If you are thinking about purchasing a bond, there are issues to consider, including the current market circumstances and interest rate sensitivity. Interest rate sensitivity refers to how much a change in interest rates will affect the expected price and maturity of an investment. To calculate the sensitivity of the interest rate, you must measure the duration. For example, if a $100,000 bond that matures in ten years pays a 5 percent coupon rate annually, then each year has a duration of 8 percent. However, if that coupon rate increase to 6 percent, the current value of that bond will fall by 8 percent. To figure this, you need to calculate the discounted weighted average of the bond's cash flows.
Instructions
1. Access your spreadsheet software or grab a piece of blank paper and a pencil. Create six columns. Label each column with these headings: Year, Cash Flows, Interest, Factor, Discount Factor, and Year X Discount Factor.
2. Create 10 rows underneath the labels and write the numbers one through 10 underneath the "Year" column. You can adjust for the period of your own investment.
3. Multiply the par value of the bond by the coupon rate and write this value underneath the "Cash Flows" column from year 1 through 9. For example, a bond with a par value of $100,000 and a coupon rate of 5 percent would have $5,000 in the cash flow column from year one to nine.
4. Add the par value of the bond to the amount calculated in the previous step and write this under the cash flow column for year 10. For example, a bond at $100,000 would add $5,000. $105,000 would be written under the cash flow column for year 10.
5. Calculate the discount factor for each row of the factor column. Use a calculator to raise the number calculated in the previous step from the interest column by the power calculated by the number in the corresponding year column. For example, the first row would calculate 1.05^1 = 1.05. Do this for each row. The last row should read 1.05^10 = 1.63.
6. Divide the discount factor into the numbers found in the cash flow. For example, row 1 would read: $5,000/1.05 = $4,726. The final row should read: $105,000/1.63 = $64,417.
7. Multiply the year number by the corresponding number in the rows for the discount factor column. For example, the first number would be 1*$4,762, which would equal $4,762. The last number would be 10*$64,417, which would equal $644,170. These results should be written in the "Year X Discount Factor" column.
8. Add all numbers in the Year X Discount Factor column. The date for the previous example would add up to a total of $810,345. Divide that total by the face value of the bond. For example, $810,345 divided by $100,000 is 8.1. This gives you the duration of the bond and represents the sensitivity of the interest rate. It means that if the interest rate rises by just one percent, the value of the bond will fall by approximately 8 percent.
Tags: cash flow, coupon rate, value bond, cash flow column, Discount Factor
