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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
semiannual at a rate of 8% convertible semiannually. The bond matures for 12,000
and has a price of 12,145.78. b. Bond B is a one year bond with semiannual 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
semiannual 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 semiannual 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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