Time Value of Money
A Fun Finance Subject
A Critical Finance Subject
Ordinary Annuity: Annuity payments are made at the end of the time period
Annuity Due: Annuity payments are made at the beginning of the time period (e.g., insurance policy payment)
Perpetual Annuity: An annuity that lasts forever (e.g., $100 a year every year . . . forever).
1. You deposit $100 in a bank on January 1, 2000 and you want to find the value of that deposit January 1, 2001. If the interest rate is 5%, what is the future value of the deposit on January 1, 2001?
2. Assume you leave the interest and deposit untouched through January 1, 2002, what will the future value of your $100 deposit be on January 1, 2002?
3. Assume you leave the interest and deposit untouched, what will the future value of $100 be on January 1, 2010?
4. Assume you leave the interest and deposit untouched and the interest rate is 6%, rather than 5%, what will the future value of your $100 deposit be on January 1, 2010?
5. Refer to question 1: If the interest rate was compounded quarterly, what would be the future value of the deposit on January 1, 2001?
6. You loan your brother $1,000 at an annual interest rate of 7% for 3 years. If he pays you back along with the interest at the end of three years, how much will you receive?
7. You loan your sister $1,000 and she agrees to pay $2,000 back in 5 years as long as you stop setting her alarm for 4:00 a.m. in the morning. Assuming you stop this prank, what will be your annual rate of return on this loan to your sister?
8. You have $150,000 in a savings account earning 5% per year, but you know in two years you will have to withdraw $100,000 to buy an engagement ring. How much money will be in your account in three years?
9. You have $15,000 in cash. You expect inflation to equal 12 percent for the next 15 years. How much cash will you need in 15 years to equal the buying power of the current $15,000?
10. If the inflation rate is 8 percent per year for 5 years, determine how much purchasing power the dollar lost. Your answer should be given as a percentage.
11. If inflation is 8% annually for the next five years, how many dollars will be needed five years from now to maintain the same purchasing power that $100 has today?
12. A major business publication reported a 12% annual rate of inflation based on a recent 1% monthly increase in the CPI (consumer price index). What is the correct annual rate of increase?
13. You are on your cell phone talking to your roommate. Your roommate tells you that you just won a million dollars. After talking with your roommate, you go in and tell your boss what you really think of him and resign immediately. Because you resigned, you forgo the year end bonus of $10,000 which you were hoping to put in the stock market. When you arrived home, you find out that you won a million doll hairs, not dollars. If you would have received a 10% annual return on your stock market investment, how much would it have turned into in 40 years?
14. EMC Corporation filed a lawsuit against IBM. To settle the lawsuit, IBM offered $10,000,000 (today). If EMC continues the process, EMC management estimates winning and receiving $20,000,000 after all expenses. However, the funds would be received in 5 years. Using a required return of 14%, should EMC accept IBM's offer.
15. You notice that all your neighbors seem to need various items (e.g., tree limbs, construction debris) hauled away. You are thinking of buying a dump truck for $35,000. You estimate you could generate $10,000 a year cash flow (end of year) after paying for all expenses including hiring someone to drive the truck. The estimated life of the truck is 7 years with no salvage value. You would like an annual return of 12%. Should you buy the dump truck?
16. You would like to open a sports store. You are considering a franchise or your own, independent store. If you decide to own a store under the franchise system (e.g., Play it Again Sports), you will generate $5,000 a year more (end-of-year) for 15 years. The initial cost will be $60,000 more versus having your own, independent store. If you would like a 7% annual return, should you start a store under a franchise system or be independent?
17. You are on the Price is Right. You just won $100,000 (today). You are offered $300,000 to be paid in 12 years if you decline the $100,000 today. You would like a 12% annual return. What should you do?
18. You smoke a pack of cigarettes a day ($4). You decide to give up smoking and in its place chew gum ($1 a day habit). You will take the $3 extra daily cash flow and invest it at a 12% annual rate. How much additional money will you have in 30 years.Use a 360 day year.
19. You are three years old. Your older sister tells you, "if you jump out the third floor and land through the basketball hoop, I will give you $500." You would like to go to Disney World when you are old enough (6 years old). You were told that it will cost $600 for you to go to Disney World. If you expect to receive an annual return of 30%, will "making a basket" allow you to go to Disney World? Assume all injuries are paid for by your parents.
20. You tell your sister, "if you move out today, I will buy you a car valued at $10,000 when you turn 18." Your sister is 16 years old. If you receive a 10% annual return, how much money do you have to set aside today to be able to buy your sister a car when she is 18?
