SOA/CAS MAY 2003 COURSE 2 EXAM SOLUTIONS · SOA/CAS MAY 2003 COURSE 2 EXAM SOLUTIONS Economics and...

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SOA/CAS MAY 2003 COURSE 2 EXAM SOLUTIONS

Economics and Finance Solutions Prepared by Keith Sharp

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Compound Interest Solutions Prepared by Sam Broverman,

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1. Kellison - Sections 1.8 and 1.9

Bruce's 6-month rate of interest is , and 7.25 years is 14.5 6-month periods.��

Bruce's accumulated value after 7.25 years is . Solving for , we get��

��

��

�� .

Peter's account grows to , so that .��

��

Then % . Answer: B� � � ��

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2. 2-21-00 Fourth Printing p. 103 M = (1/k){Q-(1-k)C-RF(r, rd )} + T Here the Fed’s portfolio of securities, Q increases by $1 billion, the reserve ratio k=0.10, so M increases by 1/0.1=$10 billion. If banks don’t lend the full allowed amount then M increases less. Could get this answer also by thinking of the infinite geometric series: 1 (1 + 0.9 + 0.92+0.93+……)= 1/(1-0.9)=10 Answer A 3...Brealey and Myers 7th. Ed. p. 195; we’ll be a little fussier than B&M and make the expectations explicit in the CAPM formula E(r) -rf = β (E(r)-rf) Now think of r as being rIND, plug in the question’s data about the industry E(rIND) – 4=E(rIND) -rf = βIND (E(rm)-rf)= X (14 – 4) (1) And plug in the data about E(rQRS) 0.5+ E(rIND) –4 = E(rQRS) -rf = βQRS (E(rm)-rf)= 0.4 (14-4) (2) Subtract (1) from (2) to get 0.5=(0.4-X) (14-4) so X= 0.35 Answer D 4. Landsburg 5 th. Ed. p. 41 – or just think it through unaided Worth of current daily production = 110*2000/(8+2)= $22,000 Could boost daily production value to 110*2000/(8)= $27,500 if hired delivery firm. So worth paying up to (27,500-22,000)=$5,500 Note from Keith Sharp: the wage level isn’t relevant here: if don’t hire delivery firm then the opportunity cost is the value of the lost production. This is clear in this case since the question says that we employ these folks anyway. Also, there is assumed to be extra (so free-of-charge) factory capacity. Answer D


5. Kellison - Section 8.5

Under the sum-of-years-digits method, the depreciated value at the end of 4 years in a 10-year

depreciation schedule is

� � � � � ��

��

�� .

We can solve for , .� � � ��

Under the straight line method for the remaining 6 years (from time 4 to time 10), the

depreciation per year will be . Answer: C��


6. Higher prices – Landsburg 5 th. Ed. p. 19 diagram A. Demand curve shifts right and up, supply curve stays in place, intersection (equilibrium) price and quantity increase. Answer A 7. Brealey and Myers 7th. Ed. p. 472 rA = (rD * (D/(D+E)) + (rE * (E/(D+E)) Here use the initial EPS=6 and number of shares 10,000/50 and initial debt interest 5,000*0.05 rA = [5,000*0.05+6*10,000/50]/[5,000 + 10,000] = 0.096666 After the change we’ll have the same rA, the same firm value 5,000+10,000=15,000 and an amount of equity 15,000 – DNEW earning the new 15%

0.0966666 = 0.05 * DNEW/15,000 + 0.15 * (15,000 – DNEW)/15,000 1450=0.05 * DNEW+ 0.15 * (15,000 – DNEW) Solve to give DNEW=8,000, an increase of $3,000 Answer B

P

Q

D

D

S

D’



We denote the 4-year rate of interest by . Then the accumulated value at the end�

of 40 years is (10 4-year periods, with valuation one full 4-year period after the� � ��

10-th deposit). The accumulated value at the end of 20 years is ��

We are given that .��

This is equivalent to , where is the 4-year discount rate��

� � � ��

� ��

equivalent to the 4-year interest rate . Factoring the left hand side of the equation, we get��

