### Fnce451 Midterm

Midterm Exam – October 17, 2012 SOLUTIONS Instructions: 1. Read the questions carefully. 2. Answer all questions on the following pages. 3. A financial calculator and a regular calculator are permitted. 4. A one-sided 8. 5” x 11” formula sheet is permitted with formulas only. 5. The midterm has 11 pages, including 2 blank pages. 6. For Part 2, show all your work. 7. Midterm duration: 75 minutes. 8. Mark allocation: Shown on exam. Print your name: _________________________________________ Sign your name: __________________________________________ Student Number: __________________________________________

Good Luck!!! Part 1: Multiple Choice Part 2: Short Answer and Problems Question 1 Question 2 Question 3 Question 4 Total /20 /4 /5 /10 /16 /55 1 Part 1 [2 points each = 20 points]: Multiple Choice. Circle the BEST answer. 1. The Double Dip Co. is expecting its ice cream sales to decline due to the increased interest in healthy eating. Thus, the company has announced that it will be reducing its annual dividend by 5% a year for the next two years. After that, it will maintain a constant dividend of $1 a share. Two weeks ago, the company paid a dividend of $1. 0 per share. What is this stock worth if you require a 9% rate of return? A. $10. 86 B. $11. 11 C. $11. 64 D. $12. 98 E. $14. 23 2. The value of common stock today depends on: A. The expected future holding period and the discount rate. B. The expected future dividends and the capital gains. C. The expected future dividends, capital gains and the discount rate. D. The expected future holding period and capital gains. E. None of the above. 3. The tax shield on CCA is calculated by: A. The quantity (1-Tc) multiplied by CCA. B. Revenues less expenses less CCA. C.

The quantity (Revenues-Expenses) multiplied by CCA. D. Revenues less expenses less taxes. E. None of the above. 4. If the project beta-IRR co-ordinates plot above the SML, the project should be: A. Accepted because it is overvalued. B. Accepted because it is undervalued. C. Rejected because it is overvalued. D. Rejected because it is undervalued. E. None of the above. 5. The opportunity set of portfolios is: A. All possible return combinations of those securities. B. All possible risk combinations of those securities. C. All possible risk-return combinations of those securities.

D. The best or highest risk-return combination. E. The lowest risk-return combination. 2 6. The combination of the efficient set of portfolios with a riskless lending and borrowing rate results in: A. The capital market line which shows that all investors will only invest in the riskless asset. B. The capital market line which shows that all investors will invest in a combination of the riskless asset and the tangency portfolio. C. The security market line which shows that all investors will invest in the riskless asset only. D.

The security market line which shows that all investors will invest in a combination of the riskless asset and the tangency portfolio. E. None of the above. 7. Stock A has an expected return of 20%, and stock B has an expected return of 4%. However, the risk of stock A as measured by its variance is 3 times that of stock B. If the two stocks are combined equally in a portfolio, what would be the portfolio’s expected return? A. 20. 0%. B. 4. 0%. . C. 12. 0%. D. Greater than 20%. E. Need more information to answer. 8. Two mutually exclusive investment opportunities require an initial investment of $8 million.

Investment A then generates $1 million per year in perpetuity, while investment B pays $500,000 in the first year, with cash flows increasing by 5% per year thereafter. Determine the NPV for which an investor would regard both opportunities as being equivalent. A. ?$1 million B. $0 C. $1 million D. $2 million E. $8 million 9. When comparing two projects with different lives, why do you compute an annuity with an equivalent present value (PV) to the net present value (NPV)? A. So that you can see which project has the greatest net present value (NPV). B.

So that the projects can be compared on their cost or value created per year. C. To reduce the danger that changes in the estimate of the discount rate will lead to choosing the project with a shorter time frame. D. To ensure that cash flows from the project with a longer life that occur after the project with the shorter life has ended are considered. E. To avoid complications arising from alternating cash inflows and outflows. 3 10. A firm is considering changing their credit terms. It is estimated that this change would result in sales increasing by $1,000,000.

This in turn would cause inventory to increase by $150,000, accounts receivable to increase by $100,000, and accounts payable to increase by $75,000. What is the firm’s expected change in net working capital? A. $1,175,000 B. $325,000 C. $250,000 D. $175,000 E. $150,000 4 Part 2 [35 points]: Short Answer and Problems. Please show all your work. Question 1 [4 points]: When two stocks have a correlation of ? 1, is it always possible to construct a portfolio with 0 standard deviation? If so, what is the weight (denoted as ? ) that always ensures that the portfolio has 0 standard deviation? Answer: Yes. 1 point) We can show this by substituting correlation of ? 1 in the portfolio variance formula: ? p2 = ? 2? 12 + (1 ? ?)2? 22 + 2? (1 ? ?)? 1,2? 1? 2 which gives, ? p2 = ? 2? 12 + (1 ? ?)2? 22 + 2? (1 ? ?)(? 1)? 1? 2 = [?? 1 ? (1 ? ?)? 2]2 (1 point for setting up the problem with the variance formula) We are interested in the standard deviation, which is the square root of the above variance. By choosing ? so that [?? 1 ? (1 ? ?)? 2] = 0 we get ? = ? 2/(? 1 + ? 2) and thus we can always ensure the portfolio has 0 standard deviation. (2 points: 1 point for setting the standard deviation equal to zero to solve for ? and 1 point for final answer) 5 Question 2 [5 points]: Storico Co. just paid a dividend of $3. 50 per share. The company will increase its dividend by 20 percent next year and will then reduce its dividend growth rate by 5 percentage points per year until it reaches the industry average of 5 percent dividend growth, after which the company will keep a constant growth rate, forever. If the required return on Storico stock is 13 percent, what will a share of stock sell for today? Answer: Here we have a stock with differential growth, where the dividend growth changes every year for the first four years.

