24W ECON 36 MIDTERM 1_SOLUTIONS

24W ECON 36 MIDTERM 1 DART ID_____________ Version 1 1 DIRECTIONS: This exam has two parts. Part 1 has 10 questions worth 3 points each (30 points total). Part 2 has 4 questions worth 4 points each (16 points total). The combined total of 46 points will be normalized to a final score out of 20. Read each question carefully, show ALL work, and follow the Dartmouth Honor Code. A calculator will be provided. WRITE YOUR DARTMOUTH ID ON EVERY PAGE. PART A: MULTIPLE CHOICE - Choose the one alternative that best completes the statement or answers the question. 1) A small craft store located in a kiosk expects to generate annual cash flows of $6,800 for the next three years. At the end of the three years, the business is expected to be sold for $15,000. What is the value of this business at a discount rate of 15 percent? A) $30,100.07 B) $29,408.27 C) $25,388.67 D) $17,409.09 E) $19,477.67

DART ID:_____________________ Version 1 2 2) Gabriel is considering two independent projects with 2-year lives. Both projects have been assigned a discount rate of 13 percent. She has sufficient funds to finance one or both projects. Project A costs $38,500 and has cash flows of $19,400 and $28,700 for Years 1 and 2, respectively. Project B costs $41,000, and has cash flows of $25,000 and $22,000 for Years 1 and 2, respectively. Which project, or projects, if either, should Gabriel accept based on the profitability index method and what is the correct reason for that decision? A) You should accept both projects since both of their PIs are positive. B) You should accept Project A since it has the higher PI and you can only select one project. C) You should accept both projects since both of their PIs are greater than 1. D) You should only accept Project A since it is the only project with a PI greater than 1. E) Neither project is acceptable.

DART ID:_____________________ Version 1 4 4) Northern Woods is considering two methods of production for a new product. The first method will require fixed assets costing $450,000 that will be depreciated straight-line to zero over the product ’ s 3-year life. Annual fixed costs are $316,000 and variable costs per unit are $8.64. The second method will require fixed assets costing $790,000, annual fixed costs of $211,000, and variable costs per unit of $6.57. The firm expects to sell 46,000 units per year at $20 per unit. The discount rate is 16 percent and the tax rate is 21 percent. Should the product be produced and if so, which method of production should be implemented and why? A) Yes; Method A; because A has the lower initial cost B) Yes; Method A; because it will break-even on a financial basis with fewer annual sales C) Yes; Method B; because it has lower annual costs D) Yes; Method B; because B has a financial break-even quantity that is less than the expected sales units E) No; Neither method of production will financially break-even within the expected life of the project.

DART ID:_____________________ Version 1 5 5) A 15-year bond has a coupon rate of 4.5 percent, a $1,000 par value, matures in 7 years, has a price of $1,105.50, and pays interest semiannually. What is the current yield? A) 1.41% B) 1.79% C) 2.04% D) 4.07% E) 2.83%

DART ID:_____________________ Version 1 7 7) The stock of Cylinder Systems is currently selling for $59.48 per share. The stock has an expected growth rate of 4.22 percent and an expected total return for the next year of 9.87 percent. How much dividend income should you expect to receive next year if you purchase 800 shares of this stock today? A) $2,309.20 B) $2,008.04 C) $2,688.50 D) $2,380.15 E) $2,001.10

DART ID:_____________________ Version 1 8 8) You want to design a portfolio that has a beta of zero. Stock A has a beta of 1.69 and Stock B's beta is also greater than 1. You are willing to include both stocks as well as a risk-free security in your portfolio. If your portfolio will have a combined value of $5,000, how much should you invest in Stock B? A) $2,630 B) $0 C) $2,959 D) $3,008 E) $1,487

DART ID:_____________________ Version 1 10 10) Andrews has a current debt-equity ratio of .52 and a target debt-equity ratio of .45. The cost of floating equity is 9.5 percent and the flotation cost of debt is 6.6 percent. What should the firm use as its weighted average flotation cost? A) 8.01% B) 8.51% C) 8.33% D) 7.76% E) 8.60%

DART ID:_____________________ Version 1 11 PART B – SHORT ANSWER: Read each question carefully. Write your answer in the space provided after each question. 11) Sparkling Water, Incorporated, expects to sell 3.8 million bottles of drinking water each year in perpetuity. This year each bottle will sell for $1.52 in real terms and will cost $.87 in real terms. Sales income and costs occur at year-end. Revenues will rise at a real rate of 1.3 percent annually, while real costs will rise at a real rate of .9 percent annually. The real discount rate is 6 percent. The corporate tax rate is 21 percent. What is the company worth today? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to the nearest whole number, e.g., 1,234,567.)

DART ID:_____________________ Version 1 13 13) Suppose stock returns can be explained by a two-factor model. The firm-specific risks for all stocks are independent. The following table shows the information for two diversified portfolios: β 1 β 2 E( R ) Portfolio A .85 1.15 16% Portfolio B 1.45 −.25 12 If the risk-free rate is 4 percent, what are the risk premiums for each factor in this model? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

DART ID:_____________________ Version 1 14 14) Cookies 'n Cream, Incorporated, recently issued new securities to finance a new TV show. The project cost $45 million, and the company paid $2.2 million in flotation costs. In addition, the equity issued had a flotation cost of 7 percent of the amount raised, whereas the debt issued had a flotation cost of 2 percent of the amount raised. If the company issued new securities in the same proportion as its target capital structure, what is the company’s target debt-equity ratio? (Do not round intermediate calculations and round your answer to 4 decimal places, e.g., 32.1616.)

