CHAPTER Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Brief Exercises Topics Questions Present value concepts 1, 2, 3, 4, 9, 17 Use of tables 5, 13, 14, 17 Present and future value problems: a Unknown future amount 7, 19 1, 5, 13 2, 3, b Unknown payments 10, 11, 12 6, 12, 15, 17 8, 16, 17 2, 4, 10, 15 c Unknown number of periods Exercises Problems d Unknown interest rate 15, 18 3, 11, 16 9, 10, 11, 14 2, e Unknown present value 6, 8, 19 2, 7, 8, 10, 14 3, 4, 5, 6, 7, 8, 11, 12, 17, 18, 19 1, 4, 7, 9, 13, 14 Value of a series of irregular deposits; changing interest rates Valuation of leases, pensions, bonds; choice between projects Deferred annuity Expected Cash Flows 3, 5, 15 7, 12, 13, 14, 15, 16 3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15 20, 21, 22 13, 14, 15 16 Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) 6-1 ASSIGNMENT CLASSIFICATION TABLE (BY LEARNING OBJECTIVE) Learning Objectives Brief Exercises Exercises Problems Identify accounting topics where the time value of money is relevant Distinguish between simple and compound interest Use appropriate compound interest tables Identify variables fundamental to solving interest problems Solve future and present value of problems 1, 2, 3, 4, 7, 2, 3, 6, 9, 10, 15 1, 2, 3, 5, 7, 9, 10 Solve future value of ordinary and annuity due problems 5, 6, 9, 13 3, 4, 6, 15, 16 2, 7 Solve present value of ordinary and annuity due problems 10, 11, 12, 14, 16, 17 3, 4, 5, 6, 11, 12, 17, 18, 19 1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 14 Solve present value problems related to deferred annuities and bonds 15 7, 8, 13, 14 6, 11, 12, 15 Apply expected cash flows to present value measurement 20, 21, 22 13, 14, 15 6-2 Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) ASSIGNMENT CHARACTERISTICS TABLE Item Description Level of Difficulty Time (minutes) E6-1 E6-2 E6-3 E6-4 E6-5 E6-6 E6-7 E6-8 E6-9 E6-10 E6-11 E6-12 E6-13 E6-14 E6-15 E6-16 E6-17 E6-18 E6-19 E6-20 E6-21 E6-22 Using interest tables Simple and compound interest computations Computation of future values and present values Computation of future values and present values Computation of present value Future value and present value problems Computation of bond prices Computations for a retirement fund Unknown rate Unknown periods and unknown interest rate Evaluation of purchase options Analysis of alternatives Computation of bond liability Computation of pension liability Investment decision Retirement of debt Computation of amount of rentals Least costly payoff Least costly payoff Expected cash flows Expected cash flows and present value Fair value estimate Simple Simple Simple Moderate Simple Moderate Moderate Simple Moderate Simple Moderate Simple Moderate Moderate Moderate Simple Simple Simple Simple Simple Moderate Moderate 5–10 5–10 10–15 15–20 10–15 15–20 12–17 10–15 5–10 10–15 10–15 10–15 15–20 15–20 15–20 10–15 10–15 10–15 10–15 5–10 15–20 15–20 P6-1 P6-2 P6-3 P6-4 P6-5 P6-6 P6-7 P6-8 P6-9 P6-10 P6-11 P6-12 P6-13 P6-14 P6-15 Various time value situations Various time value situations Analysis of alternatives Evaluating payment alternatives Analysis of alternatives Purchase price of a business Time value concepts applied to solve business problems Analysis of alternatives Analysis of business problems Analysis of lease vs purchase Pension funding Pension funding Expected cash flows and present value Expected cash flows and present value Fair value estimate Moderate Moderate Moderate Moderate Moderate Moderate Complex Moderate Complex Complex Complex Moderate Moderate Moderate Complex 15–20 15–20 20–30 20–30 20–25 25–30 30–35 20–30 30–35 30–35 25–30 20–25 20–25 20–25 20–25 Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) 6-3 LEARNING OBJECTIVES 6-4 Identify accounting topics where the time value of money is relevant Distinguish between simple and compound interest Use appropriate compound interest tables Identify variables fundamental to solving interest problems 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 and bonds Apply expected cash flows to present value measurement Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) CHAPTER REVIEW Chapter discusses the essentials of compound interest, annuities, and present value These techniques are being used in many areas of financial reporting where the relative values of cash inflows and outflows are measured and analyzed The material presented in Chapter will provide a sufficient background for application of these techniques to topics presented in subsequent chapters (L.O 1) Compound interest, annuity, and present value techniques can be applied to many of the items found in financial statements In accounting, these techniques can be used to measure the relative values of cash inflows and outflows, evaluate alternative investment opportunities, and determine periodic payments necessary to meet future obligations It is frequently used when market-based fair value information is not readily available Some of the accounting items to which these techniques may be applied are: (a) notes receivable and payable, (b) leases, (c) pensions and other post-retirement benefits, (d) long-term assets, (e) stock-based compensation, (f) business