Its micro... explain every part

8. Overhaul of a production line generates the following incremental cash inflows over the line's 5-year remaining life. C1 C2 C3 CA C's Cash inflow ($ million) +1.5 +1.3 +1.05 +0.9 +0.75 (a) What is the PV of the inflows? The cost of capital is 12%. (b) Part (a) used a nominal discount rate and the cash inflows incorporated inflation. Redo Part (a) with real cash flows and a real discount rate. The forecasted inflation rate is 3% per year. 9. You have just inherited an office building. You expect the annual rental income (net of maintenance and other cost) for the building to be $100,000 for the next year and to increase at 5% per year indefinitely. A expanding internet company offers to rent the building at a fixed annual rent for 5 years. After year 5, you could re-negotiate or rent the building to another tenant. What is the minimum acceptable fixed rental payments for this five-year agreement? Use a discount rate of 12%. 10. Two dealers compete to sell you a new Hummer with a list price of $45,000. Dealer C offers to sell it for $40,000 cash. Dealer F offers "(-percent financing:" 48 monthly payments of $937.50. (48x937.50=45,000) (a) You can finance purchase by withdrawals from a money market fund yielding 2% per year. Which deal is better? (b) You always carry unpaid credit card balances charging interest at 15% per year. Which deal is better? 11. Your sales are $10 million this and expected to grow at 5% in real terms for the next three years. The appropriate nominal discount rate is 10%. The inflation is expected to be 2% per year during the same period. What is the present value of your sales revenue for the next three years? Fall 2008 Page 2 of 66 12. Company ABC's after-tax cash flow is $10 million (at the end of ) this year and expected to grow at 5% per year forever. The appropriate discount rate is 9%. What is the value of company ABC? 13. You own three oil wells in Vidalia, Texas. They are expected to produce 7,000 barrels next year in total, but production is declining by 6 percent every year after that. Fortunately, you have a contract fixing the selling price at $15 per barrel for the next 12 years. What is the present value of the revenues from the well during the remaining life of the contract? Assume a discount rate of 8 percent. 14. A geothermal power station produces cash flow at a current rate of $14 million per year, after maintenance, all operating expenses and taxes. All the cash flow is paid out to the power stations owners. The cash flow is expected to grow at the inflation rate, which is forecasted at 2% per year. The opportunity cost of capital is 8%, about 3 percentage points above the long-term Treasury rate. (Assume this is an annually compounded rate.) The power station will operate for a very long time. Assume for simplicity that it will last forever. (a) What is the present value of the power station? Assume the first cash flow is received one year hence (b) Now assume that the power stations cash flow is generated in a continuous stream, starting immediately. What is the present value?15. A foundation announces that it will be offering one MIT scholarship every year for an indefinite number of years. The first scholarship is to be offered exactly one year from now. When the scholarship is offered, the student will receive $20,000 annually for a period of four years, beginning from the date the scholarship is offered. This student is then expected to repay the principal amount received ($80,000) in 10 equal annual installments, interest-free, starting one year after the expiration of her scholarship. This implies that the foundation is really giving an interest-free loan under the guise of a scholarship. The current interest is 6% for all maturities and is expected to remain unchanged. (a) What is the PV of the first scholarship? (b) The foundation invests a lump sum to fund all future scholarships. Determine the size of the investment today. 16. You signed a rental lease for an office space in the Back Bay for five years with an annual rent of $1 million, paid at the beginning of each year of the lease. Just before you pay your first rent, the property owner wants to use the space for another purpose and proposes to buy back the lease from you. The rent for similar space is now $1.25 million per year. What would be the minimum compensation that you would ask from the property owner? Assume the interest rate to be 6%. Fall 2008 Page 3 of 66 17. The annual membership fee at your health club is $750 a year and is expected to increase at 5% per year. A life membership is $7,500 and the discount rate is 12%. In order to justify taking out the life membership, what would be your minimum life expectancy? 