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60 Price (Shour) 10 100 200 300 400 500 600 700 800 900 1000 Quantity (hours/week) 28. The figure above illustrates the demand and supply of Economics 101 tutoring services at MSU during finals week. In a misguided attempt to help low-income Economics 101 students, suppose that MSU administrators decree that tutors cannot charge more than $20 per hour for Economics 101 tutoring at MSU. This policy will cause a. a shortage of tutoring services at MSU and a deadweight loss of student welfare of $2250 per week b. a surplus of tutoring services at MSU and a deadweight loss of student welfare of $2000 per week C. a shortage of tutoring services at MSU and a deadweight loss of student welfare of $2000 per week d. a surplus of tutoring services at MSU and a deadweight loss of student welfare of $2250 per week e. an increase in the well-being of Economics 101 students since they will now pay less for tutoring services Elves/hour Total Product (toys/hour) 0 50 2 80 3 100 4 110 5 115 6 118 29. Santa Claus hires elves to produce toys according to the production function in the table above. Santa prices his toys at $10 each and elf wages are $75 per hour. Based on this information, what is the optimum number of elves for Santa to hire? a. 5 per hour b. 6 per hour . 3 per hour d. 4 per hour e. 2 per hour 30. If the price of a good rises and the total amount that consumers spend on the good rises, then demand for the good must be a. relatively elastic b. relatively inelastic unit elastic unit inelastic ECNS 101 - Final Exam - Section 1 - Version 1-Page 7 of 13 Quantity Demanded Price Quantity Supplied (dozens/week) ($/dozen) (dozens/week 140 6 0 120 7 15 100 8 30 30 9 45 50 10 60 40 11 75 20 12 90 13 10531. As a mid-size company, you have a pension plan which pays out $10 million a year forever. The first payment is exactly one year from now. The term structure is currently flat at 5%. (a) Compute the present value of your pension liabilities. (b) Suppose that the interest rate goes down by 0.1%. How does the value of your liability change? (c) Given your answer to (b), what is the modified duration of your pension liability? (d) Suppose that the pension plan is fully funded (i.e., the value of your assets equal the value of pension liabilities). You want to invest all your assets in bonds to avoid any interest rate risk. What should the duration of your bond portfolio be? (e) Suppose that this portfolio is a single zero-coupon bond. What should its maturity and total par value be? 32. On a job interview, you were handed the following quotes on U.S. Treasuries: Bond | Maturity (years) | Coupon Rate | Yield to Maturity 5% 4.5% 5% 5.0% 0% 5.5% Assume that the par value is $100 and coupons are paid annually, with the first coupon payment coming in exactly one year from now. The yield to maturity is also quoted as an annual rate. You are then asked the following questions: (a) What should be the price of a bond with a maturity of 3 years and coupon rate of 5%, given the above information? (b) What should be the 1-year forward rate between years 2 and 3? (c) What is the modified duration of a bond portfolio with 30% invested in bond 1 and 70% invested in bond 3? (d) How much would the value of the portfolio in (c) change if the yields of all bonds increased by 0.15%? 33. You have the following data on Treasury bonds. Assume that there are no taxes, only annual coupon payments are made and the first coupon payment occurs a year from now Bond Year of Maturity Coupon Face Value at T Price Today 25 100 100.00 50 500 422.61 50 N0 - 20 300 232.28 1000 192.31 Fall 2008 Page 17 of 66 (a) Calculate the following four annualized forward rates: f from 0 to 1, f from 1 to 2, f from 2 to 3, and f from 3 to 10. (b) Is it a good investment if it costs $21 million now and yields the following risk-free cash inflows? Year 2 3 Cash Flow (in million dollars) 9 10 11 34. Which of the following investments is most affected by changes in the level of interest rates? Suppose interest rates go up or down by 50 basis points (+ 0.5%). Rank the investments from most affected (largest change in value) to least affected (smallest change in value). (a) $1 million invested in short-term Treasury bills. (b) $1 million invested in Treasury strips (zero coupons) maturing in December 2016. (c) $1 million invested in a Treasury note maturing in December 2016. The note pays a 5.5% coupon. (d) $1 million invested in a Treasury bond maturing in January 2017. The bond pays a 9.25% coupon.24. Unigene Labs has existing assets that generate an EPS of $5 per year, which is expected to remain constant if the firm does not invest except to maintain exiting assets. Unigene is all-equity financed and its stock has a beta of 1.2. You estimate the market risk premium to be 8% and the risk free rate to be 4%. Next year (year 1), the firm has the opportunity to invest $3 per share to launch a new product, which will increase its EPS earnings by $0.80 per year permanently, starting the year after (year 2). The earnings from this product are highly volatile, with an annual standard deviation to be 50% and a correlation to the market to be 0.1. The market's standard deviation is 20%. (a) What is the cost of capital for the company's existing assets? (b) What would be stock price and the price-to-earnings ratio at time zero if the firm did not plan to launch the new product? (c) What is the appropriate discount rate for the new product? Explain your answer. (d) What would be stock price and the price-to-earnings ratio at time zero if the firm did plan to launch the new product? 