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: Dollar Price=(Price Quote100)×Par Value\text{Dollar Price} = \left(\frac{\text{Price Quote}}{100}\right) \times \text{Par Value} Substituting the values: Dollar Price=(105.456100)×1,000\text{Dollar Price} = \left(\frac{105.456}{100}\right) \times 1,000 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:

  1. How does a bond's price relate to its par value?
  2. Why might a bond trade above its par value?
  3. What factors affect a bond's yield to maturity?
  4. How is the coupon rate different from the current yield?
  5. 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