PROBLEM # 1 (6 points): You have just turned 22, and you intend to start saving for your retirement. You plan to retire in 43 years when you turn 65. During your retirement you would like to have an annual income of $120,000 per year for the next 26 years (until age 91). a) Calculate how much you need to have in your account before the first withdrawal at age 66. (3 points) b) Calculate how much you would have to save annually between now and age 65 in order to finance your retirement income and to fill that account. (3 points) Make the following assumptions: Assume that the relevant compounded interest rate is 4 percent for all 69 years. You make the first payment today and the last payment on the day you turn 65. You make the first withdrawal when you turn 66 and the last withdrawal when you turn 91. PROBLEM # 2 (5 points): You just took a $315,000, 30-year loan. Payments at the end of each month are flat (equal in every month) at an annual interest rate of 3.75 percent. a) Calculate the monthly payment. (2 point) b) Provide the appropriate loan table, showing the breakdown in each month between principal repayment and interest. (3 points) FIN 3414 Spring 2019 3 PROBLEM # 3 (9 points): You are offered an asset that costs $14,000 and has cash flows as indicated below at the end of each quarter for the next 8 years. Then it will be sold for $2,500. Your cost of capital is 6.5 percent. An alternative (mutually exclusive) project is available which offers a net present value (NPV) of $5,000, an internal rate of return (IRR) of 6.0%, a profitability index (PI) of 0.98, and a profitability index (NPI) of 0.11. Year 1: $800 each quarter Year 2: $850 each quarter Year 3: $850 each quarter Year 4: $950 each quarter Year 5: $800 each quarter Year 6: $600 each quarter Year 7: $500 each quarter Year 8: $400 each quarter a) What is the IRR of the asset? (2 points) b) What is the NPV of the asset? (2 point) c) What are the profitability index (PI) and net profitability index (NPI) of the asset? (1 point) d) Should you purchase it? Base your answer on your solutions to parts a through c and explain why. (2 points) e) Compared to the alternative project, is this a more attractive opportunity? Why? (2 points)