1. E-1 Prepared by Coby Harmon University of California, Santa Barbara Westmont College W ILEY IFRS EDITION

2. E-2 APPENDIX PREVIEW Financial Accounting IFRS 3rd Edition Weygandt ● Kimmel ● Kieso Would you rather receive NT$1,000 today or a year from now? You should prefer to receive the NT$1,000 today because you can invest the NT$1,000 and earn interest on it. As a result, you will have more than NT$1,000 a year from now. What this example illustrates is the concept of the time value of money. Everyone prefers to receive money today rather than in the future because of the interest factor.

3. E-3 E LEARNING OBJECTIVES After studying this chapter, you should be able to: 1.Distinguish between simple and compound interest. 2.Solve for future value of a single amount. 3.Solve for future value of an annuity. 4.Identify the variables fundamental to solving present value problems. 5.Solve for present value of a single amount. 6.Solve for present value of an annuity. 7.Compute the present value of notes and bonds. 8.Compute the present values in capital budgeting situations. 9.Use a financial calculator to solve time value of money problems. APPENDIX Time Value of Money

4. E-4  Payment for the use of money.  Difference between amount borrowed or invested (principal) and amount repaid or collected. Elements involved in financing transaction: 1.Principal (p ): Amount borrowed or invested. 2.Interest Rate (i ): An annual percentage. 3.Time (n ): Number of years or portion of a year that the principal is borrowed or invested. LO 1 Nature of Interest Learning Objective 1 Distinguish between simple and compound interest.

5. E-5  Interest computed on the principal only. Nature of Interest Illustration: Assume you borrow NT$5,000 for 2 years at a simple interest rate of 6% annually. Calculate the annual interest cost. Interest = p x i x n = NT$5,000 x.06 x 2 = $600 2 FULL YEARS Illustration E-1 Interest computations Simple Interest LO 1

6. E-6  Computes interest on ► the principal and ► any interest earned that has not been paid or withdrawn.  Most business situations use compound interest. Compound Interest LO 1 Nature of Interest

7. E-7 Illustration: Assume that you deposit €1,000 in Bank Two, where it will earn simple interest of 9% per year, and you deposit another €1,000 in Citizens Bank, where it will earn compound interest of 9% per year compounded annually. Also assume that in both cases you will not withdraw any cash until three years from the date of deposit. Compound Interest Illustration E-2 Simple versus compound interest LO 1

8. E-8 Future value of a single amount is the value at a future date of a given amount invested, assuming compound interest. FV =future value of a single amount p =principal (or present value; the value today) i =interest rate for one period n =number of periods Illustration E-3 Formula for future value LO 2 Future Value Concepts Learning Objective 2 Solve for future value of a single amount.

9. E-9 Illustration: If you want a 9% rate of return, you would compute the future value of a €1,000 investment for three years as follows: LO 2 Illustration E-4 Time diagram Future Value of a Single Amount

10. E-10 What table do we use? LO 2 Illustration: If you want a 9% rate of return, you would compute the future value of a €1,000 investment for three years as follows: Future Value of a Single Amount Illustration E-4 Time diagram

11. E-11 What factor do we use? €1,000 Present ValueFactorFuture Value x 1.29503= €1,295.03 LO 2 Future Value of a Single Amount

12. E-12 What table do we use? Illustration : Illustration E-5 Demonstration problem— Using Table 1 for FV of 1 LO 2 Future Value of a Single Amount

13. E-13 £20,000 Present ValueFactorFuture Value x 2.85434= £57,086.80 LO 2 Future Value of a Single Amount

14. E-14 Illustration: Assume that you invest HK$2,000 at the end of each year for three years at 5% interest compounded annually. Illustration E-6 Time diagram for a three-year annuity LO 3 Learning Objective 3 Solve for future value of an annuity. Future Value of an Annuity

15. E-15 Illustration: Invest = HK$2,000 i = 5% n = 3 years LO 3 Illustration E-7 Future value of periodic payment computation Future Value of an Annuity

16. E-16 When the periodic payments (receipts) are the same in each period, the future value can be computed by using a future value of an annuity of 1 table. Illustration E-8 Demonstration problem—Using Table 2 for FV of an annuity of 1 LO 3 Future Value of an Annuity

17. E-17 What factor do we use? £2,500 PaymentFactorFuture Value x 4.37462= £10,936.55 LO 3 Future Value of an Annuity

18. E-18 The present value is the value now of a given amount to be paid or received in the future, assuming compound interest. Present value variables: 1.Dollar amount to be received (future amount). 2.Length of time until amount is received (number of periods). 3.Interest rate (the discount rate). Present Value Variables LO 4 Present Value Concepts Learning Objective 4 Identify the variables fundamental to solving present value problems.