25. PDQ Corp. is earning EPS of $3.00 next year, 15% of book value per share (BVPS) of $20.00. The companys sales revenues are expanding at 10% per year, and assets and BVPS will grow proportionally. But growth of revenues and assets will drop to 5% per year after year 5. (a) Assume earnings will continue to be 15% of BVPS. What is PDQ stock worth? The cost of capital is 10. (b) Your answer epended in part on a horizon value for the companys shares in year 5. What does that horizon value assume about the NPV of PDQs growth oppor- tunities from year 6 on? 26. Company Us earnings and dividends have been growing at a steady 15% per year. You are confident that the growth will continue for at least one more year, but the growth is not sustainable for the long run. Eventually the companys growth rate will drop below 10%. The current price is $62, and next years dividend is forecasted at $.50 per share. A security analyst forecasts the expected rate of return over the next year as: DIV1 0.50 1 = - Po 62 + 0.15 = 15.8% Explain why 15.8% is an upward-biased forecast of next years rate of return.27. Consider a company KY2. As of today, it has 1,000,(HJ shares of stoclr. outstand- 28. ing. trading at $50 per share and no debt. Assume that tomorrow the company de- cides, unexpectedly, to invest in a new project, which requires an initial investment of $10,000,\" today and is expected to produce a growing stream of cash ows, start.- ing from $1,200,000 in one year frorn now and growing at 3% per year. The cost of capital for the new project is estimated at 12%. Theae new investment plans are not yet known. The company decides to nance the new project. by issuing equity. It would lilve to issue just enough shares to raise the necessary $10,003,000 for the initial investment. {a} How many share; should the company issue? (b) What will be the share price after the new project is adopted? (c) How would your answer change if the investment in the new project was not unexpected, but rather was well l-mown to the market a month in advance? Your rich aunt has died. Her will gives you ownership of 5,000 shares of Plum Creek Timber Company, currently trading at $22 per share. But various legal complications will delay distribution of your aunts sharia to you until Octber 2008. Plum Creel: now pays an annual dividend of $1.40 per share. Assume for simplicity that the next dividend will be paid in Septearber 2003, just before you will receive the shares. [Therefore you will not receive the next dividend.) In the past Plum Creeks dividend has increased by 3% per year. This is a reasonable long-term trend, but security analysts are pessimistic for the immediate future. They forecast no growth in earnings and dividends for the next 3 years. Plum Creek is a relatively safe security. Investors are content with an 3% expected rate of return. A banlr olfers to buy the shares from you for $18.50 per share paid immediately. (The ban]: would pay $18.50 per share now and receive the shares next October.) Is this a fair offer? . Chuclry Cheese has a cost of capital of 9% per year. Its expected EPS next year is $5.00. The rm plans to plow back 40% of its earnings for new investments in the following years. The ROE on the new investments is 12%. {a} Calculate the share price and the PIE ratio of this rm. (b) If the plow-back ratio increases. will the HE ratio increase, decrease or remain unaected? State any assumptions you make and give a brief justication. c Gi-ven answer to I: what. will be ur advice to this rm. on its dividend i am: . as policy? . iDoc, a health service company. is expected to generate $1 in earnings per share next year and in the years to follow, from its existing assets. It plans to announce a new program to expand its businsm. This new program will increase its plow back ratio Fall 2008 Page 33 of 55 31. from zero to 50% next year. The retuni on equity for the new investments will be 12%. The expansion is expected to continue forever at the same rate. The cost of capital is 10%. {a} What is the expected dividend next year and its future growth under the new program? (b) What is the change in iDoc's stock price in response the announcement? (c) Is iDoc a growth company? What is its PfE ratio before and after the announce- merit? MW Co. expects earnings of $1.25 per share next year, out of which $0.50 will be paid out as dividends. Earning and dividends are expected to grow at a constant rate g- each year afterwards. MW shares are now traded at $20. The cost of capital for MW Co. is 10%. {a} What is the expected growth rate of earning 9'? (b) What is the HUB for MW\"? (c) Is MW a growth company? Justify your answer. 32. Fast Track, a local bus company providing direct scrvice hetereen New York and Boston1 had after-tax earnings of $32.5 million in the past year [year [1] and expected the same earnings forever. An investment. ban]: had valued Fast Track at $21] million. Now by allowing passengers to hook online, Fast Track Expects its after-tax earnings to grovvr at 2.5% per year, starting this year [year 1]. How much would the value of Fast Track increase by this change? [Assume the cost of capital stays the same.) 33. Dragon and Tiger Island {DTI}, an online game company, expects next year's after tax earnings to he $21] per share. Its business is still expanding. It plows back 30% of its earnings. The ROE on its new investments is 15%. Its cost of capital is 12.5%. [a] 'Wlnat is the share price of DTI? What is its eves? [In] Suppose that a new competitor come; in and cuts DTI's RUE to 12%. How would this impact DTI's investment decisions and its share price? Explain why. 34. The dividend yield for shares of the Union Pacic Railroad is 1.9%. Seourity analysts are forecasting rapid growth in Union Pacic's earnings per share (EPS], about 12.7% per year for the next three years. Dom that imply an expected rate of return of 1.9 + 12.7 = 14.6%? Explain. 35. The Northern Company is a utility company with existing assets that generates an EPS [eamings per share] of $5. If the rm only maintains existing assets, EPS is Expected to remain constant at $5 a year. Hovsever, next year, the Northern Company has the opportunity to invest $3 per share to develop a new electricity generator using solar energy. The development of the new generator will he completed next year. This investment is expected to generate a return {HOE} of 20% per year forever. The cost Fall 2003 Page 34 of HE of capital is 10%. What will be the Northern Companys share price if it decides to develop the new generator? Use the back of this page if needed to complete your answer. 36. BetaTrend is an exact match for MetaTrend except for one thing: it generates a con- tinuous stream of earnings and dividends. Thus it generates earnings in a continuous stream at 12% per year, starting immediately, and pays out half of earnings as div-i- dends. What is the present value of EetaTrend stock? The annually compounded cost of capital is 12%