combinations, (g) disclosures, and (h) environmental liabilities Nature of Interest Interest is the payment for the use of money It is normally stated as a percentage of the amount borrowed (principal), calculated on a yearly basis Simple Interest (L.O 2) Simple interest is computed on the amount of the principal only The formula for simple interest can be expressed as p × i × n where p is the principal, i is the rate of interest for one period, and n is the number of periods Compound Interest (L.O 3) Compound interest is the process of computing interest on the principal plus any interest previously earned Compound interest is common in business situations where capital is financed over long periods of time Simple interest is applied to shortterm investments and debts due in one year or less How often interest is compounded can make a substantial difference in the level of return achieved, or the cost of borrowing In discussing compound interest, the term period is used in place of years because interest may be compounded daily, weekly, monthly, and so on To convert the annual interest rate to the compounding period interest rate, divide the annual interest rate by the number of compounding periods in a year The number of periods over which interest will be compounded is calculated by multiplying the number of years involved by the number of compounding periods in a year Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) 6-5 Compound Interest Tables (L.O 3) Compound interest tables have been developed to aid in the computation of present values and annuities Careful analysis of the problem as to which compound interest tables will be applied is necessary to determine the appropriate procedures to follow The contents of the five types of compound interest tables follow: Future value of 1. Contains the amounts to which will accumulate if deposited now at a specified rate and left for a specified number of periods (Table 6-1) Present value of 1. Contains the amount that must be deposited now at a specified rate of interest to equal at the end of a specified number of periods (Table 6-2) Future value of an ordinary annuity of 1. Contains the amount to which periodic rents of will accumulate if the rents are invested at the end of each period at a specified rate of interest for a specified number of periods (This table may also be used as a basis for converting to the amount of an annuity due of 1.) (Table 6-3) Present value of an ordinary annuity of Contains the amounts that must be deposited now at a specified rate of interest to permit withdrawals of at the end of regular periodic intervals for the specified number of periods (Table 6-4) Present value of an annuity due of Contains the amounts that must be deposited now at a specified rate of interest to permit withdrawals of at the beginning of regular periodic intervals for the specified number of periods (Table 6-5) (L.O 4) Certain concepts are fundamental to all compound interest problems These concepts are: a Rate of Interest. The annual rate that must be adjusted to reflect the length of the compounding period if less than a year b Number of Time Periods. The number of compounding periods (a period may be equal to or less than a year) c Future Amount. The value at a future date of a given sum or sums invested assuming compound interest d Present Value. The value now (present time) of a future sum or sums discounted assuming compound interest (L.O 5) The remaining concepts in this chapter cover the following six major time value of money concepts: a Future value of a single sum b Present value of a single sum c Future value of an ordinary annuity 6-6 Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) d Future value of an annuity due e Present value of an ordinary annuity f Present value of an annuity due 10 Single-sum problems generally fall into one of two categories The first category consists of problems that require the computation of the unknown future value of a known single sum of money that is invested now for a certain number of periods at a certain interest rate The second category consists of problems that require the computation of the unknown present value of a known single sum of money in the future that is discounted for a certain number of periods at a certain interest rate Present Value 11 The concept of present value is described as the amount that must be invested now to produce a known future value This is the opposite of the compound interest discussion in which the present value was known and the future value was determined An example of the type of question addressed by the present value method is: What amount must be invested today at 6% interest compounded annually to accumulate $5,000 at the end of 10 years? In this question the present value method is used to determine the initial dollar amount to be invested The present value method can also be used to determine the number of years or the interest rate when the other facts are known Future Value of an Annuity 12 (L.O 6) An annuity is a series of equal periodic payments or receipts called rents An annuity requires that the rents be paid or received at equal time intervals, and