19. E-19 Present Value (PV) = Future Value ÷ (1 + i ) n Illustration E-9 Formula for present value p = principal (or present value) i = interest rate for one period n = number of periods Present Value of a Single Amount LO 5 Learning Objective 5 Solve for present value of a single amount.

20. E-20 Illustration: If you want a 10% rate of return, you would compute the present value of €1,000 for one year as follows: Illustration E-10 Finding present value if discounted for one period Present Value of a Single Amount LO 5

21. E-21 What table do we use? Illustration: If you want a 10% rate of return, you can also compute the present value of €1,000 for one year by using a present value table. Illustration E-10 Finding present value if discounted for one period Present Value of a Single Amount LO 5

22. E-22 €1,000x.90909= €909.09 What factor do we use? Future ValueFactorPresent Value Present Value of a Single Amount LO 5

23. E-23 Illustration E-11 Finding present value if discounted for two period What table do we use? Illustration: If the single amount of €1,000 is to be received in two years and discounted at 10% [PV = €1,000 ÷ (1 +.10 2 ], its present value is €826.45 [($1,000 ÷ 1.21). Present Value of a Single Amount LO 5

24. E-24 €1,000x.82645= €826.45 Future ValueFactorPresent Value What factor do we use? Present Value of a Single Amount LO 5

25. E-25 NT$100,000x.79383= NT$79,383 Illustration: Suppose you have a winning lottery ticket. You have the option of taking NT$100,000 three years from now or taking the present value of NT$100,000 now. Assuming an 8% rate in discounting. How much will you receive if you accept your winnings now? Future ValueFactorPresent Value Present Value of a Single Amount LO 5

26. E-26 Illustration: Determine the amount you must deposit today in your super savings account, paying 9% interest, in order to accumulate £5,000 for a down payment 4 years from now on a new car. Future ValueFactor Present Value £5,000x.70843= £3,542.15 Present Value of a Single Amount LO 5

27. E-27 The value now of a series of future receipts or payments, discounted assuming compound interest. Necessary to know the: 1.Discount rate, 2.Number of payments (receipts). 3.Amount of the periodic payments or receipts. Present Value of an Annuity LO 6 Learning Objective 6 Solve for present value of an annuity.

28. E-28 Illustration: Assume that you will receive €1,000 cash annually for three years at a time when the discount rate is 10%. Calculate the present value in this situation. What table do we use? Illustration E-14 Time diagram for a three-year annuity Present Value of an Annuity LO 6

29. E-29 What factor do we use? €1,000 x 2.48685 = €2,486.85 Annual ReceiptsFactorPresent Value Present Value of an Annuity LO 6

30. E-30 Illustration: Kildare Company has just signed a capitalizable lease contract for equipment that requires rental payments of €6,000 each, to be paid at the end of each of the next 5 years. The appropriate discount rate is 12%. What is the amount used to capitalize the leased equipment? €6,000 x 3.60478 = €21,628.68 Present Value of an Annuity LO 6

31. E-31 Illustration: Assume that the investor received €500 semiannually for three years instead of €1,000 annually when the discount rate was 10%. Calculate the present value of this annuity. €500 x 5.07569 = €2,537.85 Time Periods and Discounting LO 6

32. E-32 Two Cash Flows :  Periodic interest payments (annuity).  Principal paid at maturity (single sum). Present Value of a Long-term Note or Bond 01234910 5,000..... 5,000 LO 7 Learning Objective 7 Compute the present value of notes and bonds. NT$5,000 NT$100,000

33. E-33 01234910 5,000 NT$5,000..... 5,000 NT$100,000 Illustration: Assume a bond issue of 10%, five-year bonds with a face value of NT$100,000 with interest payable semiannually on January 1 and July 1. Calculate the present value of the principal and interest payments. Present Value of a Long-term Note or Bond LO 7

34. E-34 PV of Principal NT$100,000 x.61391 = NT$61,391 PrincipalFactorPresent Value Present Value of a Long-term Note or Bond LO 7

