1. Which of the following statements is an implication of the semi-strong form of the. Prices slowly adjust over time to incorporate past information.

Transcription

1 COURSE 2 MAY 2001

2 1. Which of the following statements is an implication of the semi-strong form of the Efficient Market Hypothesis? (A) (B) (C) (D) (E) Market price reflects all information. Prices slowly adjust over time to incorporate past information. Past price data should have predictive power for stock returns. Actively managed portfolios cannot consistently outperform the market. The correct answer is not given by (A), (B), (C), or (D). May Course 2

3 2. The free rider problem is considered a major reason that public goods are provided by the government rather than by the private market. Which of the following explains why the free rider problem occurs? (A) (B) (C) (D) (E) It is impossible to exclude non-paying consumers, which makes it difficult for private firms to collect sufficient revenue. The use of these goods by an additional consumer imposes extra social costs on everyone else. There are some consumers who place no value on public goods and thus are not willing to pay a positive price. These goods are too expensive to be provided by the private marketplace. The long-run marginal cost of these goods lies below the long-run average cost. Course 2 6 Form 01A

4 3. Suppose the economy is entering the contractionary phase of a business cycle. Which of the following is an indicator of this downturn in economic activity? (A) (B) (C) (D) (E) A decrease in the unemployment rate An increase in the number of new building permits for private housing units An increase in stock prices An increase in delivery lags An increase in business inventories May Course 2

5 4. A 20-year loan of 20,000 may be repaid under the following two methods: i) amortization method with equal annual payments at an annual effective rate of 6.5% ii) sinking fund method in which the lender receives an annual effective rate of 8% and the sinking fund earns an annual effective rate of j Both methods require a payment of X to be made at the end of each year for 20 years. Calculate j. (A) j 6.5% (B) 6.5% < j 8.0% (C) 8.0% < j 10.0% (D) 10.0% < j 12.0% (E) j > 12.0% Course 2 8 Form 01A

6 5. A perpetuity-immediate pays X per year. Brian receives the first n payments, Colleen receives the next n payments, and Jeff receives the remaining payments. Brian's share of the present value of the original perpetuity is 40%, and Jeff's share is K. Calculate K. (A) 24% (B) 28% (C) 32% (D) 36% (E) 40% May Course 2

7 6. Suppose a constant-cost, competitive industry is in long-run equilibrium. Now suppose the government imposes an annual licensing fee as a requirement for firms to produce in the industry. As a result of this fee, what will happen to the quantity supplied in the market and the quantity supplied by an individual firm in the long run? (A) (B) (C) (D) (E) The quantity supplied in the market will increase, and the quantity supplied by an individual firm will increase. The quantity supplied in the market will increase, but the quantity supplied by an individual firm will decrease. The quantity supplied in the market will decrease, but the quantity supplied by an individual firm will not change, as some firms go out of business. The quantity supplied in the market will decrease, and the quantity supplied by an individual firm will decrease. The quantity supplied in the market will decrease, but the quantity supplied by an individual firm will increase. Course 2 10 Form 01A

8 7. Seth, Janice, and Lori each borrow 5000 for five years at a nominal interest rate of 12%, compounded semi-annually. Seth has interest accumulated over the five years and pays all the interest and principal in a lump sum at the end of five years. Janice pays interest at the end of every six-month period as it accrues and the principal at the end of five years. Lori repays her loan with 10 level payments at the end of every six-month period. Calculate the total amount of interest paid on all three loans. (A) 8718 (B) 8728 (C) 8738 (D) 8748 (E) 8758 May Course 2

9 8. The following is given for Company X: Authorized number of shares 600,000 Common stock ($1 par value) $ 450,000 Additional paid-in capital $1,000,000 Retained Earnings $5,000,000 Treasury Stock $ 150,000 The company plans to issue an additional 100,000 shares at $3 per share. Which of the following is true? (A) Authorized number of shares will be 700,000. (B) Common stock will be $750,000. (C) Additional paid-in capital will be $1,200,000. (D) Retained earnings will be $5,200,000. (E) Treasury stock will be $50,000. Course 2 12 Form 01A

