Unformatted text preview: FIN20150 Chapter 4 and Mid‐Term #1 Review Document 1) A generous relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $3,000. Each year after that, you will receive a payment on the anniversary of the last payment that is 5% larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is 10% per year. a. What is today's value of the bequest? b. What is the value of the bequest immediately after the first payment is made? 2) You are thinking about buying a piece of art that costs $50,000. The art dealer is proposing the following deal: He will lend you the money, and you will repay the loan by making the same payment every two years for the next 20 years (i.e., a total of 10 payments). If the two‐year rate of interest is 12.36%, how much will you have to pay every two years? Assume your first payment is due two years from today. 3) You figure that the total cost of college will be $108,000 per year 18 years from today. If your discount rate is 4% compounded annually, what is the present value today of four years of college costs starting 18 years from today? 4) Assume you can earn 8.5% per year on your investments. a. If you invest $140,000 for retirement at age 30, how much will you have 35 years later for retirement? b. If you wait until age 40 to invest the $140,000 , how much will you have 25 years later for retirement? c. Why is the difference so large? 5) When Alfred Nobel died, he left the majority of his estate to fund five prizes, each to be awarded annually in perpetuity starting one year after he died (the sixth one, in economics, was added later). a. If he wanted the cash award of each of the five prizes to be $55,000 and his estate could earn 9% per year, how much would he need to fund his prizes? b. If he wanted the value of each prize to grow by 6% per year (perhaps to keep up with inflation), how much would he need to leave? Assume that the first amount was still $55,000. c. His heirs were surprised by his will and fought it. If they had been able to keep the amount of money you calculated in (b), and had invested it at 9% per year, how much would they have in 2014, 118 years after his death? 6) A rich aunt has promised you $2,000 one year from today. In addition, each year after that, she has promised you a payment (on the anniversary of the last payment) that is 2% larger than the last payment. She will continue to show this generosity for 20 years, giving a total of 20 payments. If the interest rate is 9%, what is her promise worth today? 7) Assume that your parents wanted to have $180,000 saved for college by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 6.0% per year on their investments. a. How much would they have to save each year to reach their goal? b. If they think you will take five years instead of four to graduate and decide to have $220,000 saved just in case, how much would they have to save each year to reach their new goal? 8) What is the present value of $9,000 paid at the end of each of the next 74 years if the interest rate is 10% per year? 9) You have decided to buy a perpetual bond. The bond makes one payment at the end of every year forever and has an interest rate of 8%. If the bond initially costs $4,000, what is the payment every year? 10) You want to endow a scholarship that will pay $7,000 per year forever, starting one year from now. If the school's endowment discount rate is 9%, what amount must you donate to endow the scholarship? How would your answer change if you endow it now, but it makes the first award to a student 10 years from today? 11) You plan to deposit $700 in a bank account now and $200 at the end of the year. If the account earns 6% interest per year, what will be the balance in the account right after you make the second deposit? 12) You have just taken out a five‐year loan from a bank to buy an engagement ring. The ring costs $6,200. You plan to put down $1,200 and borrow $5,000. You will need to make annual payments of $1,100 at the end of each year. Show the timeline of the loan from your perspective. How would the timeline differ if you created it from the bank's perspective? 13) Suppose you receive $130 at the end of each year for the next three years. a. If the interest rate is 6%, what is the present value of these cash flows? b. What is the future value in three years of the present value you computed in (a)? c. Suppose you deposit the cash flows in a bank account that pays 6% interest per year. What is the balance in the account at the end of each of the next three years (after your deposit is made)? How does the final bank balance compare with your answer in (b)? 14) You have an investment account that started with $3,000 10 years ago and which now has grown to $5,000. a. What annual rate of return have you earned (you have made no additional contributions to the account)? b. If the investment account earns 13% per year from now on, what will the account's value be 10 years from now? 15) The British government has a consol bond outstanding that makes a ₤1,500 coupon payment each year forever. Assume that the current interest rate in Great Britain is 6% per year, compounded annually. If you will receive your first coupon payment tomorrow, what is the value of the consol bond today? 16) Kamps4Kids LLC is considering purchasing a parcel of wilderness land near a popular historic site. This land will cost Kamps4Kids $750,000 today and it will take two years to obtain the necessary permits to operate wilderness campsites on this land. After the permits are obtained, Kamps4Kids expects to make $66,000 at the end of every year indefinitely starting in the third year (at time t=3). Assume that the appropriate discount rate is 6% per year, compounded annually. What is the Net Present Value (NPV) of this investment (Present Value of all project cash flows)? Do the benefits outweigh the costs? 17) You purchase a home that costs $450,000. You have $90,000 in cash that you will use as a down payment. The bank is offering a 30‐year mortgage that requires annual payments and has an interest rate of 5% per year compounded annually. Payments are due at the end of the year. a. What is the initial loan amount? b. What is your annual mortgage payment? c. What if, instead of buying the house, you decided the better alternative was to use the $90,000 you have saved and simply pay cash for a condo. Instead of making annual mortgage payments to the bank, you make the exact same annual payments, at the exact same times, into a retirement account earning the same 5%. At the end of 30 years, how much money will you have in your retirement account? 18) After a long and successful career in business, you are feeling quite charitable and are considering making a donation to your alma mater. After speaking with the university’s development office, you learn that the business school is trying to endow a new professorship position. The initial salary for someone in this role would be $125,000 and the university expects the salary to increase by 2% per year. Assume the salary is paid annually in one lump sum and the first payment is in one year. If the university expects to earn an interest rate of 10% on its investments, how much would your donation need to be in order to endow the professorship? 19) A bank is offering the following investment opportunity. If you deposit $15,000 today, the bank will repay you $27,500 in ten years. What is the internal rate of return (IRR) on this investment? In other words, what is the interest rate that is being implied by the combination of the initial cash flow today and the payout in 10 years? 20) After speaking with your financial advisor, you have put together a plan to save for retirement. You have decided to start investing in a retirement account. At the end of this year, you plan on depositing $5,000 in this account. You feel that, as your salary grows, you will be able to increase your annual contribution by 4% each year. You just turned 25 and hope to retire at 60. a. If your financial advisor tells you to expect investment returns of 8%, how much money can you expect to have in your account when you turn 60? b. Fast forward 25 years. You have just turned 50 and are evaluating your financial situation. You have been disciplined and have made your payments, as scheduled, and have increased your deposits by 4% annually as you had planned. However, it turns out your financial advisor was a bit optimistic and you have only experienced returns of 7% over the course of your retirement savings. How much money is in your account? c. You still want to retire at age 60. However, you live a simpler lifestyle than you had anticipated and feel you would be comfortable retiring with $1,250,000 in your retirement account at age 60 (instead of your original goal from part A). How much would you have to deposit each year for the next 10 years in order to reach your new retirement goal? Assume investment returns will be 7%. Additionally, assume you will no longer be increasing your payments, but rather will be making constant annual payments. d. Suppose you cannot afford to make the payments from part C. You can, however, afford to make annual payments of $20,000 until you reach your goal of having saved $1,250,000. How many years past your initial planned retirement age of 60 will you need to continue making annual contributions in order to reach this goal? Prior assumptions from part C are still valid. ...
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 Spring '11
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