18. You are considering buying a car worth $30,000. The dealer, who is anxious to sell the car, offers you an attractive financing package. You have to make a down-payment of $3,500, and pay the rest over 5 years with annual payments. The dealer will charge you interest at a constant annual interest rate of 2%, which may be different from the market interest rate. (a) What is the annual payment to the dealer? (b) The dealer offers you a second option: you pay cash, but get a $2,500 rebate. Should you go for the loan or should you pay cash? Assume that the market annual interest rate is constant at 5%. Note: the tradeoff between the two options is that in the first case, you can finance your purchase at a relatively low rate of interest. In the second case, you receive a lump-sum cash rebate. 19. Your brother-in-law asks you to lend him $100,000 as a second mortgage on his vacation home. He promises to make level monthly payments for 10 years, 120 payments in all. You decide that a fair interest rate is 8% compounded annually. What should the monthly payment be on the $100,000 loan? 20. Your cousin is entering medical school next fall and asks you for financial help. He needs $65,000 each year for the first two years. After that, he is in residency for two years and will be able to pay you back $10,000 each year. Then he graduates and becomes a fully qualified doctor, and will be able to pay you $40,000 each year. He promises to pay you $40,000 for 5 years after he graduates. Are you taking a financial loss or gain by helping him out? Assume that the interest rate is 5% and that there is no risk. 21. You are awarded $500,000 in a lawsuit, payable immediately. The defendant makes a counteroffer of $50,000 per year for the first three years, starting at the end of the first year, followed by $60,000 per year for the next 10 years. Should you accept the offer if the discount rate is 12%? How about if the discount rate is 8%? 22. You are considering buying a Back Bay two-bedroom apartment for $800,000. You plan to make a $200,000 down payment and take a $600,000 30-year mortgage for the rest. The interest rate on the mortgage is 6% monthly APR. Payments are due at the end of every month. (a) What is the effective annual rate? (b) What is the monthly payment?23. 25. 2E. 21'. True, false or \"it depends" (give a brief explanation]: US. Treasury securities have no risk because they give sure payoffs at xed future dates. . A 10-year German government bond [bond] has face value of 10.000 and an annual coupon rate of 5%. Assume that interest rate [in euros] is equal to 0% per year. [a] What is the bond's PV? {b} Suppose instead that the bond paid interest semiannually like a US. bond. [The bond would pay .025 x 10,000 = 250 every I0 months} What is the PV in this case? You are considering buying a two bedroom apartment in Back Bay for $000,000. You plan to males a $100,000 down payment and take out a $500,000 30-year mortgage to: the rest. The interest rate on the mortgage is 8.5% monthly APR. [a] What is the effective annual rate [EAR]? [In] What is the manthly paymmlt? (c) How much do you owe the ban]: immediately after the 00th monthly payment? John is 30 years old at the beginning of the new millennium and is thinking about getting an MBA. John is currently making $40,000 per year and expects the same for the remainder of his working years (until age 65]. I f he goes to a business school, he gives up his income for two years and1 in addition, pays $20,000 per year for tuition. In return. John aspects an increase in his salary after his MBA is completed. Suppose that the post-graduation salary increases at a 5% per year and that the discount rate is 8%. What is miminum expected starting salary after graduation that males; going to a business school a positive-NPV investment for John? For simplicity, assume that all cash ows occur at the end of each year. After doing well in your nance classes, you landed a job at the IMF. Your salary is $1I1',I3I,0001 and your contract is for 5 years. Your salary will stay the same during the 5 years and, since you are at the IMF, you are not subject to taxes. If you do well [which we assume will happen with certainty}, you will get a permanent contract. Under this contract, your salary will grow at the rate of 3% per year, until retirement. Retirernent will occur in 30 years after your contract becomes permanent. For simplicity, assume that your salary is paid at the end of each year. In other words1 Fall 2003 Pass 5 of $5 encompass} seamen + 3%? 35 $100,{Il0[1 + 3%)SCI We assume that the interest rate is 4% (and will stay at 4% forever}. {a} What is the value of your human capital? That is, what is the PV (as of today] of all your future earnings? (b) Assume that you spend 70% of your salary, and deposit the remainder in a savings account1 which pays the rate 4%. How much money will you have in the sayings account just after you received your fth salary {end of year 5]? [You deposit only 30% of that salary in the savings account.) 