See document
Nanyang Business School CF—Final Exam The following test consists of 4 questions, worth 150 points. Answer to the questions to the best of your ability. This is an individual test. You may use any reference materials you like—lectures notes, assignments, assignment solutions, other course materials provided, your own notes, textbooks, notes from other courses, etc. You may also use a calculator or a computer with appropriate software to solve these questions. The one thing you may not use is the assistance of another person. If you are unsure of what the questions are asking you to do, you may ask the instructor. You should feel free to discuss general course concepts with other members of the class (or with anyone who is willing to talk about such things with you), but you should not discuss specific issues/questions related to this test with other members of the class or anyone else, until after the due date. (Please note that the exam is due before midnight, Singapore time, on the due date.) 1. [40 points] A firm has developed a COVID-19 vaccine. This vaccine is expected to be in demand for the next four years, after which there will be no demand. The vaccine may not be stored; if not sold in the year it is produced, the excess vaccine must be destroyed. In order to produce the vaccine, a factory must be opened. The factory may be opened at the beginning of Year 1 (i.e., now), or at the beginning of Years 2, 3, or 4 (if not already open). The cost of opening a factory is e200 million, at the time it is opened. Once opened, a factory must eventually be closed. Because of the complex chemicals and biological agents involved, closing the factory is a difficult and expensive operation, costing e150 million. If the factory is opened, it must be closed by the end of Year 4 (or earlier). Each year that the factory is open, a fixed operating cost (regardless of the amount of vaccine produced) of e400 million is incurred, paid at the end of each year of operation. If the factory is closed, it may be reopened, but the opening cost must be paid again (and also the closing cost, when it is closed for a second time). The price of the vaccine is fixed by regulation at e45. Initial demand is 10 million units the first year. In each subsequent year, the demand increases by 20%, or decreases by 10%, with equal probability. The revenues are received at the end of each year of production. Example—suppose the factory is opened immediately, operated for two years, and then closed. (This strategy is presented only to illustrate the cash flows; it is not an optimal strategy.) The cash flows are as shown below, occurring at the end of the indicated years. Year 0 Year 1 Year 2 Opening cost −e200 million — — Operating cost — −e400 million −e400 million Closing cost — — −e150 million Revenues — e450 million e540 million or e405 million Assume an appropriate discount rate for all cash flows is 12% per year. All applicable taxes are already included in the numbers given. Assume throughout that the firm’s objective is to maximise firm value; it does not pursue other objectives, such as making people healthy. 1(a). [10 points] Consider the strategy of opening the factory immediately, operating it for the next four years, and closing it at the end of Year 4. What is the NPV of this strategy? Is this strategy better than never opening a factory and never producing the vaccine? Final Exam 1 04 December 2020 Nanyang Technological University Nanyang Business School Executive Education CF—Corporate Finance Semester 1, AY 2020–2021 Prof. Robert L. Kimmel 1(b). [15 points] Assume now the firm pursues the optimal strategy, opening and closing the factory at the times and in the states that maximise firm value. What is the optimal strategy? Describe when and in what states the firm should open the factory, and when and in what states it should close the factory. What is the NPV of pursuing this strategy? How does the NPV of the optimal strategy compare to the NPV of the strategy from 1(a)? 1(c). [15 points] Now assume (contrary to the assumptions given) that demand for the vaccine each year after the first increases 40% or decreases 30%, with equal probability. How do your answers to 1(b) change? Describe the optimal strategy and its NPV under these alternate assumptions. 2. [40 points] There is a firm that has an all-equity capital structure, with 200 shares of stock outstanding. Based on your macroeconomic forecasts, the value of the firm one year from now will depend on the state of the macroeconomy, as shown in the following table. State Recession Stable Expansion Probability 0.25 0.50 0.25 Market Return −10% +10% +30% Firm Value $3, 380 $4, 056 $6, 084 Assume throughout that the CAPM describes the expected returns of all assets correctly. The risk-free rate is 4.00%. The above values are after any applicable corporate income tax is paid; assume that personal taxes on all forms of investment income are at the same rate. The firm has no plan to pay any dividend before next year. 2(a). [10 points] What is the present value of the firm’s equity, today? (Answer in aggregate, i.e., the value of all 200 