Chrome File Edit View History Bookmarks People Window Help P5&6 (Interest Rates
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Chrome File Edit View History Bookmarks People Window Help P5&6 (Interest Rates and Bond ?Secure https://xlitemprod.pearsoncmg.com/api/v1/print/en-us/finance Date:6/4/18 Course: Financial Management (Fin 31 5. Bond prices. Price the bonds from the following table with semiannual coupon payments Years to Yield to Par Value Coupon Rate Maturity Maturity $1,000.00 $5,000.00 $5,000.00 $1,000.00 7% 12% 9% 11% 15 8% 996 5% 15 15 a. Find the price for the bond in the following table: (Round to the nearest cent.) Yield to Maturity 7% Years to Par Value Coupon Rate Maturity $1,000.00 8% 15 b. Find the price for the bond in the following table: (Round to the nearest cent) Yleld to Maturity 12% Years to Par Value Coupon Rate Maturity $5,000.00 9% 15 c. Find the price for the bond in the following table: (Round to the nearest cent.) Years to Yield to Par Value Coupon Rate Maturity Maturity $5,000.00 5% 9% d. Find the price for the bond in the following table: (Round to the nearest cent.) Years to Par Value Coupon Rate Maturity $1,000.00 Yield to Maturity 11% 15 1: Definition Coupon is the regular interest payment of a bond.Explanation / Answer
a. Price $ 1,091.96 Working: 1) Semi annual coupon = $ 1,000.00 x 4% = $ 40.00 2) Semi annual yield = 7% / 2 = 3.50% 3) Present value of annuity of $ 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.035)^-30)/0.035 i 3.50% = 18.392 n 30 4) Present Value of $ 1 to be received at maturity = 1+i)^-n = (1+0.035)^-30 = 0.356 5) Present Value of coupon payment = $ 40.00 x 18.392 = $ 735.68 Present Value of Par Value = $ 1,000.00 x 0.356 = $ 356.28 Present value of total cash flows from bond $ 1,091.96 6) Price of bond is the Present value of cash flows from bond.So, Price of bond is $ 1,091.96 b. Price $ 3,967.64 Working: 1) Semi annual coupon = $ 5,000.00 x 4.5% = $ 225.00 2) Semi annual yield = 12% / 2 = 6.00% 3) Present value of annuity of $ 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.06)^-30)/0.06 i 6.00% = 13.765 n 30 4) Present Value of $ 1 to be received at maturity = (1+i)^-n = (1+0.06)^-30 = 0.174 5) Present Value of coupon payment = $ 225.00 x 13.765 = $ 3,097.09 Present Value of Par Value = $ 5,000.00 x 0.174 = $ 870.55 Present value of total cash flows from bond $ 3,967.64 6) Price of bond is the Present value of cash flows from bond.So, Price of bond is $ 3,967.64 c. Price $ 4,208.73 Working: 1) Semi annual coupon = $ 5,000.00 x 2.5% = $ 125.00 2) Semi annual yield = 9% / 2 = 4.50% 3) Present value of annuity of $ 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.045)^-10)/0.045 i 4.50% = 7.913 n 10 4) Present Value of $ 1 to be received at maturity = (1+i)^-n = (1+0.045)^-10 = 0.644 5) Present Value of coupon payment = $ 125.00 x 7.913 = $ 989.09 Present Value of Par Value = $ 5,000.00 x 0.644 = $ 3,219.64 Present value of total cash flows from bond $ 4,208.73 6) Price of bond is the Present value of cash flows from bond.So, Price of bond is $ 4,208.73 d. Price $ 709.33 Working: 1) Semi annual coupon = $ 1,000.00 x 3.5% = $ 35.00 2) Semi annual yield = 11% / 2 = 5.50% 3) Present value of annuity of $ 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.055)^-30)/0.055 i 5.50% = 14.534 n 30 4) Present Value of $ 1 to be received at maturity = (1+i)^-n = (1+0.055)^-30 = 0.201 5) Present Value of coupon payment = $ 35.00 x 14.534 = $ 508.68 Present Value of Par Value = $ 1,000.00 x 0.201 = $ 200.64 Present value of total cash flows from bond $ 709.33 6) Price of bond is the Present value of cash flows from bond.So, Price of bond is $ 709.33
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