Question

Joseph’s Baseball Bats, Inc. decides to finance an additional plant expansion by borrowing in the bond market. Having learned a lesson from its earlier bond issuance, where the coupon rate was lower than the market rate, they decided to increase the coupon rate they offer.

On March 1, 2023, they issued a $6,000,000 face value, 6% coupon rate, 20-year bond. However, at this time, the 6% coupon they offered is higher than the 5% market rate of interest that bond investors demanded. The bonds mature on February 28, 2043 and pay interest on February 28th of each year.
1) How much cash did Joseph’s Baseball Bats receive; that is, what was the bond’s price? (Please show calculations).
2) If, on April 1, 2023, the U.S. Federal Reserve increases interest rates, what will likely happen to the price of Joseph’s bonds in the marketplace? Why will this happen?

Answer 1

Joseph's Baseball Bats, Inc. issued bonds above the market rate, and thus will receive more than $6,000,000. If the Federal Reserve raises interest rates, the market price for these bonds will likely fall, as new bonds will be more competitive with higher yields.

Step-by-step explanation:

Joseph’s Baseball Bats Bond Pricing

Joseph’s Baseball Bats, Inc. issued a bond with a face value of $6,000,000 at a coupon rate of 6%, which is above the market rate of 5%. To calculate the bond's price, we would have to discount the future cash flows (interest payments and the principal at maturity) back to their present value at the market rate. The bond's cash flows consist of 20 annual payments of $360,000 (6% of $6,000,000) plus the principal repayment of $6,000,000 at the end of the 20th year.

The present value of these cash flows can be calculated using the formula for the present value of an annuity for the interest payments and the present value of a lump sum for the principal repayment. However, without doing the actual calculations, we know that the bond's price will be higher than the face value ($6,000,000) since the coupon rate is higher than the market rate. Therefore, Joseph's Baseball Bats will receive more than $6,000,000 from this issuance.

Impact of Rising Interest Rates

If the U.S. Federal Reserve increases interest rates on April 1, 2023, the price of Joseph’s bonds in the marketplace will likely decrease. This happens because new bonds are likely to be issued at these higher rates, making existing bonds with lower rates less attractive. Investors will require a discount on the existing bonds for them to yield a return that is competitive with new issues at higher rates.