10 9. Which of the following statements regarding consumer goods in the marketplace is true? (A) (B) (C) (D) (E) The quantity demanded of an inferior good decreases as its price decreases. The intersection of a consumer s Engel curve and demand curve represents how much the consumer will buy given a specific income level. When the price of a normal good decreases, the increase in quantity due to the income effect cannot be greater than the substitution effect. The compensated demand curve for a normal good will be steeper than the uncompensated demand curve. The income elasticity of demand is equal to the slope of the Engel curve. May Course 2

11 10. A company is considering two projects. Project X requires an investment of 4000 today (t = 0) and will return level cash flows at the end of each year for 8 years. The IRR is 10%. Project Y also requires an investment of 4000 today (t = 0) and will return a single cash flow of 6600 at the end of 5 years. The risk-free rate is 2.5%, the market risk premium is 7% and the estimated beta is Compared to Project Y, which of the following is true? (A) Project X has a shorter payback period, a lower IRR and lower NPV. (B) Project X has a shorter payback period, a higher IRR and higher NPV. (C) Project X has a longer payback period, a lower IRR and lower NPV. (D) Project X has a longer payback period, a higher IRR and higher NPV. (E) Project X has a longer payback period, a lower IRR and higher NPV. Course 2 14 Form 01A

12 11. Machine I costs X, has a salvage value of 8 X, and is to be depreciated over 10 years using the declining balance method. Machine II costs Y, has a salvage value of 8 X, and is to be depreciated over 10 years using the sum-of-the-years digits method. The total amount of depreciation in the first seven years for Machine I equals the total amount of depreciation in the first seven years for Machine II. Calculate Y X. (A) 0.94 (B) 0.99 (C) 1.04 (D) 1.09 (E) 1.14 May Course 2

13 12. Bruce and Robbie each open up new bank accounts at time 0. Bruce deposits 100 into his bank account, and Robbie deposits 50 into his. Each account earns an annual effective discount rate of d. The amount of interest earned in Bruce's account during the 11th year is equal to X. The amount of interest earned in Robbie's account during the 17th year is also equal to X. Calculate X. (A) 28.0 (B) 31.3 (C) 34.6 (D) 36.7 (E) 38.9 Course 2 16 Form 01A

14 13. Ron has a loan with a present value of a n. The sum of the interest paid in period t plus the principal repaid in period t + 1 is X. Calculate X. (A) 1 + (B) 1 + v i n t v d n t (C) 1 + v n-t i (D) 1 + v n-t d (E) 1 + v n-t May Course 2

15 14. Which of the following statements about productivity is true? (A) (B) (C) (D) (E) Government spending on infrastructure improvements does not contribute to productivity growth because it does not increase the capital stock. Real wage growth is largely a function of productivity growth. Changes in the demographic composition of the workforce do not have any impact on productivity. If labor is growing at the same rate as capital then labor productivity will be unchanged. A shift in the economy to a greater proportion of service jobs would not be expected to affect productivity. Course 2 18 Form 01A

16 15. Tom can produce pizzas at a cost of 10 per pizza, and deliver pizzas at a cost of 2 per pizza. The equilibrium price for a pizza delivered to the door of a consumer is Tom currently produces and delivers 10 pizzas each night. Tom spends half his time producing pizzas and half his time delivering pizzas. Assuming unlimited demand at the current equilibrium price, what is the largest daily rate Tom could pay a delivery service without decreasing his profit? (A) 5 (B) 10 (C) 20 (D) 45 (E) 50 May Course 2

17 16. The money supply is determined by the combined actions of the central bank, the commercial banking system, and the public s preferences regarding how they hold money. Which of the following will result in an increase in the money supply? (A) (B) (C) (D) (E) An increase in the public s demand for currency. An exogenous increase in market interest rates. The central bank increases the discount rate. The central bank increases the reserve requirement ratio. The central bank sells bonds to the public. Course 2 20 Form 01A

18 17. At an annual effective interest rate of i, i > 0%, the present value of a perpetuity paying 10 at the end of each 3-year period, with the first payment at the end of year 6, is 32. At the same annual effective rate of i, the present value of a perpetuity-immediate paying 1 at the end of each 4-month period is X. Calculate X. (A) 38.8 (B) 39.8 (C) 40.8 (D) 41.8 (E) 42.8 May Course 2

19 18. Which of the following statements must be true for a natural monopoly? (A) (B) (C) (D) (E) Setting price equal to marginal cost would result in a loss. Marginal costs are high whereas fixed costs are low. The marginal cost curve is falling at the point where it crosses the industry demand curve. Producing at the intersection of marginal revenue and marginal cost would result in a loss. Average and marginal cost curves intersect below the industry demand curve. Course 2 22 Form 01A