� ��

� �

�

� � � � �� from which is follows that ,�

and then and , and .��

��

Then . Answer: E� � ��

��

��

�


9. 2-21-00 Fourth Printing p. 18. Capital account balance is net purchases of country X assets by non-residents. That’s 450-350=+100. Or can see it as a current account of (200-250)+(50-100)= -100 which must be balanced by an equal and opposite capital account balance. Comment by Keith Sharp: usually regarded as long-term bad news for country X: maybe it’s living beyond its means by selling to foreigners assets such as office buildings and common stock or whole companies etc.. Country X optimists (and, in early 2003, politicians hoping to be re-elected) may prefer to say that it means foreign investors like Toyota have faith in the Country X economy and want to invest there and e.g. build factories. A little controversial: what do you think? Answer D. 10. Landsburg 5th.Ed. p. 108. Don’t confuse yourself by thinking too hard on this one. Demand for fish increases, so price goes up and suppliers are willing to supply more. The demand curve for fish has moved up and right, as in question 6. For beef the demand curve moves down and left, hence lower price and lower quantity supplied. Answer C. 11. Brealey and Myers 7th. Ed. p. 189 T – though same variability if the two are perfectly correlated (but all false isn’t a possible answer) F – ‘perfectly diversified’ would, roughly, be buying all stocks in the S&P500 index. Still have market risk. F – risk added to the portfolio is the correlation with the non-diversifiable market risk. A unique risk (e.g. anti-trust action in Microsoft’s case) can be diversified away by holding only a little Microsoft stock. Answer A



The last 6 months of the 8th year is the time from the end of the 15th to the end of the 16th half-

year.

� � � � �! � � � �! " �� ! �� !

# " # # # # # # #

$

The amount of interest earned in Eric's account in the 16th half-year is the change in balance

from time to time . The balances at those points are and ��

�� 6 .

The amount of interest earned by Eric in the period is

��

� �� 6

The balance in Mike's account at the end of the 15th half-year (7.5 years) is , and��

the balance at the end of the 16th half-year (8 years) is . The interest earned by Mike��

in that period is ��

We are told that Eric and Mike earn the same amount of interest. Therefore,

�� %� � �& � ��

�� , so that . Then .

Answer: C


13. 2-21-00 Fourth Printing p. 1 F- ‘Investment’ not what’s needed T- e.g. value of policing services is estimated as equaling its cost F- Mixing supply- and demand- side definitions of GDP. F- Most countries use GDP F- GDP Answer B 14. Landsburg 5th. Ed. p. 196 Demand: P =20 - 4Q Supply: P = 10 + Q Solve to get P=12 and Q=2 New demand: P = 30-4Q Same supply: P=10+Q Solve to get P=14 and Q=4 Using the old as the ‘base’ we have % Change in quantity/% Change in price =[ (4-2)/2]/[(14-12)/12] = 6 Answer E



The amortization payment is the solution of the relationship , so that' �� '(��

' � �� . Under the sinking fund method, with loan interest rate still at 10%, the interest

payments at the end of each year are , and the sinking fund deposits are��

�� . The accumulated value of the sinking fund just before the repayment of

the loan is , and just after the 1000 loan is repaid, the balance in the sinking��

fund is 213. Answer: A


16.Brealey and Myers 7 th. Ed. p. 523 2,700 * annuity(10 years at 12%) = 15,255.6 Adjusted value = 15,255.6 – 500 – 15,000 = -244. Answer D



The timeline of deposits and withdrawals is

� ��

� ��

� � � ��

��

The dollar-weighted equation is

�� %�� "� �� &��

� �� .

Note that the withdrawal of 80 is on Oct. 15, and there are 2.5 months remaining until the end of

the year. The equation can be written as

�� %� � �� &

� %�� & � � � �� .

Solving for results in . Answer: E� � � ��


18. 2-21-00 Fourth Printing p. 32 ∆Y/Y = ∆A/A + αK ∆K/K + αN ∆N/N (1) Interpreting the question as saying, αK = 0.8 and αN = 1.2 (but see below) we have: ∆Y/Y = 0.1 + 0.8*200/800 +1.2*(-100/1200) = 0.2 Hence ∆Y =0.2*1,500=300 and the new Y is 1,800 Note that 2-21-00 Fourth Printing p. 32 says ‘assume that αK + αN =1.’ But consider equal changes in K and N, say 3%. So there’s 3% more workers, and the same capital per worker, i.e. no capital deepening. If there’s no improvement in technology, (i.e. ∆A/A =0), then it seems reasonable that output grows by 3% ∆Y/Y=0.03. Hence from (1) we have αK + αN =1 without any need to assume it. On the other hand, we could perhaps argue that we should regard N as being hours worked, and that a person could work overtime without any need for more tools. If so, we might decide that αK + αN =1 is not necessarily always true. Answer D 19. Landsburg 5th. Ed. p. 206 Accounting profit = 275,000 – 12,500 – 20,000 – 70,000 = $172,500 Economic profit = 172,500 – (150,000+25,000)=-2,500 For economic profit we subtract the opportunity cost: the salary and benefits. Answer C