outstanding shares, not the value of a single share.) As described above, the firm’s capital structure is currently 100% equity, with 200 shares of stock outstanding. However, the firm is considering selling some warrants. The sale of the warrants would have no immediate effect on the cash flows of the firm, since whatever cash is raised through the sale of the warrants, management plans to pay out to the equityholders as a one-time special dividend. However, the warrantholders have the right to exercise their warrants one year from now. For each warrant exercised, the warrantholder pays the firm $23.40, and firm gives the warrantholder a newly created share of stock. If the warrantholder chooses not to exercise the warrant one year from how, it expires worthless. The firm’s plan is to sell warrants for 100 additional shares. Assume the warrants have no effect on the amount of taxes paid. 2(b). [5 points] What is the value of a share in each of the three future states, if the warrantholders exercise their warrants? (Note—there are two effects. The warrantholders pay cash to the firm, and the number of outstanding shares increases.) In which (if any) of the three future states will the warrantholders want to exercise their warrants? 2(c). [10 points] What is the value of the warrants, today? (Note—value the warrants like you would value any other asset. Assume the warrantholders will exercise their warrants optimally, i.e., they will exercise when and only when the value they receive is greater than zero, the value they receive if they allow the warrants to expire.) 2(d). [10 points] What is the value of the existing equity, once the firm issues the warrants and pays out the special dividend? 2(e). [5 points] How does the value of the firm under the new capital structure (with 200 shares of equity and warrrants for 100 additional shares) compare to the value under the original capital structure (with only 200 shares of equity)? Does the change in capital structure increase the firm value, decrease the firm value, or leave it the same? Are the results consistent with Modigliani/Miller Proposition I? Explain briefly. 3. [40 points] Assume investors are risk-neutral, and the risk-free rate is 0.00%. The future (one year from now) values of the existing assets of a firm, and the NPV of a new project the firm is contemplating, are shown below. Final Exam 2 04 December 2020 Nanyang Technological University Nanyang Business School Executive Education CF—Corporate Finance Semester 1, AY 2020–2021 Prof. Robert L. Kimmel State A B Existing Assets £30, 940 £111, 384 NPV of New Project £3, 094 £6, 188 Management knows the true state of the firm (A or B), but has no way to credibly communicate the state to its investors, who assign probability 0.5 to each of the states. To undertake the new project, an investment of £15, 470 is needed, which the firm does not have—it would have to issue new securities to raise the necessary funds. The firm’s current capital structure consists of 1, 547 shares of equity, and £23, 205 face value of debt, which is due one year from now. Management’s objective is to maximise the welfare of its curent shareholders. 3(a). [15 points] Suppose investors believe the firm will issue equity to raise the necessary funds, and undertake the new project, in both states. If the firm issues new equity, how many new shares are needed to raise the necessary £15, 470? What should the price of these shares be? If management acts according to investor beliefs, is it maximising the welfare of its existing shareholders? 3(b). [15 points] Suppose investors believe the firm will issue equity to raise the necessary funds, and undertake the new project, only in State A. If the firm issues new equity, how many new shares are needed to raise the necessary £15, 470? What should the price of these shares be? If management acts according to investor beliefs, is it maximising the welfare of its existing shareholders? 3(c). [10 points] Is there an cost to asymmetric information in this scenario? Why or why not? Explain briefly. If there is, can the problem be resolved if the firm issues debt instead of equity? Does it matter what the priority of the debt is? Explain briefly. 4. [30 points] Assume the CAPM describes the expected returns of all assets correctly. The risk-free rate is 4%, and the expected return of the market is 12%. An all-equity firm has cash flows that are a perpetuity; each year, the firm generates a cash flow which has expected cash flow of S$4 million, after corporate income tax is paid. The beta coefficient of the firm’s equity is 0.75. The corporate tax rate is 33%. Personal tax rates on debt and equity are each 20%. 4(a). [5 points] What is the value of the firm’s equity? 4(b). [5 points] What is the WACC of the firm? Now suppose the firm issues S$10, 000, 000 market value of debt, and pays these funds to the shareholders (either through a special dividend, or by repurchasing shares). It is forecast that the debt will be risky, with a beta coefficient of 0.125. 4(c). [5 points] What is the value of the equity, after the recapitalisation is completed? 4(d). [10 points]