21. You have $150,000 in a savings account earning 5% per year, and you know in two years your fiancé/fiancée will pay you $100,000 to walk down the aisle. If you put all the money in your savings account, how much money will be in your account in three years?
22. If you loaned $1,000 to your Uncle Jean on January 1, 2000, another $1,000 to your Aunt Jean on January 1, 2001, and another $1,000 to your Cousin Jean on January 1, 2002, all at a 12% annual interest rate, how much cash will you receive if all three loans were to be paid back on January 1, 2003?
23. Your Aunt Jean will pay you $1,000 today if you promise to name your first born, Jean. Your Uncle Jean is sick of the name Jean and will pay you $2,000 if you don't name your first born, Jean; however, it will take him 4 years to give you the $2,000. If you would like an annual return of 15%, which Jean's offer should you accept?
24. Your ailing grandmother lives in Seattle. You could move her to your town at a cost of $12,000 or you could go visit her every year at a cost of $2,000 per year (end-of-year). If you expect your Grandma to live 8 more years and you like to obtain an annual return on your money of 14%, should you move grandma? You will not go to her funeral.
25. You have an offer to sell some real estate for $700,000 (immediate closing, January 1, 2000). You also have a $1,000,000 offer for that same real estate but the closing would be in 4 years (i.e., you would receive the $1 million on January 1, 2004). You need $700,000 now to go on the vacation of a lifetime. You can get a $700,000 loan for 10% annually. What should you do-- sell now or borrow the money and sell for $1 million?
26. Your rich aunt just offered you $100,000 to stop dating a specific person. Assume you can obtain a 9% annual return for the next 10 years. How much money will you have at the end of 10 years?
27. You bought a lot in a subdivision for $15,000 that you plan to sell in 15 years. You expect an annual growth rate of 12 percent. What is the expected value of the lot in the 15th year?
28. You just read in the paper that buying a home to rent out often generates no cash flow while holding the property; however, you make money because the home appreciates. If you buy a rental home for $70,000 at fair value and it appreciates at 3 percent per year, how much will the property be worth in 20 years. If you bought the rental home with a $20,000 downpayment and $50,000 mortgage and in 20 years the mortgage was paid off, what would be your annual return during the 20 year time period assuming there is no cash flow during the years of ownership?
29. You work for the Pharmaceutical Industry. You notice that people continue to go to Canada or go on-line to buy their medications from questionable suppliers. Your analysis indicates you could generate $50,000,000 more in cash flow per year (end of year) for the next five years if you ran a $300,000,000 ad campaign today. If the annual required return was 12%, would you recommend this advertising campaign?
30. You want to join the circus. You can be a clown on a donkey or you can be a clown on an elephant. Unfortunately, the elephant needs to be trained for a year before you start to get paid. The cost for either is $20,000 (today) including the training cost for the elephant. From today, the donkey and elephant will retire from show-biz in 10 years. If you can generate $30,000 a year of cash flow with the donkey and $33,000 a year of cash flow with the elephant, which should you buy? The positive cash flows are at the end of the year.Use a 10% discount rate.
31. You are dating two people, person A and person B, and would like to marry one of them. Person A should be able to make $50,000 per year (cash flow) for the next 30 years. Person B should be able to make $40,000 per year (cash flow) for 40 years. Using a discount rate of 6 percent, to which person should you propose first? Note: They have equal spending habits.
32. You are considering moving production overseas. To close down the plant, it would cost $1,000,000. However, you think the company could generate additional cash flow of $90,000 per year for 15 years. If you would like an annual return of 11%, should you close down the plant?
33. You are using outdated equipment in the plant that costs $10,000 per machine per year to maintain. You could buy new equipment at $40,000 per machine. The new machines would cost $2,000 per year to maintain. If both old and new machines have a remaining life of 10 years, should you replace the machines? You would like a 9% annual return.
34. Your rich aunt has given you $236,740. Unfortunately, she thinks that you are not mature enough to receive the money today, so the $236,740 will be given to you in 10 years. Assume a 9% discount rate. What is the value today? That is, what is the present value of the $236,740 gift?
35. What is the present value of the $236,740 if the discount rate is 7%?
36. You owe (interest free mortgage) $50,000, due in 3 years, to a company from whom you bought a warehouse. You can pay off the mortgage now or invest the money at 7.75%. How much would you be willing to offer the company if you were to pay off the mortgage today?
37. Your property taxes have just increased by $1,100 per year (payable at the end of the year). You make it a point to have the present value of the property taxes for the next three years set aside in an account. The account returns 6% annually. How much should be added to the account to assure that the property taxes for the next three years are paid?
