James Corporation is planning to issue bonds with a face value of $502,000 and a
ID: 2520419 • Letter: J
Question
James Corporation is planning to issue bonds with a face value of $502,000 and a coupon rate of 6 percent. The bonds mature in 15 years and pay interest semiannually every June 30 and December 31. All of the bonds will be sold on January 1 of this year. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use the appropriate factor(s) from the tables provided. Round your final answer to whole dollars.) Required Compute the issue (sale) price on January 1 of this year for each of the following independent cases a. Case A: Market interest rate (annual):4 percent b. Case B: Market interest rate (annual): 6 percent. c. Case C: Market interest rate (annual): 8.5 percentExplanation / Answer
CALCULATION OF PRESENT VALUE OF THE BOND IF THE INTEREST PAID SEMI ANNUALLY Answer = A) If the market rate of interest is 4% annually Step 1 : Calculation of Annual Coupon Payments Par value of the bond issued is = $5,02,000 Annual Coupon % 6.00% Annual Coupon Amount $30,120 Semi Annual Coupon Amount $15,060 Step 2: Calculate number of years to Maturity Number of years to maturity = 15 years Interest is paid semi annyally so total period = 15 Years * 2 = 30 Periods Step 3 : Caclulation of Current Market Price (intrinsic value) of the bonds Market rate of interest or Yield to Maturity or Required Return = 4% Bonds interest is paid semi annualy means so discounting factor = 4 % /2= 2 % PVF = 1 / Discount rate = 1/ 1.02 Result of above will again divide by 1.02 , repeat this lat period Period Interest Amount (In Million) PVF @ 2% PresentValue 1 Interest $15,060.00 0.9804 $14,764.71 2 Interest $15,060.00 0.9612 $14,475.20 3 Interest $15,060.00 0.9423 $14,191.37 4 Interest $15,060.00 0.9238 $13,913.11 5 Interest $15,060.00 0.9057 $13,640.31 6 Interest $15,060.00 0.8880 $13,372.85 7 Interest $15,060.00 0.8706 $13,110.64 8 Interest $15,060.00 0.8535 $12,853.56 9 Interest $15,060.00 0.8368 $12,601.53 10 Interest $15,060.00 0.8203 $12,354.45 11 Interest $15,060.00 0.8043 $12,112.20 12 Interest $15,060.00 0.7885 $11,874.71 13 Interest $15,060.00 0.7730 $11,641.87 14 Interest $15,060.00 0.7579 $11,413.60 15 Interest $15,060.00 0.7430 $11,189.80 16 Interest $15,060.00 0.7284 $10,970.39 17 Interest $15,060.00 0.7142 $10,755.29 18 Interest $15,060.00 0.7002 $10,544.40 19 Interest $15,060.00 0.6864 $10,337.65 20 Interest $15,060.00 0.6730 $10,134.95 21 Interest $15,060.00 0.6598 $9,936.22 22 Interest $15,060.00 0.6468 $9,741.40 23 Interest $15,060.00 0.6342 $9,550.39 24 Interest $15,060.00 0.6217 $9,363.13 25 Interest $15,060.00 0.6095 $9,179.53 26 Interest $15,060.00 0.5976 $8,999.54 27 Interest $15,060.00 0.5859 $8,823.08 28 Interest $15,060.00 0.5744 $8,650.08 29 Interest $15,060.00 0.5631 $8,480.47 30 Interest $15,060.00 0.5521 $8,314.19 30 Bond Principal Value $5,02,000.00 0.5521 $2,77,139.59 Total $6,14,430.21 Current Bonds Price = $6,14,430.21 Answer =A = Issue price of the bonds = $6,14,430.21 Answer = B) If the market rate of interest is 6% annually Step 1 : Calculation of Annual Coupon Payments Par value of the bond issued is = $5,02,000 Annual Coupon % 6.00% Annual Coupon Amount $30,120 Semi Annual Coupon Amount $15,060 Step 2: Calculate number of years to Maturity Number of years to maturity = 15 years Interest is paid semi annyally so total period = 15 Years * 2 = 30 Periods Step 3 : Caclulation of Current Market Price (intrinsic value) of the bonds Market rate of interest or Yield to Maturity or Required Return = 6% Bonds interest is paid semi annualy means so discounting factor = 6 % /2= 3 % PVF = 1 / Discount rate = 1/ 1.03 Result