Question

1. A corporate bond has 2 years to maturity, a coupon rate of 8%, a face value of $1,000 and pays coupons semiannually. The market interest rate for similar bonds is 9.5%.

a. What is the bond's duration in years?

b. If yields fall by 0.8 percentage points, what is the new expected bond price based on its duration (in $)?

c. What is the actual bond price after the change in yields (in $)?

d. What is the difference between the two new bond prices (in absolute $)?

2. A corporate pension plan has to make the following payments over the next few years:

Year	1	2	3	4
Amount ($ million)	19	23	29	37

The appropriate interest rate is 8%.

a. What is the duration of the liability?

b. What is the duration of a perpetuity if the yield is 8%?

c. The fund wants to immunize its interest rate risk by investing in a perpetuity and a 1-year zero coupon bond. To do so, how much should it invest in the perpetuity (in $ million)?

Answer 1

Duration of Bond:

Year (K)	Amount	Pv factor @ 4.75%	Present value( W)	K*W
1	$        40.00	0.9547	$                                    38.19	$                                    38.19
2	$        40.00	0.9114	$                                    36.45	$                                    72.91
3	$        40.00	0.8700	$                                    34.80	$                                  104.40
4	$ 1,040.00	0.8306	$                                  863.81	$                              3,455.23
		Total Values	$                                  973.25	$                              3,670.73
			Duration = Sum of KW/ Sum of W = 3670.73/973.25 = 4Years
			Modifide Duration= duration/ PV Factors = 4/(1.0475)^2 =3.65 Year

(B) If Mkt yield falls by .8 basis point then the value of bond will increase.

percentage Increase in Value of bond= 0.8*3.65= 2.92%

Value of old bond:

Year (K)	Amount	Pv factor @ 4.75%	Present value( W)
1	$        40.00	0.9547	$                                    38.19
2	$        40.00	0.9114	$                                    36.45
3	$        40.00	0.8700	$                                    34.80
4	$ 1,040.00	0.8306	$                                  863.81
		Total Values	$                                  973.25

Value of new bond= 973.25+973.25*2.92%=1001.67

C) Revise value of bond

Year (K)	Amount	Pv factor @ 4.35%	Present value( W)
1	$        40.00	0.9583	$                                    38.33
2	$        40.00	0.9184	$                                    36.73
3	$        40.00	0.8801	$                                    35.20
4	$ 1,040.00	0.8434	$                                  877.13
		Total Values	$                                  987.40