Math 373 Test 3 Fall 2013 November 7, 2013

Transcription

1 Math 373 Test 3 Fall 2013 November 7, You are given the following spot interest rate curve: Time t Spot Rate r t % % % % % % % % Calculate the accumulated value of a three year annuity immediate with annual payments of 500.

2 2. A bond has the following characteristics at 8% interest: a. Price = 10,000 b. Modified Duration = 17 c. Macaulay Convexity = 350 Estimate the price of this bond using both the duration and the convexity if the interest rate was 7%.

3 3. Telma has agreed to pay 100,000 to her parents in 8 years. She wants to fully immunize her interest rate risk by purchasing the following two zero coupon bonds: a. Bond 1 matures for 10,000 at the end of 6 years. b. Bond 2 matures for 6000 at the end of 15 years. The annual effective interest rate is 4%. Calculate the number of Bond 2 that Telma will buy. (Assume partial bonds can be purchased.)

4 4. Sarah owns a 25 year bond with annual coupons of 500 and a maturity value of 10,000. Sarah sells the bond 3 months after the 10 th coupon has been paid. The bond is sold to produce an annual yield rate of 6%. Calculate the clean value of this bond at the time of sale based on the theoretical method.

5 5. Trena has agreed to pay Jayme the following payments: a. 30,000 at the end of 2 years; b. 50,000 at the end of 5 years; and c. 10,000 at the end of 8 years. You are given that v 0.9. Calculate the Modified Duration of Trena s liability.

6 6. Trena has agreed to pay Jayme the following payments: a. 30,000 at the end of 1 years; b. 50,000 at the end of 2 years; and c. 10,000 at the end of 3 years. You are given the following three bonds: a. A one year bond with annual coupons of 100 and a maturity value of 2000 with a price of b. A two year bond with annual coupons of 80 and a maturity value of 1000 with a price of c. A three year bond with annual coupons of 50 and a maturity value of 1800 with a price of Determine the amount of the two year bond that should be purchased to exactly match the cash flows of Trena s liability. (Assume that you can purchase partial bonds.)

7 7. The common stock of Kroeger LTD pays a quarterly dividend. The next dividend is expected to be 2.00 and is payable in 3 months. Thereafter, each dividend is expected to be 0.10 larger than the previous dividend. In other words, the first dividend will be 2.00, the second dividend will be 2.10, the third dividend will be 2.20, etc. Calculate the price of Kroeger common stock to yield 12% compounded quarterly.

8 8. The Batta Insurance Company has the following two assets: a. A zero coupon bond which matures for 10,000 in five years and has an annual yield of 8%. b. A bond with a price of 20,000 which has a Macaulay Duration of 3 and a Macaulay Convexity of 11. All values were calculated at an annual effective interest rate of 8%. Let Let Port D Mod be the Modified Duration of this portfolio of assets at an interest rate of 8%. Port C Mod be the Modified Convexity of this portfolio of assets at an interest rate of 8%. Calculate C Port Mod D. Port Mod

9 9. A 20 year bond has annual coupons of 400. The bond matures for 13,000. Calculate the Macaulay Duration of this bond at an annual effective interest rate of 5.5%.

10 10. You are given the following three bonds: a. A one year bond with annual coupons of 100 and a maturity value of 2000 with a price of b. A two year bond with annual coupons of 80 and a maturity value of 1000 with a price of c. A three year bond with annual coupons of 50 and a maturity value of 1800 with a price of Determine the three year spot interest rate.

11 11. Calculate the modified convexity for a 3 year bond with annual coupons of 300 and a maturity value of 5000 using an annual effective interest rate of 8%.

12 12. Heather purchases a callable bond to yield 7% convertible semi-annually. The bond pays semiannual coupons at a rate of 8% convertible semi-annually. The bond matures at the end of 10 years for its face amount of The bond is callable at the end of 5 years for a call value of The bond is also callable at the end of 7 years for a call value of Calculate the price that Heather paid for the bond.

13 13. The preferred stock of STOAKES Inc sells has a quarterly dividend of 4 with the next dividend paid in 2 months. Calculate the price of the preferred stock to produce an annual yield of 10%.