1. Appendix A- 1

2. Appendix A- 2 Time Value of Money Managerial Accounting Fifth Edition Weygandt Kimmel Kieso

3. Appendix A- 3 study objectives 1. 1.Distinguish between simple and compound interest. 2. 2.Solve for future value of a single amount. 3. 3.Solve for future value of an annuity. 4. 4.Identify the variables fundamental to solving present value problems. 5. 5.Solve for present value of a single amount. 6. 6.Solve for present value of an annuity. 7. 7.Compute the present values in capital budgeting situations. 8. 8.Use a financial calculator to solve time value of money problems.

4. Appendix A- 4 In accounting (and finance), the term indicates that 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

5. Appendix A- 5 Payment for the use of money. Excess cash received or repaid over the amount invested or borrowed (principal). Variables involved in financing transaction: 1. Principal (p) - Amount borrowed or invested. 2. Interest Rate (i) – An annual percentage. 3. Time (n) - The number of years or portion of a year that the principal is borrowed or invested. Nature of Interest SO 1 Distinguish between simple and compound interest.

6. Appendix A- 6 Interest computed on the principal only. SO 1 Distinguish between simple and compound interest. Nature of Interest Illustration: On January 2, 2010, assume you borrow $5,000 for 2 years at a simple interest of 12% annually. Calculate the annual interest cost. Interest = p x i x n = $5,000 x.12 x 2 = $1,200 FULL YEAR Illustration A-1 Simple Interest

7. Appendix A- 7 Computes interest on  the principal and  any interest earned that has not been paid or withdrawn. Most business situations use compound interest. Nature of Interest SO 1 Distinguish between simple and compound interest. Compound Interest

8. Appendix A- 8 Illustration: Assume that you deposit $1,000 in BankOne, where it will earn simple interest of 9% per year, and you deposit another $1,000 in CityCorp, 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. Nature of Interest - Compound Interest SO 1 Distinguish between simple and compound interest. Year 1 $1,000.00 x 9%$ 90.00$ 1,090.00 Year 2 $1,090.00 x 9%$ 98.10$ 1,188.10 Year 3 $1,188.10 x 9%$106.93$ 1,295.03 Illustration A-2

9. Appendix A- 9 SO 2 Solve for future value of a single amount. The future value is the value at a future date of a given amount invested assuming compound interest. Illustration A-3 Future value computation Future Value of a Single Amount

10. Appendix A- 10 SO 2 Solve for future value of a single amount. Illustration: If you earn a 9% rate of return, compute the future value of $1,000 at the end of three years: Illustration A-4 Future Value of a Single Amount

11. Appendix A- 11 SO 2 Solve for future value of a single amount. Illustration: If you earn a 9% rate of return, compute the future value of $1,000 at the end of three years: Illustration A-4 Future Value of a Single Amount What table do we use?

12. Appendix A- 12 What factor do we use? Present ValueFactorFuture Value SO 2 Solve for future value of a single amount. Future Value of a Single Amount $1,000x1.29503=$1,295.03

13. Appendix A- 13 Illustration: John and Mary Rich invested $20,000 in a savings account paying 6% interest at the time their son, Mike, was born. The money is to be used by Mike for his college education. On his 18th birthday, Mike withdraws the money from his savings account. How much did Mike withdraw from his account? Illustration A-5 SO 2 Solve for future value of a single amount. Future Value of a Single Amount

14. Appendix A- 14 Present ValueFactorFuture Value SO 2 Solve for future value of a single amount. Future Value of a Single Amount $20,000x2.85434=$57,086.80

15. Appendix A- 15 The Future Value of an Annuity is the sum of all the payments (receipts) plus the accumulated compound interest on them. In computing the future value of an annuity, it is necessary to know 1.the interest rate, 2.the number of compounding periods, and 3.the amount of the periodic payments or receipts. SO 3 Solve for future value of an annuity. Future Value of a Annuity

16. Appendix A- 16 Illustration: Assume that you invest $2,000 at the end of each year for three years at 5% interest compounded annually. Compute the future value. Illustration A-6 SO 3 Solve for future value of an annuity. Future Value of a Annuity

17. Appendix A- 17 SO 3 Solve for future value of an annuity. Future Value of a Annuity Illustration A-7 Solution on notes page

18. Appendix A- 18 SO 3 Solve for future value of an annuity. Future Value of a Annuity Annual InvestmentFactorFuture Value $2,000x3.15250=$6,305 What factor do we use?

19. Appendix A- 19 SO 4 Identify the variables fundamental to solving present value problems. 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 paid or received in the future, 2.Length of time until amount is paid or received, and 3.Interest rate (the discount rate). Present Value Variables

20. Appendix A- 20 Present Value = Future Value / (1 + i ) n Illustration A-9 Formula for present value i = interest rate for one period n = number of periods Present Value of a Single Amount SO 5 Solve for present value of a single amount.

21. Appendix A- 21 Illustration: If you want a 10% rate of return, you would compute the present value of $1,000 for one year as follows: Illustration A-10 Present Value of a Single Amount SO 5 Solve for present value of a single amount.

