Question

Brenton, Berean and Basak (BBB) is a pension fund specialist looking for a bond with a particular duration to add to their existing portfolio in order to immunize the portfolio. Crawford, Coty and Connor (CCC) has an outstanding bond with a 8.975% coupon, 4 years to maturity, and a yield to maturity of 11.5% that meets BBB’s criterion.

11. What would be the duration of the bond above if it were a semi-annual bond? What would you expect to pay for this bond Show your calculations. (6 points)

Answer 1

Duration of the Bond Calculation:

(assume that the face value of the bond is $1000)

Year (t)	Payments (n)	Cash Flow from coupon payments (8.975%/2 of $1000)	Cash Flow from maturity amount	Total Cash Flow from coupon payments and maturity amount (CF)	Present value (PV) discounted at 11.5%/2 =5.75% semiannual yield to maturity	PV *t
0.5	1.0	$44.88		$44.88	$42.43	$21.22
1.0	2.0	$44.88		$44.88	$40.13	$40.13
1.5	3.0	$44.88		$44.88	$37.95	$56.92
2.0	4.0	$44.88		$44.88	$35.88	$71.77
2.5	5.0	$44.88		$44.88	$33.93	$84.83
3.0	6.0	$44.88		$44.88	$32.09	$96.26
3.5	7.0	$44.88		$44.88	$30.34	$106.20
4.0	8.0	$44.88	$1,000.0	$1,044.88	$668.07	$2,672.28
sum					$920.82	$3,149.59
					Bond's Price↑
				Macaulay Duration = sum of (PV*t)/sum of PVs =	$3149.59/$920.82	3.42

Duration of the bond is 3.42 years

And you expect to pay $920.82 for this bond (price of the bond)

Formulas used in excecl: