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1. You graduated from Haas and have started working at your dream job. You also just turned 30 years old and expect to work until you turn 65 (so for 35 years) and then be retired for 25 years (until you turn 90). Your pre-tax starting salary, which is paid at the end of the year (i.e., when you turn 31) is $130k. You expect your salary to grow at a constant rate of 3% per year until retirement. The (before-tax) nominal interest rate for borrowing or lending is 4% and the tax rate on both income and interest is 35%. (a) What is the present value of your lifetime after-tax earnings? (b) Suppose you want to consume a constant amount (in nominal terms), at the end of each year, throughout the rest of your life (so for 60 years, starting next year). How much should you consume each year? Are you saving or borrowing in your rst year? (Hint: the present value of your consumption plan should be the same as your answer to part(a).) (c) Upon second thought, you decide that a better strategy is to consume a constant amount, at the end of each year, in real terms throughout your life. You expect inflation to remain constant at 1.5% per year. How much can you consume each year in real terms? Are you saving or borrowing in your first year? (Hint: the present value of your consumption plan should still be the same as your answer to part (a).) (d) After a bit more thinking, you decide it would be nice to leave some money to your children in your will. Suppose you decide to bequeath an amount of $1M in real terms at the end of your life (i.e., the nominal amount of your bequeathment in 60 years has the same purchasing power as $1M does today, you can ignore estate taxes). What is the present value of your bequeathment? Redo your answer to part (c) given your newfound generosity. 2. You are the CFO of a toy company that is considering launching a new line of toys. Your financial analysts have put together the following projections. Sales from the new line are expected to be $35M at t = 1; 2, and 3 after which the new line will be discontinued. Cost of goods sold (COGS) are forecasted to be 28% of Sales. The new line of toys will require additional sales associates, whose salaries are projected to be 12% of Sales. An advertising campaign for the new line of toys is expected to cost $4M at t = 1 and $4M at t = 2. Each toy takes on average 6 months to sell. Therefore, Inventory is forecasted to be 50% of next year's COGS. The company does not sell toys to customers on credit. However, it pays its suppliers of materials after 60 days. Therefore, Accounts Payable is forecasted to be 17% of next year's COGS. Launching the new line of toys will require a capital expenditure in new equipment of $50M at t = 0. The equipment will be straight-line depreciated for tax purposes over 5 years to a salvage value of zero. At t = 3, the equipment will be sold for $15M. The asset beta for the new line of toys is estimated to be A = 1:6. The current risk-free rate is 3% (assume the yield curve is at) and the market risk premium is 5%. The toy company is 100% equity financed and faces a corporate tax rate of 35%. (a) What is an appropriate discount rate for the free cash flows from the project? (b) What are the free cash flows associated with the new line of toys. To answer this question, please complete the table in the LQ2 tab of the excel le (if you are submitting a handwritten exam, please also complete the table on the next page). (c) What is the NPV of the project? What is the IRR? For what discount rates does the project have a positive NPV? 7 3. You have the following information about stock Q and the market portfolio M. Stock Q Market Portfolio (M) Expected return ? 10% Standard deviation 40% 20% The correlation between stock Q and the market portfolio is Q;M = 0:6. The risk-free rate is 3%. For parts (a)-(c) of this question, you should assume that the CAPM holds. (a) What is the beta of Stock Q? What is the expected return of Stock Q according to the CAPM? (b) Suppose you decide to invest in a portfolio that consists of 20% in stock Q, 50% in the market portfolio and 30% in the risk-free asset. (i) What is the beta of this portfolio? (ii) What is the expected return of this portfolio? (iii) What is the standard deviation of this portfolio? (c) Instead of holding the portfolio described in part (b), you decide to find a portfolio with the same expected return as the portfolio in part (b) but with the lowest possible standard deviation. What are the optimal portfolio weights in Q, M, and the risk-free asset? What is the Sharpe ratio of this portfolio? Now suppose that the CAPM does not hold and Stock Q has a positive = 2:5%. (d) Is the Sharpe ratio of the MVE portfolio of Q and M higher or lower than the portfolio you computed in part (c)? Explain why. (e) If other investors can also easily identify Stock Q as having positive, would you expect the positive to persist? Explain why or why not? 4. Hewlett-Packard (HPQ) consists of two divisions: The Personal Systems division and the Enterprise Services division. The Personal Systems division is considering the possibility of launching a new line of 3D printers. The expected (after-tax) free cash flows from the project are given below. Date 0 1 2 3 Free Cash Flow (in $M) -100 45 45 45 HPQ's leverage policy is to maintain a constant debt-to-equity ratio of 1/4, which it achieves by rebalancing the amount of debt outstanding annually. It has a debt beta ( D) equal to 0.2 and an equity beta ( E) equal to 1.6. Two of HPQ's competitors, Canon Inc (CAJ) and Xerox Corporation (XRX), operate exclusively in Personal Systems. You have the following information about these two rms. CAJ XRX Debt (D, in $B) 10 2 Equity (E, in $B) 40 18 Debt Beta ( D) 0.2 0.1 Equity Beta ( E) 2.1 1.9 HPQ's corporate tax rate is 35%. The risk-free rate is 4%. The market risk premium is 5%. (a) Estimate the unlevered cost of capital (i.e., E(rA)) for the new line of 3D printers. (c) Given HPQ's leverage policy, what is an appropriate weighted average cost of capital for the new line of 3D printers? For simplicity, you can assume that HPQ's debt beta (and therefore its debt cost of capital) will not change if the project is undertaken. What is the NPV of the new line of 3D printers? How much of this value is due to the debt tax shield? (d) Suppose that HPQ decides to invest in the new line of 3D printers. How much additional debt should it issue at t = 0 to maintain its desired debt-to-equity ratio? (e) Suppose that instead of maintaining a constant debt-to-equity ratio for this project, HPQ decides to use a leverage policy in which the interest paid at dates 1, 2 and 3 is equal 10% of the free cash ow in that date. What is the NPV of the project under this alternative leverage policy? (Hint: it will be easier to use APV rather than WACC).