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Study Guide Chapter 9

Study Guide Chapter 9. Agricultural Economics 330 Instructor: David J. Leatham. Question 1. What is the “time value of money?” The time value of money refers to the principle that $1 received (or paid) today has a greater value than$1 received (or paid) in the future?. Question 2.

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Study Guide Chapter 9

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  1. Study GuideChapter 9 Agricultural Economics 330 Instructor: David J. Leatham

  2. Question 1 • What is the “time value of money?” • The time value of money refers to the principle that $1 received (or paid) today has a greater value than$1 received (or paid) in the future?

  3. Question 2 • Why is there a “time value of money?” • Money received today can be invested, thus, it increases over time and people prefer consumption today rather than later.

  4. Question 3 • Explain the term compounding as it relates to money. • Converts earlier (present) sums of money to future sums of money. Interest is added to principal and interest is paid on earned interest. Thus, money grows exponentially.

  5. Question 4 • Assume that the salary cap on NFL players has prevented an NFL team from hiring a valuable free agent. The star quarterback has agreed to give up $1 million dollars today so that the team can hire the free agent but the quarterback insists that he be paid an equivalent bonus amount in five years. Assume that you represent the quarterback. What should the bonus be if the quarterback can earn 12% on his investments over the five year period of time?

  6. 0 5 r = 12 % V5 -1 Mil VN = V0 (1+r)N Future Value of a Single Sum V5 = 1,000,000 (1+.12)5 i N PV FV PMT 12 ? -1,000,000 0 5 V5 = $1,762,342

  7. Question 5 • Suppose the local car dealership is running a special on a deluxe Ram truck this week. The dealership will sell you the truck for $23,000 and will let you finance the full $23,000. How much will your monthly payments be if you repay the loan in equal monthly payments over five years at an interest rate of 11% (compounded monthly)?

  8. ... 5*12=60 0 1 2 ... r =11/12=.916% -A -A -A 23,000 V0 = A [USPVr,N] Present Value of an Uniform Annuity 23,000= A [USPV0.916%, 60] i N PV FV PMT 0 23,000 ? 60 A= $500.08 • 0.916

  9. Question 6 • Suppose you represent a linebacker from Texas A&M that has been drafted by the Dallas Cowboys. In addition to the annual salary of $400,000 a year, the Cowboys are willing to pay him a signing bonus. They are willing to pay a bonus of $600,000 today or pay him a bonus of $155,000 per year for five years (end of year)

  10. Part A • If the linebacker can earn 10% on his investments, would you recommend that he take the $600,000 today or the $155,000 annuity? (hint: compare the present values.)

  11. 0 1 2 5 ... r = 10 % 155k 155k 155k -V0 V0 = A [USPVr,N] Present Value of an Uniform Annuity V0= 155k [USPV10%, 5] i N PV FV PMT 10 0 V0 155k 5 A= $587,572 Take the $600,000 bonus.

  12. Part B • If the linebacker can only earn 6% on his investments, would you recommend that he take the $600,000 today or the $155,000 annuity?

  13. 0 1 2 5 ... r = 6% 155k 155k 155k -V0 V0 = A [USPVr,N] Present Value of an Uniform Annuity V0= 155k [USPV6%, 5] i N PV FV PMT 6 0 V0 155k 5 A= $652,916 Take the annuity.

  14. Question 7 • How many years will it take for you to triple your money if you can earn 9% on your money?

  15. 0 N r = 9 % 1 3 V0 = VN (1+r)-N Present Value of a Single Sum 1= 3 (1+.09)-N i N PV FV PMT 9 3 1 0 N N = 12.7

  16. Question 8 • Suppose Mr. Agirich has made a good profit on his cattle this year and wants to put $10,000 in a savings account to pay for his son’s education. The bank pays 5% compounded annually on money in savings accounts. • A. How much will Mr. Agirich have in his savings account in fourteen years if $10,000 is put in the account today?

  17. 0 14 r = 5 % -10,000 V14 VN = V0 (1+r)N Future Value of a Single Sum V14 = 10,000 (1+.05)14 V14 = 19,799 14 5 -10,000 0 ? i% N PV PMT FV Agricultural Finance

  18. Question 9 • Suppose Mr. Agirich has made a good profit on his cattle this year and wants to put $10,000 in a savings account to pay for his son’s education. The bank pays 5% compounded annually on money in savings accounts. • B. How many years will it take for the money to triple if money is put in the savings account today (round off to the greatest year)?

