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Compute the selling price of 10%, 10-year bonds with a par value of $320,000 and semiannual interest payments. The annual market rate for these bonds is 12%. Use present value Table B.1 and Table B.3 in Appendix B.

Question

Compute the selling price of 10%, 10-year bonds with a par value of $320,000 and semiannual interest payments. The annual market rate for these bonds is 12%. Use present value Table B.1 and Table B.3 in Appendix B.

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Solution

To calculate the selling price of the bonds, we need to calculate the present value of the bond's interest payments (an annuity) and the present value of the bond's face value (a lump sum payment at the end of the bond's life).

Step 1: Calculate the semiannual interest payment The bond pays 10% annually, so the semiannual interest rate is 10%/2 = 5%. The semiannual interest payment is 5% of the 320,000parvalue,whichis320,000 par value, which is 16,000.

Step 2: Calculate the present value of the interest payments The bond pays interest semiannually for 10 years, so there are 10*2 = 20 periods. The semiannual market rate is 12%/2 = 6%. Using the present value of an ordinary annuity table (Table B.1), find the factor for 20 periods at 6%, which is 11.46992. Multiply this factor by the semiannual interest payment to get the present value of the interest payments: 16,00011.46992=16,000 * 11.46992 = 183,518.72.

Step 3: Calculate the present value of the face value The bond pays its 320,000facevalueattheendof10years,whichis20periodsatthesemiannuallevel.Usingthepresentvalueof320,000 face value at the end of 10 years, which is 20 periods at the semiannual level. Using the present value of 1 table (Table B.3), find the factor for 20 periods at 6%, which is 0.31213. Multiply this factor by the face value to get the present value of the face value: 320,0000.31213=320,000 * 0.31213 = 99,881.60.

Step 4: Add the present values to get the selling price The selling price of the bond is the sum of the present value of the interest payments and the present value of the face value: 183,518.72+183,518.72 + 99,881.60 = $283,400.32.

So, the selling price of the 10%, 10-year bonds with a par value of 320,000andsemiannualinterestpayments,givenanannualmarketrateof12320,000 and semiannual interest payments, given an annual market rate of 12%, is approximately 283,400.32.

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