Final answer:
To calculate the present value of the bonds at issuance, you need to discount the future cash flows from the bonds to their present value. The present value of the bonds at issuance is $287,175.28.
Step-by-step explanation:
To calculate the present value of the bonds at issuance, we need to discount the future cash flows from the bonds to their present value. In this case, the bonds pay semiannual interest at a rate of 6% on a $200,000 bond principal for 10 years. We can use the formula for present value of an annuity to calculate the present value of the interest payments, and add it to the present value of the principal payment.
The present value of an annuity formula is: PV = C * (1 - (1 + r)^-n) / r, where PV is the present value, C is the periodic cash flow, r is the interest rate per period, and n is the number of periods.
Using this formula, the present value of the interest payments can be calculated as follows:
Interest Payment = (Bond Principal) * (Interest Rate / 2) = $200,000 * 6% / 2 = $6,000
Using the present value of an annuity formula, with a rate of 4% (half of the 8% yearly market interest rate), and a duration of 20 periods (10 years * 2 payments per year), the present value of the interest payments is:
PV of Interest Payments = $6,000 * (1 - (1 + 4%)^-20) / (4%) = $87,175.28
The present value of the principal payment is simply the face value of the bonds, since the principal is repaid at the end of the bond term. Therefore, the present value of the bonds at issuance is:
Present Value of Bonds at Issuance = PV of Interest Payments + Bond Principal = $87,175.28 + $200,000 = $287,175.28