ACT 2020, MIDTERM #1ECONOMIC AND FINANCIAL APPLICATIONS

FEBRUARY 11, 2009HAL W. PEDERSEN

You have 70 minutes to complete this exam. When the invigilator instructs you tostop writing you must do so immediately. If you do not abide by this instruction youwill be penalised. All invigilators have full authority to disqualify your paper if, intheir judgement, you are found to have violated the code of academic honesty.

Each question is worth 10 points. Provide sufficient reasoning to back up your answerbut do not write more than necessary.

This exam consists of 8 questions. Answer each question on a separate page of theexam book. Write your name and student number on each exam book that you useto answer the questions. Good luck!

Question 1. Bill and Jim enter into a binding contract involving the exchange ofan asset in nine months time. The current market price of the asset is $100. Thecontinuously compounded interest rate is r = 0.10. The contract calls for Jim to sellthe asset to Bill at that time for a price of 105. Furthermore, Jim and Bill agreethat the fair value of the contract at initiation is to be zero and that, if necessary,an amount will be fixed at contract initiation that one will pay to the other in ninemonths time so that this condition is met. If the price of the asset in nine monthstime is $104 what is Jim’s total profit or loss at the time the asset is sold?

Question 2. Assume that you open a 100 share short position in Jiffy Inc. commonstock at the bid-ask price of $32.00 - $32.50. When you close your position afterexactly one-year, the bid-ask prices are $29.50 - $30.25. Jiffy Inc. common stock paida dividend of $1.15 exactly 3 months after you opened your short position. If youpay a commission rate of 1.5%, and the continuously compounded interest rate is 3%,calculate your profit or loss on this trade at the time the position is closed?

1

2 ACT 2020 – MIDTERM #1

Question 3. John has just purchased a home for $100,000. The insurance policy willcover any losses due to fire subject to a deductible of $10,000. The one-year premiumon the insurance policy is $1,000 which is due at the start of the policy year.

(1) [5 points] Let M denote the market value of John’s home at the end of the policyyear.1 Draw a chart of the net value of John’s home and insurance policy versus Mat the end of the policy year. Assume the continuously compounded interest rate isr = 0.10.

(2) [3 points] Explain in what sense there is a put option implicit in this transaction,possibly drawing an appropriate chart.

(3) [2 points] At what value of M would John have the same wealth with and withoutthe above insurance policy? If there is no such value of M explain why.

Question 4. Barkley Corporation (BC) has decided to issue a mandatory convertiblebond. The bond matures at time T , pays a 5% annual coupon on a $1,000 notionalface amount, and the share price at that time is denoted ST . The mandatory con-vertible bond pays the bondholder 25 shares at bond maturity if the share price isbelow $40, it pays the bondholder (25 · 40)/ST BC shares at bond maturity if theshare price is between $40 and $60 and it pays the bondholder 16 and 2/3 shares atbond maturity if the share price is above $60.

(1) [3 points] Draw a chart of the payoff at bond maturity to the owner of the BarkleyCorporation mandatory convertible bond. (As was done in class, your chart shouldnot include the interest component of the bond.)

(2) [2 points] If it turns out that ST = 39, compute the dollar amount of the payoff atbond maturity to the owner of the Barkley Corporation mandatory convertible bond.

(3) [5 points] The President of Barkley Corporation, is also interested in the possi-bility of issuing a convertible bond. This bond would pay a 2% annual coupon ona $1,000 notional face amount, and would permit the bondholder to receive the faceamount of $1,000 at maturity or 25 shares in Barkley Corp., to be determined at thebondholder’s discretion. Assume that T = 2 for this bond and the mandatory con-vertible bond and that the continuously compounded force of interest is r = 0.04. Forwhat value of the share price at bond maturity, i.e. S2, would a person that boughtthe mandatory convertible bond have the same payoff as a person that bought theconvertible bond? If there is no such value for S2 explain why.

1If there is a devastating fire the market value of John’s home could be close to zero. If there isno fire and the real estate market soars then the market value of John’s home could be more thanJohn’s purchase price of $100,000.

ACT 2020 - MIDTERM #1 3

Question 5. The Federated Bank of Canada is offering a structured product thatguarantees a continuously compounded return of 3% on the investor's capital at theend of 5 years. The continuously compounded interest rate is r = 0.08. The indexunderlying the structured product is currently at 1200 (i.e. So = 1200). The currentmarket price of one at-the-money European call on the underlying index expiring in5 years is $450.

