1. 1 Accounting and the Time Value of Money Instructor Adnan Shoaib PART II: Corporate Accounting Concepts and Issues Lecture 24

2. 2 1. 1.Identify accounting topics where the time value of money is relevant. 2. 2.Distinguish between simple and compound interest. 3. 3.Use appropriate compound interest tables. 4. 4.Identify variables fundamental to solving interest problems. 5. 5.Solve future and present value of 1 problems. Learning Objectives

3. 3 Future value of a single sum Present value of a single sum Solving for other unknowns Basic Time Value Concepts Single-Sum Problems Applications The nature of interest Simple interest Compound interest Fundamental variables Accounting and the Time Value of Money

4. 4  A relationship between time and money.  A dollar received today is worth more than a dollar promised at some time in the future. Basic Time Value Concepts Time Value of Money LO 1 Identify accounting topics where the time value of money is relevant.

5. 5 1. Notes 2. Leases 3. Pensions and Other Postretirement Benefits 4. Long-Term Assets Applications to Time Value Concepts: Basic Time Value Concepts 5. Shared-Based Compensation 6. Business Combinations 7. Disclosures 8. Environmental Liabilities LO 1 Identify accounting topics where the time value of money is relevant.

6. 6  Payment for the use of money.  Excess cash received or repaid over the amount borrowed (principal). The Nature of Interest Basic Time Value Concepts LO 1 Identify accounting topics where the time value of money is relevant.

7. 7  Interest computed on the principal only. LO 2 Distinguish between simple and compound interest. Basic Time Value Concepts Simple Interest Illustration: Barstow Electric Inc. borrows $10,000 for 3 years at a rate of 8% per year. Compute the total interest to be paid for the 1 year. Federal law requires the disclosure of interest rates on an annual basis. Interest = p x i x n = $10,000 x.08 x 1 = $800 Annual Interest

8. 8  Interest computed on the principal only. LO 2 Distinguish between simple and compound interest. Basic Time Value Concepts Simple Interest Illustration: Barstow Electric Inc. borrows $10,000 for 3 years at a rate of 8% per year. Compute the total interest to be paid for the 3 years. Federal law requires the disclosure of interest rates on an annual basis. Interest = p x i x n = $10,000 x.08 x 3 = $2,400 Total Interest

9. 9 LO 2 Distinguish between simple and compound interest. Basic Time Value Concepts Simple Interest Illustration: On October 1, 2012, Barstow Electric Inc. borrows $10,000 for 3 months at a rate of 7% per year. Compute the total interest to be paid for the year ended Dec. 31, 2012. Interest = p x i x n = $10,000 x.08 x 3/12 = $200 Partial Year  Interest computed on the principal only.

10. 10 LO 2 Distinguish between simple and compound interest. Basic Time Value Concepts Compound Interest  Computes interest on ► principal and ► interest earned that has not been paid or withdrawn.  Most business situations use compound interest.

11. 11 Future Value of a Single Amount The future value of a single amount is the amount of money that a dollar will grow to at some point in the future. Assume we deposit $1,000 for three years that earns 6% interest compounded annually. $1,000.00 × 1.06 = $1,060.00 and $1,060.00 × 1.06 = $1,123.60 and $1,123.60 × 1.06 = $1,191.02

12. 12 Future Value of a Single Amount Writing in a more efficient way, we can say.... $1,191.02 = $1,000 × [1.06] 3 FV = PV (1 + i) n Future Value Future Value Amount Invested at the Beginning of the Period Interest Rate Interest Rate Number of Compounding Periods Number of Compounding Periods

13. 13 Using the Future Value of $1 Table, we find the factor for 6% and 3 periods is 1.19102. So, we can solve our problem like this... FV = $1,000 × 1.19102 FV = $1,191.02 Future Value of a Single Amount

14. 14 Present Value of a Single Amount Instead of asking what is the future value of a current amount, we might want to know what amount we must invest today to accumulate a known future amount. This is a present value question. Present value of a single amount is today’s equivalent to a particular amount in the future.

15. 15 Present Value of a Single Amount Remember our equation? FV = PV (1 + i) n We can solve for PV and get.... FV (1 + i ) n PV =

16. 16 Present Value of a Single Amount Assume you plan to buy a new car in 5 years and you think it will cost $20,000 at that time. What amount must you invest today in order to accumulate $20,000 in 5 years, if you can earn 8% interest compounded annually?

