Homework_3_Solution

# Homework_3_Solution - FIN340 HOMEWORK#3 SOLUTION 1 If the...

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FIN340 HOMEWORK #3 SOLUTION 1. If the term structure of interest rates is flat, all yields are the same (at 3% in this problem). In general, the price of a bond is the present value of its future cash flows (coupon payments and principal repayment). Since all the yields are the same, we can use the annuity formula to find the value of the coupons and then add in the present value of principal payment. If the interest rates were not all the same, you can’t use the annuity formula. You have to discount each cash flow individually using the appropriate yield-to-maturity for each corresponding maturity/cash flow and then add them up.) a) 10-year bond with a 2% coupon: ⎡⎤ ×− + ⎢⎥ ⎣⎦ 20 20 10 1 1,000 PV = 1 = 914.16 0.015 (1+0.015) (1+0.015) b) 10-year bond with a 4% coupon: + 20 20 20 1 1,000 PV = 1 =1,085.84 0.015 (1+0.015) (1+0.015) c) 10-year bond with a 2% coupon: + 20 20 15 1 1,000 PV = 1 =1,000 0.015 (1+0.015) (1+0.015) d) When the coupon rate is lower than the yield, the bond price is lower than the face value and hence it is sold at a discount . When the coupon rate is higher than the yield, the bond price is higher than the face value and hence it is sold at a premium . Only when the rates are equal, the bond sells at par .

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2. See also the Excel File for more calculations and for more details. a) We begin by finding the price of the 6% coupon bond using the mathematical definition of YTM: ⎡⎤ ×− + ⎢⎥ ⎣⎦ 22 60 1 1,000 PV = 1 =1,037.72 0.04 (1+0.04) (1+0.04) Next we can find the yield of the 1-year zero-coupon bond given by.
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Homework_3_Solution - FIN340 HOMEWORK#3 SOLUTION 1 If the...

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