  19. 0 N r = 5 % -10,000 30,000 VN = V0 (1+r)N Future Value of a Single Sum 30,000= 10,000 (1+.05)N N = 22.5 ? 5 -10,000 0 30,000 i% N PV PMT FV Agricultural Finance

  20. Question 10 • Suppose Mr. Agirich has made a good profit on his cattle this year and wants to put $10,000 in a savings account to pay for his son’s education. The bank pays 5% compounded annually on money in savings accounts. • C. Suppose Mr. Agirich want $40,000 in the bank account in fourteen years. How much does he need to put in the bank today?

  21. 0 14 r = 5 % -V0 40,000 V0 = VN (1+r)-N Present Value of a Single Sum V0 = 40,000 (1+.05)-14 V0 = 20,203 14 5 V0 0 40,000 i% N PV PMT FV Agricultural Finance

  22. Question 11 • Suppose Mr. Agirich has made a good profit on his cattle this year and wants to put $10,000 in a savings account to pay for his son’s education. The bank pays 5% compounded annually on money in savings accounts. • D. Suppose Mr. Agirich decides to put $1,000 in the savings account at the end of each of the next 14 years. How much will be in the college fund in fourteen years?

  23. ... 0 1 2 14 ... r = 5 % -1,000 -1,000 -1,000 V14 VN = A [USFVr,N] Future Value of an Uniform Annuity V14 = 1,000 [USFV5%,14] V14 = $19,599 14 5 0 -1,000 ? i% N PV PMT FV

  24. Question 12 • Suppose Mr. Agirich, a wealthy rancher, has the opportunity to buy a prize-winning bull. Mr. Agirich wants to make a 14% rate of return on investments (discount rate =14%). • A. If Mr. Agirich plans on receiving $4,000 and the end of the next five years from breeding fees (profit after expenses), how much should he pay for this bull?

  25. ... 0 1 2 5 ... r = 14 % 4,000 4,000 4,000 -V0 V0 = A [USPVr,N] Present Value of an Uniform Annuity V0 = 4,000 [USPV14%, 5] V0 = $13,732 5 14 ? 4,000 0 i% N PV PMT FV Agricultural Finance

  26. Question 13 • Suppose Mr. Agirich, a wealthy rancher, has the opportunity to buy a prize-winning bull. Mr. Agirich wants to make a 14% rate of return on investments (discount rate =14%). • B. If Mr. Agirich plans on receiving $4,000 and the end of the next five years from breeding fees (profit after expenses) and he believes that he can sell the bull at the end of five years for $30,000, how much should he pay for this bull?

  27. ... 0 1 2 5 ... r = 14 % 4,000 4,000 4,000 -V0 30,000 Mixed Cash Flows: An Annuity and a Single Sum V0 = A [USPVr,N] Present Value of an Uniform Annuity V0 = VN(1+r)-N Present Value of a Single Sum of Money V0 = 4,000 [USPV14%, 5] + 30,000(1+.14)-5 V0 = $29,313 5 14 ? 4,000 30,0000 i% N PV PMT FV Agricultural Finance

  28. Question 14 • Suppose the local car dealership is running a special on a deluxe Ram truck this week. The dealership will sell Mr. Agirich the truck for $30,000 and will let him finance the full $30,000. How much will the monthly payments be if the loan is repaid in equal monthly payments over five years at an interest rate of 9%?

  29. 5*12=60 0 1 2 ... r =9/12=0.75% -A -A -A 30,000 V0 = A [USPVr,N] Present Value of an Uniform Annuity 30,000= A [USPV0.75%, 60] A = $622.75 60 0.75 30,000 ? 0 i% N PV PMT FV

  30. Question 15 • Suppose Mr. Agirich has a daughter that just married and her husband (Rick) wants to start ranching. Mr. Agirich has agreed to lend Rick $80,000 at the beginning of the next five years. Mr. Agirich will only charge Rick 4% interest compounded annually. At the end of five years, Rick agrees to pay Mr. Agirich the full outstanding amount. Also suppose that Rick must borrow the money from the bank to pay off the loan to Mr. Agirich. The bank agrees to let Rick pay off the loan over 7 years (seven annual payments) at 12% interest. Payments will start at the end of the sixth year: interest starts accruing at 12% at the end of the 5th year. Calculate the annual loan payments.

