For each of the following pairs of treasury securities (each with $1000 par value), identify which will have the higher price: a. a three-year zero-coupon bond or a five-year zero coupon bond? b. a three-year zero-coupon bond or a three-year 4% coupon bond? c. a two-year 5% coupon bond or a two-year 6% coupon bond?

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(a)0.04317 (b) 3672 which will be paid by the payer to the receiver (c) -399. so, the 399 which will be paid by the receiver to the payer (d) 2659.38 Explanation: Solution (a) Swap Rate (R) = (1 – P₃)/(P₁+P₂+P₃) = (1 – 0.88)/(0.97 + 0.93 + 0.88) = 0.04317 (b) The payer pays the fixed interest rate and gets the variable interest rate. Then, the fixed interest rate is known as the swap rate which is 4.317%. Now, The variable rate is the one year spot rate for the first year of the loan. which is r₁ = 1/P₁ -1 = 1/0.97 – 1 = 0.03093 Thus, The net swap payment becomes (300,000)(0.04317) – (300,000)(0.03093) = 3672 which will be paid by the payer to the receiver. (c) The payer pays the fixed interest rate and receives the variable interest rate. The fixed interest rate is the swap rate which is 4.317%. Thus, The variable rate is the one year spot rate for the second year of the loan is 4.45%. So, The net swap payment becomes (300,000)(0.04317) – (300,000)(0.04450) = -399. Therefore, the 399 which will be paid by the receiver to the payer. (d) The market value is the present value of expected future cash flows. under this swap, the variable rate has been swapped for the constant swap rate. There is one year left under the swap. Then, The expectation is that the swap owner will pay (300,000)(0.04317) and receive (300,000)(0.0525). these payments would be made at the end of one year. Therefore, the market value will be: {(300,000)(0.0525) – (300,000)(0.04317)}/1.0525 = 2799/1.0525 = 2659.38

The Market Price of Bond C Coupon (R) = 5% x 1,000 = $50 Bond yield Kd = 5% = 0.05 Po = R(1-(1+r)-n)/k + FV/ (1+r)n Po = 50(1-(1+0.05)-2)/0.05 + 1,000/(1 + 0.05)2 Po = 50(1-(1.05)-2)/0.05 + 1,000/

(1.05)2 Po = 50(1-(0.9070))/0.05 + 1,000/

(1.05)2 Po = 50/1.86 + 907.03 Po = 26.88 + 907.03 Po = $933.91 Explanation: The market price of bond C equals present value of the coupon plus the present value of the face value. The present value of the coupon is obtained by discounting the coupon at the present value of annuity factor of 5% for 2 years. The 5% bond yield is used because the bonds belong to the same risk class and the yield of this class is 5%. The present value of the face value of the bond is determined by discounting the face value at the present value factor of 5% for 2 years. The aggregate of the two present values give the current market price of Bond C.

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