Question

You are required to produce a table showing bond values and the impact of changes in interest rate over the life of a bond and a diagram demonstrating the link between the changes in values (due to changes in interest rate) and time to maturity.

The bond has a face value of $1,000, pays a coupon rate of 7% p.a paid annually and it is issued with 10 years to maturity. All calculations should be executed in excel.

Your table should show the following:

• The value of the bond, year by year (from date of issue until its maturity), assuming all other things remain the same.

• The value of the bond, year by year, from date of issue until its maturity, assuming that market interest rate increases by 1.5% (hence yield to maturity increases by 1.5%), all other things remain the same.

• The potential % change in value, year by year, from the date of issue until its maturity.

The % change in value demonstrates the impact of the increase in interest rate on the bond value (or interest rate risk), for each year of maturity.

• From your table produce a diagram that demonstrates the relationship between % change in value and time to maturity.

The initial market interest rate (yield to maturity) to be used is 10%.

Answer 1

First we will calculate the Present Value of the bond with Interest rate of 10%, coupon rate of 7% paid annually, face value of $1,000 and no of years as 10 years.

Particulars	Amount
Face Value of the Bond	-1000
Coupon	-70
No of years	10
Interest rate	10%
Present Value of the Bond	815.66

We have taken the face value and coupon as negative only for calculation purpose and we have to use the PV formula in excel. Now we will calculate the changes in price of the bond due to change in interest rate.

Please find the table and the graph for the same:

No of years	Face value of the bond	Coupon	Inerest Rate	Present value of the Bond
10	-1000	-70	10.00%	₹ 815.66
9	-1000	-70	11.50%	₹ 755.60
8	-1000	-70	13.00%	₹ 712.07
7	-1000	-70	14.50%	₹ 683.23
6	-1000	-70	16.00%	₹ 668.37
5	-1000	-70	17.50%	₹ 667.89
4	-1000	-70	19.00%	₹ 683.37
3	-1000	-70	20.50%	₹ 717.84
2	-1000	-70	22.00%	₹ 776.27
1	-1000	-70	23.50%	₹ 866.40