(1) [4 points] Assuming that the Federated Bank of Canada charges the investor afront-end load of 1% for this contract (i. e. the haircut is 1%), compute the participa­tion rate for the structured product.

(2) [3 points] Now consider exactly the same contract and market data except thatthe investor is now guaranteed to receive 90% of their capital at the end of 5 years.Assuming that the Federated Bank of Canada charges the investor a front-end loadof 1% for this contract (i. e. the haircut is 1%), compute the participation rate for thestructured product.

(3) [3 points] At what effective rate of return for the index over the five-year periodwill an investor receive the same rate of return on either of the contracts defined in

(1) and (2) above? If no such rate of return exists, explain why.

Question 6. Barkley & Ruff Cereal Company sells "Sugar Corns" for $2.50 per box.The company will need to buy 20,000 bushels of corn in 6 months to produce 40,000boxes of cereal. Non-corn costs total $60,000. 'What is the company's profit if theypurchase call options at $0.12 per bushel with a strike price of $1.60? Assume the6-month interest rate is 4.0% and the spot price in 6 months is $1.65 per bushel.

Happy Jalapenos, LLC has an exclusive contract to supply jalapeno peppers to theorganizers of the annual jalapeno eating contest. The contract states that the contestorganizers will take delivery of 10,000 jalapenos in one year at the market price. Itwill cost Happy Jalapenos 1,000 to provide 10,000 jalapenos and today's market priceis 0.12 for one jalapeno. The continuously compounded risk-free interest rate is 6%.

Happy Jalapenos has decided to hedge as follows (both options are one-year,European):

Buy 10,000 0.12-strike put options for 84.30 and sell 10,000 0.14-stike call optionsfor 74.80.

Happy Jalapenos believes the market price in one year will be somewhere between0.10 and 0.15 per pepper. Which interval represents the range of possible profit oneyear from now for Happy Jalapenos?

A. -200 to 100B. -11 0 to 190C. -100 to 200D. 190 to 390E. 200 to 400

You are given the following information:

• The current price to buy one share of ABC stock is 100• The stock does not pay dividends• The risk-free rate, compounded continuously, is 5%

• European options on one share of ABC stock expiring in one year have thefollowing prices:

Strike Price Call option pricePut oPtion price90

14.630.24

100

6.801.93110

2.176.81

A butterfly spread on this stock has the following profit diagram.

8

6420do

8590 / 95

100105 \. 1101151tO

-2-4

Which of the following will NOT produce this profit diagram?

A. Buy a 90 put, buy a 110 put, sell two 100 putsB. Buy a 90 call, buy a 110 call, sell two 100 callsC. Buy a 90 put, sell a 100 put, sell a 100 call, buy a 110 callD. Buy one share of the stock, buy a 90 call, buy a 110 put, sell two 100 putsE. Buy one share of the stock, buy a 90 put, buy a 110 call, sell two 100 calls.

Question 1. The easiest way to approach this problem is to note that after thepayment is made rendering this a zero cost contract that Jim and Bill have agreed toa forward contract. Jim has agreed to deliver the asset and he is therefore going tohave to purchase the asset at its market price on the delivery date in order to fulfilhis committment to deliver the asset to Bill. Therefore, Jim's profit or loss dependson the forward price less the market price of the asset to be delivered on the deliverydate.

The forward price is 100 . eO.1O(0.75) = 107.79. Jim's profit is 107.79 - 104.00 = 3.79.

Answer = 3.79

One can also look at the problem in the following way. Let the value of the asset attime 0.75 be denoted SO.75. Jim will receive the cash flow 105 - SO.75 at time 0.75.The value of this cash flow today is

105· e-O.1O(0.75) - So = 105· e-O.075 - 100 = -2.59

Therefore, Bill must pay Jim 2.59 . eO.1O(0.75) = 2.79 at time 0.75 for this to be a zerovalue contract. Jim's profit is then the sum of this payment and his net cost to deliverthe asset at time 0.75. Therefore, Jim's profit is

2.79 + (105 - 104) = 3.79

D

Question 2. The proceeds from the short sale at time 0 are

100(32.00)(1 - 0.015) = 3152.00

The accumulated value of the short sale proceeds after 1 year is

3152 . eO.03(1) = 3247.99

The accumulated value at time 1 of the dividend payment that you must make attime 0.25 because you are short the shares is

1.15(100) . eO.03(0.75) = 117.62

The cost to cover your position (i. e. repurchase the shares you are short) at time 1 is

100(30.25)(1 + 0.015) = 3070.38

Your profit or loss is equal to the "accumulated value of the short sale proceeds" lessthe "accumulated value of required dividend payments made" less the "cost to coveryour position". Therefore, your profit is

3247.99 - 117.62 - 3070.38 = 59.99

Answer = 59.99D

q ill e. s.f. " 0 V\ .;.

