Consider a 10-year corporate bond with $500,000 face value and semi-annual coupons of8% APR. Given the credit rating of this company, the appropriate yield is 7.5% (APR)Without doing any calculations, do you expect this bond to sell at a premium or aa.discount to face value? Price the bond to confirm your suspicions. If the yield for the bond were 8.5%, do you expect the bond to sell at a premium or adiscount? Calculate the bond price.

First, let's understand the concept. A bond sells at a premium when its coupon rate is higher than its yield and at a discount when its coupon rate is lower than its yield.

1. For the first scenario, the coupon rate is 8% and the yield is 7.5%. Since the coupon rate is higher than the yield, we expect the bond to sell at a premium.

Let's confirm this by calculating the bond price:

Step 1: Calculate the semi-annual coupon payment Coupon payment = (8%/2) * $500,000 =$20,000

Step 2: Calculate the semi-annual yield Yield = 7.5%/2 = 3.75%

Step 3: Calculate the present value of the coupon payments The bond pays $20,000 every six months for 10 years, which is 20 periods. We discount these payments back to the present using the semi-annual yield. PV of coupons =$20,000/(1+3.75%) + $20,000/(1+3.75$20,000/(1+3.75%)^20

Step 4: Calculate the present value of the face value The bond will pay $500,000 at the end of 10 years, which is 20 periods from now. We discount this back to the present using the semi-annual yield. PV of face value =$500,000/(1+3.75%)^20

Step 5: Add the present value of the coupon payments and the face value to get the price of the bond. Price of bond = PV of coupons + PV of face value

2. For the second scenario, if the yield were 8.5%, the yield is now higher than the coupon rate. Therefore, we expect the bond to sell at a discount.

You can calculate the bond price using the same steps as above, but replace the yield with 8.5%/2 = 4.25%.