Questions: Present Value of Bonds Payable; Premium Moss Co. issued 42,000,000 of five-year, 11% bonds, with interest payable semiannually, at a market (effective) interest rate of 9%. Determine the present value of the bonds payable using the present value tables in Exhibit 5 and Exhibit 7. Round to the nearest dollar.

Solution Steps

To determine the present value of the bonds payable, we need to calculate the present value of the interest payments and the present value of the principal repayment. The interest payments are an annuity, and the principal repayment is a lump sum. We will use the present value of an annuity formula and the present value of a lump sum formula, considering the market interest rate and the number of periods.

The semiannual coupon payment can be calculated using the formula: \[ \text{Semiannual Coupon Payment} = \frac{\text{Face Value} \times \text{Coupon Rate}}{\text{Periods per Year}} = \frac{42000000 \times 0.11}{2} = 2310000 \]

The total number of periods for the bond is given by: \[ \text{Total Periods} = \text{Years} \times \text{Periods per Year} = 5 \times 2 = 10 \]

The semiannual market interest rate is calculated as: \[ \text{Semiannual Market Rate} = \frac{\text{Market Rate}}{\text{Periods per Year}} = \frac{0.09}{2} = 0.045 \]

The present value of the annuity can be calculated using the formula: \[ PV_{\text{annuity}} = \text{Semiannual Coupon Payment} \times \left(1 - (1 + \text{Semiannual Market Rate})^{-\text{Total Periods}}\right) / \text{Semiannual Market Rate} \] Substituting the values: \[ PV_{\text{annuity}} = 2310000 \times \left(1 - (1 + 0.045)^{-10}\right) / 0.045 \approx 18278378.9891 \]

The present value of the lump sum can be calculated using the formula: \[ PV_{\text{lump sum}} = \frac{\text{Face Value}}{(1 + \text{Semiannual Market Rate})^{\text{Total Periods}}} \] Substituting the values: \[ PV_{\text{lump sum}} = \frac{42000000}{(1 + 0.045)^{10}} \approx 27044962.6453 \]

The total present value of the bonds is the sum of the present value of the annuity and the present value of the lump sum: \[ \text{Present Value of Bonds} = PV_{\text{annuity}} + PV_{\text{lump sum}} \approx 18278378.9891 + 27044962.6453 \approx 45323341.6344 \] Rounding to the nearest dollar gives: \[ \text{Present Value of Bonds} \approx 45323342 \]

Final Answer