Considering investing in either of two corporate bonds - One will give you with an annual 8% interest payment, while
the other will provide you with 6%. Assume that the market rate in
effect on the day you purchase either of the bonds is 7%. Explain how
you will earn 7% on your investment, regardless of which bond you
purchase.
To earn 7% on your investment, regardless of which bond you purchase, you would need to consider the concept of bond pricing and yield.
Bond prices are determined by the market based on several factors, including the prevailing interest rates and the creditworthiness of the issuer. When the bond's interest rate is higher than the prevailing market rate, it is considered to be priced at a premium. Conversely, if the bond's interest rate is lower than the market rate, it is considered to be priced at a discount.
In this scenario, both bonds have interest rates higher than the market rate (8% and 6% versus a market rate of 7%). This implies that both bonds are priced at a premium, which means the bond price is higher than its face value (the amount you pay to purchase the bond).
To earn 7% on your investment, you would need to compare the prices of both bonds and determine which bond offers a higher initial yield based on the purchase price.
Let's calculate this:
1) For the bond offering an 8% interest payment:
Assuming the face value of the bond is $1,000, and the market rate is 7%, you can use the following formula to calculate the bond's price:
Price = Coupon Payment / Market Rate = $80 / 7% = $1,142.86
Since the bond is priced at $1,142.86, which is higher than its face value, you are paying more upfront. However, when you receive the annual interest payment of $80, it would be more than the 7% market rate on your initial investment of $1,142.86. Thus, your effective yield would be equal to the market rate (7%).
2) For the bond offering a 6% interest payment:
Using the same formula and assuming a face value of $1,000, you can calculate the bond's price:
Price = Coupon Payment / Market Rate = $60 / 7% = $857.14
This bond is priced at a discount since its price is lower than its face value. However, when you receive the annual interest payment of $60, it would be less than the 7% market rate on your initial investment of $857.14. Nevertheless, the bond's discounted price compensates for the lower interest payment, resulting in an effective yield of 7%.
In both cases, you would earn an effective yield of 7% on your investment, even though the interest payments are different. This is due to the pricing and yield dynamics of bonds in relation to prevailing market rates.