Bond Price
Coupon amount	$60	$60	$60	$60	$60
Maturity value	0	0	0	0	$1,000
Total cash flow	$60	$60	$60	$60	$1,060
Present Value @ 8%	$56.07	$52.41	$48.98	$45.77	$755.77	$959.00
proportion	5.85%	5.46%	5.11%	4.77%	78.81%

if yield declines to 7%, bond price = $959.00