1. 1 Accounting and Annuities Instructor Adnan Shoaib PART II: Corporate Accounting Concepts and Issues Lecture 25

2. 2 1. 1.Solve future value of ordinary and annuity due problems. 2. 2.Solve present value of ordinary and annuity due problems. 3. 3.Solve present value problems related to deferred annuities and bonds. 4. 4.Apply expected cash flows to present value measurement. Learning Objectives

3. 3 Annuities More Complex Situations Present Value Measurement Future value of ordinary annuity Future value of annuity due Examples of FV of annuity Present value of ordinary annuity Present value of annuity due Examples of PV of annuity Deferred annuities Valuation of long-term bonds Effective- interest method of bond discount/ premium amortization Choosing an appropriate interest rate Example of expected cash flow Accounting and the Time Value of Money

4. 4 Basic Annuities An annuity is a series of equal periodic payments. Period 1Period 2Period 3Period 4 $10,000

5. 5 AnnuitiesAnnuities (1)Periodic payments or receipts (called rents) of the same amount, (2)Same-length interval between such rents, and (3)Compounding of interest once each interval. Annuity requires: LO 1 Solve future value of ordinary and annuity due problems. Ordinary Annuity - rents occur at the end of each period. Annuity Due - rents occur at the beginning of each period. Two Types

6. 6 LO 1 Solve future value of ordinary and annuity due problems. Future Value of an Ordinary Annuity  Rents occur at the end of each period.  No interest during 1st period. AnnuitiesAnnuities 01 Present Value 2345678 $20,00020,000 Future Value

7. 7 LO 1 Solve future value of ordinary and annuity due problems. Illustration: Assume that $1 is deposited at the end of each of 5 years (an ordinary annuity) and earns 12% interest compounded annually. Following is the computation of the future value, using the “future value of 1” table (Table 6-1) for each of the five $1 rents. Future Value of an Ordinary Annuity

8. 8 R = periodic rent FVF-OA = future value factor of an ordinary annuity i = rate of interest per period n = number of compounding periods A formula provides a more efficient way of expressing the future value of an ordinary annuity of 1. Where: n,i LO 1 Solve future value of ordinary and annuity due problems. Future Value of an Ordinary Annuity

9. 9 Illustration: What is the future value of five $5,000 deposits made at the end of each of the next 5 years, earning interest of 12%? = $31,764.25 LO 1 Solve future value of ordinary and annuity due problems.

10. 10 Future Value of an Ordinary Annuity Illustration: What is the future value of five $5,000 deposits made at the end of each of the next 5 years, earning interest of 12%? LO 1 Solve future value of ordinary and annuity due problems. What table do we use? Alternate Calculation

11. 11 $5,000 DepositsFactorPresent Value x 6.35285= $31,764 What factor? Future Value of an Ordinary Annuity i=12% n=5 LO 1 Solve future value of ordinary and annuity due problems.

12. 12 Gomez Inc. will deposit $30,000 in a 12% fund at the end of each year for 8 years beginning December 31, 2012. What amount will be in the fund immediately after the last deposit? 01 Present Value What table do we use? Future Value of an Ordinary Annuity 2345678 $30,00030,000 Future Value LO 1 Solve future value of ordinary and annuity due problems.

13. 13 Future Value of an Ordinary Annuity DepositFactorFuture Value LO 1 Solve future value of ordinary and annuity due problems. $30,000x 12.29969= $368,991 i=12% n=8

14. 14 LO 1 Solve future value of ordinary and annuity due problems. Future Value of an Annuity Due  Rents occur at the beginning of each period.  Interest will accumulate during 1 st period.  Annuity Due has one more interest period than Ordinary Annuity.  Factor = multiply future value of an ordinary annuity factor by 1 plus the interest rate. AnnuitiesAnnuities 012345678 20,000 $20,000 Future Value

15. 15 LO 1 Solve future value of ordinary and annuity due problems. Future Value of an Annuity Due Comparison of Ordinary Annuity with an Annuity Due

16. 16 Future Value of an Annuity Due Illustration: Assume that you plan to accumulate $14,000 for a down payment on a condominium apartment 5 years from now. For the next 5 years, you earn an annual return of 8% compounded semiannually. How much should you deposit at the end of each 6- month period? R = $1,166.07 LO 1 Solve future value of ordinary and annuity due problems. Computation of Rent

17. 17 Future Value of an Annuity Due Computation of Rent $14,000 = $1,166.07 12.00611 Alternate Calculation LO 1 Solve future value of ordinary and annuity due problems.

18. 18 Future Value of an Annuity Due Illustration: Suppose that a company’s goal is to accumulate $117,332 by making periodic deposits of $20,000 at the end of each year, which will earn 8% compounded annually while accumulating. How many deposits must it make? LO 1 Solve future value of ordinary and annuity due problems. Computation of Number of Periodic Rents 5.86660

19. 19 Future Value of an Annuity Due Illustration: Mr. Goodwrench deposits $2,500 today in a savings account that earns 9% interest. He plans to deposit $2,500 every year for a total of 30 years. How much cash will Mr. Goodwrench accumulate in his retirement savings account, when he retires in 30 years? LO 1 Solve future value of ordinary and annuity due problems. Computation of Future Value

20. 20 Illustration: Bayou Inc. will deposit $20,000 in a 12% fund at the beginning of each year for 8 years beginning January 1, Year 1. What amount will be in the fund at the end of Year 8? 01 Present Value What table do we use? Future Value of an Annuity Due 2345678 $20,00020,000 Future Value LO 1 Solve future value of ordinary and annuity due problems.