20 19. Consider the following project: Time Net cash flow Assuming a 20% opportunity cost of capital, the NPV is zero. Calculate the expected economic income in the second year. (A) 192 (B) 388 (C) 436 (D) 526 (E) 628 May Course 2

21 20. Suppose that in the long run, real output is growing at 2.75% per year and the velocity of money is growing at 1.0% per year. Further suppose that the monetary authorities have a target rate of inflation between 0.0% and 1.0% per year. Which of the following is most consistent with the goal of the monetary authorities? (A) (B) (C) (D) (E) Money supply growth should be less than 1.75% per year. Money supply growth should be between 1.75% and 2.75% per year. Money supply growth should be between 2.75% and 3.75% per year. Money supply growth should be greater than 3.75% per year. Money supply growth does not matter; in the long run, the price level is determined by technological change and the growth of labor and capital inputs. Course 2 24 Form 01A

22 21. In the market for personal computers, the demand and supply are neither perfectly elastic nor perfectly inelastic. Suppose there is an exogenous increase in the wages of workers who manufacture computer chips used in personal computers. What will happen to price and quantity in the personal computer market? (A) (B) (C) (D) (E) Neither the price nor the quantity exchanged will change. Price will decrease, and the quantity exchanged will increase. Price will decrease, and the quantity exchanged will decrease. Price will increase, and the quantity exchanged will increase. Price will increase, and the quantity exchanged will decrease. May Course 2

23 22. A company invests 20,000 in a project. The project is expected to have cash flows of 3000 at the end of each year for 15 years, with the first cash flow expected one year after the initial investment. Using the project s after-tax weighted average cost of capital, the project has a net present value of The following gives additional information about the company: (i) The company is financed with 40% equity and 60% debt. (ii) The company s marginal tax rate is 25%. (iii) re = 2rD, where r E is the cost of equity and r D is the cost of debt. Calculate r E. (A) 10.25% (B) 12.40% (C) 13.25% (D) 14.60% (E) 16.40% Course 2 26 Form 01A

24 23. Suppose that there is an overall increase in both real income and interest rates observed in the economy. Using the IS/LM framework, this observation can best be explained by which of the following events? (A) (B) (C) (D) (E) A rightward shift in the LM curve caused by an expansionary monetary policy. A leftward shift in the LM curve due to an exogenous increase in the domestic price level. A leftward shift in the IS curve due to an exogenous increase in savings as more people become concerned about retirement. An increase in government spending for national defense that results in a rightward shift in the IS curve. An increase in personal income taxes to reduce the deficit. May Course 2

25 24. A company has an asset with a depreciation basis of 100,000 which can be depreciated by the following schedule: Year Percent The marginal tax rate is 35% and the pretax borrowing rate is 12%. Calculate the present value of the tax shields created by the depreciation. (A) 26,045 (B) 28,156 (C) 30,267 (D) 32,633 (E) 35,000 Course 2 28 Form 01A

26 25. Which of the following must be true for a competitive firm to continue operating in the short run? I. Total Revenue Total Costs + Fixed Costs > 0 II. III. Marginal Costs > Average Costs Price > Average Variable Costs (A) (B) (C) (D) (E) III only I and II only I and III only II and III only I, II, and III May Course 2

27 26. Susan invests Z at the end of each year for seven years at an annual effective interest rate of 5%. The interest credited at the end of each year is reinvested at an annual effective rate of 6%. The accumulated value at the end of seven years is X. Lori invests Z at the end of each year for 14 years at an annual effective interest rate of 2.5%. The interest credited at the end of each year is reinvested at an annual effective rate of 3%. The accumulated value at the end of 14 years is Y. Calculate Y X. (A) 1.93 (B) 1.98 (C) 2.03 (D) 2.08 (E) 2.13 Course 2 30 Form 01A

28 27. 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. (A) 12% (B) 16% (C) 18% (D) 20% (E) 24% May Course 2

29 28. Assume that a monopolist s demand and marginal cost functions are given by the following formulas: Demand: P = 10 - Q Marginal Cost: MC = Q + 1 where P is price and Q is quantity. What price will the monopolist charge? (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 Course 2 32 Form 01A

