PMBA 8135 Take Home Problem Set 3 Spring 2014 Directions: Determine or compute an answer for each question/problem on this problem set. After you have computed an answer for every question, enter your answers online via the quiz function entitled THPS 3 ANSWER SUBMISSION FORM. I will post a detailed solution key to the problem set right after the Answer Submission Form closes. If you do not post your answers by midnight on due date as per the course calendar, you will receive a grade of 0 on the problem set I cannot accept any answers after I post the solution key. All work on this problem set is to be yours alone. No cooperation of any sort is allowed. This problem set is governed by the GSU honor code. If you have any questions concerning the problem set, attend the chat session or send me questions via GSU email. I will hold a D2L chat session (see course calendar) during which I will answer any questions asked about the problems on this sheet. Please verify BEFORE the chat session class that you are able to enter the D2L chat room. The main rule of the chat room is that I type in CAPS and you type in lower case. NOTE: All questions are equally weighted. PART I: MULTIPLE CHOICE Choose the letter of the most correct answer for each question. 1. Assume that you have the following information on project A: (i) it will yield cash flows of $935 per year forever; (ii) the IRR is 12%; (iii) the required rate of return is 10.35%.What is the NPV of this project? a. $935,000,000 b. $1,282.45 c. $1,242.15 d. $1,397.65 e. Not enough information is provided 2. A cost that has already been paid, or the liability to pay has already been incurred, is a(n): a. salvage value expense. b. net working capital expense. c. sunk cost. d. opportunity cost. e. erosion cost. 3. The most valuable investment given up if an alternative investment is chosen is a(n): a. salvage value expense. b. net working capital expense. c. sunk cost. d. opportunity cost. e. erosion cost. 4. You are considering two independent projects with the following cash flows. The required return for both projects is 10%. Given this information, which one of the following statements is correct? a. You should accept project B since it has the higher IRR and reject project A because you cannot accept both projects. b. You should accept project A because it has the lower NPV and reject project B. c. You should accept project A because it has the higher NPV and you cannot accept both projects. d. You should accept project B because it has the higher IRR and reject project A. e. You should accept both projects if the funds are available to do so since both NPV's are > 0.
5. You are considering two independent projects both of which have been assigned a discount rate of 8%. Based on the profitability index, what is your recommendation concerning these projects? 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. c. You should accept both projects since both of their PIs are greater than 1. d. You should only accept project B since it has the largest PI and the PI exceeds 1. e. Neither project is acceptable. 6. Consider the following projects, for a firm using a discount rate of 10%: Project NPV IRR PI A $200,000 12.2% 1.04 B $200,001 11% 1.01 C $60,000 10.1% 1.61 D $(235,000) 9%.95 If the projects are mutually exclusive, which, if any, project(s) should the firm accept? a. Project A b. Project B c. Project D d. Projects B and D e. Projects A, B and C 7. Consider the following projects, for a firm using a discount rate of 10%: Project NPV IRR PI A $200,000 12.2% 1.04 B $200,001 11% 1.01 C $60,000 10.1% 1.61 D $(235,000) 9%.95 If the projects are independent, which, if any, project(s) should the firm accept? a. Project A b. Project B c. Project D d. Projects B and D e. Projects A, B and C
PART II: PROBLEMS Compute and record on the answer sheet a numerical answer for each of the problems in this section. Round return answers as percent values rounded to one decimal place (thus, record.0837 as 8.4%), round dollar answers to two decimal places (thus, record $2,342.36984 as $2,342.37), and enter any other answers as instructed in the question. As discussed in the instructions on the first page, you MUST attach pages to the answer sheets that show your worked out solutions for EVERY problem in this section. USE THE DATA BELOW TO ANSWER THE FOLLOWING 6 QUESTIONS Historical returns for stock G and the market portfolio are shown below (assume that the data provided below is the entire population of returns): Year Stock G Market Portfolio 1 22% 12% 2 34% 24% 3-13% 0% 4 44% 18% 5 0% -11% 6-23% 6% 7 11% 12% 8 18% 32% 8. What is the geometric mean return of Stock G over the time period in the chart? 9. What is the geometric mean return of the Market Portfolio over the time period in the chart? 10. What is the arithmetic mean return of Stock G over the time period in the chart? 11. What is the arithmetic mean return of the Market Portfolio over the time period in the chart? 12. What is the standard deviation of Stock G over the time period in the chart? 13. What is the standard deviation of the Market Portfolio over the time period in the chart? 14. What is the covariance between Stock G and the Market Portfolio over time period in the chart? 15. What is Stock G s beta coefficient over the time period in the chart? USE THE INFORMATION BELOW TO ANSWER THE FOLLOWING 2 QUESTIONS Stock X has an expected return of 14% and a standard deviation of 36%. Stock Y has an expected return of 18% and a standard deviation of 48%. The covariance between stock X and stock Y is 1250. Assume you create a portfolio made up of 35% of stock X and 65% of stock Y. 16. What is the expected return of your portfolio? 17. What is the standard deviation of returns of your portfolio? USE THE INFORMATION BELOW TO ANSWER THE FOLLOWING 2 QUESTIONS You hold a diversified portfolio consisting of 20 stocks. Ten of your stocks have a value of $10,000 each and the other ten stocks that you hold have a value of $20,000 each. Thus, the total value of your portfolio is (10)($10,000) + (10)($20,000) = $300,000. The current beta of your portfolio is 1.0 and the expected return on your portfolio (according to the CAPM) is 14.0%. The risk-free rate is 3%. The average beta of your ten stocks that each has a value of $10,000 is 0.7. You are considering selling one of your $10,000 stocks (this stock has a beta of 1.2) and one of your $20,000 stocks (this stock has a beta of 0.7). You then plan to take the proceeds from your sale (i.e., $30,000) and buy a stock with a beta of 2.5. 18. If you complete these transactions, what will be the beta of your new portfolio? 19. If you complete these transactions, what will be the expected return on your new portfolio?