( 000/

~g11. '6" ~

8g/ ~11.~:>

~JO$.11

qD ",00" ••, 000// , .

Iht,01 j.:.br(\" (...~"'ffr~~5,o'"

~rt~LJ '-ll ~ h J c:- L,,. f.

~s.

M(9()oo:>-M)

- I ooC>. fo {,j

'fe.

~ ,t./

::. MAx ('0 ooo~) - "OS.I'?/ ./ ~

',S

~o •..• .[JL', •.s ••rn"e '- ~oJ.. 7c .. .[hL ""nrket vtol", " ef tJL

S'£,-./fL a,"L 0+ 9::'-°00

(II~L

~ol-- Ll -,S 0r-f05'{ o~0'0

\"'~lI'rn ••..C(..

l~~~()rkl.-l ~L

CV\

\lC. w(l. ,fJ, c> I'" L

W·J.[~

~(..Hdt1:h (.~ V\ j~-ft~L

~o I·, Lj

e-1rlJ(+0

1~"r-

(q~ooo - 1\1)+

-'/ j 0 S . J I

A

~L{e-f-L~Lcr~tar o·r. l'I S :

ffj)f,·/;

f( 8 ~1 ~.F;j.,/

~I IOS,;1/

S OM e.. J-.>c",~'~o ...

~L ',.s O}""7J' ~('-l~czr-

~,,~.rn •• C'- jf'O,,·.J-<r<-J.

I.<;J ~. 1\ ,....~rft t.-i >J" It.( ~

'-tk,.,.

(I> II 0 ~\ 'J

-, '"~••t t.

~flu Jd PL •••. {~

5'') ..,,-f. L /1" -f

~r~ t: I ~j'";10. {~!.

1\0

art.

M - ) 105,17~

.eo

co 9 ~ 000 -/ J J c5 .) 7 ;;:./~ 891. t>/

'000

l~L ~\L.£ •.•.rc.. \111~(3q);; q15

O~L Cc",JJ

u IJ {b~ft \ (. 0 II J

ral-{t;;bwt- {~~ s

2- S S - 2~ (~ - 'to) + I e ~ (-~ - b " )T 'T + .::> T '/-t

-,"> t\ Q t 1\ ~ C t.. > .s CI r J ~ l r (. .

1-0'2... 0 + 10 <> 0 + 2 S ( S 2.. - 'I,,)+

J" s c. kJ > L J ~k

k tI .s (I c: ••.J t..

t

o 1.

C/I1>~ .{~c- r-~'o..~I:~"..

fl. ~ •r "I -t-o ;

fooD + (~.s ~2.. - /(00)+

IGOO + 2-S(>2.-/.fo)+

11L C!45h

COI\."tri-;~It... tire...

2.

~\I~etc...

reSt-):=lSS'L - 25(5L-'10)+ "I- 110 ~(>z.-[,o)-t

c(l

rI>(1..$yla(,o-Io.,...•

-tl--e...c ~ IIr-l~D~{,j

0

00Ir-''-Yd..(.. J

lo-P~J$"2-50-i kl'-{

'1 ,0'/1.-° €. + to + }00'O -+

S1...

.>. Iv < J 0 Irb '.0 coil J .J"ol:L l~tlt i~l.

6Tf/5\

Or£-

rl./n t-'O •...s~"1 ~> t. c •• r "I t ",LJ

(;v h·, '} t-",t -15t

.5ll\lrl1 \~ o-t l

Sk..( l- ",} [5" ,z",,'t -+;.