that compound interest be applied The future value of an annuity is the sum (future value) of all the rents (payments or receipts) plus the accumulated compound interest on them If the rents occur at the end of each time period, the annuity is known as an ordinary annuity If rents occur at the beginning of each time period, it is an annuity due Thus, in determining the amount of an annuity for a given set of facts, there will be one less interest period for an ordinary annuity than for an annuity due Present Value of an Annuity 13 (L.O 7) The present value of an annuity is the single sum that, if invested at compound interest now, would provide for a series of equal withdrawals for a certain number of future periods If the annuity is an ordinary annuity, the initial sum of money is invested at the beginning of the first period and withdrawals are made at the end of each subsequent period If the annuity is an annuity due, the initial sum of money is invested at the beginning of the first period and withdrawals are made at the beginning of each period Thus, the first rent withdrawn in an annuity due occurs on the day after the initial sum of money is invested When computing the present value of an annuity, for a given set of facts, there will be one less discount period for an annuity due than for an ordinary annuity Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) 6-7 Deferred Annuities 14 (L.O 8) A deferred annuity is an annuity in which two or more periods have expired before the rents will begin For example, an ordinary annuity of 10 annual rents deferred five years means that no rents will occur during the first five years, and that the first of the 10 rents will occur at the end of the sixth year An annuity due of 10 annual rents deferred five years means that no rents will occur during the first five years, and that the first of the 10 rents will occur at the beginning of the sixth year The fact that an annuity is a deferred annuity affects the computation of the present value However, the future value of a deferred annuity is the same as the future value of an annuity not deferred because there is no accumulation or investment on which interest may accrue 15 A long-term bond produces two cash flows: (1) periodic interest payments during the life of the bond, and (2) the principal (face value) paid at maturity At the date of issue, bond buyers determine the present value of these two cash flows using the market rate of interest 16 (L.O 9) Concepts Statement No introduces an expected cash flow approach that uses a range of cash flows and incorporates the probabilities of those cash flows to provide a more relevant measurement of present value The FASB takes the position that after computing the expected cash flows, a company should discount those cash flows by the risk-free rate of return, which is defined as the pure rate of return plus the expected inflation rate Financial Calculators *17 Business professionals, after mastering the above concepts, will often use a financial (business) calculator to solve time value of money problems When using financial calculators, the five most common keys used to solve time value of money problems are: NN II PV PV PMT PMT FV FV where: N = number of periods I = interest rate per period (some calculators use I/YR or i) PV = present value (occurs at the beginning of the first period) PMT = payment (all payments are equal in amount, and the time between each payment is the same) FV = future value (occurs at the end of the last period) 6-8 Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) LECTURE OUTLINE This chapter can be covered in two to three class sessions Most students have had previous exposure to single sum problems and ordinary annuities, but annuities due and deferred annuities will be new material for most students T EACHING T IP Illustration 6-5 can be distributed to students as a self-contained 6-page handout It uses 10 sample problems to demonstrate a 4-step solution method that can be used to solve any of the problems discussed in the chapter Some students with a background in math or finance courses may prefer to use exponential formulas rather than interest tables to find interest factors Other students with financial calculators may prefer to “let the calculator the work.” Remind students that whether they use interest tables, exponential formulas, or internal calculator routines, they cannot solve problems correctly unless they can correctly identify the type of problem, the number of periods, and the interest rate involved Students often have no difficulty with problems that are worded: “At 6%, what is the present value of an annuity due of 20 payments of $10,000 each?” but they may not know how to proceed if the same problem is worded: “What amount must be deposited now in an account paying 12% if it is desired to make 20 semiannual withdrawals of $10,000 each, beginning today?” Emphasize to students the importance of properly setting up the problem The second and third class sessions can be used for determining solutions to more complex problems, including deferred annuities, bond valuation and other accounting applications Some of the journal