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Unformatted text preview: Math 370 (Z) UNIVERSITY OF ILLINOIS AT URBANA—CHAMPAIGN
Actuarial Science Program
DEPARTMENT OF MATHEMATICS Prof. Rick Gorvett Exam 2/F M Preparation Topic A: Stock Pricing 1) 2) 3) 39 Stock Pricing and Short Sales
Review Problems DH: 1‘3 Gordon Growth Model : RJ = The stock of Company X sells for 75 per share assuming an annual effective interest rate of 1'. Annual dividends will be paid at the end of each year forever. The ﬁrst dividend is 6, with
each subsequent dividend 3% greater than the previous year’s dividend. Calculate i. 6 .— .——u————" . \ __ I
(B)9% 37‘s — Lao; ‘5 r. 0./I on. ll /. 10%
11%
912% You are considering the purchase of a share of stock. If you buy the share, you will expect to
receive the following dividends: $2 one year from now, $2.50 two years from now, $3 three
years from now, and thereafter annual dividends increase by 5% per year. If the effective
annual interest rate is 11%, what is the current value of this share of stock? (From a prior
Math 210 class) 1 2 ‘ rd 3 l
pa=————+——‘—);+( .o =w.w I.” 0“ ulnar .u The dividends of a cornmon stock are expected to be 1 at the end of each of the next 5 years
and 2 for each of the following 5 years. The dividends are expected to grow at a ﬁxed rate of
2% per year thereafter. Assume an annual effective interest rate of 6%. Calculate the price of this stock using the dividend discount model. (May 2005 FM Exam, question # 23) (A)29 P_ I + r 20.02.! _
C(32)? ° ‘ eta06 '2 0‘3.“ .Vmé + '°‘"'°" (November 2005 FM Exam, question # 20) W : 3319‘: w Topic B: Short Sales 4) 5) (Po—Pl)+iM—DIV General a roach : r =
PP M M = margin = P0 x (margin%) Eric and Jason each sell a different stock short at the beginning of the year for a price of 800.
The margin requirement for each investor is 50% and each Will earn an annual effective
interest rate of 8% on his margin account. Each stock pays a dividend of 16 at the end of the
year. Immediately thereafter, Eric buys back his stock at a price of (800  2X), and Jason buys
back his stock at a price of (800 + X). Eric’s annual effective yield, 1‘, on the short sale is twice J ason’s annual effective yield. Calculate i.
Mamnu ''' .50 (too) = 4°“ EA) 4% Infant" = 913060!) = 3 7
6% . Yoo  (3'00 4.1.) +32. 46 Lif
(C) 8% E : L 2‘: '3 100 (D) 10% 1‘46 9‘00
(E) 12% (2005 sample question # 38)
a, “J”. _ 909(ha+&)+32.16 : Mex
A: 0H 1 Ifoo 4'00
101:
=3 $2? =3 t, :o‘oé
Jose and Chris each sell a different stock short for the same price. For each investor, the
margin requirement is 50% and interest on the margin debt is paid at an annual effective rate
of 6%. Each investor buys back his stock one year later at a price of 760. Jose’s stock paid a
dividend of 32 at the end of the year while Chris’s stock paid no dividends. During the 1—
year period, Chris’s return on the short sale is i, which is twice the return earned by Jose.
Calculate i. __
MAMm = .5'0 ~ 7’ Wienerr  ,5‘0 'P (.95)
(A) 12%
16% ‘ z P‘V‘O + ~03? _ LO3PWéo
(D) 20%
(E) 24% (2005 sample question # 39)
7. “3,; _ Pwno  Maw—nae.
0" ' 3' I So? . 6) Bill and Jane each sell a different stock short for a price of 1000. For both investors, the 7) 3) D) 875 w. ‘
900 margin requirement is 50%, and interest on the margin is credited at an annual effective rate
of 6%. Bill buys back his stock one year later at a price of P. At the end of the year, the stock
paid a dividend of X. Jane also buys back her stock after one year, at a price of (P —— 25). At
the end of the year, her stock paid a dividend of 2X. Both investors earned an annual
effective yield of 21% on their short sales. Calculate P. Marten» a ,6’ (mac) 25130. E33332 Iﬂ‘m‘“? =~ .oﬁfno) = 30.
((1)850 loco ~49 +3o X :5 x 1 9 an? (2005 sample question # 40) leoo—QPZS’)+30 2x ,9 x, 02"“! . 0. = 50 D 97 'P = 52 00
On January 1, 2004, Karen sold stock A short for 50 with a margin requirement of 80%. On December 31, 2004, the stock paid a dividend of 2, and an interest amount of 4 was credited
to the margin account. On January 1, 2005, Karen covered the short sale at a price of X, earning a 20% return. Calculate X. ‘°"‘*"“2 => x=ji (A 40
4 o 2'0 = ‘t o
C) 48
(D) 52
(E) 56 (May 2005 FM Exam, question # 22) Theo sells a stock short with a current price of 25,000 and buys it back forX at the end of 1
year. Govermnental regulations require the short seller to deposit margin of 40% at the time
of the short sale. The prevailing interest rate is an 8% annual rate, and Theo earns a 25% yield on the transaction. Calculate X. 25709::  X 'l‘ .0?(4(2S;mo\> ' (A) 19,550 I
(B) 20,750 ' 2 5‘ " . 4 (1.8099)
C 22,500
3,300
(B) 24,500 (November 2005 FM Exam, question # I 7)
.7!) x .. 2. 3! 3 no ﬁre1' _..——n——. 2.. ...
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 margin requirement, short sales

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