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In 2021, a baseball player signed a contract worth $57 million. The contract called for $10.5 million immediately and a salary of $2.6 million in 2022, $7.7 million in 2023, $10.5 million in 2024, $8.5 million in 2025 and 2026, and $8.7 million in 2027. If the appropriate interest rate is 8 percent, what kind of deal did the player dig out of the dirt? Assume all payments other than the first $10.5 million are paid at the end of the contract year.

User ViaTech
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Final answer:

If current interest rates are higher than a bond's coupon rate, as is the case with the local water company's bond where the market rate is 9% and the bond's coupon rate is 6%, the bond will sell for less than its face value. For a $10,000 bond, one year before maturity, the price you'd be willing to pay considering the current interest rate would be $9,724.77.

Step-by-step explanation:

When considering the purchase of a bond on the secondary market, the prevailing interest rates will significantly impact the price you pay. If the current interest rates are higher than the bond's coupon rate, the bond will be sold at a discount; conversely, if the current interest rates are lower, the bond will be sold at a premium.

Given a $10,000 ten-year bond with a 6% interest rate that is approaching its maturity with one year remaining, and current market interest rates have risen to 9%, you would expect to pay less than the face value of the bond because the bond's fixed interest payments are less attractive compared to newer issues at 9%.

To calculate the actual price you'd be willing to pay for the bond:

  1. Determine the bond's remaining cash flows, which, in this case, include the interest payment for the last year and the face value repayment at maturity.
  2. Discount these future cash flows back to their present value using the current 9% market interest rate.

Here's an example calculation:

Bond's future value cash flows:

  • $600 (6% of $10,000) in interest after one year.
  • $10,000 face value at the end of the year.

Present value of these cash flows:

  • $600 / (1 + 0.09)^1 = $550.46
  • $10,000 / (1 + 0.09)^1 = $9,174.31

Sum of the present values: $550.46 + $9,174.31 = $9,724.77

Therefore, the price you would be willing to pay for the bond considering the higher interest rate would be $9,724.77.

User Exacerbatedexpert
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