DART ID:_____________________ Version 1 16 5) D Current yield = [.045($1,000)]/$1,105.50 Current yield = .0407, or 4.07% 6) B P 0 = [$1.97(1.028)]/(.17 − .028) P 0 = $14.26 7) C Dividend income = (.0987 − .0422)($59.48)(800) Dividend income = $2,688.50 8) B Your entire portfolio should be invested in risk-free securities to obtain a portfolio beta of zero. 9) D (.1234 − .126) = .9(.014) + 1.1( F GNP ) F GNP = − .0138, or − 1.38% 10) E ƒ = (1/1.45)(.095) + (.45/1.45)(.066) ƒ = .0860, or 8.60%

DART ID:_____________________ Version 1 17 PART B – SHORT ANSWER: Read each question carefully. Write your answer in the space provided after each question. 11) Sparkling Water, Incorporated, expects to sell 3.8 million bottles of drinking water each year in perpetuity. This year each bottle will sell for $1.52 in real terms and will cost $.87 in real terms. Sales income and costs occur at year-end. Revenues will rise at a real rate of 1.3 percent annually, while real costs will rise at a real rate of .9 percent annually. The real discount rate is 6 percent. The corporate tax rate is 21 percent. What is the company worth today? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to the nearest whole number, e.g., 1,234,567.)? Explanation: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. To determine the value of a firm, we can find the present value of the firm’s future cash flows. No depreciation is given, so we can assume depreciation is zero. Using the tax shield approach, we can find the present value of the aftertax revenues, and the present value of the aftertax costs. The required return, growth rates, price, and costs are all given in real terms. Subtracting the costs from the revenues will give us the value of the firm’s cash flows. We must calculate the present value of each separately since each is growing at a different rate. First, we will find the present value of the revenues. The revenues in Year 1 will be the number of bottles sold, times the price per bottle, or: Aftertax revenue in Year 1 in real terms = (3,800,000 × $1.52)(1 − .21) Aftertax revenue in Year 1 in real terms = $4,563,040 Revenues will grow at 6 percent per year in real terms forever. Applying the growing perpetuity formula, we find the present value of the revenues is: PV of revenues = C 1 /( R − g ) PV of revenues = $4,563,040/(.06 − .013) PV of revenues = $97,085,957 The real aftertax costs in Year 1 will be: Aftertax costs in year 1 in real terms = (3,800,000 × $.87)(1 − .21) Aftertax costs in year 1 in real terms = $2,611,740 Costs will grow at .9 percent per year in real terms forever. Applying the growing perpetuity formula, we find the present value of the costs is:

DART ID:_____________________ Version 1 19 12) When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh flowers on her grave every Sunday as long as he lived. The week after she died in 1962, a bunch of fresh flowers that the former baseball player thought appropriate for the star cost about $7. Based on actuarial tables, “ Joltin ’ Joe ” could expect to live for 30 years after the actress died. Assume that the EAR is 6.8 percent. Also, assume that the price of the flowers will increase at 3.5 percent per year, when expressed as an EAR. Assume that each year has exactly 52 weeks and Joe began purchasing flowers the week after Marilyn died. What is the present value of this commitment? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to the nearest whole number, e.g., 1,234,567.)? Explanation: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. To find the present value, we need to find the real weekly interest rate. To find the real return, we need to use the effective annual rates in the Fisher equation. So, we find the real EAR is: (1 + R ) = (1 + r )(1 + h ) 1 + .068 = (1 + r)(1 + .035) r = .0319, or 3.19% Now, to find the weekly interest rate, we need to find the APR. Using the equation for discrete compounding: EAR = [1 + (APR/ m )] m − 1 We can solve for the APR. Doing so, we get: APR = m [(1 + EAR) 1/ m − 1] APR = 52[(1 + .0319) 1/52 − 1] APR = .0314, or 3.14% So, the weekly interest rate is: Weekly rate = APR/52 Weekly rate = .0314/52 Weekly rate = .00060, or .060% Now we can find the present value of the cost of the flowers. The real cash flows are an ordinary annuity, discounted at the real interest rate. So, the present value of the cost of the flowers is: PVA = C ({1 − [1/(1 + r ) t ]}/ r ) PVA = $7({1 − [1/(1 + .00060) 30(52) ]}/.00060) PVA = $7,072.20

DART ID:_____________________ Version 1 20 13) Suppose stock returns can be explained by a two-factor model. The firm-specific risks for all stocks are independent. The following table shows the information for two diversified portfolios: β 1 β 2 E( R ) Portfolio A .85 1.15 16% Portfolio B 1.45 −.25 12 If the risk-free rate is 4 percent, what are the risk premiums for each factor in this model? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Explanation: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. We can express the multifactor model for each portfolio as: E( R P ) = R F + β 1 F 1 + β 2 F 2 where F 1 and F 2 are the respective risk premiums for each factor. Expressing the return equation for each portfolio, we get: 16% = 4% + .85 F 1 + 1.15 F 2 12% = 4% + 1.45 F 1 − .25 F 2 We can solve the system of two equations with two unknowns. Multiplying each equation by the respective F 2 factor for the other equation, we get: 4.00% = 1.0% + .2125 F 1 + .2875 F 2 13.8% = 4.6% + 1.6675 F 1 −.2875 F 2 Summing the equations and solving for F 1 gives us: 17.8% = 5.6% + 1.88 F 1 F 1 = 6.49% And now, using the equation for Portfolio A, we can solve for F 2 , which is: 12% = 4% + 1.45(6.49%) − .25 F 2 F 2 = 5.64%