A tax-exempt bond was recently issued at an annual 12 percent coupon rate and matures 20 years from today. The par value of the bond is $1,000. a. If a required market rates are 12 percent, what is the market price of the bond? b. If required market rates fall to 6 percent, what is the market price of the bond? c.If required market rates rise to 18 percent, what is the market price of the bond? d.At what required market rate (6 percent, 12 percent or percent) does the above bond sell at a discount? At a premium?

a. To calculate the market price of the bond when the required market rates are 12 percent, we need to discount the future cash flows generated by the bond. The bond pays an annual coupon rate of 12 percent on a par value of $1,000 for a total of 20 years.

Using the formula for present value of a bond's cash flows:

Market Price = (Coupon payment / (1 + Required Market Rate)^1) + (Coupon payment / (1 + Required Market Rate)^2) + ... + (Coupon payment + Par value / (1 + Required Market Rate)^20)

Substituting the values:
Coupon Payment = 12% * $1,000 = $120
Required Market Rate = 12% (annual rate)

Market Price = ($120 / (1 + 0.12)^1) + ($120 / (1 + 0.12)^2) + ... + ($120 / (1 + 0.12)^20)

You can calculate the above equation to find the market price of the bond when required market rates are 12 percent.

b. To calculate the market price of the bond when required market rates fall to 6 percent, we follow the same steps as in part a, but now the required market rate is 6 percent. Substituting the values into the formula above, you can calculate the market price of the bond when required market rates are 6 percent.

c. Again, follow the same steps as in part a, but now the required market rate is 18 percent. Substituting the values into the formula, you can calculate the market price of the bond when required market rates are 18 percent.

d. The bond sells at a discount when its market price is lower than its par value. This occurs when the required market rate is higher than the coupon rate of 12 percent.

The bond sells at a premium when its market price is higher than its par value. This occurs when the required market rate is lower than the coupon rate of 12 percent.

By comparing the required market rates with the coupon rate, you can determine whether the bond sells at a discount or premium.

To determine the market price of the bond, we need to calculate the present value of its future cash flows. The cash flows consist of periodic coupon payments and the final principal payment.

a. If the required market rate is 12 percent (equal to the coupon rate), the bond will be priced at its par value because the coupon rate is equal to the required rate. Therefore, the market price will be $1,000.

b. If required market rates fall to 6 percent (below the coupon rate), the bond will be priced at a premium. To calculate the market price, we need to discount the future cash flows at the new rate of 6 percent. The coupon payments of 12 percent of $1,000 will now have a higher present value, resulting in a higher market price than the par value.

c. If required market rates rise to 18 percent (above the coupon rate), the bond will be priced at a discount. Again, we need to discount the future cash flows at the new rate of 18 percent. The coupon payments of 12 percent will have a lower present value, resulting in a market price lower than the par value.

d. To determine at what required market rate the bond sells at a discount or a premium, we need to compare the market price to the par value.

- If the market price is higher than the par value, the bond is selling at a premium.
- If the market price is lower than the par value, the bond is selling at a discount.
- If the market price is equal to the par value, the bond is selling at its face value.

In this case, when required market rates fall to 6 percent, the market price will be higher than the par value, indicating a premium. When required market rates rise to 18 percent, the market price will be lower than the par value, indicating a discount.