  31. 5 0 1 4 ... r = 4% 80,000 80,000 80,000 V5 Solve as Mixed Cash Flows: An Annuity and Single Sums VN = A [USFVr,N] Future Value of an Uniform Annuity VN = Vn(1+r)N-n Future Value of a Single Sum of Money V5 = 80,000 [USFV4%, 4](1+.04) + 80,000(1+.04)5 V5 = 353,305 + 97,332 = $450,638= Outstanding Loan Agricultural Finance

  32. ... 0 1 5 6 12 r = 12 % ... -A 437,049 -A V0 = A [USPVr,N] Present Value of an Uniform Annuity 450,638= A [USPV12%, 7] A = $98,743 7 12 450,638 ? 0 i% N PV PMT FV Agricultural Finance

  33. Question 16 • Suppose that you have just graduated from TAMU and you have a job paying $38,000 per year. You would like to save $20,000 so that you can make a downpayment on a house in 5 years. How much would you have to put in the bank each month if the bank pays 6 percent on savings accounts (assume you put the money in the bank at the end of the month and interest is compounded monthly)?

  34. 5*12=60 0 1 2 ... r =6/12=0.5% -A -A -A 20,000 V0 = A [USFVr,N] Future Value of an Uniform Annuity 20,000= A [USFV0.5%, 60] A = $286.66 60 0.5 0 ? 20,000 i% N PV PMT FV

  35. Question 17 • Suppose that you have an opportunity to buy a house for $100,000. You have enough money in your bank account to make a $20,000 downpayment. Suppose you borrow $80,000 to buy the house and will repay the loan over 30 years. The annual interest on the loan is eight percent. The bank requires equal monthly payments. • A. Calculate the monthly payments.

  36. 30*12=360 0 1 2 ... r =8/12=0.67% -A -A -A 80,000 V0 = A [USPVr,N] Present Value of an Uniform Annuity 80,000= A [USPV0.67%, 360] A = $587.01 360 0.67 80,000 ? 0 i% N PV PMT FV

  37. Question 17 Conintued • Suppose that you have an opportunity to buy a house for $100,000. You have enough money in your bank account to make a $20,000 downpayment. Suppose you borrow $80,000 to buy the house and will repay the loan over 30 years. The annual interest on the loan is eight percent. The bank requires equal monthly payments. • B. How much interest will you pay on this loan if you keep the loan for 30 years?

  38. Interest • Total Payments=587.01*360 = • 211,324 • Total Interest = 211,324-80,000 = • 131,324.2

  39. Question 18 • Suppose that you have an opportunity to start a computer business in the shadow of TAMU. You are sure it will be a successful business but you don’t have any money to get it started. Your parents have agreed to lend you $100,000 today so that you can start the business. They will charge you six-percent interest and require that you pay the loan back, principal and interest, at the end of five years. • A. How much money will you owe your parents in five years?

  40. 0 5 r = 6% 100,000 -V5 VN = V0 (1+r)N Future Value of a Single Sum V5 = 100,000 (1+.06)5 V5 = 133,822.56 5 6 100,000 0 V5 i% N PV PMT FV

  41. Question 18 Continued • Part B • Suppose at the end of five years you don’t have the money to pay your parents the money you owe them (Part A.). A friendly bank will lend you the money. The annual interest rate is 12 percent. The bank will lend you the money for 10 years and requires equal annual payments. Calculate the annual payments.

  42. 10 0 1 2 ... r =12% -A -A -A 133,822.56 V0 = A [USPVr,N] Present Value of an Uniform Annuity 133,822.56= A [USPV12%, 10] A = $23,684.47 10 12 133,822 ? 0 i% N PV PMT FV

  43. Question 18 Continued • Part C • Suppose at the end of five years you don’t have the money to pay your parents the money you owe them (Part A.). You agree to take out a loan with the local bank to pay your parents as much as you can. The annual interest rate is 12 percent. The bank will lend you the money for 10 years and requires equal annual payments. The maximum annual payment you can make is $10,000. What is the maximum amount of money that you can borrow from the bank?

  44. 10 0 1 2 ... r =12% -10k -10k -10k V0 V0 = A [USPVr,N] Present Value of an Uniform Annuity V0 = 10,000 [USPV12%, 10] V0=56,502.23 10 12 V0 10,000 0 i% N PV PMT FV

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