22. Appendix A- 22 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 A-10 Present Value of a Single Amount What table do we use? SO 5 Solve for present value of a single amount.

23. Appendix A- 23 What factor do we use? Future ValueFactorPresent Value $1,000x.90909=$909.09 Present Value of a Single Amount SO 5 Solve for present value of a single amount.

24. Appendix A- 24 Illustration: If you receive the single amount of $1,000 in two years, discounted at 10% [PV = $1,000 / 1.10 2 ], the present value of your $1,000 is $826.45. Illustration A-11 What table do we use? Present Value of a Single Amount SO 5 Solve for present value of a single amount.

25. Appendix A- 25 Present Value of a Single Amount What factor do we use? Future ValueFactorPresent Value $1,000x.82645=$826.45 SO 5 Solve for present value of a single amount.

26. Appendix A- 26 Present Value of a Single Amount Illustration: Suppose you have a winning lottery ticket and the state gives you the option of taking $10,000 three years from now or taking the present value of $10,000 now. The state uses an 8% rate in discounting. How much will you receive if you accept your winnings now? Future ValueFactorPresent Value $10,000x.79383=$7,938.30 SO 5 Solve for present value of a single amount.

27. Appendix A- 27 Illustration: Determine the amount you must deposit now in a savings account, paying 9% interest, in order to accumulate $5,000,000 four years from today. Future ValueFactorPresent Value $5,000,000x.70843=$3,542,150 Present Value of a Single Amount SO 5 Solve for present value of a single amount.

28. Appendix A- 28 The value now of a series of future receipts or payments, discounted assuming compound interest. 01 Present Value 2341920 $100,000100,000..... 100,000 SO 6 Solve for present value of an annuity. Present Value of an Annuity

29. Appendix A- 29 Illustration: Assume that you will receive $1,000 cash annually for three years at a time when the discount rate is 10%. What table do we use? Illustration A-14 SO 6 Solve for present value of an annuity. Present Value of an Annuity

30. Appendix A- 30 Illustration A-15 Solution on notes page SO 6 Solve for present value of an annuity. Present Value of an Annuity

31. Appendix A- 31 Annual ReceiptsFactorPresent Value $1,000x2.48685=$2,486.85 What factor do we use? SO 6 Solve for present value of an annuity. Present Value of an Annuity

32. Appendix A- 32 Illustration: Christel Company has just signed an agreement to purchase equipment for installment 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 present value of the installment payments? PaymentsFactorPresent Value $6,000x3.60478=$21,628.68 SO 6 Solve for present value of an annuity. Present Value of an Annuity

33. Appendix A- 33 Illustration: When the time frame is less than one year, you need to convert the annual interest rate to the applicable time frame. Assume that the investor received $500 semiannually for three years instead of $1,000 annually when the discount rate was 10%. $500 x 5.07569 = $2,537.85 Time Periods and Discounting SO 6 Solve for present value of an annuity.

34. Appendix A- 34 The decision to make long-term capital investments is best evaluated using discounting techniques that recognize the time value of money. To do this, many companies calculate the present value of the cash flows involved in a capital investment. Present Value in a Capital Budgeting Decision SO 7 Compute the present values in capital budgeting situations.

35. Appendix A- 35 Illustration: Nagel-Siebert Trucking Company, a cross- country freight carrier in Montgomery, Illinois, is considering adding another truck to its fleet because of a purchasing opportunity. Navistar Inc., 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 salvage 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? Present Value in a Capital Budgeting Decision SO 7 Compute the present values in capital budgeting situations.

36. Appendix A- 36 Present Value in a Capital Budgeting Decision The cash flows that must be discounted to present value are: Cash payable on delivery (today): $154,000. Net cash flow from operating the rig: $40,000 for 5 years. Cash received from sale of rig at the end of 5 years: $35,000. Illustration A-17 SO 7 Compute the present values in capital budgeting situations.

37. Appendix A- 37 Present Value in a Capital Budgeting Decision Notice the present value of the net operating cash flows is discounting an annuity, while computing the present value of the $35,000 salvage value is discounting a single sum. Illustration A-18 Accepted SO 7 Compute the present values in capital budgeting situations.

38. Appendix A- 38 SO 8 Use a financial calculator to solve time value of money problems. Using Financial Calculators Illustration C-20 Financial calculator keys N = number of periods I = interest rate per period PV = present value PMT = payment FV = future value

39. Appendix A- 39 Using Financial Calculators Illustration A-21 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. SO 8 Use a financial calculator to solve time value of money problems.

40. Appendix A- 40 Using Financial Calculators Illustration A-22 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%. SO 8 Use a financial calculator to solve time value of money problems.

41. Appendix A- 41 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. Using Financial Calculators Illustration A-23 Useful Applications – Auto Loan SO 8 Use a financial calculator to solve time value of money problems.

42. Appendix A- 42 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? Illustration A-24 SO 8 Use a financial calculator to solve time value of money problems.

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