30 29. In a country that does not trade with the rest of the world, the marginal propensity to consume is 0.7, and the income tax rate is 30%. What is the country s government expenditure multiplier? (A) 1.10 (B) 1.96 (C) 2.04 (D) 3.33 (E) 4.76 May Course 2

31 30. A stock price can go up by 20% or down by 15% over the next period. The current stock price is greater than 70. You own a one-period put on the stock. The put has an exercise price of The risk-free rate is 11.25%. If the put is exercised today, the amount received will be X. The price of the put today (unexercised) is also X. Calculate the current stock price. (A) (B) (C) (D) (E) Course 2 34 Form 01A

32 31. You are given the following information about an investment account: Date Value Immediately Before Deposit Deposit January 1 10 July 1 12 X December 31 X Over the year, the time-weighted return is 0%, and the dollar-weighted return is Y. Calculate Y. (A) -25% (B) -10% (C) 0% (D) 10% (E) 25% May Course 2

33 32. Which of the following statements about the short-run supply curve for a competitive industry is FALSE? (A) (B) (C) (D) (E) As price rises, industry output goes up because firms in the industry increase production. As price rises, firms not previously producing will start up production and thereby further increase industry output. As price rises, entry of new firms tends to make the industry supply curve more elastic than the supply curve of typical firms in the industry. As price and output increase for the industry, the factor-price effect is likely to make the industry supply curve less elastic. As price and output increase for the industry, the marginal cost curve of each firm in the industry will likely shift down because of the factor-price effect. Course 2 36 Form 01A

34 33. You are given: Current Liabilities Long Term Liabilites Shareholder Equity Total Assets EBIT Depreciation Interest Taxes The company s Payout Ratio is 10%. Determine the company s Internal Growth Rate. (A) 7.1% (B) 8.1% (C) 8.9% (D) 9.1% (E) 10.9% May Course 2

35 34. Suppose there is an economy that produces only one good, X, and suppose that the competitive supply and demand functions for X are: Supply: Demand: Q = 5P Q = 20 5P where P is price and Q is quantity. Further suppose that the government imposes a price ceiling of 1, which is perfectly enforced at no cost. Assuming that the supply curve does not shift due to the price ceiling, what is the deadweight loss from the price ceiling? (A) 2.5 (B) 5.0 (C) 10.0 (D) 15.0 (E) 20.0 Course 2 38 Form 01A

36 35. Which of the following are true? I. The variance of equity returns in an equal-weighted portfolio is proportional to the number of stocks held. II. III. Beta is the correlation between the returns on an asset and the returns on the market portfolio. In empirical tests, the slope of the CAPM is estimated to be steeper than theory would suggest. (A) (B) (C) (D) (E) None I only II only III only I, II, and III May Course 2

37 36. Suppose that over the past year, the nominal exchange rate increased from 1.25 German marks per U.S. dollar to Further suppose that over this period the U.S. inflation rate was 3% and the German rate was 2%. What is the change in the real exchange rate? (A) +1% (B) +19% (C) +21% (D) +23% (E) +25% Course 2 40 Form 01A

38 37. Seth borrows X for four years at an annual effective interest rate of 8%, to be repaid with equal payments at the end of each year. The outstanding loan balance at the end of the second year is and at the end of the third year is Calculate the principal repaid in the first payment. (A) 444 (B) 454 (C) 464 (D) 474 (E) 484 May Course 2

39 38. You are the chief actuary for a small, all-equity financed insurer. The current book value of equity is In years 1 and 2, you will earn a Return on Equity (ROE) of 20% and reinvest all earnings. Starting in year 3 (and every year thereafter), your company s ROE will be 15%, your free cash flow will be 50% of annual earnings, and you will pay a dividend equal to 100% of free cash flow. You have been approached by another insurer who would like to buy your company. Assuming an opportunity cost of capital equal to 15%, use Discounted Cash Flow to find the value of your company. (A) 1000 (B) 1089 (C) 1264 (D) 1440 (E) 1444 Course 2 42 Form 01A

40 39. A firm has a debt ratio of 0.4. The firm also has a debt beta of 0.75 and an equity beta of The expected return on the market is currently 11% and the risk-free interest rate is 5%. What is the required return on an investment project that expands the firm s existing operations while maintaining the current target capital structure? (A) 10% (B) 11% (C) 12% (D) 14% (E) 15% May Course 2

