An investor has two bonds in his portfolio that have a face value of $1,000 and
ID: 1171890 • Letter: A
Question
An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 9% annual coupon. Bond L matures in 13 years, while Bond S matures in 1 year.
Assume that only one more interest payment is to be made on Bond S at its maturity and that 13 more payments are to be made on Bond L.
What will the value of the Bond L be if the going interest rate is 4%? Round your answer to the nearest cent.
$
What will the value of the Bond S be if the going interest rate is 4%? Round your answer to the nearest cent.
$
What will the value of the Bond L be if the going interest rate is 8%? Round your answer to the nearest cent.
$
What will the value of the Bond S be if the going interest rate is 8%? Round your answer to the nearest cent.
$
What will the value of the Bond L be if the going interest rate is 14%? Round your answer to the nearest cent.
$
What will the value of the Bond S be if the going interest rate is 14%? Round your answer to the nearest cent.
$
Explanation / Answer
1) Value of bond L $ 1,499.28 Working: a. Value of bond is the present value of cash flow from bond. Present Value of couon payment $ 90 x 9.985648 = $ 898.71 Present Value of Par Value $ 1,000 x 0.600574 = $ 600.57 Present Value of cash flow from bond $ 1,499.28 b. Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.04)^-13)/0.04 i 4% = 9.985648 n 13 c. Present Value of payment of 1 at maturity = = (1+i)^-n = (1+0.04)^-13 = 0.600574 d. Annual coupon = Par Value x Coupon rate = $ 1,000 x 9% = $ 90 2) Value of bond S $ 1,048.08 Working: a. Value of bond is the present value of cash flow from bond. Present Value of couon payment $ 90 x 0.961538 = $ 86.54 Present Value of Par Value $ 1,000 x 0.961538 = $ 961.54 Present Value of cash flow from bond $ 1,048.08 b. Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.04)^-1)/0.04 i 4% = 0.961538 n 1 c. Present Value of payment of 1 at maturity = = (1+i)^-n = (1+0.04)^-1 = 0.961538 d. Annual coupon = Par Value x Coupon rate = $ 1,000 x 9% = $ 90 3) Value of bond L $ 1,079.04 Working: a. Value of bond is the present value of cash flow from bond. Present Value of couon payment $ 90 x 7.903776 = $ 711.34 Present Value of Par Value $ 1,000 x 0.367698 = $ 367.70 Present Value of cash flow from bond $ 1,079.04 b. Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.08)^-13)/0.08 i 8% = 7.903776 n 13 c. Present Value of payment of 1 at maturity = = (1+i)^-n = (1+0.08)^-13 = 0.367698 d. Annual coupon = Par Value x Coupon rate = $ 1,000 x 9% = $ 90 4) Value of bond S $ 1,009.26 Working: a. Value of bond is the present value of cash flow from bond. Present Value of couon payment $ 90 x 0.925926 = $ 83.33 Present Value of Par Value $ 1,000 x 0.925926 = $ 925.93 Present Value of cash flow from bond $ 1,009.26 b. Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.08)^-1)/0.08 i 8% = 0.925926 n 1 c. Present Value of payment of 1 at maturity = = (1+i)^-n = (1+0.08)^-1 = 0.925926 d. Annual coupon = Par Value x Coupon rate = $ 1,000 x 9% = $ 90 5) Value of bond L $ 707.88 Working: a. Value of bond is the present value of cash flow from bond. Present Value of couon payment $ 90 x 5.842362 = $ 525.81 Present Value of Par Value $ 1,000 x 0.182069 = $ 182.07 Present Value of cash flow from bond $ 707.88 b. Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.14)^-13)/0.14 i 14% = 5.842362 n 13 c. Present Value of payment of 1 at maturity = = (1+i)^-n = (1+0.14)^-13 = 0.182069 d. Annual coupon = Par Value x Coupon rate = $ 1,000 x 9% = $ 90 6) Value of bond S $ 956.14 Working: a. Value of bond is the present value of cash flow from bond. Present Value of couon payment $ 90 x 0.877193 = $ 78.95 Present Value of Par Value $ 1,000 x 0.877193 = $ 877.19 Present Value of cash flow from bond $ 956.14 b. Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.14)^-1)/0.14 i 14% = 0.877193 n 1 c. Present Value of payment of 1 at maturity = = (1+i)^-n = (1+0.14)^-1 = 0.877193 d. Annual coupon = Par Value x Coupon rate = $ 1,000 x 9% = $ 90
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