of above will again divide by 1.03 , repeat this lat period Period Interest Amount (In Million) PVF @ 3% PresentValue 1 Interest $15,060.00 0.9709 $14,621.36 2 Interest $15,060.00 0.9426 $14,195.49 3 Interest $15,060.00 0.9151 $13,782.03 4 Interest $15,060.00 0.8885 $13,380.61 5 Interest $15,060.00 0.8626 $12,990.89 6 Interest $15,060.00 0.8375 $12,612.51 7 Interest $15,060.00 0.8131 $12,245.16 8 Interest $15,060.00 0.7894 $11,888.50 9 Interest $15,060.00 0.7664 $11,542.24 10 Interest $15,060.00 0.7441 $11,206.05 11 Interest $15,060.00 0.7224 $10,879.66 12 Interest $15,060.00 0.7014 $10,562.78 13 Interest $15,060.00 0.6810 $10,255.13 14 Interest $15,060.00 0.6611 $9,956.43 15 Interest $15,060.00 0.6419 $9,666.44 16 Interest $15,060.00 0.6232 $9,384.89 17 Interest $15,060.00 0.6050 $9,111.55 18 Interest $15,060.00 0.5874 $8,846.16 19 Interest $15,060.00 0.5703 $8,588.51 20 Interest $15,060.00 0.5537 $8,338.36 21 Interest $15,060.00 0.5375 $8,095.49 22 Interest $15,060.00 0.5219 $7,859.70 23 Interest $15,060.00 0.5067 $7,630.78 24 Interest $15,060.00 0.4919 $7,408.52 25 Interest $15,060.00 0.4776 $7,192.74 26 Interest $15,060.00 0.4637 $6,983.24 27 Interest $15,060.00 0.4502 $6,779.85 28 Interest $15,060.00 0.4371 $6,582.38 29 Interest $15,060.00 0.4243 $6,390.66 30 Interest $15,060.00 0.4120 $6,204.52 30 Bond Principal Value $5,02,000.00 0.4120 $2,06,817.35 Total $5,02,000.00 Current Bonds Price = $5,02,000.00 Answer =B = Issue price of the bonds = $5,02,000.00 Answer = C) If the market rate of interest is 8.5 % annually Step 1 : Calculation of Annual Coupon Payments Par value of the bond issued is = $5,02,000 Annual Coupon % 6.00% Annual Coupon Amount $30,120 Semi Annual Coupon Amount $15,060 Step 2: Calculate number of years to Maturity Number of years to maturity = 15 years Interest is paid semi annyally so total period = 15 Years * 2 = 30 Periods Step 3 : Caclulation of Current Market Price (intrinsic value) of the bonds Market rate of interest or Yield to Maturity or Required Return = 8.5% Bonds interest is paid semi annualy means so discounting factor = 8.5 % /2= 4.25 % PVF = 1 / Discount rate = 1/ 1.0425 Result of above will again divide by 1.0425 , repeat this lat period Period Interest Amount (In Million) PVF @ 4.25% PresentValue 1 Interest $15,060.00 0.9592 $14,446.04 2 Interest $15,060.00 0.9201 $13,857.12 3 Interest $15,060.00 0.8826 $13,292.20 4 Interest $15,060.00 0.8466 $12,750.31 5 Interest $15,060.00 0.8121 $12,230.51 6 Interest $15,060.00 0.7790 $11,731.91 7 Interest $15,060.00 0.7473 $11,253.63 8 Interest $15,060.00 0.7168 $10,794.85 9 Interest $15,060.00 0.6876 $10,354.77 10 Interest $15,060.00 0.6595 $9,932.63 11 Interest $15,060.00 0.6326 $9,527.70 12 Interest $15,060.00 0.6069 $9,139.28 13 Interest $15,060.00 0.5821 $8,766.70 14 Interest $15,060.00 0.5584 $8,409.30 15 Interest $15,060.00 0.5356 $8,066.48 16 Interest $15,060.00 0.5138 $7,737.63 17 Interest $15,060.00 0.4928 $7,422.19 18 Interest $15,060.00 0.4727 $7,119.60 19 Interest $15,060.00 0.4535 $6,829.36 20 Interest $15,060.00 0.4350 $6,550.94 21 Interest $15,060.00 0.4173 $6,283.88 22 Interest $15,060.00 0.4002 $6,027.70 23 Interest $15,060.00 0.3839 $5,781.97 24 Interest $15,060.00 0.3683 $5,546.25 25 Interest $15,060.00 0.3533 $5,320.14 26 Interest $15,060.00 0.3389 $5,103.26 27 Interest $15,060.00 0.3250 $4,895.21 28 Interest $15,060.00 0.3118 $4,695.64 29 Interest $15,060.00 0.2991 $4,504.22 30 Interest $15,060.00 0.2869 $4,320.59 30 Bond Principal Value $5,02,000.00 0.2869 $1,44,019.67 Total $3,96,711.67 Current Bonds Price = $3,96,711.67 Answer =C = Issue price of the bonds = $3,96,711.67
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