1 / 34

The Time Value of Money: Future Amounts and Present Values

The Time Value of Money: Future Amounts and Present Values. Appendix B. The Concept. An amount of money available today can be safely invested to accumulate to a larger amount in the future. 0. 1. 2. 3. 4. The Concept. $630 × 1.08. $583 × 1.08. $540 × 1.08. $500 × 1.08.

brita
Download Presentation

The Time Value of Money: Future Amounts and Present Values

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Time Value of Money:Future Amounts and Present Values Appendix B

  2. The Concept An amount of money available today can be safely invested to accumulate to a larger amount in the future.

  3. 0 1 2 3 4 The Concept $630 × 1.08 $583 × 1.08 $540 × 1.08 $500 × 1.08 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.

  4. 0 1 2 3 4 Relationships between Present Values and Future Amounts $630 × 1.08 $583 × 1.08 $540 × 1.08 $500 × 1.08 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.

  5. Applications of the Time Value of Money Concept Investors, accountants, and other decision makers apply the time value of money in three basic ways. 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

  6. Future Amount Present Value Future Amounts A future amount is simply the dollar amount to which a present value will accumulate over time.

  7. $500 Present Value× 1.360 Factor = $680 Future Amount 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?

  8. $680 Future Amount1.360 Factor $500 Present Value= 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?

  9. Annuity Payment Annuity Payment Annuity Payment Annuity Payment Annuity Payment The Future Amount of an Annuity An annuity is a series of equal periodic payments. Future Amount

  10. $500 Periodic Payment× 4.506 Factor =$2,253 Future Amount of an Annuity 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?

  11. $2,253 Future Amount of an Annuity 4.506 Factor $500 Periodic Payment= 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?

  12. 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.

  13. Future Amount Present Value Present Value The present value is today’s value of funds to be received in the future.

  14. $680 Future Amount × .735 Factor = $500 Present Value (rounded) Present Values What would you pay today for the opportunity to receive $680 in 4 years, assuming an 8% interest rate?

  15. 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.

  16. Annuity Payment Annuity Payment Annuity Payment Annuity Payment Annuity Payment The Present Value of an Annuity Present Value

  17. $500 Periodic Payment× 3.312 Factor =$1,656 Present Value of an Annuity 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?

  18. 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.

  19. Valuation of Financial Instruments 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. Cash Equity Contracts 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.

  20. Appear in the balance sheet at their fair 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. Valuation of Financial Instruments Investments in Securities Accounts Receivable Accounts Payable

  21. Interest-Bearing Receivables 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.

  22. “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.

  23. * 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. “Non-Interest-Bearing” Notes Assume that on 1 January 2009, 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 31 December 2009. 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.

  24. “Non-Interest-Bearing” Notes

  25. Market Prices of Bonds Calculate the Present Value of the Lump-sum Maturity Payment (Face Value) On 1 January 2009, 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 30 June 2009. Calculate the Present Value of the Annuity Payments (Interest) 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.

  26. Market Prices of Bonds Calculate the Present Value of the Lump-sum Maturity Payment (Face Value) On 1 January 2009, 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 30 June 2009. Calculate the Present Value of the Annuity Payments (Interest)

  27. Market Prices of Bonds

  28. Finance Leases A finance 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.

  29. Finance Leases Assume that on 1 December, Pace Tractor uses a finance 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 31 December. 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.

  30. $1,000 Periodic Payment× 21.243 Factor = $21,243 Present Value of an Annuity Finance Leases

  31. $24,000 - $21,243 = $2,757  24 months = $114.88 per month Finance Leases

  32. Finance Leases $1,000 Periodic Payment× 21.243 Factor = $21,243 Present Value of an Annuity

  33. 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.

  34. End of Appendix B

More Related