20. Brealey and Myers 7 th. Ed I- T p. 386 II- F p. 383 III-F-p. 48 e.g. interest rate risk Answer A 21. Landsburg 5th. Ed. p. 328; efficiency wage is higher to ensure the person wants to keep the job. Answer B Interest theory



The timeline of the payments is

� � � � � " � � � � � � � "

# " " # # # # # # #

Pmt. � � � � � � � �

The schedule of payments can be written as the combination of two series

Time � � � � " � � � � � � �

� � � � � � � � �

� � � ��

In other words, the perpetuity can be written as a level perpetuity immediate of per year� minus

a decreasing -year annuity-immediate whose payments start at and decrease by 1 per year.� �

The present value of the perpetuity can be formulated as the combination of the two present

values.

') � �( � �*(� � ��

��

�� .

Therefore . Answer: C( � ��


23. Brealey and Myers 7th. Ed. p. 195, 472 CAPM: E(r) – 4.5 = E(r) -rf = β (E(r)-rf) = 0.9 (12.3) (p. 195) Hence E(r) = 15.57% rA = (rD * (D/(D+E)) + (rE * (E/(D+E)) (p. 472) 11= (7*(800/(800+E)) + (15.57*(E/(800+E)) 8800 + 11E = 5,600 + 15.57E E=700; E+D=700+800=1,500 Answer B 24. 2-21-00 Fourth Printing p. 68 IS: r=12-2Y LM: r=Y Solve to give r=4%=$4trillion =Y in initial equilibrium The money expansion moves LM right and down. Increased government spending moves IS right and up. Effect on r is uncertain Y certainly increases from $4 trillion.. Answer D. 25. Brealey and Myers 7 th. Ed. p. 625: Put option to abandon. Answer C

r

Y

IS(G, T, NX)

LM(M/P)



The progression of fund and deposits to fund are described in the following timeline.� !

Fund earns interest at rate 6%.�

� � � � � � � � ��

Amt. in ��

Fund �

Dep. to level ��

Fund +int. � ��

The deposits into Fund consist of a combination of level deposits of 100 each for 10 years,!

along with decreasing deposits. The accumulated value in Fund is!

�� *�� . Answer: C


27. Landsburg 5th. Ed. p. 203. Use q for quantity produced by a firm; Q for the market.

AC=q+(25/q), so

TC=q*AC=q2 + 25, of which q2 is variable

MC=d(TC)/dq=2q

AVC=q2/q=q

P=50-4Q

If competitive with n identical firms we have QMARKET =nq and equimarginal principle says

2q=MC=MR=P=50-4 Q=50-4nq

Solve to get q=50/(2+4n), P=50-200n/(2+4n).

Profitable if n=2 competing firms?

P=50-200n/(2+4n)=10,

q=50/(2+4n)=5

TR=PQ=50

TC=q2+25=50.

Hence TR=TC. Each of the two firms breaks even. If we interpret the question as including

‘breaking even’ in ‘supporting two companies this gives: Answer C

28. Brealey and Myers 7th. Ed. p. 475. Ignore the book value information. Take a weighted average using market values: βA = (D/(D+E))*βD + (E/(D+E))*βE (p. 475) 0.78 = (D/(D+E)) * 0.3 + (1-(D/(D+E))) * 1.5 Solve to give (D/(D+E)) = (1.5-0.78)/(1.2)=0.6 Cost of capital is the weighted average of the debt 10% and equity 15% expected returns, 0.6*10+0.4*15=12% Answer B


29. 2-21-00 4 th. printing p.94-95 The question uses M for the more conventional ∆M/M. Sticking with the conventional notation, MV=PY (∆M/M) + (∆V/V) = (∆P/P) + (∆Y/Y) (∆M/M) + 2% = (1% to 2%) + 4% (∆M/M) = 3% to 4% Answer E



Under the three methods, the deposit grows according to the following rates

��

' �� % % %

+ �� % %

, �� % % %

The portfolio yield rates are found in the final column. For 1997 we use % , etc.� � ��

The new money rates are from the first column of the investment year table for years 1997, 1998

and 1999 .

