Young Co. issues $800,000 of 10% bonds dated January 1, Year 1. Interest is payable semiannually on June 30 and December 31. The bonds mature in 5 years. The current market rate for similar bonds is 8%. The entire issue is sold on the date of issue. The following values are given:Present Value ofOrdinary AnnuityPresent Valueof $1N=10; i=0.048.110900.67556N=10; i=0.057.721730.61391What amount of proceeds on the sale of bonds should Young report?
Question
Young Co. issues 1N=10; i=0.048.110900.67556N=10; i=0.057.721730.61391What amount of proceeds on the sale of bonds should Young report?
Solution 1
Young Co. should report the amount of proceeds on the sale of bonds as follows:
Step 1: Determine the present value of the bond's future cash flows. To calculate the present value of the bond's future cash flows, we need to find the present value of the interest payments and the present value of the principal repayment.
Step 2: Calculate the present value of the interest payments. The bond pays semiannual interest at a rate of 10%. Since the market rate is 8%, we can use the present value of an ordinary annuity formula to calculate the present value of the interest payments.
Using the given values, we find that the present value of an ordinary annuity with N=10 and i=0.048 is 8.1109. Therefore, the present value of the interest payments is 8.1109 * (10% * 64,887.20.
Step 3: Calculate the present value of the principal repayment. At maturity, the bond will repay the principal amount of 1 formula.
Using the given values, we find that the present value of 800,000 = $491,128.80.
Step 4: Calculate the total present value of the bond's future cash flows. To find the total present value of the bond's future cash flows, we add the present value of the interest payments and the present value of the principal repayment.
Total present value = 491,128.80 = $556,016.
Step 5: Determine the amount of proceeds on the sale of bonds. The amount of proceeds on the sale of bonds is equal to the total present value of the bond's future cash flows. Therefore, Young Co. should report $556,016 as the amount of proceeds on the sale of bonds.
Solution 2
Young Co. should report the amount of proceeds on the sale of bonds as follows:
Step 1: Determine the present value of the bond's future cash flows. To calculate the present value of the bond's future cash flows, we need to find the present value of the interest payments and the present value of the principal repayment.
Step 2: Calculate the present value of the interest payments. The bond pays semiannual interest at a rate of 10%. Since the market rate is 8%, we can use the present value of an ordinary annuity formula to calculate the present value of the interest payments.
Using the given values, we find that the present value of an ordinary annuity with N=10 and i=0.048 is 8.1109. Therefore, the present value of the interest payments is 8.1109 * (10% * 64,887.20.
Step 3: Calculate the present value of the principal repayment. At maturity, the bond will repay the principal amount of 1 formula.
Using the given values, we find that the present value of 800,000 = $491,128.80.
Step 4: Calculate the total present value of the bond's future cash flows. To find the total present value of the bond's future cash flows, we add the present value of the interest payments and the present value of the principal repayment.
Total present value = Present value of interest payments + Present value of principal repayment Total present value = 491,128.80 Total present value = $556,016.00
Step 5: Calculate the amount of proceeds on the sale of bonds. The amount of proceeds on the sale of bonds is equal to the total present value of the bond's future cash flows.
Therefore, Young Co. should report the amount of proceeds on the sale of bonds as $556,016.00.
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