;: • , •..••,...•I.tt.A

v"I •.( ,f- c_( ••.J"

Po1uffS~f~ \ S

10 <!. " c.'" t 1.0 "

c..wrvV

Uo ~ S <. Go.( 'L-

+

~ .ctf ,.;>°e t-~o + )000

fooo -

L5(>l--'tc) :;:C,'.2.2Lj'!>

~

52- ;~'L. Lf5

0'~Lr

--,. 'fZ.~-

'to

•'-0

~ J:TftOttTCc~f 0 (\tS

-Ih·.~ f,.ra U -t~1I·1 'I)

,t.&s ..•• {I-e...S1.. .

r "- .s", J ~ tJ I (I (\'t ~ •••• f .{~r

i ~" t j -f "" t K f -,..• (I t t J.. £.

ty-~"''-I. clJlI "6t/c.~J'

M~I-l: Ii- c ~ lt~5',J{ IkJCX~dlArt\~ ;[Y',Je')'l-cr f-c." ....-{J

.::

;rYl"l>~"r ~7·(fL"'\~lJ ba Jt\Ac;.

Io ( , -

tf$o

(+::r:~v c..).f. l'

~t..*\I't"1'\

~. o~('S) I+(, - e.' O;(»e-·o8{S.!-. c) I) , led (R..r..b)()- e-.-

t.fS .•• +IoS-

.',~

r4rl; c- ~4-/;"0'"

(2. /\ t L- :;. S:(,~2-

~<r ~

s(,~

A\5o ). ,~ I 8

A l.r (c. t c.. t\. J c ••I ..,..(.1) #'\ c.{ :

r . r ~ ~'.« . L·~ I'~ L

( I .0 ~ ( ~) - •u s-( S) )\..-e. e -.01 :: .5G'}2..

·t

10 (.10)

-.c~(5) )I.(I-.?Ge - .01 (.s~-I'l..o)tt.f50

- . ,,, + I'].. 00

Y5tJ

( _.oe-csJ_.O() /1-0<)\..1 - . fo ~ LjSo

(d

. Ib I 6 + . .5 ~ ') L -b

-./0 + /.03/7- -2:-

-~l- ==.5S7;

~ ;:r",tfl.)C :;