' � ��

+ � ��

, � �� .

We see that . This relationship could be determined by comparing the interest rates, - ' - +

in the table above without doing the actual calculations. Answer: D


31. Brealey and Myers 7th. Ed. p. 206 I-T p. 206.2 (2/10 way down page 206) II-F maybe: p. 207-208 arguably the statement is true but is not an advantage III-F – 207.9; APT equations longer than CAPM, anyway Answer A 32. Landsburg 5th. Ed. p. 91 Consumption has decreased as income decreased and price decreased. So, if non- Giffen, consumption would have decreased if price stayed same. (We have to say ‘if non-Giffen’ because we want to use the property that quantity decreases less if price goes down) So, if non Giffen, income effect gives a decrease in quantity with decrease in income. So if non Giffen, then it’s normal. Is Giffen possible? Yes, e.g. income might have decreased 0.00001% and price might have decreased 90%, and we have decreased quantity. So it’s either normal or Giffen. That’s one of the answers, so in a multiple-choice environment let’s thankfully stop there and pick Answer E.



Annuity (i) has present value .��(��

The present value of annuity (ii) can be formulated as

��( � ��. ( � ��. (�� .

Note that annuity (i) can also be written as .��( � ��( � ��. (��

Both annuities have the same present value , so that�

��( � ��. ( � ��( � ��. ( � ��. (�� .

After canceling the factor , the equation becomes(��

�� . � �� . � ��. . � /�� . With , this becomes the quadratic equation

��/ � �/ � �� / � / � � � � / � �� , or equivalently . The roots are .

We ignore the negative root for . Therefore, so that , and then. � / . � �� . � ��

� � �� ( � �� . Finally, . Answer: A��


34. Brealey and Myers 7th. Ed. p. 494. Double taxation on profits going to equity holders. Relative tax advantage of debt = (1-Tp)/[(1-TpE)(1-TC)]=(1-0.38)/[(1-0.38)(1-0.35)]=1.54 Answer D 35. Landsburg 5th. Ed. T - p. 472 e.g. the park doesn’t get cleaned up T - p. 494 Pigou tax ‘internalizes the externalities’:e.g. pays for the crowding that your presence impose on others T - p. 505 the ‘mayor and the streetlight’ example Answer E



Eric must deposit 400 into the margin account (50% of the initial value of the stock being sold

short). Eric's balance at the end of the year is

�� . Eric's yield is ��

� ��

(in this context, yield refers to overall growth in the initial investment of 400).

Jason also deposits 400 in his margin account. Jason's balance at the end of the year is

�� . Jason's yield is .��

� ��

We are told that Eric's yield is twice Jason's yield.

Therefore, . Solving for results in .��

Eric's yield is then . Answer: B� � � � ��


37. Brealey and Myers 7th. Ed. e.g. p. 97..This comes from the general logic of using discounted cash value to value assets (bonds, stocks, businesses, ….) or liabilities (mortgages, insurance company reserves…). This is done in numerous applications, especially by actuaries. Here the stock price at different dates is assumed to always use the same rate of discounting. So the resulting purchase prices of assets give the ‘all holding periods give the same return’ property. If you want to see more verification, please go to Keith Sharp’s site, www.sharpwaterloo.com (Course 2 page, ‘unwinding’). Answer D.

38. 2-21-00 4 th. printing p. 108. If the Fed is decreasing interest rates it’s probably trying to boost the economy by encouraging interest-dependent spending, and it’s not too worried about inflation. This is most likely to be the Fed’s mood during a period of economic contraction or low growth. Lowering the discount rate and buying bonds are both ways for the Fed to decrease interest rates. Answer A



During the first 10 years, interest only is paid. Therefore, after each interest payment, the

outstanding balance remains unchanged at 1000. At the end of 10 years the outstanding balance

is still 1000. To see what happens during the second 10 years we consider a general situation

with a loan of amount at annual interest rate and annual payments equal to0 �

�� Interest due . The interest due is equal to the previous outstanding balance multiplied by

the interest rate. The schedule of payments is as follows

� � � � � "

