This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 2year 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 ....
View
Full
Document
 Fall '06
 BOGAN,V.

Click to edit the document details