2. Time Value of Money Managerial Accounting, Fourth Edition Appendix A

3. 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. Study Objectives

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. Payment for the use of money. Excess cash received or repaid over the amount 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 outstanding. Nature of Interest Basic Time Value Concepts

6. Interest computed on the principal only. SO 1 Distinguish between simple and compound interest. Simple Interest ILLUSTRATION: On January 2, 2007, Tomalczyk borrows $20,000 for 3 years at a rate of 7% per year. Calculate the annual interest cost. Principal $20,000 Interest ratex 7% Annual interest$ 1,400 FULL YEAR

7. Simple Interest ILLUSTRATION continued: On March 31, 2007, Tomalczyk borrows $20,000 for 3 years at a rate of 7% per year. Calculate the interest cost for the year ending December 31, 2007. Principal $20,000 Interest ratex 7% Annual interest$ 1,400 Partial year x 9/12 Interest for 9 months$ 1,050 PARTIAL YEAR SO 1 Distinguish between simple and compound interest.

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 Computes interest on  the principal and  any interest earned that has not been paid or withdrawn.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

9. ILLUSTRATION: On January 2, 2007, Tomalczyk borrows $20,000 for 3 years at a rate of 7% per year. Calculate the total interest cost for all three years, assuming interest is compounded annually. Compound Interest SO 1 Distinguish between simple and compound interest.

10. SO 2 Solve future value of a single amount. Future Value Concepts Future Value of a Single Amount The value at a future date of a given amount invested assuming compound interest. FV = p x (1 + i )n Illustration C-3 Formula for future value FV = future value of a single amount p = principal (or present value) i = interest rate for one period n = number of periods

11. SO 2 Solve future value of a single amount. Future Value Concepts Future Value of a Single Amount The value at a future date of a given amount invested assuming compound interest. Illustration: Exercise: Steve Allen invested $10,000 today in a fund that earns 8% compounded annually. To what amount will the investment grow in 3 years?

12. 0123456 Present Value $10,000 What table do we use? Future Value? SO 2 Solve future value of a single amount. Future Value Concepts

13. Table 1 What factor do we use? SO 2 Solve future value of a single amount. Future Value Concepts

14. Table 1 $10,000 x 1.25971 = $12,597 Present ValueFactorFuture Value SO 2 Solve future value of a single amount. Future Value Concepts

15. PROOF - Future Value of a Single Sum Exercise: Steve Allen invested $10,000 today in a fund that earns 8% compounded annually. To what amount will the investment grow in 3 years? SO 2 Solve future value of a single amount. Future Value Concepts

16. Exercise: Steve Allen invested $10,000 today in a fund that earns 8% compounded semiannually. To what amount will the investment grow in 3 years? 0123456 Present Value $10,000 What table do we use? Future Value? SO 2 Solve future value of a single amount. Future Value Concepts

17. Table 1 What factor do we use? 6 compounding periods 4% interest per period Future Value Concepts SO 2 Solve future value of a single amount.

18. Table 1 $10,000 x 1.26532 = $12,653 Present ValueFactorFuture Value Future Value Concepts SO 2 Solve future value of a single amount.

19. (1) Periodic payments or receipts of the same amount, (2) Same-length interval between payments or receipts, (3) Compounding of interest each interval. Annuity requires the following: SO 3 Solve for future value of an annuity. The future value of an annuity is the sum of all the payments (receipts) plus the accumulated compound interest on them. Future Value Concepts

20. Future Value of an Annuity Rents occur at the end of each period. No interest during 1 st period. 01 Present Value 2345678 $20,00020,000 Future Value Future Value Concepts SO 3 Solve for future value of an annuity.

21. Exercise: Bayou Inc. will deposit $20,000 in a 12% fund at the end of each year for 8 years beginning December 31, Year 1. What amount will be in the fund immediately after the last deposit? 01 Present Value What table do we use? 2345678 $20,00020,000 Future Value SO 3 Solve for future value of an annuity. Future Value Concepts

22. Table 2 What factor do we use? SO 3 Solve for future value of an annuity. Future Value Concepts

23. Table 2 $20,000 x 12.29969 = $245,994 DepositFactorFuture Value SO 3 Solve for future value of an annuity. Future Value Concepts

24. 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 received in the future, 2.Length of time until amount is received, and 3.Interest rate (the discount rate). Present Value Concepts

25. Present Value of a Single Amount PV = FV / (1 + i )n Illustration C-9 Formula for present value PV = present value of a single amount FV = future value of a single amount p = principal (or present value) i = interest rate for one period n = number of periods Present Value Concepts SO 5 Solve for present value of a single amount.

26. Present Value of a Single Amount Multiply the present value factor by the future value. Illustration: Exercise: Itzak Perlman needs $20,000 in 4 years. What amount must he invest today if his investment earns 12% compounded annually? Present Value Concepts

27. Exercise: Itzak Perlman needs $20,000 in 4 years. What amount must he invest today if his investment earns 12% compounded annually? 0123456 Present Value? What table do we use? Future Value $20,000 SO 5 Solve for present value of a single amount. Present Value Concepts

28. Table 3 What factor do we use? SO 5 Solve for present value of a single amount. Present Value Concepts

29. Table 3 $20,000 x.63552 = $12,710 Future ValueFactorPresent Value SO 5 Solve for present value of a single amount. Present Value Concepts

30. Exercise: Itzak Perlman needs $20,000 in 4 years. What amount must he invest today if his investment earns 12% compounded quarterly? 0123456 Present Value? What table do we use? Future Value $20,000 SO 5 Solve for present value of a single amount. Present Value Concepts

31. Table 3 What factor do we use? SO 5 Solve for present value of a single amount. Present Value Concepts

32. Table 3 $20,000 x.62317 = $12,463 Future ValueFactorPresent Value SO 5 Solve for present value of a single amount. Present Value Concepts

33. Present Value of an Annuity 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 Concepts

34. 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..... 100,000 SO 6 Solve for present value of an annuity. Present Value Concepts

35. Table 4 What factor do we use? SO 6 Solve for present value of an annuity. Present Value Concepts

36. Table 4 $100,000 x 9.81815 = $981,815 ReceiptFactorPresent Value SO 6 Solve for present value of an annuity. Present Value Concepts

37. Present Value Concepts - Capital Budgeting Example 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? SO 7 Compute Present Values in Capital Budgeting

38. Present Value Concepts - Capital Budgeting Example SO 7 Compute Present Values in Capital Budgeting

39. Present Value Concepts - Capital Budgeting Example SO 7 Compute Present Values in Capital Budgeting

40. Present Value Concepts - Capital Budgeting Example SO 7 Compute Present Values in Capital Budgeting

41. LO 8 Use a financial calculator to solve time value of money problems. Using Financial Calculators Illustration C-22 Financial calculator keys PV = present value of a single amount N = number of periods I = interest rate per period PV = present value PMT = payment FV = future value

42. LO 8 Use a financial calculator to solve time value of money problems. Using Financial Calculators Illustration C-23 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.

43. LO 8 Use a financial calculator to solve time value of money problems. Using Financial Calculators Illustration C-24 Calculator solution for present value of an annuity 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%.

44. LO 8 Use a financial calculator to solve time value of money problems. Using Financial Calculators Illustration C-25 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.

45. LO 8 Use a financial calculator to solve time value of money problems. 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 C-26

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