. S59'}

o(L

"55.9'1;0

~~~ ~

5S.7Yf)

G'~~~r 0 \

·F:r"' ../"t·.tlt\. :

-r: -11\.,(yt"",,~t ~C{ ,-l-"11

It>; --," .•-l-. t'l -,1'\. v~.A·.,...~...i,rh -

c:

,.,.... I-l-.a1t ~t- -'n..\&'r,( 'I"V~~"'(H+ l~Df.•S JW\-'r (\ •.•.t ...~J

c' .-i::~~G'>/ 1 c. t"('" J c,{ r. t ~ ,-( ~.t ~r<JthO~FCkf/ c..~",,,-r>S'l'''' /fr, ..-I::.-e~J !tJ4i 11 o/c

o t 'i't 'l -b /I ( ~ v u+ t"" {.. u- t-

~r'I""<" ~+ tlf-{~<..-r(> •..t-l ct1/( 0Nl'"... 6#f£-ht. 1r1\~(..'"{1""1 ~v"'''>~t'-~",t I>t-'<..~

"\ ~ " & ; <r ( ~ ~ e 1< , ~ v~ I

ex - s -~

1; )C a •...tit.> '''' G:

101~ •+ ',"',+> /J. i ',t'- \Id~ f"\ t. ••..-{ r~.f1J.r•.• ;"'flrtlj.. {. C. t..: r;:::.. o. f' c

Off) rt.tloopt (;.c.. 10010 rd::HM -.f (!"Q~;.fdt) : (; ~ J.co

l.ey':) )vllra •••.~(t~ C-Q••.+·/ •...•.•o • .s'j CCll",,,I •.rI rct-"rl1.: G=- e·d2..(r)

:r...,uJ+i"'t,,- f -;'" ~ .....JJb f" ~ (;•..."r"•...1( (.

C 0 to\.,..... 55', 0'" : Io ~A •....•",•..f- A-voJ.\'ll t-.. f",rcl,.../C-

Al-·IJ,t..-f'\(»O.Lj ClJU 0fMtI"'5

Io G ..•. C I~ - Io , e-- r T- ;Ieh ) ( ~"T - 5 e) +C.

Etf i.-c.+>V t. (l '-fCrl'" t\

,.... r",'t.~ Ort

t.o -1"'./ _J

,s .• _ I-50

.::r to. \12){,,.. t;.r.(' H..~"C--f~I" f.fld"r-", 0" [:0/7)

-To

•.If-I)-+( 1- G e-_c-,-I,) SO

( ~ ".J,~)- L~TJ +C

~to,;"TJ

=-(G -I) +( J - G'e.-rT-h) 5. C tC"·h )c C,/,J +-

C I - G e-- c- T - h) _5~c

Ct;»f of Ccr;o..

tIt 6"'''r .•.•l t~" 'f. <~

<;; •.•.t:~ ">ac;.f fr.cct. .}Itbc oiL Str./f"-

/00 0 DO

./

FOf"" f'" III

A~r. ~c-k:

~Pf.t

-::;

RC"l" "'L-C •.,:>-1:.5

r(l\(l"'\.ofL ;:

f f', l. Lfc!r(),..~+

:: 1 . .50 ')(. Yo 000 -;;: / 0 ~ 000/ ../

u~kld)ld

~(! J,tJ (0)+

(;0 000 +/'

Ct\~k f/e..-

~~jL

f, 0 t-.-/: ~ ',"}:l,.,

~tjL

-- --

--- I~ 0 000/ [ bo 000 -T 1--0 000 S~-z..../ ./

_ [-2,/000( >'f'- - J.bo)+

- ~/o'c(./1.)(J.O'f)J Jro r 5 'f\.- ;; I. t 5/

f-hd)~d

;::

Ie D 000

~pf-t/

....-- 5 50i ./

-~lf?j,\7 (e,.,. bi- fit-y

l~<.. 1c;..fo W·-,cc-

~~ f... i\ L+

-f 5 (\ l-J l\ 1<\1 t.

7... coo 0 (. 0 S) - 2-(; c: ~ 0 C . 1 'L-) (1.·1) ~/ /

.[k<- cOI"\n~) •..•,,/d k",,'• .f r ,....+ I ,J'J' -) j iv t " Iv k.r <..c~sl. (.d .

Answer is D

The accumulated cost of the hedge is (84.30-74.80)exp(.06) = 10.09.Let x be the market price.If x < 0.12 the put is in the money and the payoff is 10,000(0.12 - x) = 1,200 - 10,000x.

The sale of the jalapenos has a payoff of 1O,OOOx - 1,000 for a profit of 1,200 - 10,000x

+ IO,OOOx - 1,000 - 10.09 = 190.From 0.12 to 0.14 neither option has a payoff and the profit is 1O,OOOx - 1,000 - 10.09 =IO,OOOx - 1,010.

If x >0.14 the call is in the money and the payoff is -1 O,OOO(x - 0.14) = 1,400 - 10,000x.

The profit is 1,400 - I O,OOOx + I O,OOOx - 1,000 - 10.09 = 390.The range is 190 to 390. (Pages 33-41)

Answer is D

This is based on Exercise 3.18 on Page 89. To see that D does not produce the desiredoutcome, begin with the case where the stock price is 8 and is below 90. The payoff is 8+ 0 + (110 - S) - 2( I00 - S) = 28 - 90 which is not constant and so cannot produce thegiven diagram. On the other hand, for example, answer E has a payoff of 8 + (90 - S) + 0- 2(0) = 90. The cost is 100 + 0.24 + 2.17 - 2(6.80) = 88.81. With interest it is 93.36.The profit is 90 - 93.36 = -3.36 which matches the diagram.