21. 21 DepositFactorFuture Value LO 1 Solve future value of ordinary and annuity due problems. Future Value of an Annuity Due 12.29969 x 1.12 = 13.775652 i=12% n=8 $20,000x 13.775652= $275,513

22. 22 LO 2 Solve present value of ordinary and annuity due problems. Present Value of an Ordinary Annuity  Present value of a series of equal amounts to be withdrawn or received at equal intervals.  Periodic rents occur at the end of the period. AnnuitiesAnnuities 01 Present Value 2341920 $100,000100,000..... 100,000

23. 23 LO 2 Solve present value of ordinary and annuity due problems. Illustration: Assume that $1 is to be received at the end of each of 5 periods, as separate amounts, and earns 12% interest compounded annually. Present Value of an Ordinary Annuity

24. 24 A formula provides a more efficient way of expressing the present value of an ordinary annuity of 1. Where: Present Value of an Ordinary Annuity LO 2 Solve present value of ordinary and annuity due problems.

25. 25 Present Value of an Ordinary Annuity Illustration: What is the present value of rental receipts of $6,000 each, to be received at the end of each of the next 5 years when discounted at 12%? LO 2 Solve present value of ordinary and annuity due problems.

26. 26 Illustration: Jaime Yuen wins $2,000,000 in the state lottery. She will be paid $100,000 at the end of each year for the next 20 years. How much has she actually won? Assume an appropriate interest rate of 8%. 01 Present Value What table do we use? 2341920 $100,000100,000 Present Value of an Ordinary Annuity..... LO 2 Solve present value of ordinary and annuity due problems. 100,000

27. 27 LO 2 Solve present value of ordinary and annuity due problems. Present Value of an Ordinary Annuity $100,000 ReceiptsFactorPresent Value x 9.81815= $981,815 i=5% n=20

28. 28 LO 2 Solve present value of ordinary and annuity due problems. Present Value of an Annuity Due  Present value of a series of equal amounts to be withdrawn or received at equal intervals.  Periodic rents occur at the beginning of the period. AnnuitiesAnnuities 01 Present Value 2341920 $100,000100,000..... 100,000

29. 29 Present Value of an Annuity Due Comparison of Ordinary Annuity with an Annuity Due LO 2 Solve present value of ordinary and annuity due problems.

30. 30 Illustration: Space Odyssey, Inc., rents a communications satellite for 4 years with annual rental payments of $4.8 million to be made at the beginning of each year. If the relevant annual interest rate is 11%, what is the present value of the rental obligations? LO 2 Solve present value of ordinary and annuity due problems. Present Value of an Annuity Due

31. 31 Illustration: Jaime Yuen wins $2,000,000 in the state lottery. She will be paid $100,000 at the beginning of each year for the next 20 years. How much has she actually won? Assume an appropriate interest rate of 8%. 01 Present Value What table do we use? 2341920 $100,000100,000..... LO 2 Solve present value of ordinary and annuity due problems. 100,000 Present Value of an Annuity Due

32. 32 LO 2 Solve present value of ordinary and annuity due problems. $100,000 ReceiptsFactorPresent Value x 10.60360= $1,060,360 Present Value of an Annuity Due i=8% n=20

33. 33 Illustration: Assume you receive a statement from MasterCard with a balance due of $528.77. You may pay it off in 12 equal monthly payments of $50 each, with the first payment due one month from now. What rate of interest would you be paying? LO 2 Solve present value of ordinary and annuity due problems. Present Value of an Annuity Due Computation of the Interest Rate Referring to Table 6-4 and reading across the 12-period row, you find 10.57534 in the 2% column. Since 2% is a monthly rate, the nominal annual rate of interest is 24% (12 x 2%). The effective annual rate is 26.82413% [(1 +.02) - 1]. 12

34. 34 Solving for Unknown Values in Present Value Situations In present value problems involving annuities, there are four variables: Present value of an ordinary annuity or Present value of an annuity due The amount of the annuity payment The number of periods The interest rate If you know any three of these, the fourth can be determined.

35. 35 Solving for Unknown Values in Present Value Situations Assume that you borrow $700 from a friend and intend to repay the amount in four equal annual installments beginning one year from today. Your friend wishes to be reimbursed for the time value of money at an 8% annual rate. Assume that you borrow $700 from a friend and intend to repay the amount in four equal annual installments beginning one year from today. Your friend wishes to be reimbursed for the time value of money at an 8% annual rate. What is the required annual payment that must be made (the annuity amount) to repay the loan in four years? TodayEnd of Year 1 Present Value $700 End of Year 2 End of Year 3 End of Year 4

36. 36 Solving for Unknown Values in Present Value Situations Assume that you borrow $700 from a friend and intend to repay the amount in four equal annual installments beginning one year from today. Your friend wishes to be reimbursed for the time value of money at an 8% annual rate. What is the required annual payment that must be made (the annuity amount) to repay the loan in four years?

