Math Problem Statement
Calculate the value of a bond that matures in 16 years and has a $ 1 comma 000 par value. The annual coupon interest rate is 9 percent and the market's required yield to maturity on a comparable-risk bond is 13 percent. The value of the bond is $ enter your response here. (Round to the nearest cent.)
Solution
To calculate the value of a bond, we can use the present value formula for bonds. The value of a bond is the sum of:
- The present value of the coupon payments.
- The present value of the par value at maturity.
Given Data:
- Par value (): $1,000
- Coupon rate (): 9% of $1,000 = $90 per year
- Yield to maturity (): 13% or 0.13
- Time to maturity (): 16 years
Steps:
-
Calculate the present value of the coupon payments:
- The coupon payments are an annuity, so we use the present value of an annuity formula:
-
Calculate the present value of the par value:
- The par value is a lump sum payment, so we use the present value of a single sum formula:
Now let me calculate these values for you.The value of the bond is approximately $735.84.
Would you like more details or have any questions?
Here are 5 related questions to explore further:
- How does a change in the market interest rate affect the bond's value?
- What happens to the bond price if the coupon rate matches the yield to maturity?
- How is the yield to maturity (YTM) different from the coupon rate?
- What is the relationship between bond prices and interest rate risk?
- How would semi-annual coupon payments affect the bond value?
Tip: A bond’s price moves inversely to changes in the market interest rate. When rates rise, bond prices fall, and vice versa.
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Math Problem Analysis
Mathematical Concepts
Present Value
Bond Valuation
Annuity
Interest Rates
Formulas
PV_{coupons} = C \times \left(1 - \frac{1}{(1 + r)^t}\right) \div r
PV_{par value} = F \div (1 + r)^t
Theorems
Present Value Theorem
Suitable Grade Level
College-Level Finance
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