41 40. You are interested in purchasing a call option on a common stock that is currently trading at a price of 100 per share. You are given the following information: (i) (ii) (iii) the standard deviation of the continuously compounded annual rate of return on the stock is 0.4; the time to maturity of the call is 3 months (0.25 years); and Current Share Price ln = 0.08, at the risk-free rate. Present Value of the Exercise Price Calculate the price of each call option using Black-Scholes. (A) 0.8 (B) 1.8 (C) 2.8 (D) 3.8 (E) 4.8 Course 2 44 Form 01A

42 41. Bill buys a 10-year 1000 par value 6% bond with semi-annual coupons. The price assumes a nominal yield of 6%, compounded semi-annually. As Bill receives each coupon payment, he immediately puts the money into an account earning interest at an annual effective rate of i. At the end of 10 years, immediately after Bill receives the final coupon payment and the redemption value of the bond, Bill has earned an annual effective yield of 7% on his investment in the bond. Calculate i. (A) 9.50% (B) 9.75% (C) 10.00% (D) 10.25% (E) 10.50% May Course 2

43 42. The supply and demand functions for a good are: Supply: Demand: P = 1 + 4Q P = 4 2Q where P is price and Q is quantity. Now suppose an increase in the price of an input causes the supply function to become: Supply: P = 2 + 4Q What is the price elasticity of demand at the initial equilibrium? (A) (B) (C) (D) (E) Course 2 46 Form 01A

44 43. The market value of a company s liabilities consists of 40 of debt and 80 of equity, for total liabilities of 120. The b for the company s debt and equity are 0.3 and 1.65, respectively. The expected return on the company s debt is 9%. The company has a weighted average cost of capital of 14%. Which of the following statements are true, ignoring the effect of taxes? I. If the proceeds from issuing additional equity of 10 are used to retire 10 of debt, the company s cost of capital will increase to 14.6%. II. If a proposed new project has a b of 1.05, the project is riskier than the company s existing business. III. If the risk-free rate is 8%, then the expected risk premium on the market is 5%. (A) (B) (C) (D) (E) I only II only III only I and II only I and III only May Course 2

45 44. A company has Earnings Before Interest and Taxes (EBIT) of 11,560. The company has 100,000 of 6% debt outstanding. The company s corporate tax rate is 35%. The company paid out 1000 as a dividend and had an average equity of 20,912 during the year. Determine the Return on average Equity (ROE) for the company s stock. (A) 7.2% (B) 12.5% (C) 14.2% (D) 17.3% (E) 35.9% Course 2 48 Form 01A

46 45. At time t = 0, 1 is deposited into each of Fund X and Fund Y. Fund X accumulates at 2 t a force of interest δ t =. Fund Y accumulates at a nominal rate of discount of 8% per k annum convertible semiannually. At time t = 5, the accumulated value of Fund X equals the accumulated value of Fund Y. Determine k. (A) 100 (B) 102 (C) 104 (D) 106 (E) 108 May Course 2

47 46. A utility-maximizing consumer has indifference curves of the form: U = XY where U is the consumer s utility, X is the number of units of meat consumed, and Y is the number of units of bread consumed. The consumer buys only meat and bread. Meat costs 5 per unit, and bread costs 3 per unit. If the consumer s utility is 12, how many units of meat are purchased? (A) 1.7 (B) 2.7 (C) 4.5 (D) 7.2 (E) 20.0 Course 2 50 Form 01A

48 47. Which of the following is most consistent with the monetarists long-run view of the macroeconomy? (A) (B) (C) (D) (E) The growth of real output is determined by technology and the growth of inputs. The growth of real output is determined by changes in the velocity of money. The growth of real output is determined by the growth in the wage rate. Inflation is determined by the wage-price spiral. Inflation is determined by changes in the velocity of money. May Course 2

49 48. A company s stock is currently selling for Its next dividend, payable one year from now, is expected to be 0.50 per share. Analysts forecast a long-run dividend growth rate of 7.5% for the company. Tomorrow the long-run dividend growth rate estimate changes to 7%. Calculate the new stock price. (A) 22.2 (B) 23.8 (C) 25.9 (D) 28.0 (E) 28.5 Course 2 52 Form 01A

