You have been notified that you will be receiving an amount of $2,000 a year for the next 2 years (end of period cash flows), which the first cash flow occurring 1 year from today. The appropriate discounting rate is 12%. A typical question is: What is the present value today of this stream of cash flows? However, since this is a practice example, lets solve this problem step by step. It takes at least 9 steps or questions to get to the answer.

Problem for LN-1 material. You have been notified that you will be receiving an amount of $2,000 a year for the next 2 years (end of period cash flows), which the first cash flow occurring 1 year from today. The appropriate discounting rate is 12%. A typical question is: What is the present value today of this stream of cash flows? However, since this is a practice example, lets solve this problem step by step. It takes at least 9 steps or questions to get to the answer. One of the first thing to ask ourselves is: 1. What is the frequency of payment (called "p") - the number of times the cash flows occur in a year? 1 A 2. Another question to ask is: Is this series of cash flows an A/ 3. Is it an ordinary annuity? Answer either yes or no (lower case) yes annuity? Answer either yes or no (lower case). yes A 4. What is the APR for this problem? Do not enter the % sign and round to and use 2 decimals. for example, if the answer is 5.275% then enter 5.28; if your answer is 4% you must enter 4.00, if it is 3.4% you must enter 3.40 A/ 5. What is the frequency compounding (m) ? A 6. What is the discounting rate per period? Do not enter the % sign and round to and use 2 decimals. for example, if the answer is 5.275% then enter 5.28; if your answer is 4% you must enter 4.00, if it is 3.4% you must enter 3.40 A 7. What is the number of periods for this annuity (n)? 8: What is the value of the annuity discounting factor (PVIFA) to use in the discounting process of this annuity? Use 4 decimals in your answer. A/ 9. Now we can answer the question 'What is the present value today of the given stream of cash flows? Use comma to separate thousands, don't use decimals (round to the nearest dollar), and do not use the dollar ($) sign. For example if your answer is $1,240.34, then enter 1,240 A Now let's modify the problem in several ways. First, let's change the frequency of payment and the frequency of compounding. The cash flows are to be paid every 6 months and the APR is still 12% but now it compounds semi-annually. Thus, the problem now read as "You have been notified that you will be receiving an amount of $2,000 semi-annually for the next 2 years (end of period cash flows), which the first cash flow occurring 6 months from today. The appropriate discounting rate is 12% compounding semi-annually." 10. What is now the frequency of payment (p)? A 11. What is now the frequency of compounding (m)? A/ 12. What is the discounting rate per period? Do not enter the % sign and round to and use 2 decimals. for example, if the answer is 5.275% then enter 5.28; if your answer is 4% you must enter 4.00, if it is 3.4% you must enter 3.40 flows? A/ 13. What is the number of periods for discounting these cash A 14: What is the value of the annuity discounting factor (PVIFA) to use in the discounting process of this annuity? Use 4 decimals in your A 15. What is the present value today of the given stream of cash flows? Use comma to separate thousands, don't use decimals (round to the nearest dollar), and do not use the dollar ($) sign. For example if your answer is $1,240.34, then enter 1,240 answer. A Now let's modify again the problem. Everything the same except that the first cash flow occurs today. Thus, the problem now read as "You have been notified that you will be receiving an amount of $2,000 semi-annually for the next 2 years (beginning of period cash flows), which the first cash flow occurring today. The appropriate discounting rate is 12% compounding semi-annually." 16. What is the present value today of the given stream of cash flows? Use comma to separate thousands, don't use decimals (round to the nearest dollar), and do not use the dollar ($) sign. For example if your answer is $1,240.34, then enter 1,240 Now let's modify again the problem. Everything the same except that the first cash flow occurs today. Thus, the problem now read as "You have been notified that you will be receiving an amount of $2,000 semi-annually for the next 2 years (beginning of period cash flows), which the first cash flow occurring today. The appropriate discounting rate is 12% compounding semi-annually." 16. What is the present value today of the given stream of cash flows? Use comma to separate thousands, don't use decimals (round to the nearest dollar), and do not use the dollar ($) sign. For example if your answer is $1,240.34, then enter 1,240 A/ Now let's modify again the problem. Instead of the first cash flow occurring today, let's go back to previous set up (first cash flow starts in 6 months and every cash flow thereafter is every 6 months, APR is still 12% and compounded semi-annually just as before). However, the cash flows go forever (every 6 months). Thus, the problem now read as "You have been notified that you will be receiving an amount of $2,000 semi-annually forever (end of period cash flows), which the first cash flow occurring six months from today. The appropriate discounting rate is 12% compounding quarterly." 