Present value can be used to determine the fair price -or value - of a bond. In the examples that follow, assume you are working with zero-coupon bond and that there are no transaction costs. A zero-coupon bond is one that pays all interest and the principal when the bond matures. a. For example, suppose somebody offers to sell you a bond that will pay a future value of $225 – interest included - when it matures in two years. If the current market interest rate is 3%, then what would be a fair price for you to pay for this bond? The value of a bond changes whenever the current market interest rates change. For example, suppose you bought a bond in 2015 that promises to pay you 5% annual interest until it matures in 2020. The value of your bond (i.e., the price that you can sell it for if you choose to sell it before maturity) will change if the market interest rate changes. To understand why, work through the following examples. b. Suppose you purchased a bond for $181.82 that will pay $200 (interest included) when it matures one year from now. What is the return on this bond? c. What will happen to the value of your bond (that promises to pay $200 in one year) if the market interest rate suddenly changes to 7%? How much is your bond worth after the interest rate changes? Provide an explanation for why the value of your bond changed in this direction?
Present value can be used to determine the fair price -or value - of a bond. In the examples that follow, assume you are working with zero-coupon bond and that there are no transaction costs. A zero-coupon bond is one that pays all interest and the principal when the bond matures. a. For example, suppose somebody offers to sell you a bond that will pay a future value of $225 – interest included - when it matures in two years. If the current market interest rate is 3%, then what would be a fair price for you to pay for this bond? The value of a bond changes whenever the current market interest rates change. For example, suppose you bought a bond in 2015 that promises to pay you 5% annual interest until it matures in 2020. The value of your bond (i.e., the price that you can sell it for if you choose to sell it before maturity) will change if the market interest rate changes. To understand why, work through the following examples. b. Suppose you purchased a bond for $181.82 that will pay $200 (interest included) when it matures one year from now. What is the return on this bond? c. What will happen to the value of your bond (that promises to pay $200 in one year) if the market interest rate suddenly changes to 7%? How much is your bond worth after the interest rate changes? Provide an explanation for why the value of your bond changed in this direction?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:**Understanding Present Value and Its Role in Determining Bond Prices**
1. **Present Value and Bonds**:
- The present value is a financial concept used to determine the fair price or value of a bond. It takes into account future cash flows discounted back to their value today.
2. **Zero-Coupon Bonds**:
- In these examples, we consider a zero-coupon bond, which pays all interest and principal at maturity, with no transaction costs assumed.
3. **Example Calculations**:
a. **Future Value Calculation**:
- Suppose you are offered a bond that will pay $225 in two years, including interest. If the market interest rate is 3%, what would be a fair price today for this bond?
4. **Interest Rate Impact on Bond Value**:
- Bond values fluctuate with market interest rate changes. For instance, if you bought a bond in 2015 with a 5% annual return, the sellable value before maturity in 2020 would shift with interest rate changes.
b. **Return on Investment Example**:
- You purchased a bond for $181.82 that matures at $200 in one year. Determine the return on this bond.
c. **Interest Rate Scenario (7%)**:
- What happens to your bond’s value if the market interest rate suddenly shifts to 7%? Calculate your bond’s new worth and explain why the value shifted.
d. **Interest Rate Scenario (10% to 12%)**:
- If the market rate changes from 10% to 12%, what is the new value of your bond? Provide insight into the directional value change due to interest rate variations.
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