37. 37 LO 3 Solve present value problems related to deferred annuities and bonds.  Rents begin after a specified number of periods.  Future Value - Calculation same as the future value of an annuity not deferred.  Present Value - Must recognize the interest that accrues during the deferral period. More Complex Situations 012341920 100,000..... Future Value Present Value Deferred Annuities

38. 38 LO 3 Solve present value problems related to deferred annuities and bonds. Two Cash Flows:  Periodic interest payments (annuity).  Principal paid at maturity (single-sum). 01234910 140,000 $140,000..... 140,000 2,000,000 Valuation of Long-Term Bonds More Complex Situations

39. 39 Clancey Inc. issues $2,000,000 of 7% bonds due in 10 years with interest payable at year-end. The current market rate of interest for bonds of similar risk is 8%. What amount will Clancey receive when it issues the bonds? 01 Present Value 234910 140,000 $140,000..... 140,000 Valuation of Long-Term Bonds 2,140,000 LO 3 Solve present value problems related to deferred annuities and bonds.

40. 40 LO 3 Solve present value problems related to deferred annuities and bonds. $140,000 x 6.71008 = $939,411 Interest PaymentFactorPresent Value Valuation of Long-Term Bonds PV of Interest i=8% n=10

41. 41 LO 3 Solve present value problems related to deferred annuities and bonds. $2,000,000 x.46319 = $926,380 PrincipalFactorPresent Value Valuation of Long-Term Bonds PV of Principal i=8% n=10

42. 42 Clancey Inc. issues $2,000,000 of 7% bonds due in 10 years with interest payable at year-end. Valuation of Long-Term Bonds LO 3 Solve present value problems related to deferred annuities and bonds. Present value of Interest $939,411 Present value of Principal 926,380 Bond current market value $1,865,791

43. 43 Valuation of Long-Term Bonds LO 3 Solve present value problems related to deferred annuities and bonds.

44. 44 Valuation of Long-term Leases Certain long-term leases require the recording of an asset and corresponding liability at the present value of future lease payments.

45. 45 Valuation of Long-term Leases On January 1, 2011, Todd Furniture Company signed a 20-year non- cancelable lease for a new retail showroom. The lease agreement calls for annual payments of $25,000 for 20 years beginning on January 1, 2011. The appropriate rate of interest for this long-term lease is 8%. Calculate the value of the asset acquired and the liability assumed by Todd (the present value of an annuity due at 8% for 20 years).

46. 46 Valuation of Pension Obligations Some pension plans create obligations during employees’ service periods that must be paid during their retirement periods. The amounts contributed during the employment period are determined using present value computations of the estimate of the future amount to be paid during retirement.

47. 47 Valuation of Pension Obligations On January 1, 2011, Todd Furniture Company hired a new sales manger for the new showroom. The sales manager is expected to work 30 years before retirement on December 31, 2040. Annual retirement benefits will be paid at the end of each year of retirement, a period that is expected to be 25 years. The sales manager will earn $2,500 in annual retirement benefits for the first year worked, 2011. How much must Todd contribute to the company pension fund in 2011 to provide for $2,500 in annual pension benefits for 25 years that are expected to begin in 30 years. Todd’s pension fund is expected to earn 5%.

48. 48 Valuation of Pension Obligations This is a two part calculation. The first part requires the computation of the present value of a 25-year ordinary annuity of $2,500 as of December 31, 2040. Next we calculate the present value of the December 31, 2040 amount. This second present value is the amount Todd will contribute in 2011 to fund the retirement benefit earned by the sales manager in 2011.

49. 49 Expected cash flow approach that uses a range of cash flows and incorporates the probabilities of those cash flows. Choosing an Appropriate Interest Rate Three Components of Interest:  Pure Rate  Expected Inflation Rate  Credit Risk Rate LO 4 Apply expected cash flows to present value measurement. Present Value Measurement Risk-free rate of return. IASB states a company should discount expected cash flows by the risk- free rate of return.

50. 50 Keith Bowie is trying to determine the amount to set aside so that she will have enough money on hand in 2 years to overhaul the engine on her vintage used car. While there is some uncertainty about the cost of engine overhauls in 2 years, by conducting some research online, Angela has developed the following estimates. LO 4 Apply expected cash flows to present value measurement. Present Value Measurement Instructions: How much should Keith Bowie deposit today in an account earning 6%, compounded annually, so that she will have enough money on hand in 2 years to pay for the overhaul?

51. 51 LO 4 Apply expected cash flows to present value measurement. Present Value Measurement Instructions: How much should Keith Bowie deposit today in an account earning 6%, compounded annually, so that she will have enough money on hand in 2 years to pay for the overhaul?

52. 52 End of Lecture 25