Consider The Following Three Bond Quotes With Solutions
With Solutionconsider The Following Three Bond Quotes A Treasury Bond
Consider the following three bond quotes: a Treasury bond quoted at 103:21, a corporate bond quoted at 96.10, and a municipal bond quoted at 100.50. If the Treasury and corporate bonds have a par value of $1,000 and the municipal bond has a par value of $5,000, what is the price of these three bonds in dollars? (Do not round intermediate calculations and round your final answers to 2 decimal places.)
Paper For Above instruction
The process of calculating the actual price of bonds based on their quotes and par values is fundamental in bond valuation. Bond quotes are typically expressed in relation to their face value, often in terms of percentage of face value plus a specific fraction representing additional pricing components. In this context, understanding how to interpret these quotes and convert them into dollar amounts is essential for investors and financial analysts.
Given the bond quotes and their par values, the first step involves interpreting the quotes correctly. For Treasury bonds and corporate bonds, the quotes are expressed as a percentage of face value with a fractional component (e.g., 103:21). This notation implies a percentage price with 21/32 parts. For municipal bonds, the quote is straightforward as a percentage of face value.
Specifically, a quote of 103:21 indicates 103 and 21/32 percent of face value. To find the dollar price, we convert this to a decimal by adding the fraction, then multiply by the par value. The calculation involves converting the fraction to its decimal form, which is 21 divided by 32.
The second quote, 96.10, reflects 96.10 percent of par value, a direct percentage. The third quote, 100.50, similarly indicates 100.50 percent of face value, applicable to the municipal bond.
Conversion of bond quotes to dollar prices
For the Treasury bond quoted at 103:21:
- Convert the fractional quote: 21/32 = 0.65625
- Combine with the whole number part: 103 + 0.65625 = 103.65625%
- Calculate the dollar price: 103.65625% of $1,000
- $1,036.56
For the corporate bond quoted at 96.10:
- Convert percentage directly: 96.10% of $1,000
- $961.00
For the municipal bond quoted at 100.50:
- Convert percentage directly: 100.50% of $5,000
- $5,025.00
Therefore, the prices of these bonds are:
- Treasury bond: $1,036.56
- Corporate bond: $961.00
- Municipal bond: $5,025.00
This process demonstrates how bond quotes are interpreted and converted into actual dollar prices, which are crucial for investment decisions and portfolio management.
References
- Bodie, Z., Kane, A., & Marcus, A. J. (2021). Investments (12th ed.). McGraw-Hill Education.
Financial Management: Theory & Practice (15th ed.). Cengage Learning. - Journal of Financial Economics, 115(3), 708-722.