MA373 F15 Homework Chapter 9 Solutions

# MA373 F15 Homework Chapter 9 Solutions - Chapter 9 Section...

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November 5, 2015 Copyright Jeff Beckley 2013, 2014, 2015 Chapter 9, Section 1 1. (S09T3) John must pay Kristen 10,000 at the end of 1 year. He also must pay Ahmad 30,000 at the end of year 2. John wants to exactly match his liabilities by purchasing the following two bonds: a. Bond A is a one year zero coupon bond maturing for 1000. b. Bond B is a two year bond with annual coupons of 200 and a maturity value of 1000. Calculate the amount of each bond that John should buy. Solution: John needs to make the cash flows going out equal to the cash flows coming in. To do this, we can set up two equations where a is the amount of bond A and b is the amount of bond B. We know that at the end of year 1 John will pay 10,000 and he will receive 1000 from every bond A and 200 from every bond B. Then at the end of year two when he needs to pay 30000, he will be receiving 1200 for every bond B. 10000 1000 200 30000 1200 a b b Simply solve this system algebraically. 30000 1200 25 10000 1000 200(25) 5 b b a a

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November 5, 2015 Copyright Jeff Beckley 2013, 2014, 2015 2. (S08T3) Yvonne must make a payment of 80,000 at the end of one year. Additionally, she must make a payment of 40,000 at the end of two years. Finally, she must make a payment of 60,000 at the end of 3 years. She wants to purchase bonds to exactly match her payments. She can purchase the following three bonds: Bond Number Term of Bond Annual Coupon Maturity Value 1 1 Year 0 1000 2 2 Years 60 1000 3 3 Years 70 1200 Calculate the amount of Bond 2 which Yvonne should purchase. Solution: Once again, we just need to set up equations that will match the cash flows. 80000 1000 60 70 40000 1060 70 60000 1270 a b c b c c Now we need to solve, starting with c. 60000 1270 60000 40000 1060 70 1270 34.616 c b b
November 5, 2015 Copyright Jeff Beckley 2013, 2014, 2015 3. (F11HW) Rivera Insurance Company has committed to paying 10,000 at the end of one year and 40,000 at the end of two years. It’s Chief Financial Officer, Miguel, wants to exactly match this obligation using the following two bonds: Bond A is a one year bond which matures at par of 1000 and pays an annual dividend at a rate of 6%. This bond can be bought to yield 6% annually. Bond B is a two year bond which matures at par of 1000 and pays an annual dividend at a rate of 10%. This bond can be bought to yield 7% annually. Calculate the amount of each bond that Rivera should purchase. Calculate the cost of Rivera to exactly match this obligation. Solution: 10000 1060 100 40000 1100 a b b Solving, 36.363636 6.0034305 b a Now, let’s find the price of each bond in order to find the total cost to match. Price of Bond 1: 1 / 6% 60 1000 1000 N I Y PMT FV CPT PV Note: We could also know this intuitively because the coupon rate is the same as the yield. Price of Bond 2: 2 / 7 100 1000 1054.240545 N I Y PMT FV CPT PV Now we can find the total price 6.0034305(1000) 36.363636(1054.240545) 44339.45

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November 5, 2015 Copyright Jeff Beckley 2013, 2014, 2015 4. (F11HW) Wang Life Insurance Company issues a three year annuity that pays 40,000 at the end of each year. Wang uses the following three bonds to absolutely match the cash flows under this annuity: a. A zero coupon bond which matures in one year for 1000.
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• Spring '08
• Staff
• Math, Zero-coupon bond, Jeff Beckley, Copyright Jeff Beckley

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