Math Problem Statement
Question content area top Part 1 Bond prices and yields Assume that the Financial Management Corporation's $1 comma 000 -par-value bond has a 7.100 %
coupon, matures on May 15, 2027, has a current price quote of 105.456
and a yield to maturity (YTM) of 5.712 % . Given this information, answer the following questions: a. What was the dollar price of the bond? b. What is the bond's current yield? c. Is the bond selling at par, at a discount, or at a premium? Why? d. Compare the bond's current yield calculated in part b to its YTM and explain why they differ. Question content area bottom Part 1 a. The dollar price of the bond is $enter your response here . (Round to the nearest cent.)
Solution
To solve these questions, let's address each part step by step. The given information is as follows:
- Par value (Face value of the bond) = $1,000
- Coupon rate = 7.100% annually
- Maturity date = May 15, 2027
- Current price quote = 105.456
- Yield to Maturity (YTM) = 5.712%
Part a: Dollar Price of the Bond
The bond's dollar price is determined by its price quote. Price quotes for bonds are expressed as a percentage of the bond's par value. So, if the price quote is 105.456, the bond is selling for 105.456% of its par value.
The dollar price of the bond can be calculated as: Substituting the values: Let me calculate that.The dollar price of the bond is $1,054.56.
Do you have any questions so far or would you like to proceed with the next part?
Here are some related questions:
- How does a bond's price relate to its par value?
- Why might a bond trade above its par value?
- What factors affect a bond's yield to maturity?
- How is the coupon rate different from the current yield?
- What happens to bond prices as the maturity date approaches?
Tip: Bonds with a price quote above 100 are selling at a premium, while those below 100 are at a discount.
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Math Problem Analysis
Mathematical Concepts
Bond Pricing
Yield to Maturity (YTM)
Current Yield
Percentage Calculations
Formulas
Dollar Price = (Price Quote / 100) × Par Value
Current Yield = (Annual Coupon Payment / Current Bond Price) × 100
Theorems
Relationship between Price and YTM
Bond Pricing at Premium, Discount, or Par
Suitable Grade Level
College/University Level
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