50 49. Tawny makes a deposit into a bank account which credits interest at a nominal interest rate of 10% per annum, convertible semiannually. At the same time, Fabio deposits 1000 into a different bank account, which is credited with simple interest. At the end of 5 years, the forces of interest on the two accounts are equal, and Fabio's account has accumulated to Z. Determine Z. (A) 1792 (B) 1953 (C) 2092 (D) 2153 (E) 2392 May Course 2

51 50. The present values of the following three annuities are equal: (i) (ii) (iii) perpetuity-immediate paying 1 each year, calculated at an annual effective interest rate of 7.25% 50-year annuity-immediate paying 1 each year, calculated at an annual effective interest rate of j% n-year annuity-immediate paying 1 each year, calculated at an annual effective interest rate of j - 1% Calculate n. (A) 30 (B) 33 (C) 36 (D) 39 (E) 42 Course 2 54 Form 01A

52 Course 2 May 2001 Answer Key 1 D 26 C 2 A 27 B 3 E 28 C 4 E 29 B 5 D 30 B 6 E 31 A 7 D 32 All 8 C 33 E 9 D 34 D 10 C 35 A 11 B 36 C 12 E 37 A 13 D 38 B 14 B 39 C 15 D 40 E 16 B 41 B 17 B 42 A 18 A 43 C 19 A 44 D 20 B 45 B 21 E 46 B 22 E 47 A 23 D 48 A 24 C 49 B 25 C 50 A A 10 B 13 C 9 D 9 E 9 Course 2 Solutions 1 May 2001

53 1. D According to the semi-strong version of the efficient market theory, prices accurately reflect all publicly available information about a security. Thus, by this theory, actively managed portfolios should not be able to consistently outperform the rest of the market. All available information has already been incorporated into the current market price. 2. A The private market does not usually provide public goods since it is impossible to exclude non-paying customers. This often makes it impossible for a private firm to collect sufficient revenue to cover the cost. 3. E An increase in business inventories indicates that demand is not as high as businesses anticipated, resulting in inventory accumulation. The decrease in demand is a reflection of the downturn in economic activity. 4. E X = = a , = + (0.08)(20, 000) S20 j S = j j = 14.18% 5. D X B= X a = 0.4 n i n C = v Xan 2n X J = v i 0.4 n a = v = 0.6 n i X J = 0.36 i Course 2 Solutions 2 May 2001

54 6. E The licensing fee works the same as an increase in fixed costs; it shifts the market supply upward, increasing price and decreasing quantity demanded. At the firm level, however, it increases average costs without changing marginal costs; therefore, the representative firm increases output. This apparent paradox is resolved by the fact that in the long run some firms will go out of business. 7. D Seth = = = Janice = 5000 ( 0.06)( 10) = Lori = P(10) 5000 = where P = = a The sum is C Additional paid-in capital will be $1,200,000 (($3 per share - $1 par value) 100,000 shares = $200,000 increase). 9. D For a normal good, a price decline results in a positive income effect and a quantity increase larger than would be the case for a compensated price decline. 10. C Project X: Annual cash flows of (immediate annuity at 10% with PV = 4000). Payback 4000 in 6 th year. NPV discount rate = (0.07) = 0.06 Annuity at 6% of cash flows of 4000, ,, = Project Y: Payback in 5 th year IRR is interest rate such that: 4000 = 6600v 5 Æ IRR = 10.5% NPV = /(1.06) 5 = % Course 2 Solutions 3 May 2001

55 11. B decl bal 10 X 1 d = ( ) ( 1 d ) = ( 0.125) 7 1 X 8 1/10 ( ) Depr = X X = X 7/10 sum of yrs digits 10 1 i = first 7 yrs depr = 55 7 X 49 Depr = Y X X = Y X = Y 12. E Bruce's interest, year 11: = X (1 d) ( 1 d) Robbie's interest, year 17: ( 1 d ) 16 = X = 1 1 d ( 1 d ) 10 1 d ( d) = d = 10.91% 2 X = = ( ) D If you assume: Annual repayments of interest and principal repayments are level. Year (t + 1) principal repaid = v n t Year t interest repaid = i an + = 1 - v n t+1 t 1 Total = 1 v n t+1 + v n t = 1 v n t (v 1) = 1 v n t (-(1 v)) = 1 + v n t (d) 14. B Real wages can grow only when there is labor productivity growth or labor s share of product increases. The latter has remained relatively constant for long periods so the former is the primary source of real wage growth. Course 2 Solutions 4 May 2001

