Present Value Calculation for Regatta Inc. Bonds
How can we calculate the present value of Regatta, Inc.'s bonds?
Investors buying the bond today can expect to earn a yield to maturity of 6.8 percent. How much will you be willing to pay for Regatta's bond today?
Calculation of Present Value for Regatta, Inc.'s Bonds
Rounding the final answer to the nearest dollar, you would be willing to pay approximately $1,124 for Regatta, Inc.'s bond today. Among the given answer options, none matches the calculated price.
To calculate the price you would be willing to pay for Regatta, Inc.'s bond, we need to find the present value of its future cash flows using the yield to maturity of 6.8 percent. Let's break down the information:
Coupon rate: 8.25% (0.0825)
Yield to maturity: 6.8% (0.068)
Number of years to maturity: 6
To calculate the price, we need to determine the present value of the coupon payments and the principal repayment at maturity. Since the bond has annual coupon payments, we'll use the formula for the present value of an ordinary annuity:
Present Value of Coupon Payments = Coupon Payment * [(1 - (1 + r)^(-n)) / r]
where:
Coupon Payment = Coupon Rate * Face Value
= 0.0825 * Face Value
Face Value is the amount paid back at maturity. It is not provided in the given information, so we'll assume it to be $1,000 (par value).
Using the given values, let's calculate the present value of the coupon payments:
Present Value of Coupon Payments = 0.0825 * 1,000 * [(1 - (1 + 0.068)^(-6)) / 0.068]
To find the present value of the principal repayment, we'll use the formula for the present value of a future value:
Present Value of Principal Repayment = Face Value / (1 + r)^n
Present Value of Principal Repayment = 1,000 / (1 + 0.068)^6
Now, let's calculate these values:
Present Value of Coupon Payments = 0.0825 * 1,000 * [(1 - (1 + 0.068)^(-6)) / 0.068]
≈ $376.62
Present Value of Principal Repayment = 1,000 / (1 + 0.068)^6
≈ $747.83
To determine the total price you would be willing to pay for the bond today, we need to sum the present value of the coupon payments and the principal repayment:
Total Price = Present Value of Coupon Payments + Present Value of Principal Repayment
= $376.62 + $747.83
≈ $1,124.45