35. E-35 NT$5,000 x 7.72173 = NT$38,609 PaymentFactorPresent Value PV of Interest Present Value of a Long-term Note or Bond LO 7

36. E-36 Illustration: Assume a bond issue of 10%, five-year bonds with a face value of NT$100,000 with interest payable semiannually on January 1 and July 1. Present value of principal NT$61,391 Present value of interest 38,609 Present value of bondsNT$100,000 Present Value of a Long-term Note or Bond LO 7

37. E-37 Illustration: Now assume that the investor’s required rate of return is 12%, not 10%. The future amounts are again NT$100,000 and NT$5,000, respectively, but now a discount rate of 6% (12% ÷ 2) must be used. Calculate the present value of the principal and interest payments. Illustration E-20 Present value of principal and interest—discount Present Value of a Long-term Note or Bond LO 7

38. E-38 Illustration: Now assume that the investor’s required rate of return is 8%. The future amounts are again NT$100,000 and NT$5,000, respectively, but now a discount rate of 4% (8% ÷ 2) must be used. Calculate the present value of the principal and interest payments. Illustration E-21 Present value of principal and interest—premium Present Value of a Long-term Note or Bond LO 7

39. E-39 Illustration: Nagel-Siebert Trucking Company, a cross-country freight carrier, is considering adding another truck to its fleet because of a purchasing opportunity. Nagel-Siebert’s primary supplier of overland rigs is overstocked and offers to sell its biggest rig for £154,000 cash payable upon delivery. Nagel- Siebert knows that the rig will produce a net cash flow per year of £40,000 for five years (received at the end of each year), at which time it will be sold for an estimated residual value of £35,000. Nagel-Siebert’s discount rate in evaluating capital expenditures is 10%. Should Nagel-Siebert commit to the purchase of this rig? Computing the Present Values in a Capital Budgeting Decision LO 8 Learning Objective 8 Compute the present values in capital budgeting situations.

40. E-40 The cash flows that must be discounted to present value by Nagel-Siebert are as follows.  Cash payable on delivery (today): £154,000.  Net cash flow from operating the rig: £40,000 for 5 years (at the end of each year).  Cash received from sale of rig at the end of 5 years: £35,000. The time diagrams for the latter two cash flows are shown in Illustration E-22. PV in a Capital Budgeting Decision LO 8

41. E-41 The time diagrams for the latter two cash are as follows: PV in a Capital Budgeting Decision LO 8 Illustration E-22 Time diagrams for Nagel-Siebert Trucking Company

42. E-42 The computation of these present values are as follows: The decision to invest should be accepted. PV in a Capital Budgeting Decision LO 8 Illustration E-23 Present value computations at 10%

43. E-43 Assume Nagle-Siegert uses a discount rate of 15%, not 10%. The decision to invest should be rejected. PV in a Capital Budgeting Decision LO 8 Illustration E-24 Present value computations at 15%

44. E-44 LO 9 Illustration E-25 Financial calculator keys N = number of periods I = interest rate per period PV = present value PMT =payment FV = future value Using Financial Calculators Learning Objective 9 Use a financial calculator to solve time value of money problems.

45. E-45 Using Financial Calculators Illustration E-26 Calculator solution for present value of a single sum Present Value of a Single Sum Assume that you want to know the present value of €84,253 to be received in five years, discounted at 11% compounded annually. LO 9

46. E-46 Using Financial Calculators Present Value of an Annuity Assume that you are asked to determine the present value of rental receipts of €6,000 each to be received at the end of each of the next five years, when discounted at 12%. LO 9 Illustration E-27 Calculator solution for present value of a annuity

47. E-47 Using Financial Calculators Useful Applications – AUTO LOAN The loan has a 9.5% nominal annual interest rate, compounded monthly. The price of the car is €6,000, and you want to determine the monthly payments, assuming that the payments start one month after the purchase. LO 9 Illustration E-28 Calculator solution for auto loan payments.79167 9.5% ÷ 12

48. E-48 Using Financial Calculators Useful Applications – MORTGAGE LOAN You decide that the maximum mortgage payment you can afford is €700 per month. The annual interest rate is 8.4%. If you get a mortgage that requires you to make monthly payments over a 15-year period, what is the maximum purchase price you can afford? LO 9 Illustration E-29 Calculator solution for mortgage amount.70 8.4% ÷ 12

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