17. 17 Present Value of a Single Amount i =.08, n = 5 Present Value Factor =.68058 $20,000 ×.68058 = $13,611.60 If you deposit $13,611.60 now, at 8% annual interest, you will have $20,000 at the end of 5 years. Present Value of $1 Table

18. 18 FV = PV (1 + i ) n Future Value Future Value Present Value Present Value Interest Rate Interest Rate Number of Compounding Periods Number of Compounding Periods There are four variables needed when determining the time value of money. If you know any three of these, the fourth can be determined. Solving for Other Values

19. 19 Determining the Unknown Interest Rate Suppose a friend wants to borrow $1,000 today and promises to repay you $1,092 two years from now. What is the annual interest rate you would be agreeing to? a.3.5% b.4.0% c.4.5% d.5.0% Present Value of $1 Table $1,000 = $1,092 × ? $1,000 ÷ $1,092 =.91575 Search the PV of $1 table in row 2 (n=2) for this value.

20. 20 Illustration: Tomalczyk Company deposits $10,000 in the Last National Bank, where it will earn simple interest of 9% per year. It deposits another $10,000 in the First State Bank, where it will earn compound interest of 9% per year compounded annually. In both cases, Tomalczyk will not withdraw any interest until 3 years from the date of deposit. Year 1 $10,000.00 x 9%$ 900.00$ 10,900.00 Year 2 $10,900.00 x 9%$ 981.00$ 11,881.00 Year 3 $11,881.00 x 9%$1,069.29$ 12,950.29 LO 2 Distinguish between simple and compound interest. Basic Time Value Concepts

21. 21 LO 3 Use appropriate compound interest tables. Table 1 - Future Value of 1 Table 2 - Present Value of 1 Table 3 - Future Value of an Ordinary Annuity of 1 Table 4 - Present Value of an Ordinary Annuity of 1 Table 5 - Present Value of an Annuity Due of 1 Compound Interest Tables Number of Periods = number of years x the number of compounding periods per year. Compounding Period Interest Rate = annual rate divided by the number of compounding periods per year. Basic Time Value Concepts

22. 22 LO 3 Use appropriate compound interest tables. How much principal plus interest a dollar accumulates to at the end of each of five periods, at three different rates of compound interest. Basic Time Value Concepts Compound Interest

23. 23 LO 3 Use appropriate compound interest tables. Basic Time Value Concepts Formula to determine the future value factor (FVF) for 1: Where: = future value factor for n periods at i interest n = number of periods i= rate of interest for a single period FVF n,i Compound Interest

24. 24 LO 3 Use appropriate compound interest tables. Basic Time Value Concepts Determine the number of periods by multiplying the number of years involved by the number of compounding periods per year. Compound Interest

25. 25 LO 3 Use appropriate compound interest tables. 9% annual interest compounded daily provides a 9.42% yield. Effective Yield for a $10,000 investment. Basic Time Value Concepts Compound Interest

26. 26 LO 4 Identify variables fundamental to solving interest problems.  Rate of Interest  Number of Time Periods  Future Value  Present Value Fundamental Variables Basic Time Value Concepts

27. 27 LO 5 Solve future and present value of 1 problems. Single-Sum Problems Unknown Future Value Two Categories Unknown Present Value

28. 28 Value at a future date of a given amount invested, assuming compound interest. LO 5 Solve future and present value of 1 problems. Single-Sum Problems FV =future value PV =present value (principal or single sum) =future value factor for n periods at i interest FVF n,i Where: Future Value of a Single Sum

29. 29 LO 5 Solve future and present value of 1 problems. Future Value of a Single Sum Illustration: Bruegger Co. wants to determine the future value of $50,000 invested for 5 years compounded annually at an interest rate of 11%. = $84,253

30. 30 LO 5 Solve future and present value of 1 problems. Future Value of a Single Sum What table do we use? Alternate Calculation Illustration: Bruegger Co. wants to determine the future value of $50,000 invested for 5 years compounded annually at an interest rate of 11%.

31. 31 What factor do we use? $50,000 Present ValueFactorFuture Value x 1.68506= $84,253 Future Value of a Single Sum Alternate Calculation i=11% n=5 LO 5 Solve future and present value of 1 problems.

32. 32 Bob Anderson invested $15,000 today in a fund that earns 8% compounded annually. To what amount will the investment grow in 3 years? 0123456 Present Value $15,000 What table do we use? Future Value? LO 5 Solve future and present value of 1 problems. Future Value of a Single Sum

33. 33 LO 5 Solve future and present value of 1 problems. Present ValueFactorFuture Value $15,000x 1.25971= $18,896 Future Value of a Single Sum i=8% n=3

34. 34 LO 5 Solve future and present value of 1 problems. PROOF Bob Anderson invested $15,000 today in a fund that earns 8% compounded annually. To what amount will the investment grow in 3 years? Future Value of a Single Sum

35. 35 Bob Anderson invested $15,000 today in a fund that earns 8% compounded semiannually. To what amount will the investment grow in 3 years? 0123456 Present Value $15,000 What table do we use? Future Value? LO 5 Solve future and present value of 1 problems. Future Value of a Single Sum

