Final answer:
The value of a bond is determined using the present value formula by discounting future cash flows, which include annual coupon payments and face value at maturity, at the given required return. The value changes when the required return changes, showcasing the inverse relationship between bond prices and market interest rates.
Step-by-step explanation:
To determine the value of a bond, we use the present value formula which discounts future cash flows back to their value in today's dollars. In the case of IBM's bond with a 3.4% annual coupon rate, a face value of $1,000, and maturity in 11 years, the value of the bond will change based on the required return, or the market interest rate.
To calculate the bond's value for each required return scenario, you would perform the following steps:
- Calculate the annual coupon payment by multiplying the face value by the coupon rate ($1,000 x 3.4% = $34).
- Discount each of these annual coupon payments to present value using the required return.
- Discount the face value, which is the amount you receive at maturity, to its present value using the formula PV = FV / (1 + r)^n, where PV is present value, FV is face value, r is the required return, and n is the number of years to maturity.
You would perform these calculations separately for each required return (5%, 6%, and 7%) to find the respective bond values.
As a general rule, when market interest rates rise, the value of existing bonds with lower interest rates tend to decrease. Conversely, if market interest rates fall, the value of these bonds will generally increase. This inverse relationship is fundamental to bond pricing.