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Present Value and Future Value Formulas Future Value (single period) Value n = Value 0 *(1 + r ) n or Value n = Value 0 * FVFn (1 + r ) n - 1 Future Value (annuity) Value n = CFannuity * or Value n = CFannuity * FVFannuity r 1 Present Value (single period) Value 0 = Value n * or Value 0 = Value n * PVFn (1 + r ) n 1 1- (1 + r ) n Present Value (annuity) Value 0 = CFannuity * or Value 0 = CFannuity * PVFannuity r Assumption of Cash Flows Deferred basis: The cash flows are assumed to take place at the end of the year. Almost all present value and future value tables that you will ever see are on a deferred basis. Due basis: The cash flows are assumed to take place at the beginning of the year. Remember: The annuity present value table simply sums up the values from the single period table. When working a time value of money problem, ask yourself two questions: 1. What is the unknown - the value today (Value0) or the value in the future (Value n)? If the unknown is the value today, then the problem is a present value type of problem. If the unknown is the value in the future, the problem is a future value type of problem. 2. Is there an annuity involved? An annuity is defined as a fixed amount of money in consecutive periods. If no annuity is involved, you will use the single period tables (or formulas). Time Value of Money Page 2 Problems: (Some may be worked with the tables; others must be worked with a calculator that has a yx function.) 1. If you have 100 rabbits now that are growing at a rate of 10% a year, how many rabbits will you have three years from now? The unknown amount lies in the future, therefore the problem is a future value problem. There is no annuity involved, so it is a single period type of problem. Therefore, the appropriate formula is: Value n = Value 0 *(1 + r) n = 100 * (1 + 010) 3 . . = 100 * 1331 . = 1331 rabbits (Assuming that you can have 1/10 of a rabbit!) 2. If you have $100 in the bank now that is growing at a rate of 4% a year, how many dollars will you have in the bank 10 years from now? Value n = Value 0 * (1 + r ) n = $ 100 * (1+.04) 10 . = $ 100 * 1480 = $ 148.00 3. A company currently pays a dividend of $10.00 per share. Determine how much the company’s dividend will be in 10 years, assuming a 5% annual rate of growth. Value n = Value 0 * (1 + r) n = $ 10 * 10510 . . = $ 10 * 1629 = $ 16.29 4. How much will you have in your savings account at the end of five years if you deposit $1,000 now and it compounds at a rate of 1 1/2% quarterly? Value n = Value 0 * (1 + r) n = $ 1,000 * 101520 . . = $ 1,000 * 1347 = $ 1,347.00 Time Value of Money Page 3 5. How much must you have in the bank now in order to have $100 in the bank five years from now? (Assume that the money you have in the bank will grow at a rate of 4% per year.) 1 Value 0 = Value n * (1 + r ) n 1 = $ 100 * (104) 5 . = $ 100 * 0.822 = $ 82.20 6. You would like to put some money aside for your newborn baby’s college education. How much must you deposit in a savings account now if the account grows at a rate of 6% a year and you desire a balance of $20,000 eighteen years from now? 1 Value 0 = Value n * (1 + r ) n 1 = $ 20,000 * (1+.06)18 = $ 20,000 * 0.350 = $ 7,000 7. If you put $100 in the bank in each of the next five years (you put the money in at the end of each year), how much money will you have in the bank at the end of the fifth year, assuming a 4% rate of interest. (1 + r ) n - 1 Value n = CFannuity * r 5 . (104 ) - 1 = $ 100 * .04 = $ 100 * 5.416 . = $ 54160 Time Value of Money Page 4 8. You have just won the state of Kentucky’s lottery for $1 million. However, when you read the fine print, you are actually to receive $50,000 per year for the next 20 years. How much does the state of Kentucky have to put in the bank today to allow you to withdraw $50,000 per year, assuming a 6% interest rate? 1 1- (1 + r ) n Value 0 = CFannuity * r 1 1- (1+.06) 20 = $ 50,000 * .06 . = $ 50,000 * 11470 = $ 573,500 9. What is the present value of $10,000 to be received (as per gift agreement) ten years from now assuming a 6% required rate of return? Value 0 = CFn * PFVn 1 Value 0 = $ 10,000 * 10 . (106) = $ 10,000 * 0.558 = $ 5,580.00 10. How much must you have now in a savings account that grows at a rate of 6% per year to be able to withdraw $30,000 a year at the end of each of the next thirty years? 1 1- (1 + r) n Value 0 = CFannuity * r 1 1- (1+.06) 30 = $ 30,000 * .06 = $ 30,000 * 13.765 = $ 412,950.00 Time Value of Money Page 5 11. What must be paid for an investment which provides $1,000 annually for ten years plus $5,000 after ten years and yields 10%? Value 0 = CF * PFVannuity + Value n * PFVn . = $ 1,000 * 6145 + $5,000 * 0.386 = $6,145.00 + $1,930.00 = $8,075.00 12. The monthly payment on a 24-month installment auto loan (payments due at the end of each month) is $100. The interest rate on this loan is 1% per month. What is the amount borrowed? Value 0 = CFannuity * PVFannuity = $100 * 21.243 = $ 2,124.30 13. What will be the price of a ten-year bond be if it has to yield 8% to the buyer? The bond has a face value of $1,000 and pays $10 interest on a quarterly basis. Value 0 = CFannuity * PVFannuity + Vn * PVFn = $ 10 * 27.355 + $ 1,000 * 0.453 . . = $ 27355 + $ 45300 . = $ 72655 14. What will the price of a bond in #13 be if it is to yield 6% to the buyer? Value 0 = CFannuity * PVFannuity + Vn * PVFn = $ 10 * 29.916 + $1,000 * 0.551 . = $ 299.16 + $ 55100 . = $ 85016 15. You are ready to buy a new car. Given an annual percentage rate of 8%, how much can you borrow if you can afford to repay $300 each month for 60 months (paid at the end of each month)? Value 0 = CFannuity * PVFannuity = $300* 49.318 = $14,795.40

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Present Value, future value, interest rate, time value of money, Cash Flow, discount rate, present value of an annuity, two years, three years, amount of money

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posted: | 7/7/2011 |

language: | English |

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Present Value, Future Value, and Annuity document sample

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