36. 36 LO 5 Solve future and present value of 1 problems. Present ValueFactorFuture Value $15,000x 1.26532= $18,980 Future Value of a Single Sum What factor? i=4% n=6

37. 37 Value now of a given amount to be paid or received in the future, assuming compound interest. Single-Sum Problems Present Value of a Single Sum LO 5 Solve future and present value of 1 problems. Where: FV =future value PV =present value (principal or single sum) =present value factor for n periods at i interest PVF n,i

38. 38 LO 5 Solve future and present value of 1 problems. Present Value of a Single Sum Illustration: What is the present value of $84,253 to be received or paid in 5 years discounted at 11% compounded annually? = $50,000

39. 39 Present Value of a Single Sum LO 5 Solve future and present value of 1 problems. What table do we use? Illustration: What is the present value of $84,253 to be received or paid in 5 years discounted at 11% compounded annually? Alternate Calculation

40. 40 $84,253 Future ValueFactorPresent Value x.59345= $50,000 Present Value of a Single Sum What factor? i=11% n=5 LO 5 Solve future and present value of 1 problems.

41. 41 Caroline and Clifford need $25,000 in 4 years. What amount must they invest today if their investment earns 12% compounded annually? LO 5 Solve future and present value of 1 problems. Present Value of a Single Sum 0123456 Present Value? What table do we use? Future Value $25,000

42. 42 $25,000 Future ValueFactorPresent Value x.63552= $15,888 Present Value of a Single Sum What factor? i=12% n=4 LO 5 Solve future and present value of 1 problems.

43. 43 0123456 Present Value? Present Value of a Single Sum Future Value $25,000 LO 5 Solve future and present value of 1 problems. What table do we use? Caroline and Clifford need $25,000 in 4 years. What amount must they invest today if their investment earns 12% compounded quarterly?

44. 44 $25,000 Future ValueFactorPresent Value x.62317= $15,579 Present Value of a Single Sum i=3% n=16 LO 5 Solve future and present value of 1 problems.

45. 45 Single-Sum Problems Solving for Other Unknowns LO 5 Solve future and present value of 1 problems. Example—Computation of the Number of Periods The Village of Somonauk wants to accumulate $70,000 for the construction of a veterans monument in the town square. At the beginning of the current year, the Village deposited $47,811 in a memorial fund that earns 10% interest compounded annually. How many years will it take to accumulate $70,000 in the memorial fund?

46. 46 Single-Sum Problems LO 5 Solve future and present value of 1 problems. Example—Computation of the Number of Periods Using the future value factor of 1.46410, refer to Table 6-1 and read down the 10% column to find that factor in the 4-period row.

47. 47 Single-Sum Problems LO 5 Solve future and present value of 1 problems. Example—Computation of the Number of Periods Using the present value factor of.68301, refer to Table 6-2 and read down the 10% column to find that factor in the 4-period row.

48. 48 Single-Sum Problems Solving for Other Unknowns LO 5 Solve future and present value of 1 problems. Example—Computation of the Number of Periods The Village of Somonauk wants to accumulate $70,000 for the construction of a veterans monument in the town square. At the beginning of the current year, the Village deposited $47,811 in a memorial fund that earns 10% interest compounded annually. How many years will it take to accumulate $70,000 in the memorial fund?

49. 49 Single-Sum Problems Solving for Other Unknowns LO 5 Solve future and present value of 1 problems. Example—Computation of the Interest Rate Advanced Design, Inc. needs $1,409,870 for basic research 5 years from now. The company currently has $800,000 to invest for that purpose. At what rate of interest must it invest the $800,000 to fund basic research projects of €1,409,870, 5 years from now?

50. 50 Single-Sum Problems LO 5 Solve future and present value of 1 problems. Using the future value factor of 1.76234, refer to Table 6-1 and read across the 5-period row to find the factor. Example—Computation of the Interest Rate

51. 51 Single-Sum Problems LO 5 Solve future and present value of 1 problems. Using the present value factor of.56743, refer to Table 6-2 and read across the 5-period row to find the factor. Example—Computation of the Interest Rate

52. 52 Some notes do not include a stated interest rate. We call these notes noninterest-bearing notes. Even though the agreement states it is a noninterest-bearing note, the note does, in fact, include interest. We impute an appropriate interest rate for noninterest-bearing notes. Accounting Applications of Present Value Techniques—Single Cash Amount

53. 53 Statement of Financial Accounting Concepts No. 7 “Using Cash Flow Information and Present Value in Accounting Measurements” The objective of valuing an asset or liability using present value is to approximate the fair value of that asset or liability. Expected Cash Flow Approach

54. 54 End of Lecture 24