entries for the accounting applications can be discussed briefly A (L.O 1) Basic Time Value Concepts Discuss the importance of the time value of money Describe accounting applications of time value concepts: long-term assets, pensions, leases, long-term notes, stock-based compensation, business combinations, disclosures, and environmental liabilities Describe personal applications of time value concepts: purchasing a home, planning for retirement, evaluating alternative investments B (L.O 1) Nature of Interest Interest is payment for the use of money It is the excess cash received or repaid over and above the principal (amount loaned or borrowed) Interest rates are stated on an annual basis unless indicated otherwise Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) 6-9 C (L.O 2) Simple Interest T EACHING T IP Illustration 6-1 can be used to distinguish between simple interest and compound interest Simple interest is computed on the amount of the principal only Simple interest = p × i × n where p = principal i = rate of interest for a single period n = number of periods D (L.O 3) Compound Interest Compound interest is computed on the principal and on any interest earned that has not been paid or withdrawn The power of time and compounding (E.g., “What the numbers mean?” on text page 291 indicates that at 5% compounded annually, $1,000 grows to $23,839 in 65 years At 5% simple interest, $1,000 would grow to only $4,250 in 65 years.) $4,250 = $1,000 + ($1,000 × 05 × 65) The term period should be used instead of years a Interest may be compounded more than once a year: If interest is compounded Annually Semiannually Quarterly Monthly b Number of compounding periods per year 12 Adjustment when interest is compounded more than once a year (1) Compute the compounding period interest rate: Divide the annual interest rate by the number of compounding periods per year (2) Compute the total number of compounding periods: Multiply the number of years by the number of compounding periods per year 6-10 Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) K (L.O 8) Bond Valuation Problems Discuss the distinction between the stated interest rate and the market or effective interest rate: a The stated interest rate is used to determine the periodic amount of cash interest paid b The market or effective interest rate is used to value the bonds This is the rate which is used to locate the factor in the present value tables The example in the text demonstrates valuation of bonds which pay interest annually T EACHING T IP Illustration 6-6 provides an example of a bond valuation problem in which bond interest is paid semiannually L (L.O 9) Expected Cash Flow Approach Introduced by Concepts Statement No Uses a range of cash flows and their related probabilities to provide a more relevant measurement of present value Choosing an appropriate interest rate: a Is not always obvious b Three components of interest: (1) Pure rate of interest (2%–4%) (2) Expected inflation rate of interest (0%–?%) (3) Credit risk rate of interest (0%–5%) T EACHING T IP Use Illustration 6-7 to provide a basis for discussing how to apply the expected cash flow approach After computing the expected cash flows, a company discounts these cash flows by the risk-free rate of return This rate is the pure rate of return plus the expected inflation rate Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) 6-17 ILLUSTRATION 6-1 SIMPLE INTEREST VS COMPOUND INTEREST 6-18 Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) ILLUSTRATION 6-2 FUNDAMENTAL VARIABLES IN COMPOUND INTEREST PROBLEMS Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) 6-19 ILLUSTRATION 6-3 SINGLE SUM TIME DIAGRAMS 6-20 Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) ILLUSTRATION 6-3 (continued) ANNUITY TIME DIAGRAMS Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) 6-21 ILLUSTRATION 6-4 STEPS IN SOLVING COMPOUND INTEREST PROBLEMS 6-22 Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) PR OB LE MS SO LU TIO NS ILLUSTRATION 6-5 EXAMPLES OF COMPOUND INTEREST PROBLEMS Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) 6-23 ILLUSTRATION 6-5 (continued) 6-24 Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) ILLUSTRATION 6-5 (continued) Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) 6-25 ILLUSTRATION 6-5 (continued) 6-26 Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) ILLUSTRATION 6-5 (continued) Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) 6-27 ILLUSTRATION 6-5 (continued) 6-28 Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) 6-29 ILLUSTRATION 6-6 BOND VALUATION 6-30 Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) ILLUSTRATION 6-7 EXPECTED CASH FLOWS AND PRESENT VALUE Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) 6-31 ... Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For... Inc. Kieso, Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) 6-25 ILLUSTRATION 6-5 (continued) 6-26 Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, ... Intermediate Accounting, 15/e Instructor’s Manual (For Instructor Use Only) ILLUSTRATION 6-3 (continued) ANNUITY TIME DIAGRAMS Copyright © 2013 John Wiley & Sons, Inc. Kieso, Intermediate Accounting,