On April 20, 2008 your wealthy aunt will give you a bond with a par value (or a maturity value) of $10,000. Your aunt purchased the bond in 2003, and it matures on April 20, 2009. The bond pays a coupon rate of 8 percent. When it arrives, the bond will have one remaining coupon.

a. If the current relevant rate of interest is 6 percent for the type of bond your aunt is giving you, what will the market value of the bond be on the day you receive it? Why?

b. Given the prospect of new wealth, you decide to check the business section of the newspaper. It suggests that the Bank of Canada soon will reduce interest rates in Canada by one half of one percentage point. If the relevant interest rate for the bond you will receive drops by one half of one percentage point, what will be its market value on the day you receive it? Why?

c. You read further in the business section and discover that the company that issued the bond in 2003 used the $10,000 it received to issue subprime mortgages in the U.S. In other words, the company used the funds it received by issuing bonds to give mortgages to homebuyers who had very poor credit ratings. Participants in the bond market now fear that defaults on mortgages have greatly increased the risk that the original issuer will not be able to pay the par value of the bonds when they mature. As a result, a large risk premium has raised the market rate of interest on your type of bond to 20 percent. What will its value be on the day you receive it?

To calculate the market value of the bond on the day you receive it, we need to consider the current relevant rate of interest, any changes to that rate, and the risk associated with the bond. Let's go through each scenario:

a. If the current relevant rate of interest is 6 percent, and the bond pays a coupon rate of 8 percent, the bond offers a higher interest rate than the market rate. This means the bond is more attractive to investors. When a bond offers a higher interest rate, its market value increases. To calculate the market value, we can use the present value formula for a bond:

Market Value = (Coupon payment / (1 + Current interest rate)) + (Coupon payment / (1 + Current interest rate)^2) + ... + (Coupon payment + Par value / (1 + Current interest rate)^N)

Where:
- Coupon payment: The annual coupon payment (8% of the bond's par value)
- Current interest rate: The market rate of interest (6%)
- N: Number of periods until maturity (1)

Using this formula, we can calculate the market value of the bond.

b. If the relevant interest rate drops by one half of one percentage point, from 6% to 5.5%, the bond becomes even more attractive to investors. As the interest rate decreases, the market value of the bond increases. To calculate the new market value, we can use the same formula as in scenario a, but with the updated interest rate (5.5%).

c. If the market rate of interest on the bond increases to 20% due to the increased risk associated with the subprime mortgage investments, the bond becomes significantly less attractive to investors. This increase in the market rate indicates a higher risk premium, which leads to a decrease in the bond's market value. Using the same formula as before, but with the new interest rate (20%), we can calculate the market value of the bond.

Please provide the par value of the bond, and I can help you calculate the market values in each scenario.