38. Company A owes Company B $1,000 to be paid in 4 years. The annual rate of interest is 6%, paid annually. Company B wants to sell these streams of cash flows (interest payments plus the principal) to you. You would like an annual return of 8 percent. How much would you be willing to pay company B for these cash flow stream?
39. Question 38 follow-up-- If you would like an annual return of 6.5%, how much would you be willing to pay? What happens to the value of these cash flows?
40. You anticipate graduating in 4 years. Your parents have promised you a graduation gift of $10,000 four years from now. Alternatively, you can take $2,000 per year (end of year) for the next four years. Assuming a 9% discount rate, which alternative would you choose?
41. Solve question 40 using Future Value analysis. Would your answer change?
42. Today, January 1, 2003, you are thinking of buying the ice cream kiosk on the corner of Elm and Main for $30,000. Your required rate of return is 10 percent. At the end of year 3, the equipment will be obsolete (no value) and the city's laws are changing-- kiosks will be banned. Your projected annual net cash inflows from the investment are:
January 1, 2004: $ 8,000
January 1, 2005: $15,000
January 1, 2006: $18,000
Should you make this investment?
43. Ten years ago you bought shares of Ford Motor Company at $100 and today you sold the shares for $236.74. What was your annual rate of return (assume no dividends, no commissions)?
44. Fourteen years ago, you bought a Barry Bonds baseball card for 40 cents. You expect to sell the card next year for $3,000. What would be your annual rate of return?
45. Eleven years ago your parents put $5,000 in a bank account for your use today. Your deposit now has a current worth of $9,626.50. What was the annual interest rate?
46. ABC was considering buying a new machine. The old machine would be recycled (no cash received). The new machine would save the company $2000 in each of the first four years (end of year). If the machine costs $4000, lasts four years, and has no resale/disposal value, what will be the rate of return on this investment?
Year Savings PV at __% Present Value of Savings
1 $2000 X X
2 $2000 X X
3 $2000 X X
4 $2000 X X
47. Your salary was $12,000 in 1991 and 8 years later it is $36,700. If your percentage increase in your wages equals the annual inflation rate, what was the annual average inflation rate for the past 8 years?
48. Your client has just invested $30,000 for his one-year old daughter. He intends to use this fund for her college education 17 years from now. He estimates he will need $400,000 at that time. What annual rate of return will your client need to achieve?
49. You have a goal to obtain an annual rate of return of 25.99%. If you consistently reach your goal, how many years will it take to double your money?
50. Britney started with $1,000 and is now worth $10,314,478. Madonna started with $1,000 and is now worth $5,157,447.50. Both individuals net worth was generated totally from the original $1,000. Both individuals earned a 25.99% annual return. How long ago did Britney and Madonna start investing their $1,000?
51. You have $100,000 today. You expect an annual return 10 percent. You would like to retire when you are a millionaire. How many years will it take before you can retire?
52. The past five years you have been managing the family fortune that was left to you by your grandparents-- value $15,000,000 (5 years ago). Unfortunately, the assets have been decreasing at a rate of 8% per year. You promised your family that you would let someone else manage the assets if the investments ever fell to one-half the original value. If you keep losing money at 8% per year, how many years do you have left before you give up your money management position?
53. You are considering renovating an office building. You can leave the old toilets installed or replace them with efficient, 1.6 gallon toilets. The toilet will cost $300. You expect to save $30 per year in water bills if you buy the new toilet. Assuming you plan to own the building for 15 more years, what would be your annual return? Assume the building would sell for the same price regardless of which toilet is installed.
54. You just won the lottery. You will receive $10,000 per year for the next 20 years beginning in 12 months. Using an 8% discount rate, what is the present value of your lottery winnings?
55. Assume you are just starting an MBA program that will take one year to complete. You read that an MBA will earn you about $6,000 per year (ordinary annuity) more than just an undergraduate degree. Using a discount rate of 8.5%, what is the value today of the extra income if you decide to work 44 years after receiving your MBA?
56.1 + 1 = X
57. You can subscribe to an investment newsletter for $8.50 per year (annuity due) or $200 for a lifetime membership. Assume you will live 50 more years. You could invest at a 7.5% return. Which subscription method should you use?
58. What would be the present value of an $8.50 perpetual annuity discounted at 5%?
59. On a timeline, the present value is always ______the future value.
60. You and your partner have been knocking heads the last five years so you want to sell your portion of the business to her. She has offered you two choices: 1) $6000 a month for the next 3 years or 2) $140,000 today. Which offer would you choose? Use an annual discount rate of 24%.
61. When you retire, you want to receive an annuity of $800,000 (you are planning on having fun during your retirement years) at the end of each year for 10 years. The interest rate is 8 percent. How much must you have saved when you retire?