Question

On January 1, 2020, our company sold bonds with a face value of $100,000,000. These bonds are due in 8 years. The stated annual interest rate is 10% per year, payable semiannually on June 30 and December 31. The bonds were sold to yield the investor 8%. Using the information above, along with the PV tables in this assignment, the amount of cash received from the issuance of the bonds on January 1, 2020 would be? (enter whole dollars with no dollar sign but with commas) note: use the PV tables included in this assignment if you get feedback that your answer is incorrect (your calculator will likely come up with a more precise but different calculation due to the # of digits behind the decimal place)

Answer 1

The cash received from the bond issuance is determined by calculating the present value of the interest payments and the principal repayment using the present value tables provided. The cash received is the sum of the present value of semiannual interest payments and the principal amount, both discounted at the yield rate of 8%.

Step-by-step explanation:

To determine the amount of cash received from the issuance of the bonds on January 1, 2020, we must calculate the present value of both the interest payments and the principal repayment at the yield rate (discount rate in this context) of 8%. The bonds have a stated annual interest rate of 10% per year, payable semiannually, which amounts to $5,000,000 every six months. Given the bonds are due in 8 years, there will be 16 interest payments in total.

We'll use the present value (PV) of an annuity formula for the interest payments and the present value of a lump sum formula for the principal. Using the tables provided in this assignment, we find the PV factors at an 8% yield for 16 periods (semiannual) for the annuity and for 8 periods (annual) for the lump sum. To compute the total cash received, we sum the present value of the interest payments and the principal repayment.

Assuming the tables show a PV of an annuity factor of 'X' and a PV of a lump sum factor of 'Y', the total cash received would be:

• 
  
• $5,000,000 * X (Annuity PV factor for 16 periods at 8%)
• 
  
• +$100,000,000 * Y (Lump sum PV factor for 8 periods at 8%)

The sum of these two amounts will give us the cash received from the bond issuance on January 1, 2020.