1. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin The Time Value of Money: Future Amounts and Present Values Appendix B

2. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Learning Objective LO1 To explain what is meant by the phrase time value of money.

3. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin The Concept An amount of money available today can be safely invested to accumulate to a larger amount in the future.

4. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin The Concept 01234 Assume you invest $500 in a savings account that earns interest at the rate of 8% per year. This graph illustrates the growth in your savings account balance at the end of each of the next four years. $500 × 1.08 $540 × 1.08 $583 × 1.08 $630 × 1.08

5. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Learning Objective LO2 To describe the relationships between present value and future amounts.

6. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Relationships between Present Values and Future Amounts 01234 In this example, your initial investment of $500 is the present value. It is invested for four years at 8% interest. Over the four years, the value of your investment increases to $680, the future amount. $500 × 1.08 $540 × 1.08 $583 × 1.08 $630 × 1.08

7. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Learning Objective LO3 To explain three basic ways in which decision makers apply the time value of money.

8. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Applications of the Time Value of Money Concept Determine the amount to which an investment will accumulate over time Determine the amount that must be invested every period to accumulate a required future amount Determine the present value of cash flows expected to occur in the future Investors, accountants, and other decision makers apply the time value of money in three basic ways.

9. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Learning Objective LO4 To compute future amounts and the investments necessary to accumulate future amounts.

10. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Future Amounts Present Value Future Amount The Future Amount of a Single Investment

11. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Future Amounts Assume you invest $500 in a savings account that earns interest at the rate of 8% per year. What will be the future amount at the end of 4 years? $500 Present Value × 1.360 Factor = $680 Future Amount

12. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Computing the Required Investment Assume you need $680 at the end of 4 years. If you can invest at 8% per year, what is the present value? $680 Future Amount 1.360 Factor $500 Present Value =

13. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin An annuity is a series of equal periodic payments. The Future Amount of an Annuity

14. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin The Future Amount of an Annuity Future Amount Annuity Payment

15. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin The Future Amount of an Annuity Assume you invest $500 in a savings account at the end of each of the next 4 years. The account earns interest at the rate of 8% per year. What will be the balance in your account at the end of 4 years? $500 Periodic Payment × 4.506 Factor = $2,253 Future Amount of an Annuity

16. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin The Future Amount of an Annuity Assume you need $2,253 at the end of 4 years. If you can invest at 8% per year, what is the amount of required periodic payment? $2,253 Future Amount of an Annuity 4.506 Factor $500 Periodic Payment =

17. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Interest Periods of Less than One Year In our computations, we have assumed that interest is paid (compounded) or payments are made annually. Investment payments or interest payments may be made on a more frequent basis, such as monthly, quarterly, or semiannually.

18. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Learning Objective LO5 To compute the present values of future cash flows.

19. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Present Value Future Amount Present Value of a Single Investment

20. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Present Values What would you pay today for the opportunity to receive $680 in 4 years, assuming an 8% interest rate? $680 Future Amount ×.735 Factor = $500 Present Value (rounded)

21. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin What is the Appropriate Discount Rate? All investments involve some degree of risk that actual future cash flows may turn out to be less than expected. Investors will require a rate of return that justifies taking this risk.

22. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin The Present Value of an Annuity Present Value Annuity Payment

23. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin The Present Value of an Annuity Assume you need cash flows of $500 at the end of each of the next 4 years. If your investment earns interest at the rate of 8% per year, what amount do you need to invest today to achieve your cash flow needs? $500 Periodic Payment × 3.312 Factor = $1,656 Present Value of an Annuity

24. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Discount Periods of Less than One Year The present value tables can be used with discount periods of any length, but the discount rate must be for that length of time.

25. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Learning Objective LO6 To discuss accounting applications of the concept of present value.

26. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Valuation of Financial Instruments CashEquity Contract s Accountants use the phrase financial instruments to describe cash, equity investment in another business, and any contracts that call for receipts or payments of cash. Whenever the present value of a financial instrument differs significantly from the sum of the expected future cash flows, the instrument is recorded in the accounting records at its present value—not at the expected amount of the future cash receipts or payments.

27. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Valuation of Financial Instruments Marketable Securities Accounts Receivable Accounts Payable Appear in the balance sheet at their current market values, which represents their present value. Appear in the balance sheet at the amounts expected to be collected or paid in the near future. Technically, these are future amounts but they are usually received or paid within 30 or 60 days so the differences between these future amounts and their present values simply are not material.

28. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Interest-Bearing Receivable and Payables Interest-bearing receivables and payables initially are recorded in accounting records at the present value of the future cash flows— also called the “principal amount” of the obligation. This present value is often substantially less than the sum of the expected future amounts.

29. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin “Non-Interest-Bearing” Notes If the difference between the present value of a note and its face amount is material, the note initially is recorded at its present value.

30. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin “Non-Interest-Bearing” Notes Assume that on January 1, 2005, Elron Corporation purchases land from U.S. Development Company. As full payment for this land, Elron issues a $300,000 installment note payable, due in 3 annual installments of $100,000, beginning December 31, 2005. There is no mention of an interest rate. Elron should use the present value of this note—not the face amount—in determining the cost of the land and reporting its liability. Assume that a realistic interest rate for financing land over a 3 year period currently is 10% per year. $100,000 Periodic Payment × 2.487 Factor = $248,700 Present Value of an Annuity * Interest expense is determined by multiplying 10% times the last unpaid balance. In the last period, interest expense is equal to the amount of the final payment minus the remaining unpaid balance. This compensates for using factors carried to only three decimal places.

31. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin “Non-Interest-Bearing” Notes

32. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Market Prices of Bonds Calculate the Present Value of the Lump-sum Maturity Payment (Face Value) Calculate the Present Value of the Annuity Payments (Interest) On January 1, 2007, Driscole Corporation issues $1,000,000 of 10-year, 10% bonds when the going market rate of interest is 12%. Interest is paid semiannually beginning on June 30, 2007. Because bond interest is paid semiannually, we must use 20 semiannual periods as the life of the bond issue and a 6% semiannual market rate of interest in our present value calculations.

33. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Market Prices of Bonds Calculate the Present Value of the Lump-sum Maturity Payment (Face Value) Calculate the Present Value of the Annuity Payments (Interest) On January 1, 2007, Driscole Corporation issues $1,000,000 of 10-year, 10% bonds when the going market rate of interest is 12%. Interest is paid semiannually beginning on June 30, 2007.

34. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Market Prices of Bonds

35. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Capital Leases A capital lease is regarded as a sale of the leased asset by the lessor to the lessee. At the date of this sale, the lessor recognizes sales revenue equal to the present value of the future lease payments receivable, discounted at a realistic rate of interest. The lessee also uses the present value of the future payments to determine the cost of the leased asset and the valuation of the related liability.

36. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Capital Leases Assume that on December 1, Pace Tractor uses a capital lease to finance the sale of a tractor to Kelly Grading Company. The tractor was carried in Pace Tractor’s perpetual inventory records at a cost of $15,000. Terms of the lease call for Kelly Grading Company to make 24 monthly payments of $1,000 each, beginning on December 31. These lease payments include an interest charge of 1% per month. At the end of the 24-month lease, title to the tractor will pass to Kelly Grading Company at no additional cost. Let’s look at the entries for Pace Tractor.

37. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Capital Leases $1,000 Periodic Payment × 21.243 Factor = $21,243 Present Value of an Annuity

38. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Capital Leases $24,000 - $21,243 = $2,757  24 months = $212 per month

39. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Capital Leases $1,000 Periodic Payment × 21.243 Factor = $21,243 Present Value of an Annuity

40. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Obligations for Postretirement Benefits Any unfunded obligation for postretirement benefits appears in the balance sheet at the present value of the expected future cash outlays to retired employees.

41. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Disclosure of Up-to-Date Present Value Information The FASB requires companies to disclose the current values of financial instruments whenever these values differ significantly from recorded amounts.

42. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin Deferred Income Taxes The only long-term liability not shown at the present value of the expected future payments is the obligation for deferred income taxes.

43. © The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin End of Appendix B