OB 0 0�� 0�� 0�� 0��

Int. due 0� 0�� 0��

Pmt. ��0� ��0�� 0��

Princ. paid �0� 0�� 0��

OB 0 � �0� $ 0�� $ 0�� $� �

We see that the principal repaid in a particular payment is always multiplied by the previous��

outstanding balance, and therefore, the new outstanding balance is multiplied by the� � ��

previous outstanding balance. As long as the payments follow the pattern of

�� Interest due , the successive outstanding balances will form the geometric series given in

the top line of the table above. The factor ".5" could be changed and a similar pattern would

occur. For instance, if we had been told that each payment is 125% of the amount of interest due

then the successive outstanding balances would form the geometric series

0 0�� 0�� 0�� 0�� " , .� � �

In this example, we have noted above that the balance at the end of 10 years is still 1000. Then

during the second 10 years the payments are Interest due . With interest rate ,��

we get , and the successive outstanding balances form the geometric series��

�� "(at time 10) (time 11) , (time 12) �

(time 20) ." ��

For the final 10 years, the payment is , so the outstanding balance of 598.74 at time 20 must be�

equal to (prospective form of outstanding balance).�(��

Therefore, . Answer: D�( � ��


40. Brealey and Myers 7th. Ed. p. 603 and tables on p. 1016

d1 ={ loge[PStock/PV(EX)]}/(σt0.5) + σ t0.5/2 = {0.2}/(0.2 * 10.5) + 0.2 * 10.5 /2 = 1.1 d2 = d1 - σ t0.5=1.1 - 0.2 * 10.5 = 0.9

C = PStock [N(d1)] – EX e-rt [N(d2)]

and we again use the question’s data loge[PStock/PV(EX)]= 0.2

C = 122 N(1.1) – 122 e-0.2 N(0.9) = 122 * 0.8643 - 122 * 0.8187 * 0.8159 =23.95 Answer E 41. Landsburg 5th. Ed. p. 12 Notation used here: P is price paid by consumer. So with $5 tax: Supply: Q=25+5(P-5) Demand: Q=100-5P Solve supply=demand to give P= 10 and Q=50 so tax collected=5*50=250 Answer C



Bond amortization is algebraically identical to loan amortization.

The interest portion of the 7th coupon is , where is the amortized (book) value�) � � �)� �

just after the 6-th coupon, and is the yield rate on the bond. In this case .� � � ��

Since this is a 10 year bond, just after the 6th coupon there are 4 coupon periods remaining, so

the amortized value is the present value of the remaining bond payments (this is just like the

prospective outstanding balance), where present value is found using the yield rate .� � ��

The annual coupon is 800. .�) � �� . � ��( � ��

Interest in the 7th coupon is . Answer: B�) � � � ��


43. Brealey and Myers 7 th. Ed. I -T- p.351; strong-form efficiency means that private info reflected in prices too II -T- p.351 III -T- p.351 Answer E 44. Landsburg 5th. Ed. p. 128 Supply: P=10+Q Demand: P=5-Q Solve to give Q=-2.5, P=7.5. Consider what this negative Q means. There is one demander willing to pay $4 (=5-1). But the market supply curve indicates no supply till prices reach 10, which they won’t. The individual firms, if they look at this situation, will decide to produce none. The marginal cost of producing one is 10+100*1=110, and it gets even more expensive per item as quantity grows. This ‘no market exists’ situation could be realistic: what quantity is sold of expensively hand-etched microchips as good as machine-etched? So each firm produces zero, Answer A



The present value of the perpetuity-immediate of 100 per year is ��

Immediately after the 5th payment, the present value of the perpetuity is still 1,250 .

To say the perpetuity is "exchanged" for the 25-year annuity means that they have the same

present value at the time of the exchange.

The 25 year annuity-immediate has geometrically increasing payments. The geometric increase

is at 8%, which is the same as the interest rate used for present value. In this special case (when

geometric increase rate is equal to interest rate) the present value of the geometric annuity-

immediate is . This can be seen from the following explanation.��. � ��

The series of geometric payments is � � ��

The present value (one year before the first payment) is

�. ��. � �� . �"�� .��

� �. ��. ��. �"�. � ��. .

