Question

1. Find the duration of the following bond: Face Value: 1,000.00. Time to maturity, 6 years; coupon rate, 8%; Coupon payment, annual; Market interest rate, 8%. Explain and develop your immunization strategy if you invested in the bond.

2. Assume you reinvest all your coupon income until the holding period based on your strategy in question 1, calculate the accumulated value of invested payment(or receipt) when market interest rate is 8%, 9%, and 7%, respectively.

If you can, use excel to answer questions & provide excel spreadsheet used to solve questions (with formulas displayed)

Thank you!

Answer 1

Answer:

1.

First we calculate the Present value of Bond

Year	Particulars	Amount	Discount Factor @ 8%	Discounted Flow
0	Investment in Bond	-1,000.00	1	-1,000.00
1-6	Interest on Bond	= 1,000 x 8% = 80	4.6229	369.83
6	Bond maturity value	=1,000	0.630169	630.17
	Present Value			0

Strategy, as the market rate and coupon rate is same therefore it, is advisable to invest in the bond to earn higher return than Bond.

Here, we immunize the investment in bond as interest on bond reinvested in bond to earn higher rate of return than market return.

2.  Assume we reinvest all coupon income until the holding period based on your strategy in question 1,

Then , calculation of the the accumulated value of invested payment(or receipt) when market interest rate is 8%, 9%, and 7%, respectively

Accumulated value of Investment = Addition of Present value of Interest on bond till maturity + Addition of Present Value of Reinvestment of Interest on Bond + Present Value of Bond Maturity - Investment in Bond at year 0

1. When Market Interest is 8% :

Accumulated value of Investment = ( 1000 X 8% ) x ( DISCOUNT FACTOR @ 8% for 6 years )+ ( 1000 X 8% X 8%) X ( DISCOUNT FACTOR @ 8% for 2-6 years ) + ( 1,480 ) X  Discount factor @ 8% in 6th year - 1,000

= ( 80 X 4.6229 ) + ( 6.4 X 3.6970 ) + (1,480 X 0.6302 ) -1,000 = 326.19

2.

When Market Interest is 9% :

Accumulated value of Investment = ( 1000 X 8% ) x ( DISCOUNT FACTOR @ 9% for 6 years )+ ( 1000 X 8% X 8%) X ( DISCOUNT FACTOR @ 9% for 2-6 years ) + ( 1,480 ) X  Discount factor @ 9% in 6th year - 1,000

= ( 80 X 4.4859 ) + ( 6.4 X 3.5685 ) + (1,480 X 0.5963 ) -1,000 = 264.23

3.

When Market Interest is 7% :

Accumulated value of Investment = ( 1000 X 8% ) x ( DISCOUNT FACTOR @ 7% for 6 years )+ ( 1000 X 8% X 8%) X ( DISCOUNT FACTOR @ 7% for 2-6 years ) + ( 1,480 ) X  Discount factor @ 7% in 6th year - 1,000

= ( 80 X 4.7665 ) + ( 6.4 X 3.8320 ) + (1,480 X 0.6663 ) -1,000 = 391.97

Here, we analyse the above situation as follows:

1. When Market rate of interest is more then the coupon rate then bond value will be decreased and vice versa