Intermediate Accounting Seventeenth Edition Kieso ● Weygandt ● Warfield Chapter Accounting and the Time Value of Money This slide deck contains animations Please disable animations if they cause issues with your device Learning Objectives After studying this chapter, you should be able to: Describe the fundamental concepts related to the time value of money Solve future and present value of problems Solve future value of ordinary and annuity due problems Solve present value of ordinary and annuity due problems Solve present value problems related to deferred annuities, bonds, and expected cash flows Copyright ©2019 John Wiley & Sons, Inc Preview of Chapter Accounting and the Time Value of Money Basic Time Value Concepts • Applications • The nature of interest • Simple interest • Compound interest • Fundamental variables Copyright ©2019 John Wiley & Sons, Inc Preview of Chapter Single-Sum Problems • Future value of single sum • Present value of single sum • Solving for other unknowns Annuities (Future Value) • Future value of ordinary annuity • Future value of annuity due • Examples of FV of annuity Copyright ©2019 John Wiley & Sons, Inc Preview of Chapter Annuities (Present Value) • Present value of ordinary annuity • Present value of annuity due • Examples of PV of annuity Copyright ©2019 John Wiley & Sons, Inc Preview of Chapter Other Time Value of Money Issues • Deferred annuities • Valuation of long-term bonds • Effective-interest method of bond discount/premium amortization • Present value measurement Copyright ©2019 John Wiley & Sons, Inc Learning Objective Describe the Fundamental Concepts Related to the Time Value of Money LO Copyright ©2019 John Wiley & Sons, Inc Basic Time Value Concepts Time Value of Money • A relationship between time and money • A dollar received today is worth more than a dollar promised at some time in the future When deciding among investment or borrowing alternatives, it is essential to be able to compare today’s dollar and tomorrow’s dollar on the same footing—to “compare apples to apples.” LO Copyright ©2019 John Wiley & Sons, Inc Applications of Time Value Concepts Present Value-Based Accounting Measurements LO Notes Leases Benefits Long-Term Assets Pensions and Other Postretirement Copyright ©2019 John Wiley & Sons, Inc Shared-Based Compensation Business Combinations Disclosures Environmental Liabilities The Nature of Interest • Payment for the use of money • Excess cash received or repaid over the amount lent or borrowed (principal) Variables in Interest Computation Principal The amount borrowed or invested Interest Rate A percentage of the outstanding principal Time The number of years or fractional portion of a year that the principal is outstanding LO Copyright ©2019 John Wiley & Sons, Inc 10 Present Value of an Annuity Due Illustration Space Odyssey, Inc., rents a communications satellite for years with annual rental payments of $4.8 million to be made at the beginning of each year If the relevant annual interest rate is 5%, what is the present value of the rental obligations? LO Copyright ©2019 John Wiley & Sons, Inc 71 Present Value of an Annuity Due Additional Illustration Jaime Yuen wins $4,000,000 in the state lottery She will be paid $200,000 at the beginning of each year for the next 20 years How much has she actually won? Assume an appropriate interest rate of 8% What table we use? LO Copyright ©2019 John Wiley & Sons, Inc 72 Present Value of an Annuity Due Table 6.5 Present Value of an Annuity Due of $200,000 Receipts LO × 10.60360 Factor Copyright ©2019 John Wiley & Sons, Inc = $2,120,720 Present Value 73 Present Value of Annuity Problems Computation of the Interest Rate Illustration: Assume you receive a statement from MasterCard with a balance due of $528.77 You may pay it off in 12 equal monthly payments of $50 each, with the first payment due one month from now What rate of interest would you be paying? Future value of an ordinary annuity = R( PVF - OAn,i ) $538.77 = $50( PVF - OA12,i ) ( PVFOA12 ,i ) = $528.77 = 10.57540 $50 Referring to Table 6.4 and reading across the 12-period row, you find 10.57534 in the 2% column Since 