17. What is the present value today of the given stream of cash flows? Use comma to separate thousands, don't use decimals (round to the nearest dollar), and do not use the dollar ($) sign. For example if your answer is $1,240.34, then enter 1,240 A Problem for LN-1 material. You have been notified that you will be receiving an amount of $2,000 a year for the next 2 years (end of period cash flows), which the first cash flow occurring 1 year from today. The appropriate discounting rate is 12%. A typical question is: What is the present value today of this stream of cash flows? However, since this is a practice example, lets solve this problem step by step. It takes at least 9 steps or questions to get to the answer. One of the first thing to ask ourselves is: 1. What is the frequency of payment (called "p") - the number of times the cash flows occur in a year? 1 A 2. Another question to ask is: Is this series of cash flows an A/ 3. Is it an ordinary annuity? Answer either yes or no (lower case) yes annuity? Answer either yes or no (lower case). yes A 4. What is the APR for this problem? Do not enter the % sign and round to and use 2 decimals. for example, if the answer is 5.275% then enter 5.28; if your answer is 4% you must enter 4.00, if it is 3.4% you must enter 3.40 A/ 5. What is the frequency compounding (m) ? A 6. What is the discounting rate per period? Do not enter the % sign and round to and use 2 decimals. for example, if the answer is 5.275% then enter 5.28; if your answer is 4% you must enter 4.00, if it is 3.4% you must enter 3.40 A 7. What is the number of periods for this annuity (n)? 8: What is the value of the annuity discounting factor (PVIFA) to use in the discounting process of this annuity? Use 4 decimals in your answer. A/ 9. Now we can answer the question 'What is the present value today of the given stream of cash flows? Use comma to separate thousands, don't use decimals (round to the nearest dollar), and do not use the dollar ($) sign. For example if your answer is $1,240.34, then enter 1,240 A Now let's modify the problem in several ways. First, let's change the frequency of payment and the frequency of compounding. The cash flows are to be paid every 6 months and the APR is still 12% but now it compounds semi-annually. Thus, the problem now read as "You have been notified that you will be receiving an amount of $2,000 semi-annually for the next 2 years (end of period cash flows), which the first cash flow occurring 6 months from today. The appropriate discounting rate is 12% compounding semi-annually." 10. What is now the frequency of payment (p)? A 11. What is now the frequency of compounding (m)? A/ 12. What is the discounting rate per period? Do not enter the % sign and round to and use 2 decimals. for example, if the answer is 5.275% then enter 5.28; if your answer is 4% you must enter 4.00, if it is 3.4% you must enter 3.40 flows? A/ 13. What is the number of periods for discounting these cash A 14: What is the value of the annuity discounting factor (PVIFA) to use in the discounting process of this annuity? Use 4 decimals in your A 15. What is the present value today of the given stream of cash flows? Use comma to separate thousands, don't use decimals (round to the nearest dollar), and do not use the dollar ($) sign. For example if your answer is $1,240.34, then enter 1,240 answer. A Now let's modify again the problem. Everything the same except that the first cash flow occurs today. Thus, the problem now read as "You have been notified that you will be receiving an amount of $2,000 semi-annually for the next 2 years (beginning of period cash flows), which the first cash flow occurring today. The appropriate discounting rate is 12% compounding semi-annually." 16. What is the present value today of the given stream of cash flows? Use comma to separate thousands, don't use decimals (round to the nearest dollar), and do not use the dollar ($) sign. For example if your answer is $1,240.34, then enter 1,240 Now let's modify again the problem. Everything the same except that the first cash flow occurs today. Thus, the problem now read as "You have been notified that you will be receiving an amount of $2,000 semi-annually for the next 2 years (beginning of period cash flows), which the first cash flow occurring today. The appropriate discounting rate is 12% compounding semi-annually." 16. What is the present value today of the given stream of cash flows? Use comma to separate thousands, don't use decimals (round to the nearest dollar), and do not use the dollar ($) sign. For example if your answer is $1,240.34, then enter 1,240 A/ Now let's modify again the problem. Instead of the first cash flow occurring today, let's go back to previous set up (first cash flow starts in 6 months and every cash flow thereafter is every 6 months, APR is still 12% and compounded semi-annually just as before). However, the cash flows go forever (every 6 months). Thus, the problem now read as "You have been notified that you will be receiving an amount of $2,000 semi-annually forever (end of period cash flows), which the first cash flow occurring six months from today. The appropriate discounting rate is 12% compounding quarterly." 17. What is the present value today of the given stream of cash flows? Use comma to separate thousands, don't use decimals (round to the nearest dollar), and do not use the dollar ($) sign. For example if your answer is $1,240.34, then enter 1,240 A