-, '"

~ ~-& Cy

1'/ t:(l:-

,.( 1J.. L

N ~{IL :

(JJ~e ~

It.(i-t.o

o ~ J

tJvl

io

~t

tI •• nJ7~·"f'j (ort..(t>/·,.5 c.t'i~ ~t5 f io ""'Ovc.. r;.., .....

-, •. .t ~(,. I'" •• " It 1 t. .:> eI'" f

1\ nj~~ /;-.. J£.('~ if C ,-c-

o~ i ~(, M~" c1) .(~Y fw-h

~ ~ -t 5fl', k~ d 0-1 J -lJ..c.

.[~L v",Au '7\ ") .

A.

leo

110

" 0 ~

:C..• i....(..~"l.1/;0 c> ~ 6- , f .f~&..

'-"(.1 1I5. JL,w"', l.> I';;~l..r.

I/O

1II (')

sk. [i ot

-lJL ~q·Ci

5~ff- ~

CtI.sk FI., •...>

0.••j ("at"-·

~ l-t Lo5.t ~+·f;.r ;I:.•fat) .(-

c::::.. 0

~o c {\}lflo,",cJ(jr ~5k.f&do,",,'" .

Sk.-\l

=.- >.50 s -ftl"r~tf(...\\ I<-'(-/0-}.35f ~~ =

t;,. '5 .r -To

\\ }It

~,. 0 bit 1"") .(. r5>f

/', '" I'!...5., v (.. -t\--.,>

II \« ttl a'~

~Sf...f-. •.A c ~ ,,-•.<>"d1"",,<" ~ ")

it t-.5JV t-r . J

o'u v', 0 ~ 5},)) .{h(.. <? )(0(( 5?O~

d~d"O\'-' \,t.f"(.... '.>

-,.>

~. Cd II5t~',hL -#=- Call.>- 1!)J" 0

-2" 0

S("f~ ;:;D-.,1 1

q~'" "" <>

7c .

C"Il>L~·\kc....JFL(lI/.>-J tJ 0

-ItJLt

C ,,>t-j..).c.. 0I , <'

I5', t' C '-c.(/c.,,) "7 c.(/fO) .

,~. '"

f I( {. 5'.t.--, \( '- ~ f K-i>

I" 0

I-I

tJ t t to» f- 'i> ~ 0

5~~~ (.. f(/.f») '7 ~(qo)

/ ••oft..

D- r~~S-tr: k~ .:#=- fcAs

'''0

-2II~

f~t

C/l5h

FI..""s:

I"" II0

(I T L

IS :

'f 5

t >""ri A t\S ~H-:

{,V.:.. on .... >~.,+ 1-

to" - f ..k c••••J I.')()WI~ II~-J...f. To )~&-lk ~crrL c.. clIJk flvv/i-- t.. IIU J tJ....... ClIJ t.. f'j ••••

[.,.0"'- Jo:) "ilL. r .. -« ...l.""f1,(. C.1I>~ r/~", -Frat'- loro,0"'«- S"-l>r( .. ~'sf:,."it lI ••.l

I,,) Ct\(... p"'-« ..•.I- .x~t'cr-l~ $(J"'~ en 1)..( ct\)h

·ft",., .fro,.., lJ 90.«--r. J.~ ('vt £O~f"~c..-f ..

...f.") Q~J--cl7K ~4rl~t-1'

o0"

I"

C 9r. - >T) T::-10 - .5 T+- (S-r - 9c)-+

-tkt..

~ (tjk.f L> !AI.f;- 0 •••·fJ."lY',,-~u.fj;

"(..cJl.. JC (I""Ctl> 0

pL.o ~ ttl~...God

~~'r ")q90 - ClI (j

5~ r fc. •••..J."L-/c+ >+. c..../t..

a~ J~Kf+. r-J

.6-<-~V"1+ tt~

./.,ht

~1I1l11...( i..{..b~1&~<> •• d

t"-li fir r -,JJ:'("' '10)..

Cfo - 5.,.- of (5"1" -?o)+

Cfo

$.•..

, 00

II 0

4f. LtI 115

- 2.

lJ to. k~o(.V.t~lIt-/;~ }'"" .{~L "'.U.r.fJj

5«U(lJ

cCl~h.(10 ~5/."~ tHl.J t# oJJ

t.~L

c d> ~{I,,~jfr 0 C'-dq.o - C (I If .

"-e...

J.vc....t'\Ll-Jl ~t.ctlJk·rf.~'"s{;o~(I

70- Cl'll .( q D - S,) 1"" t S-r

.;( S7 - 90) of-t tfc

C o)l .fJo~.r;.. p C'-t

b~1~'")01'1 c....

.5~-r L~I 5.{-..,C/t-

(1"" J

Ct1 l-?o - ~w t IS iJ...L- >Qf\~ (1.$

l~L

~(I>~'(Jo~ fro,." ~~t.,,) Q Cjo ~ coli

.,.,/"'o

0b"" JI'" Q .f •..T' I ~ +:r C;0 .-

C o}>t ~.{-

fos..{-. "•.•.• ·.-th

J"~P~~f

( .s-r -10) + + 10 + ( >., - "0) + - L (>,- - 10" ) +I •..•...

- q; 5~

= t~t{u f'J 5'~f l 114

CdJ1.. FI 0 .-J

L

"::t ~'- _/1O

r t->.:.tl.: 1\-L- tly.i~QC itS ~ f/o .,.. ,f;,-.. -l11.

~~ t' J 3d-s '\"iUL, J

o~t'( .('\ -th. ~I''''''''''''d d) •..s+ •..c.. •• t •...~CM

" L cO"'d~tt. fr Q.{i { .J