28. Retirement planning: Mr. Jones is contemplating retirement. He is 55 and his net worth now is $2 million. He hopes that after retirement he can maintain a lifestyle that costs him $100,000 per year in today's dollars (i.e., real dollars, inflation adjusted). If he retires, he will invest all his net worth in government bonds that yield a safe annual return of 5%. Inflation is expected to be 2% per year. Ignore taxes. (a) Is Mr. Jones rich enough to retire today if he lives until (i) 80 (ii) 100 (iii) 115? (b) Mr. Jones thinks he will live until about 100. What advice will you give him about retiring? 29. Suppose you invest $50,000 for ten years at a nominal rate of 7.5% per year. If the annual inflation rate is 3% for the next ten years, what is the real value of your investment at the end of ten years? 30. Fill in the blanks. (a) ...... continuously compounded is equivalent to annual interest rate of 12%. (b) 5% continuously compounded is equivalent to annual interest rate of ......%. (c) .....% continuously compounded is equivalent to annual interest rate of 9%. 31. A 10-year U.S. Treasury bond with a face value of $10,000 pays a coupon of 5.5% (2.75% of face value every 6 months). The semi-annually compounded interest rate is 5.2 % (a 6-month discount rate of 5.2/2 = 2.6%). Fall 2008 Page 6 of 66 (a) What is the present value of the bond? (b) Generate a graph or table showing how the bond's present value changes for semi-annually compounded interest rate between 1% and 15%. 32. The Reborn VW Beetle. You are considering the purchase of a new car, the reborn VW Beetle, and you have been offered two different deals from two different dealers. Dealer A offers to sell you the car for $20,000, but allows you to put down $2,000 and pay back $18,000 over 36 months (fixed payment each month) at a rate of 8% compounded monthly. Dealer B offers to sell you the car for $19,500 but requires a down payment of $4,000 with repayment of the remaining $15,500 over 36 months at 10% compounded monthly. Which deal would you choose? (Hint: Find ranges of market interest rates that make one deal more attractive than the other.) 33. Dear Financial Adviser, My spouse and I are each 62 and hope to retire in 3 years. After retirement we will receive $5,000 per month after taxes from our employers pension plans and $1000 per month after taxes from Social Security. Unfortunately our monthly living expenses are $15,000. Our social obligations preclude further economies. We have $1,200,000 invested in a high-grade corporate-bond mutual fund. Unfortu nately the after-tax return on the fund has dropped to 3.5% per year. We plan to make annual withdrawals from the fund to cover the difference between our pension and social security income and our living expenses. How long will the money last? Sincerely, Luxury Challenged Marblehead, MA 34. The annually compounded discount rate is 5.5%. You are asked to calculate the present value of a 12-year annuity with payments of $50,000 per year. Calculate PV for each of the following cases. (a) The annuity payments arrive at one-year intervals. The first payment arrives one year from now. (b) The first payment arrives in 6 months. Following payments arrive at one-year intervals, at 18 months, 30 months, etc.34. The annually compounded discount rate is 5.5%. You are asked to calculate the present value of a 12-year annuity with payments of $50,000 per year. Calculate PV for each of the following cases. (a) The annuity payments arrive at one-year intervals. The first payment arrives one year from now. (b) The first payment arrives in 6 months. Following payments arrive at one-year intervals, at 18 months, 30 months, etc. 35. IRA Accounts and Taxes. An Individual Retirement Account (IRA) allows you to set aside a limited amount of money each year for retirement. These funds will have a special tax status that Fall 2008 Page 7 of 66 depends on several factors. (These factors include your marital status, whether you have other sources of retirement savings, your income, etc.) Suppose that you have $2,000 in pretax income to contribute to the IRA at the end of each year (starting with the end of the current year, i.e., year 1). You will retire in 30 years, and your marginal tax rate will be 28% for all years. Suppose that the account returns a fixed 6% each year until you retire. For simplicity, assume that you withdraw all money at your retirement, and any tax-deferred income is taxed at that time. (a) How much money will you have in year 30 if neither the contribution nor the in- terest income is tax-deferred? (In this case, you can withdraw the money without paying any additional tax at year 30.) (b) How much money will you have in 30 years if the contribution is not tax-deferred but the interest income is? (In this case, only the cumulative interest is taxed at year 30.) (c) How much money will you have in 30 years if both the contribution and the interest income are tax-deferred? (d) Would you expect the benefit of tax deferral to increase or decrease as the tax rate increases? Why