Setting this equal to 1,250 , we solve for , getting Immediately after the 10-th� � � ��

payment of the geometric series, there are 15 payments remaining. The series of remaining

payments is ��

(note that the 10th payment was , so the 11th payment is , etc.).��

The present value of the remaining 15 payments (valued at time 10, which is one year before the

first of the remaining 15 payments) is

�� . � �� . �" � �� . � �� .

This is exchanged for a perpetuity-immediate paying per year. The present value of this!

perpetuity-immediate is . Therefore, .! � � ��! ��! � �� ! � ��

The following series of time lines illustrate the annuities.


45. continued

Original perpetuity

� � � � " � � � "

# # # # # # #

��

At the end of 5 years, the perpetuity

� � � � "

# # # #

��

is exchanged for the 25 year geometric annuity

� � � � " �� " ��

# # # # # # #

� ��

At the end of 10 more years, the remaining 15 payments of the geometric annuity

�� " ��

# # # #

��

is exchanged for the perpetuity

�� "

# # # #

! ! ! "

Answer: C


46. Brealey and Myers 7th. Ed. p. 823; Current assets=Cash & securities + receivables + inventory (p. 819) Current ratio=Current assets/current liabilities Quick ratio= (Cash & short-term securities + receivables)/Current liabilities Inventory is up by $100,000 so the current ratio is up but the quick ratio stays the same. You may have been able to do this question if you had noticed and managed to remember (good luck!) that inventory is not regarded as ‘quick’. Answer E 47. 2-21-00 4 th. printing p. 73; Authorities are reducing interest rates, which tends to reduce the attractiveness of the country to foreign investors. Indeed, the question indicates that the fixed-exchange-rate policy has been superseded by a policy of depreciating the currency. Some currency depreciation can be achieved also by ‘talking down’ the currency. (Comment by Keith Sharp: This overall situation, arguably, represents United States policy in early 2003, which may be why the examiners chose this question. The Fed has been lowering interest rates and U.S. officials seem to be quietly encouraging a rise in foreign currencies. This is a move away from the 1990s ‘strong dollar’ policy. That had been to maintain the dollar’s value by indicating a willingness to boost interest rates and use U.S. foreign currency reserves to buy dollars to support its value if necessary. Under the apparent new policy the Euro rose startlingly from $US 0.84 in March 2002 to $US 1.18 in May 2003. So more U.S. computers bought in Paris and fewer U.S. tourists in Rome. And people buying Fords rather than BMWs in Chicago. All good for NX and U.S. GDP). So investment is up because of the low interest rates. Net exports are up too. Answer B 48. Landsburg 5th. Ed. p. 103; Price elasticity of demand =-0.75. Actual market price up by 3%. Quantity down by 0.75*3=2.25% Answer B 49. Brealey and Myers 7th.Ed. I-F p. 437; Linter assumes that managers focus on dividend changes II-T p. 441; M&M (1961) thought that in the absence of taxes etc dividend policy is irrelevant to firm value. (Comment by Keith Sharp: this wouldn’t be true if the managers could use retained dividends to make very high-return business investments. But this possibility could be regarded as an ‘imperfection’ in markets) III-T maybe; p. 439-441 Stock repurchase could mean that business investment opportunities are so scarce that the managers have nothing better to do with retained earnings. Or it could mean that the managers think the stock is cheap. Answer D?



The initial deposit of 10 grows to at the end of 10 years (40 quarters),��

and then continues to grow at 3% per half year after that. The accumulated value of the initial

deposit of 10 at the end of 30 years is (20 more years, is 40 more��

��

half-years at 3% per half-year).

The second deposit is 20 made at time 15. The accumulated value of the second deposit at time

30 (15 years after the second deposit) is (15 years is 30 half-years).��

The total accumulated value at the end of 30 years is

��

�� . Solving for results in .


Note: Keith Sharp FSA produced the above solutions for the economics and finance questions and Sam Broverman produced the solutions f ro interest theory in the May 2003 Course 2 exam. The solutions are in no way an official SoA or CAS view. If you have comments, suggested changes, questions or disagreements please email Keith via his site www.sharpwaterloo.com and e-mail Sam at [email protected] .

SOA/CAS MAY 2003 COURSE 2 EXAM SOLUTIONS · SOA/CAS MAY 2003 COURSE 2 EXAM SOLUTIONS Economics and...

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