2% is a monthly rate, the nominal annual rate of interest is 24% (12 × 2%) The effective annual rate is LO Copyright ©2019 John Wiley & Sons, Inc 26.82413%[(1 + 02)12 − 1] 74 Present Value of Annuity Problems Computation of Periodic Rent Illustration: Norm and Jackie Remmers have saved $36,000 to finance their daughter Dawna’s college education They deposited the money in the Bloomington Savings and Loan Association, where it earns 4% interest compounded semiannually What equal amounts can their daughter withdraw at the end of every months during her college years, without exhausting the fund? Future value of an ordinary annuity = R( PVF - OAn,i ) $36.000 = R( PVF - OA8,2% ) $36, 000 = R(7.32548) R = $4,914.35 LO Copyright ©2019 John Wiley & Sons, Inc 75 Learning Objective Solve Present Value Problems Related to Deferred Annuities, Bonds, and Expected Cash Flows LO Copyright ©2019 John Wiley & Sons, Inc 76 Other Time Value of Money Issues Deferred Annuities LO • Rents begin after a specified number of periods • Future Value of a Deferred Annuity - Calculation same as future value of an annuity not deferred • Present Value of a Deferred Annuity - Must recognize interest that accrues during deferral period Copyright ©2019 John Wiley & Sons, Inc 77 Other Time Value of Money Issues Valuation of Long-Term Bonds Two Cash Flows: LO • Periodic interest payments (annuity) • Principal paid at maturity (single-sum) Copyright ©2019 John Wiley & Sons, Inc 78 Valuation of Long-Term Bonds Illustration Alltech Corporation on January 1, 2020, issues $100,000 of 5% bonds due in years with interest payable annually at year-end The current market rate of interest for bonds of similar risk is 6% What will the buyers pay for this bond issue? LO Copyright ©2019 John Wiley & Sons, Inc 79 Valuation of Long-Term Bonds Present Value of Interest TABLE 6.4 PRESENT VALUE OF AN ORDINARY ANNUITY OF $5,000 × 4.21236 Factor = $21,061.80 Present Value Interest Payment LO Copyright ©2019 John Wiley & Sons, Inc 80 Valuation of Long-Term Bonds Present Value of Principal TABLE 6.2 PRESENT VALUE OF (PRESENT VALUE OF A SINGLE SUM) $100,000 Principal LO ì 74726 Factor Copyright â2019 John Wiley & Sons, Inc = $74,726.00 Present Value 81 Valuation of Long-Term Bonds Principal plus Interest Alltech Corporation issues $100,000 of 5% bonds due in years with interest payable at year-end Present value of Interest $21,061.80 Present value of Principal 74,726.00 Bond current market value $95,787.80 Date Blank LO Account Title Cash Debit Credit 95,787.80 Blank Discount on bonds payable Blank Bonds payable 4,212.20 100,000.00 Copyright ©2019 John Wiley & Sons, Inc 82 Valuation of Long-Term Bonds LO Copyright ©2019 John Wiley & Sons, Inc 83 Present Value Measurement Concept Statement No introduces an expected cash flow approach that uses a range of cash flows and incorporates the probabilities of those cash flows Choosing an Appropriate Interest Rate Three Components of Interest: LO • Pure Rate • Expected Inflation Rate Credit Risk Rate Copyright â2019 John Wiley & Sons, Inc 84 Copyright Copyright © 2019 John Wiley & Sons, Inc All rights reserved Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Act without the express written permission of the copyright owner is unlawful Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc The purchaser may make back-up copies for his/her own use only and not for distribution or resale The Publisher assumes no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein Copyright ©2019 John Wiley & Sons, Inc 85 ... Compound Interest Tables Frequency of Compounding Determine number of periods by multiplying number of years involved by number of compounding periods per year 12% Annual Interest Rate over Years... Copyright ©2019 John Wiley & Sons, Inc Applications of Time Value Concepts Present Value-Based Accounting Measurements LO Notes Leases Benefits Long-Term Assets Pensions and Other Postretirement... the number of compounding periods per year Compounding Period Interest Rate = annual rate divided by the number of compounding periods per year LO Copyright ©2019 John Wiley & Sons, Inc 16 Compound