56 15. D Currently Tom is making a profit of 5 a day. If he outsources delivery, Tom could double output and earn a profit of 50 excluding the delivery cost. Hence Tom could pay the delivery service up to 45 without decreasing his profit. 16. B An increase in market interest rates will result in banks lending out excess reserves which lowers free reserves and increases the money supply. 17. B v = 32; 10v = 32 3 ( 1+ i) ( i) ( i) ( i) = ± 2304 ( 1+ i) = = i = 7.72% 1 1 X = = 1/3 1 = ( 1+ i) ( ) 18. A At the competitive price, a natural monopoly cannot cover its costs because price is below average cost at this point. 19. A Economic income = Cash flow plus change in NPV NPV 1 = 628.4/ /(1.2) 2 = NPV 2 = 628.4/1.2 = Economic income = ( ) = B The relationship between money, velocity, prices, and real output is such that if real output is rowing at 2.75% per year, and velocity is increasing at 1.00% per year, and the inflation target is 0 to 1.00%, then in order to maintain the identity M + v = P + Y, where each variable is a growth rate, then it must be that money growth is between 1.75% and 2.75%. Course 2 Solutions 5 May 2001

57 21. E The increase in the price of an input, in this case labor, drives up the marginal cost of producing chips; therefore, it leads to a decrease in the supply of chips and an increase in the price of chips. Similarly, since chips are used to make computers, the supply of computers falls, the equilibrium price of computers increases, and the quantity exchanged decreases. 22. E Let i = after-tax WACC 3000 a 15 i - 20,000 = \ a 15 i = fi i = 10.25%. After-tax WACC = = r E (0.4) + r D (1 T x )(0.6) = 0.4 r E + ½ r E (1 0.25)(0.6) = 0.4r E r E \ r E = 16.4%. 23. D An increase in government spending shifts the IS curve to the right and increases both income and interest rates. 24. C Year 1 Year 2 Year 3 Year 4 Dollar deductions 33,330 44,450 14,810 7,410 Tax shields 11,666 15,558 5,184 2,594 After tax rate = 0.12(0.65) = Present value = 11,666/ ,558/ ,184/ ,594/ = 30, C II is not true A firm will not shut down unless Marginal Costs are less than Average VARIABLE costs. 26. C Z = 100 s 6 66% Accumulated Value = X = 100( ( Is) ) = % 0.06 = (23.23) = s % Y = 100( ( Is) ) = % ( ) = Y/X = Course 2 Solutions 6 May 2001

58 27. B ( P0 760) P0(0.06) 1.03P0 760 Chris s return = = 0.5P0 0.5P0 ( P0 760) P0(0.06) P0 792 Jose s return = = 0.5P0 0.5P0 Chris s return = 2 [Jose s return] 1.03P [1.03P0 792] = 0.5 P0 0.5 P0 1.03P 0 = 824 fi P 0 = P (800) 760 i = = = 64/400 = 16%. 0.5P 0.5(800) 28. C Set up table: 0 Q P TR MR MC Monopolist will produce the largest quantity such that MR MC. At a quantity of 3, the demand curve produces a price of 7. Solution is the same if you assume Q is continuous. 29. B With net exports set to zero, the government expenditure multiplier is equal to y 1 C (1 T ) = 1 0.7(1 0.3) = 1 0.7(0.7) = = = B (p 20) + (1 p) ( -15) = Æ p = 0.75 Put value if exercised now = X ( X ) Put value if not exercised now = Equate the above two, we get X = 75. Course 2 Solutions 7 May 2001

59 31. A Time-weighted return = 0% means: 12 X = 1 => 12X = X 10 (12 + X ) X = 60 Dollar-weighted return: I = X X 10 = Y = = = 25% (60) E As a result of the factor-price effect, the marginal cost curves of the firms do not shift down but up. 33. E Assets = Liabilities + Shareholder Equity = = Net income = EBIT Interest Taxes = = 290. (Note depreciation has already been subtracted to get EBIT) Payout Ratio = 0.l0 = dividends = dividends net income 290 Dividends = 29. Retained Earnings = Net Income dividends = Retained Earnings 261 Internal Growth Rate = = = %. Assets D Competitive equilibrium occurs at Q = 10, P = 2 Consumer surplus = ½ ( 4 2) 10 = 10 Producer surplus = ½ (2 0) 10 = 10 Total surplus = 20 At constrained P = 1 producers will only supply Q = 5 so producer surplus = ½ (1 0) 5 = 2.5 The full price to consumer (including waiting time, etc.) will be bid up to P = 3 to eliminate excess demand. So consumer surplus = ½ (4 3) 5 = 2.5 Total surplus = 5 Deadweight loss = 20 5 = 15. Course 2 Solutions 8 May 2001

