MA373 F15 Quiz 4 Solution

MA373 F15 Quiz 4 Solution - MATH 373\7/0(Mr V O/S 7 Quiz 4...

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Unformatted text preview: MATH 373 \7/0 (Mr V O/S 7% Quiz 4 Fall 2015 November 1, 2015 1. You can buy the following two bonds in the market: a. Bond A matures in six months. The bond has a par value of 10,000 and pays dividends semi-annual at a rate of 8% convertible semi-annually. The bond matures for 12,000 and has a price of 12,145.78. b. Bond B is a one year bond with semi-annual coupons of 1000 and a maturity value of 20,000. The price of this bond is 20,830.15. Calculate the one year spot interest rate. Solution: a: Fr =10000(9%) = 400 Price = 12145.78 = (12000 + 400)(1+ r05)“ ==> r05 = 0042299548 20830.15 =1000(1+ r0_5)‘°‘5 + (20000 +1000)(1+ rlyl ==> r1 = 0057899781 November 13, 2015 CopyrightJeff Beckley 2015 2. The stock of ZHANG CO pays an annual dividend. The first dividend is payable in 6 months. The first dividend is expected to be 20. The second dividend is expected to be 21. The third dividend is expected to be 22. The dividends continue to increase in the same pattern until the 215‘dividend is 40. Dividends will stay level thereafter. Using the dividend discount method and an annual effective discount rate of 20%, calculate the expected price of ZHANG CO Stock. Solution: There are several ways to do this problem. The following is just one. PV = (P1 + P2)(1 + i)°'5 where P1 is the present value of the first 20 dividends assuming the first dividend is paid in one year and P2 is the present value of the dividends after the first 20 dividends when they become level at 30 also assuming that the first dividend is paid in one year. Multiplying by (1+ i)°'S adjusts for the first dividend being paid at 6 months instead of one year. p. = p... .gmm -20.») - — (20)(1 + 1')'2° J P2 =39<1+ir2° l I gave credit for two answers. I had intended that students use an interest rate of i = 20%. However, the wording that I used stated that d = 20%. Even so if you used 1' = 20%, the answer that you got was 136.22 and you received full credit. If you used d = 10%, then i = i = 0.25 and the answer that you would get is 107.13. November 13, 2015 Copyrightleff Beckley 2015 3. You are given the following spot interest rate curve: Calculate the accumulated value of a 3 year annuity due with annual payments of 1000 at the beginning of each year. Solution: 1000 1000 1000 1000 + =1000+—+ 2 1+1»l 1+r2 1.03 1.035 PV =1000 + = 2904384487 AV = PV(1+ r3)3 = 29043844870 .041)3 = 3276.47 November 13, 2015 CopyrightJeff Beckley 2015 MATH 373 Quiz 4 Fall 2015 November 1, 2015 1. You are given the following spot interest rate curve: Calculate the accumulated value ofa 3 year annuity due with annual payments of 1000 at the beginning of each yea r. Solution: 1000 1000 1000 1000 + Z=1000+——+ 2 1+r1 (1+r2) 1.02 1.023 PV=1000+ == 2935.93185 A V = PV(1+ r3)3 = 2935931850 .027)3 = 3180.22 November 13, 2015 Copyright Jeff Beckley 2015 2. You can buy the following two bonds in the market: a. Bond A matures in six months. The bond has a par value of 10,000 and pays dividends semi-annual at a rate of 8% convertible semi—annually. The bond matures for 12,000 and has a price of 12,145.78. b. Bond B is a one year bond with semi-annual coupons of 1000 and a maturity value of 20,000. The price of this bond is 20,830.15. Calculate the one year spot interest rate. Solution: a: Fr =10000[%J = 400 Price = 12145.78 = (12000 + 400)(1+ r05 )4” ==> r05 = 0042299548 20830.15 =1000(1+ r05)“ + (20000 +1000)(1+ r1)_1 ==> r1 = 0057899781 November 13, 2015 Copyright Jeff Beckley 2015 3. The stock of ZHANG CO pays an annual dividend. The first dividend is payable in 6 months. The first dividend is expected to be 10. The second dividend is expected to be 11. The third dividend is expected to be 12. The dividends continue to increase in the same pattern until the 215tdividend is 30. Dividends will stay level thereafter. Using the dividend discount method and an annual effective discount rate of 10%, calculate the expected price of ZHANG CO Stock. Solution: There are several ways to do this problem. The following is just one. PV = (P1 + PZ)(1 + i)°'5 where P1 is the present value of the first 20 dividends assuming the first dividend is paid in one year and P2 is the present value of the dividends after the first 20 dividends when they become level at 30 also assuming that the first dividend is paid in one year. Multiplying by (1 + i)°'5 adjusts for the first dividend being paid at 6 months instead of one year. 1—(1+z’)‘20 + - —20 P1 = Pa20 +91%] —20v2°) =10 l l l l —(20)(1+i)'2°) P. =3—.°(1+z')-2° l I gave credit for two answers. I had intended that students use an interest rate of i = 10%. However, the wording that I used stated that d = 10%. Even so if you used 1' = 10%, the answer that you got was 194.17 and you received full credit. If you used of =10%, then i = l—d—d =% and the answer that you would get is 169.87. November 13, 2015 Copyright Jeff Beckley 2015 ...
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