Question

Pharoah Corporation issues $590,000 of 9% bonds, due in 10 years, with interest payable semiannually. At the time of issue, the market rate for such bonds is 10%. Compute the issue price of the bonds. (Round present value foctor calculations to 5 decimal places, eg. 1.25124 and the final answer to 0 decimal places es. 58,971.)

Answer 1

The issue price for the bonds is $705,109.

Step-by-step explanation:

To calculate the issue price of the bonds, we need to calculate the present value of the future cash flows. The cash flows for the bonds are the periodic interest payments and the final principal payment at maturity. The present value factor is calculated using the market interest rate and the number of periods until each cash flow is received. The formula to calculate the present value factor is given by:

Present value factor = 1 / (1 + r/n)^(n*t)

Where r is the market interest rate, n is the number of compounding periods per year, and t is the number of years until each cash flow is received.

First, let's calculate the present value of the interest payments:

Annual interest payment = Bond face value * Coupon rate = $590,000 * 9% = $53,100

Semiannual interest payment = Annual interest payment / 2 = $53,100 / 2 = $26,550

Number of periods = Number of years * Number of compounding periods per year = 10 * 2 = 20

Present value factor for each semiannual interest payment = 1 / (1 + 10%/2)^(2*1) = 1 / (1 + 5%)^2 = 1 / 1.05^2 = 0.90703

Total present value of the interest payments = Present value factor * Semiannual interest payment * Number of periods = 0.90703 * $26,550 * 20 = $483,007

Next, let's calculate the present value of the final principal payment:

Present value factor for the principal payment at maturity = 1 / (1 + 10%/2)^(2*10) = 1 / (1 + 5%)^20 = 1 / 1.05^20 = 0.37689

Present value of the principal payment = Present value factor * Bond face value = 0.37689 * $590,000 = $222,102

The issue price of the bonds is the sum of the present values of the interest payments and the principal payment:

Issue price = Total present value of interest payments + Present value of principal payment = $483,007 + $222,102 = $705,109

Answer 2

To calculate the issue price of the bonds, we need to use the present value formula. The present value of interest payments and the principal payment are calculated using the present value factors. The issue price of the bonds is the sum of the present value of interest payments and the present value of the principal payment.

Step-by-step explanation:

To calculate the issue price of the bonds, we need to use the present value formula. The formula is:

Issue Price = Present Value of Future Cash Flows

The present value of future cash flows can be calculated by discounting each semiannual interest payment and the principal payment. In this case, the interest payments are $590,000 * 9% / 2 = $26,550, and there are a total of 10 * 2 = 20 semiannual periods. Using the present value factor for a 10% interest rate from the present value of the annuity table, the factor is 7.72173. Hence, the present value of interest payments is $26,550 * 7.72173 = $204,886.15.

The principal payment of $590,000 is due at the end of the 10th year, so we need to discount it back to the present value using the present value factor for 10 years at a 10% interest rate. The factor is 0.38554. Hence, the present value of the principal payment is $590,000 * 0.38554 = $227,615.70.

The issue price of the bonds is the sum of the present value of interest payments and the present value of the principal payment: $204,886.15 + $227,615.70 = $432,501.85. Therefore, the issue price of the bonds is $432,501.85.