60 35. A I. Only if correlations are zero. II. Beta doesn t measure correlation, it is an estimated first derivative. III. Flatter 36. C The change in the real exchange rate is equal to the change in the nominal rate times the ratio of the inflation rates. [1.5/ /1.02] 1 = 21%. 37. A 1 B 3 = = Pa = P P = X = Pa40.08 X = PR 1 = v 4 = B Year Starting Book equity ROE 20% 20% 15% 15% 15% Æ Earnings Dividends Plowback Free C-F Starting in year 3 Dividend growth rate g = Plowback ROE = (0.5)(0.15) = t = 2 of future dividends = t = 2 of free cash-flow = 108/( ) = 1440 t = 0 of free cash-flow = 1440(1.15) Course 2 Solutions 9 May 2001

61 39. C Since the project is to expand the firm s existing operations, the risk of the new project is the same as that of the firm s existing operations. According to MM capital structure theory, to compute the asset beta, which measures the risk of the firm s existing assets in place, we add the equity beta and the debt beta, each weighted by its proportion in the firm s capital structure. b project = 0.60 b E b D = 0.60(1.5) (0.75) = 1.2. Then, the CAPM may be applied to find the cost of capital: R = ( ) = = E 1 st, calculate Present value(exercise Price) (or PV[EX]): Current Share Price Since ln = -0.08, at the risk-free rate, Present Value of the Exercise Price and the Current Share Price = 100, the PV(EX) = In addition: t = 0.25, and σ = 0.4. Note that [σ * Square Root (t)] = 0.2 Based on these inputs, it is easy to calculate d 1 and d 2 : d 1 = -0.3, and d 2 = -0.5 (Exactly) Black-Scholes: N(d1)*(Current Price) N(d2)*(PV[EX]) = N(-0.3)*100 N(-0.5)* = 100(0.3821) (0.3085) = B Price of bond = 1000 ( i) ( i) 10 ( ) S ( i) = S 1/ /2 = = i = 9.75% 1/ A The correct answer follows from the definition of the price elasticity of demand. The percentage change in price from the initial equilibrium is 1/9, and the percentage change in quantity demanded is -1/3; hence the price elasticity of demand is One can also solve the problem directly using the differential calculus: elasticity = (dq/dp)(p/q). Course 2 Solutions 10 May 2001

62 43. C I. Cost of capital remains at 14% fi false. II. b C = D/V b D + E/V b E = 1/3 (0.3) + 2/3 (1.65) = 1.2. b C = 1.20 > 1.05 fi Project is less risky fi false. III. r c = r f + b C (r m r f ) 0.14 = X fi X = 0.05 = 5% fi true. 44. D EBIT 11,560 -Int 6,000 = 100, ,560 -Tax 1,946 = 5, ,614 = Amount available to shareholders 45. B ROE = 3, , t 2 dt k e = t 5 3k 0 e = k e = k = k = B Slope of indifference curve is dy/dx = -Y/X Budget line is of form 5X + 3Y = I Y = (1/3)I (5/3)X Slope of budget line = -5/3 = -Y/X Y = (5/3)X (5/3)X*X = 12 X 2 = 7.2 X = A Monetarists believe that in the long run, real output is not affected by monetary growth, but is affected by technology and the growth of inputs. Course 2 Solutions 11 May 2001

63 48. A Current capitalization rate is: P 0 = DIV 1 /(r g) = 0.50/(r 0.075) r = 0.50/28.50 = r = When the long-run growth rate changes, current price should adjust to reflect this change, and to keep the expected rate of return constant. P 0 = 0.50/( ) = B ann eff 2 i = ( 1.05) 1 = Tawny: δ = ln ( ) = Y At t = 5, = δ t = 5 = Y = Y Z = ( ) = A 1 = a = a 50 j n j j = 7.00%, soa = n 6% n = 30.2 Course 2 Solutions 12 May 2001