Final answer:
Harpo Co. would receive proceeds lower than the face value of the bonds due to the higher yield rate; the exact amount would require a present value calculation. When buying a bond with a market interest rate higher than the bond's coupon rate close to maturity, you would pay less than its face value, and a specific calculation based on the current interest rate would provide the exact price you would be willing to pay.
Step-by-step explanation:
Harpo Co. sold bonds at a discount due to the yield rate being higher than the interest rate. The proceeds from the bond sale are calculated using present value cash flows, considering the bond's coupon payments and the principal repayment at maturity, discounted at the yield to maturity, which is 10% in this case.
When you are considering purchasing a bond one year before its maturity and the market interest rates have risen, you would expect the price of the bond to be lower than its face value. This is because the bond's fixed interest payments are less attractive when new bonds are available that pay higher interest. Consequently, the bond's price must decrease to offer a competitive yield to potential buyers.
To calculate what you would be willing to pay for a $10,000 10-year bond with a 6% interest rate when market interest rates are 9%, you would discount the bond's remaining cash flows - 1 year of interest payments and the principal repayment - back to present value using the new interest rate of 9%. The calculation would look like this:
PV = $600 / (1 + 0.09)^1 + $10,000 / (1 + 0.09)^1
This results in a present value of:
PV = $550.46 + $9174.31
So, the price you would be willing to pay for the bond would be approximately $9724.77.