Final answer:
To find out what a simple two-year bond is worth in the present, we use the present discounted value formula, adjusting the calculations whether the discount rate is 8% or rises to 11%. These present values, when compared to the bond's face value, determine if the bond sold at a premium or discount.
Step-by-step explanation:
Computing Cash Proceeds from Bond Issues for Pear Inc.
To calculate how much a bond is worth in the present, we use the concept of Present Discounted Value (PDV). A simple two-year bond issued for $3,000 at an 8% interest rate results in yearly interest payments of $240. The present value of these payments is determined by discounting them back to their value in today's dollars at a given interest rate, also known as the discount rate.
Using an 8% discount rate, the present value of the first year's $240 interest is calculated as $240 / (1 + 0.08), and the present value of the second year's combined $3,240 (interest plus principal) as $3,240 / (1 + 0.08)^2. If the discount rate is increased to 11%, the calculations change to $240 / (1 + 0.11) for the first year and $3,240 / (1 + 0.11)^2 for the second year.
Comparing the calculated present value to the bond's face value will tell us whether the bond sold at a discount or a premium. If the present value is higher than the face value, the bond sold at a premium. If it is lower, it sold at a discount. These calculations are essential in financial markets for investors making decisions based on future cash flows of bonds and stocks.