pay interest semiannually every June 30 December 31. All of the bonds will be so
ID: 2536361 • Letter: P
Question
pay interest semiannually every June 30 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 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 Step 1 : Calculation of Annual Coupon Payments Par value of the bond issued is = $5,08,000 Annual Coupon % 6.00% Annual Coupon Amount $30,480.00 Semi Annual Coupon Amount $15,240.00 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 $15,240.00 0.9804 $14,941.18 2 Interest $15,240.00 0.9612 $14,648.21 3 Interest $15,240.00 0.9423 $14,360.99 4 Interest $15,240.00 0.9238 $14,079.40 5 Interest $15,240.00 0.9057 $13,803.34 6 Interest $15,240.00 0.8880 $13,532.68 7 Interest $15,240.00 0.8706 $13,267.34 8 Interest $15,240.00 0.8535 $13,007.19 9 Interest $15,240.00 0.8368 $12,752.15 10 Interest $15,240.00 0.8203 $12,502.11 11 Interest $15,240.00 0.8043 $12,256.97 12 Interest $15,240.00 0.7885 $12,016.64 13 Interest $15,240.00 0.7730 $11,781.02 14 Interest $15,240.00 0.7579 $11,550.02 15 Interest $15,240.00 0.7430 $11,323.54 16 Interest $15,240.00 0.7284 $11,101.51 17 Interest $15,240.00 0.7142 $10,883.84 18 Interest $15,240.00 0.7002 $10,670.43 19 Interest $15,240.00 0.6864 $10,461.20 20 Interest $15,240.00 0.6730 $10,256.08 21 Interest $15,240.00 0.6598 $10,054.98 22 Interest $15,240.00 0.6468 $9,857.83 23 Interest $15,240.00 0.6342 $9,664.54 24 Interest $15,240.00 0.6217 $9,475.04 25 Interest $15,240.00 0.6095 $9,289.25 26 Interest $15,240.00 0.5976 $9,107.11 27 Interest $15,240.00 0.5859 $8,928.54 28 Interest $15,240.00 0.5744 $8,753.47 29 Interest $15,240.00 0.5631 $8,581.83 30 Interest $15,240.00 0.5521 $8,413.56 30 Bond Principal Value $5,08,000.00 0.5521 $2,80,452.01 Total $6,21,773.99 Current Bonds Price = $6,21,774 Answer = 1 =Issue price of the bond= $6,21,774 CALCULATION OF PRESENT VALUE OF THE BOND IF THE INTEREST PAID SEMI ANNUALLY Step 1 : Calculation of Annual Coupon Payments Par value of the bond issued is = $5,08,000 Annual Coupon % 6.00% Annual Coupon Amount $30,480.00 Semi Annual Coupon Amount $15,240.00 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 $15,240.00 0.9709 $14,796.12 2 Interest $15,240.00 0.9426 $14,365.16 3 Interest $15,240.00 0.9151 $13,946.76 4 Interest $15,240.00 0.8885 $13,540.54 5 Interest $15,240.00 0.8626 $13,146.16 6 Interest $15,240.00 0.8375 $12,763.26 7 Interest $15,240.00 0.8131 $12,391.51 8 Interest $15,240.00 0.7894 $12,030.60 9 Interest $15,240.00 0.7664 $11,680.19 10 Interest $15,240.00 0.7441 $11,339.99 11 Interest $15,240.00 0.7224 $11,009.70 12 Interest $15,240.00 0.7014 $10,689.03 13 Interest $15,240.00 0.6810 $10,377.70 14 Interest $15,240.00 0.6611 $10,075.44 15 Interest $15,240.00 0.6419 $9,781.98 16 Interest $15,240.00 0.6232 $9,497.06 17 Interest $15,240.00 0.6050 $9,220.45 18 Interest $15,240.00 0.5874 $8,951.89 19 Interest $15,240.00 0.5703 $8,691.16 20 Interest $15,240.00 0.5537 $8,438.02 21 Interest $15,240.00 0.5375 $8,192.25 22 Interest $15,240.00 0.5219 $7,953.64 23 Interest $15,240.00 0.5067 $7,721.98 24 Interest $15,240.00 0.4919 $7,497.07 25 Interest $15,240.00 0.4776 $7,278.71 26 Interest $15,240.00 0.4637 $7,066.71 27 Interest $15,240.00 0.4502 $6,860.88 28 Interest $15,240.00 0.4371 $6,661.05 29 Interest $15,240.00 0.4243 $6,467.04 30 Interest $15,240.00 0.4120 $6,278.68 30 Bond Principal Value $5,08,000.00 0.4120 $2,09,289.27 Total $5,08,000.00 Current Bonds Price = $5,08,000 Answer = 2 =Issue price of the bond= $5,08,000 CALCULATION OF PRESENT VALUE OF THE BOND IF THE INTEREST PAID SEMI ANNUALLY Step 1 : Calculation of Annual Coupon Payments Par value of the bond issued is = $5,08,000 Annual Coupon % 6.00% Annual Coupon Amount $30,480.00 Semi Annual Coupon Amount $15,240.00 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 $15,240.00 0.9592 $14,618.71 2 Interest $15,240.00 0.9201 $14,022.74 3 Interest $15,240.00 0.8826 $13,451.07 4 Interest $15,240.00 0.8466 $12,902.70 5 Interest $15,240.00 0.8121 $12,376.69 6 Interest $15,240.00 0.7790 $11,872.13 7 Interest $15,240.00 0.7473 $11,388.13 8 Interest $15,240.00 0.7168 $10,923.87 9 Interest $15,240.00 0.6876 $10,478.53 10 Interest $15,240.00 0.6595 $10,051.35 11 Interest $15,240.00 0.6326 $9,641.58 12 Interest $15,240.00 0.6069 $9,248.52 13 Interest $15,240.00 0.5821 $8,871.48 14 Interest $15,240.00 0.5584 $8,509.81 15 Interest $15,240.00 0.5356 $8,162.89 16 Interest $15,240.00 0.5138 $7,830.11 17 Interest $15,240.00 0.4928 $7,510.90 18 Interest $15,240.00 0.4727 $7,204.70 19 Interest $15,240.00 0.4535 $6,910.98 20 Interest $15,240.00 0.4350 $6,629.24 21 Interest $15,240.00 0.4173 $6,358.98 22 Interest $15,240.00 0.4002 $6,099.74 23 Interest $15,240.00 0.3839 $5,851.07 24 Interest $15,240.00 0.3683 $5,612.54 25 Interest $15,240.00 0.3533 $5,383.73 26 Interest $15,240.00 0.3389 $5,164.25 27 Interest $15,240.00 0.3250 $4,953.72 28 Interest $15,240.00 0.3118 $4,751.77 29 Interest $15,240.00 0.2991 $4,558.05 30 Interest $15,240.00 0.2869 $4,372.23 30 Bond Principal Value $5,08,000.00 0.2869 $1,45,741.02 Total $4,01,453.24 Current Bonds Price = $4,01,453 Answer = 3 =Issue price of the bond= $4,01,453
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