Suppose you buy a 7% coupon, 20 year bond today when it's first issued. If interest rates suddenly rise to 15%, what happens to the value of your bond?
Suppose you buy a 5% coupon, 20 year bond today when it is first issued. If interest rates suddenly rise to 8%, what happens to the value of your bond? (coupon payments are semi-annually).
To determine what happens to the value of your bond when interest rates rise, we need to understand how bond prices and interest rates are related. When interest rates increase, the value of the bond's fixed future cash flows decreases. This is because the bond's fixed coupon rate becomes less attractive compared to the prevailing higher interest rates in the market.
To calculate the change in bond value, we need to compare the coupon rate of the bond with the new prevailing interest rate:
1. Calculate the present value of the bond's future cash flows: The bond has a 7% coupon rate, which means it pays 7% of its face value as annual interest. The cash flow from the bond consists of annual coupon payments (7% of face value) for 20 years, plus the face value at maturity.
2. Calculate the present value of the bond's cash flows using the current market interest rate: Assuming the current market interest rate is 15%, we discount the bond's future cash flows at this rate to determine their present value.
3. Compare the present value of the bond's cash flows with its market price: If the present value of the bond's cash flows is higher than its market price, the bond is selling at a discount. If the present value is lower than the market price, the bond is selling at a premium.
4. Determine the change in bond value: If interest rates suddenly rise to 15%, the present value of the bond's cash flows will decrease. As a result, the bond's value will decrease, assuming no other factors affecting the bond's value change.
Note: Calculation of bond value can be complex and may require the use of financial formulas and models. Factors like bond duration, convexity, and market conditions can also impact bond pricing.