20. Consider a project with the following cash flows: Year t = 0 t =1 t = 2 t = 3 t = 4??? $3,500 $12,500 $15,000 $15,000 The Payback Period of this project is 2.3 years. The appropriate discount rate is 11%. Find the Net Present Value of the project. (Note that the cash flow for t=0 is not provided to you that is, you must first solve for it with the information given in order to then find the NPV of this project). 21. Consider a project with the following cash flows: Year t = 0 t =1 t = 2 t = 3 t = 4 t = 5??? $4,000 $12,000 $15,000 $15,000 $18,000 The IRR of this project is 11.5% and the appropriate discount rate for the project is 15%. Find the Net Present Value of the project. (Note that the cash flow for t = 0 is not provided to you that is, you must first solve for it with the information given in order to then find the NPV of this project). 22. If the cost of capital for the project shown below is 2.5 percentage points less than the project s IRR (for example, if the project s IRR is 10%, the cost of capital is 7.5%), what is the NPV of the project? Year Cash Flow 0 ($210,000) 1 $40,000 2 $50,000 3 $60,000 4 $60,000 5 $70,000 6 $70,000 23. You are analyzing two mutually exclusive projects and have developed the following information. What is the incremental IRR between project A and project B? Note that the incremental IRR is the rate of return on the cash flows of (Project A Project B). USE THE INFORMATION BELOW TO ANSWER THE FOLLOWING 3 QUESTIONS Dexter, Inc. has 10 million shares of common stock outstanding and 120,000 bonds with an 8%, semiannually payable coupon and a par value of $1,000 each. The common stock currently sells for $40 per share and has a beta of 1.25. The bonds have 10 years remaining to maturity and sell for 90% of par value. The risk-free rate is 4%, the market risk premium is 8%, and the tax rate is 35%. 24. What is the debt weight (i.e., W d ) that Dexter should use to compute its WACC? 25. What is the equity weight (i.e., W e ) that Dexter should use to compute its WACC? 26. What is Dexter s WACC?
27. Margarite's Enterprises is considering a new project. The project will require $325,000 for new fixed assets, $160,000 for additional inventory and $35,000 for additional accounts receivable. Short-term debt is expected to increase by $100,000 and long-term debt is expected to increase by $300,000. The project has a 5-year life. The fixed assets will be depreciated straight-line to a zero book value over the life of the project. At the end of the project, the fixed assets can be sold for 25% of their original cost. The net working capital returns to its original level at the end of the project. The project is expected to generate annual sales of $554,000 and costs of $430,000. The tax rate is 35% and the required rate of return is 15%. Compute the project s NPV. USE THE INFORMATION BELOW TO ANSWER THE FOLLOWING 4 QUESTIONS Assume you are the Chief Financial Officer of Pepa Kola. The marketing department has presented you with a proposal to introduce a new soft drink. You have the following information: Cost of new plant and equipment = $35,000,000. The new plant will be built on land that the company already owns. The land was purchased five years ago for $4,000,000. The company was just offered $6,000,000 to sell the land. The plant and equipment will be depreciated on a straight line basis to a $5,000,000 salvage value over the 6 year estimated life of the project. The company plans to operate the plant for 6 years and then will sell the plant and equipment for $5,000,000. If the company decides to go forward with the project, the land will be sold (6 years from today) for $4,000,000 (this is in addition to the $5,000,000 for the sale of the plant and equipment). Annual sales of the new soft drink are projected to be $50,000,000 per year for each of the next 6 years; however, the company estimates that sales revenue from existing products will decrease by $5,000,000 per year. Incremental variable costs associated with the project are estimated to be $15,000,000 per year. The project will require an increase in current assets of $14,000,000 and an increase in current liabilities of $4,000,000. All working capital will be recovered at the end of the life of the project. Annual incremental interest expenses associated with the project will be $1,000,000 per year. The corporate tax rate is 40% and the appropriate discount rate for this project is 14%. 28. What is the initial cash flow (i.e., CF0) that should be used to evaluate this project? 29. What is the annual operating cash flow for year 1 for this project? 30. What is the final year non-operating cash flow for this project?