We can find the price of the stock in Year 3 since the dividend growth rate is constant after the third dividend. The price of the stock in Year 3 will be the dividend in Year 4, divided by the required return minus the constant dividend growth rate. So, the price in Year 3 will be: P3 = $3. 50(1. 20)(1. 15)(1. 10)(1. 05) / (. 13 – . 05) = $69. 73 (2 points: 1 point for set up and 1 point for answer) The price of the stock today will be the PV of the first three dividends, plus the PV of the stock price in Year 3, so: P0 = $3. 50(1. 20)/(1. 13) + $3. 50(1. 20)(1. 15)/1. 132 + $3. 50(1. 20)(1. 15)(1. 0)/1. 133 + $69. 73/1. 133 (2 points for set up) P0 = $59. 51 (1 point) 6 Question 3 [10 points]: The expected return of the S&P 500, which you can assume is the market portfolio, is 16% and has a standard deviation of 25% per year. The expected return of Microsoft is unknown, but it has a standard deviation of 20% per year and a covariance with the S&P 500 of 0. 10. The risk-free rate is 6 percent per year. a. [2 points] Compute Microsoft’s beta. Answer: ? Microsoft = Cov(RMicrosoft, RM) / var(RM) ? Microsoft = 0. 10 / (0. 25)2 = 1. 60 (2 points: 1 point for set up and 1 point for final answer) . [2 points] What is Microsoft’s expected return given the beta computed in part (a)? We know from the CAPM: E(R) = Rf + ? (E(RM) – Rf) Therefore, E(RMicrosoft) = 0. 06 + (1. 60)(0. 16? 0. 06) = 0. 220 or 22. 0% (2 points: 1 point for set up and 1 point for final answer) c. [2 points] If Intel has half the expected return of Microsoft, then what is Intel’s beta? From the CAPM, we can solve for ? : E(R) = Rf + ? (E(RM) – Rf) 0. 11 = 0. 06 + ? Intel(0. 16 – 0. 06) ? Intel = 0. 50 (2 points: 1 point for set up and 1 point for final answer) 7 d. [2 points] What is the beta of the following portfolio? . 25 weight in Microsoft; 0. 10 weight in Intel; 0. 75 weight in the S&P 500; ? 0. 20 weight in GM (where ? GM = 0. 80); 0. 10 weight in the risk-free asset. Answer: The beta of the portfolio is the weighted average of the betas of the assets that comprise the portfolio: ? P = (0. 25)(1. 60) + (0. 10)(0. 50) + (0. 75)(1. 0) + (? 0. 20)(0. 80) + (0. 10)(0) = 1. 04 (2 points: 1 point for set up and 1 point for final answer) e. [2 points] What is the expected return of the portfolio in part (d)? Answer: From the CAPM, we can solve for E(RP) E(RP) = Rf + ? E(RM) – Rf) = 0. 06 + (1. 04)(0. 16 – 0. 06) = 0. 164 or 16. 4% (2 points: 1 point for set up and 1 point for final answer) 8 Question 4 [16 points]: Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $6 million. Ignore the CCA system and assume that the equipment will be depreciated straight-line over 5 years to a value of zero, but in fact it can be sold after 5 years for $500,000. The firm believes that working capital at each date must be maintained at a level of 10 percent of next year’s (i. e. he following year’s) forecast sales. The firm estimates production costs equal to $1. 50 per trap and believes that the traps can be sold for $4 each. Sales forecasts are given in the following table below. The project will come to an end in five years, when the trap becomes technologically obsolete. The firm’s tax bracket is 35 percent, and the required rate of return on the project is 12 percent. What is project NPV? Year Sales (millions of traps) 0 0 1 0. 5 2 0. 6 3 1. 0 4 1. 0 5 0. 6 Thereafter 0 Answer: YEAR: Sales (traps) Revenue ($4. 00 ? Sales) Expense ($1. 50 ?

Sales) Working capital Change in Wk Cap CF from Operations: Revenue Expense Depreciation Pretax profit Tax After-tax profit CF from operations Cash Flow CF: capital investments CF from working capital CF from operations Total CF PV @ 12% Net present value 0 0. 00 0. 00 0. 00 0. 20 0. 20 1 0. 50 2. 00 0. 75 0. 24 0. 04 2 0. 60 2. 40 0. 90 0. 40 0. 16 3 1. 00 4. 00 1. 50 0. 40 0. 00 4 1. 00 4. 00 1. 50 0. 24 –0. 16 5 0. 60 2. 40 0. 90 0. 00 –0. 24 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 2. 0000 0. 7500 1. 2000 0. 0500 0. 0175 0. 0325 1. 2325 2. 400 0. 900 1. 200 0. 300 0. 05 0. 195 1. 3950 4. 000 1. 500 1. 200 1. 300 0. 455 0. 845 2. 0450 4. 000 1. 500 1. 200 1. 300 0. 455 0. 845 2. 0450 2. 400 0. 900 1. 200 0. 300 0. 105 0. 195 1. 3950 (5 points) –6. 00 –0. 20 0. 00 –6. 20 –6. 20 –0. 1817 0. 0000 –0. 0400 1. 2325 1. 1925 1. 0647 0. 0000 –0. 1600 1. 3950 1. 2350 0. 9845 0. 0000 0. 0000 2. 0450 2. 0450 1. 4556 0. 0000 0. 1600 2. 0450 2. 2050 1. 4013 0. 3250 0. 2400 1. 3950 1. 9600 1. 1122 (2 points) (6 points) (3 points) 9 This page is left blank on purpose. Use it if you need it. 10 This page is left blank on purpose. Use it if you need it. 11