The managing partner, Karen Thompson, has asked you to do some quick calculations for her. She wants you to use the current yield curve, flat at 4%, in your calculations.

Client Annie Inc. has a pension plan that pays pension benefits annually at a rate of $50 million per year, starting one year from today. The pension obligation will end in 35 years. Karen wants to know the duration of these required pension payments.

Client Billy Mack Co. wants to immunize its pension obligations (present value = $100 million with a duration of 25 years) with two $1000 face value bonds. The first bond is a 7-year 3% annual coupon bond issued by Jaime Corp. The second bond issuer, Kari Ltd., has issued a consol bond paying a 6% annual coupon perpetually. Ms. Thompson wants you to calculate the money Billy Mack should allocate to each of these bonds to immunize its pension against interest rate risk.

1. What is the duration of Annies required pension payments?

Hint: Starting with Spreadsheet 16.1 of Bodie_9Ce_Ch16.xlsx, copy the formulas for coupon bonds, adjusting them to extend for the full 40 years of payments, and determine the duration.

Inputs
Settlement date	2000-01-01
Maturity date	2035-01-01
Coupon rate	0.08
Yield to maturity	0.04
Coupons per year	2
Outputs
Macaulay duration	16.8561
Modified duration	16.5255

2. Calculate the money Billy Mack should allocate to each of these bonds to immunize its pension against interest rate risk. (Again, modify Spreadsheet 16.1 for the coupon bonds duration.)

		Time until		PV of CF		Column (C)
		Payment		(Discount rate =		times
	Period	(Years)	Cash flow	5% per period)	Weight*	Column (F)
A. 8% coupon bond	1	0.5	40	38.095	0.0395	0.0197
	2	1.0	40	36.281	0.0376	0.0376
	3	1.5	40	34.554	0.0358	0.0537
	4	2.0	1040	855.611	0.8871	1.7741
Sum:				964.540	1.0000	1.8852
B. Zero-coupon bond	1	0.5	0	0.000	0.0000	0.0000
	2	1.0	0	0.000	0.0000	0.0000
	3	1.5	0	0.000	0.0000	0.0000
	4	2.0	1000	822.702	1.0000	2.0000
Sum:				822.702	1.0000	2.0000
Semiannual int rate:	0.05
*Weight = Present value of each payment (Column E) divided by the bond price