hw2_answers_Solutions - ANSWERS TO HOMEWORK QUESTIONS - HW...

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Unformatted text preview: ANSWERS TO HOMEWORK QUESTIONS - HW #2 Answers for Chapter 4 - Questions 2 & 10 2. Calculate the requested measures in parts (a) through (f) for bonds A and B (assume that each bond pays interest semiannually). Needed bond details are below. Bond A Bond B Coupon 8% 9% Yield to maturity 8% 8% Maturity (years) 2 5 Par value $100.00 $100.00 Price $100.00 $104.055 (a) What is the price value of a basis point for bonds A and B? For Bond A , we get a bond quote of $100.00 for our initial price if we have a 2-year maturity, an 8% coupon rate and an 8% yield H we change the yield one basis point so the yield is 8.01%, then we have the following variables and values: C = $40, y = 0.0801/2 = 0.04005 and n = 2*(2) = 4. Inserting these values into the present value of the coupon payments formula, we get: 179 . 145 $ 004005 . ) 04005 . 1 ( 1 1 * 40 $ ) 1 ( 1 1 * 4 = = + = r r C P n Computing the present value of the par or maturity value of $1,000 gives: 640 . 854 $ ) 04005 . 1 ( 000 , 1 $ ) 1 ( 4 = = + n r M If we add a basis point to the yield, we get the value of Bond A as: P = $145.179 + $854.640= $999.819 with a bond quote of $99.9819. For bond A the price value of a basis point is about $100- $99.9819 = $0.0181 per $100. Using the bond valuation formulas as just completed above, the value of bond B with a yield of 8%, a coupon rate of 9%, and a maturity of 5 years is: P = $364.990 + $675.564 = $1,040.554 with a bond quote of $104.0554. If we add a basis point to the yield, we get the value of Bond B as: P = $364.899 + $675.239 = $1,040.139 with a bond quote of $104.0139. For bond B , the price value of a basis point is $104.0554 - $104.0139 = $0.0416 per $100. (b) Compute the Macaulay durations for the two bonds. For bond A with C = $40, n = 4, Y = 0.04, P = $1,000 and M = $1,000, we have: 1 77509 . 3 000 , 1 $ 09 . 775 , 3 $ 000 , 1 $ ) 04 . 1 ( ) 000 , 1 ($ 4 ) 04 . 1 ( ) 40 ($ 4 ... ) 04 . 1 ( ) 40 ($ 2 04 . 1 ) 40 ($ 1 ) 1 ( ) 1 ( ... ) 1 ( 2 1 1 ) ( 4 4 2 2 = = + + + + = = + + + + + + + + = P y nM y nC y C y C years half duration Macaulay n n Macaulay duration (years) = Macaulay duration (half years) /2= 3.77509 / 2 = 1.8875 . For bond B with C = $45, n = 10, Y = 0.04, P= $1,040.55 and M = $1,000, we have: 3084 . 8 55 . 040 , 1 $ 2929 . 645 , 8 $ 55 . 040 , 1 $ ) 04 . 1 ( ) 000 , 1 ($ 10 ) 04 . 1 ( ) 45 ($ 10 ... ) 04 . 1 ( ) 45 ($ 2 04 . 1 ) 45 ($ 1 ) 1 ( ) 1 ( ... ) 1 ( 2 1 1 ) ( 10 10 2 2 = = + + + + = = + + + + + + + + = P y nM y nC y C y C years half duration Macaulay n n Macaulay duration (years) = Macaulay duration (half years) / 2 = 8.3084/2 = 4.1542 ....
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hw2_answers_Solutions - ANSWERS TO HOMEWORK QUESTIONS - HW...

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