ACCT550 Ch 6 Summary for Students

8/10/2019 ACCT550 Ch 6 Summary for Students

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CHAPTER 6

Accounting and the Time Value of Money

LEARNING OBJECTIVES

1. Identify accounting topics where the time value of money is relevant.2. Distinguish between simple and compound interest.

3. Use appropriate compound interest tables.

4. Identify variables fundamental to solving interest problems.

5. Solve future and present value of 1 problems.

6. Solve future value of ordinary and annuity due problems.

7. Solve present value of ordinary and annuity due problems.

8. Solve present value problems related to deferred annuities and bonds.

9. Apply expected cash flows to present value measurement.

CHAPTER REVIEW

1. Chapter 6 discusses the essentials of compound interest, annuities, and present vaThese techniques are being used in many areas of financial reporting where the relavalues of cash inflows and outflows are measured and analyzed. The material presenin Chapter 6 will provide a sufficient background for application of these techniquestopics presented in subsequent chapters.

2. (L.O. 1)Compound interest, annuity, and present value techniques can be appliemany of the items found in financial statements. In accounting, these techniques can

used to measure the relative values of cash inflows and outflows, evaluate alternainvestment opportunities, and determine periodic payments necessary to meet futobligations. It is frequently used when market-based fair value information is not reaavailable. Some of the accounting items to which these techniques may be applied a(a) notes receivable and payable, (b) leases, (c) pensions and other post-retirembenefits, (d) long-term assets, (e) stock-based compensation, (f) busincombinations, (g) disclosures, and (h) environmental liabilities.

Nature of Interest

3. Interest is the payment for the use of money. It is normally stated as a percentage of

amount borrowed (principal), calculated on a yearly basis.

Simple Interest

4. (L.O. 2)Simple interest is computed on the amount of the principal only. The formulasimple interest can be expressed as p i n where p is the principal, i is the ratinterest for one period, andn is the number of periods.

Copyright 2013 John Wiley & Sons, Inc. K ieso, Intermediate Accounting,15/e Instructors Manual ( For Instructor Use Only)


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Compound Interest

5. (L.O. 3)Compound interest is the process of computing interest on the principal plusany interest previously earned. Compound interest is common in business situationswhere capital is financed over long periods of time. Simple interest is applied to short-term investments and debts due in one year or less. How often interest is compoundedcan make a substantial difference in the level of return achieved, or the cost of borrowing.

6. In discussing compound interest, the term period is used in place of years becauseinterest may be compounded daily, weekly, monthly, and so on. To convert the annualinterest rate to the compounding period interest rate, divide the annual interest rateby the number of compounding periods in a year. The number of periods over whichinterest will be compounded is calculated by multiplying the number of years involved bythe number of compounding periods in a year.

Compound Interest Tables

7. (L.O. 3) Compound interest tables have been developed to aid in the computation ofpresent values and annuities. Careful analysis of the problem as to which compound

interest tables will be applied is necessary to determine the appropriate procedures tofollow. The contents of the five types of compound interest tables follow:

Future value of 1.Contains the amounts to which 1 will accumulate if deposited nowat 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 rateof interest to equal 1 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 periodicrents of 1 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 beused as a basis for converting to the amount of an annuity due of 1.) (Table 6-3)

Present value of an ordinary annuity of 1. Contains the amounts that must bedeposited now at a specified rate of interest to permit withdrawals of 1 at the end ofregular periodic intervals for the specified number of periods. (Table 6-4)

Present value of an annuity due of 1. Contains the amounts that must be depositednow at a specified rate of interest to permit withdrawals of 1 at the beginning of regularperiodic intervals for the specified number of periods. (Table 6-5)

8. (L.O. 4) Certain concepts are fundamental to all compound interest problems. Theseconcepts are:

a. Rate of Interest.The annual rate that must be adjusted to reflect the length of thecompounding period if less than a year.

b. Number of Time Periods. The number of compounding periods (a period may beequal to or less than a year).

6-2 Copyright 2013 John Wiley & Sons, Inc. K ieso, Intermediate Accounting,15/e Instructors Manual ( For Instructor Use Only)


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c. Future Amount.The value at a future date of a given sum or sums invesassuming compound interest.

d. Present Value. The value now (present time) of a future sum or sums discounassuming compound interest.

9. (L.O. 5) The remaining concepts in this chapter cover the following six major time valumoney concepts:

a. Future value of a single sum.

b. Present value of a single sum.

c. Future value of an ordinary annuity.

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 consof problems that require the computation of the unknown future value of a known sinsum of money that is invested now for a certain number of periods at a certain interrate. The second category consists of problems that require the computation of unknown present value of a known single sum of money in the future that is discounfor 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 nowproduce a known future value. This is the opposite of the compound interest discussiowhich the present value was known and the future value was determined. An examplthe type of question addressed by the present value method is: What amount mustinvested today at 6% interest compounded annually to accumulate $5,000 at the end10 years? In this question the present value method is used to determine the initial doamount to be invested. The present value method can also be used to determine 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 rentsannuity requires that the rents be paid or received at equal time intervals, and tcompound interest be applied. The future value of an annuity is the sum (future vaof all the rents (payments or receipts) plus the accumulated compound interest on thIf the rents occur at the end of each time period, the annuity is known as an ordinannuity. If rents occur at the beginning of each time period, it is an annuity due. Thusdetermining the amount of an annuity for a given set of facts, there will be one linterest period for an ordinary annuity than for an annuity due.



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Present Value of an Annuity

13. (L.O. 7) The present value of an annuity is the single sum that, if invested at compoundinterest now, would provide for a series of equal withdrawals for a certain number of futureperiods. If the annuity is an ordinary annuity, the initial sum of money is invested atthe beginning of the first period and withdrawals are made at the end of each subsequentperiod. 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 ofmoney is invested. When computing the present value of an annuity, for a given set offacts, there will be one less discount period for an annuity due than for an ordinaryannuity.

Deferred Annuities

14. (L.O. 8) A deferred annuity is an annuity in which two or more periods have expired beforethe rents will begin. For example, an ordinary annuity of 10 annual rents deferred fiveyears 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 deferredfive years means that no rents will occur during the first five years, and that the first of the10 rents will occur at the beginning of the sixth year. The fact that an annuity is a deferredannuity affects the computation of the present value. However, the future value of adeferred annuity is the same as the future value of an annuity not deferred becausethere 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 lifeof the bond, and (2) the principal (face value) paid at maturity. At the date of issue, bondbuyers determine the present value of these two cash flows using the market rate ofinterest.

16. (L.O. 9)Concepts Statement No. 7introduces an expected cash flow approach that usesa range of cash flows and incorporates the probabilities of those cash flows to providea more relevant measurement of present value. The FASB takes the position that aftercomputing the expected cash flows, a company should discount those cash flows by therisk-free rate of return,which is defined as the pure rate of return plus the expectedinflation 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 financialcalculators, the five most common keys used to solve time value of money problems are:

where:


N I PV PMT FV


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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 paymis the same).FV = future value (occurs at the end of the last period).

ILLUSTRATION 6-1SIMPLE INTEREST VS. COMPOUND INTERES



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LLUSTRATION 6-2FUNDAMENTAL VARIABLES IN COMPOUNDNTEREST PROBLEMS



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ILLUSTRATION 6-3SINGLE SUM TIME DIAGRAMS



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LLUSTRATION 6-3 (continued)ANNUITY TIME DIAGRAMS



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ILLUSTRATION 6-4STEPS IN SOLVING COMPOUND INTEREST PROBLEMS



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LLUSTRATION 6-5EXAMPLES OF COMPOUND INTEREST PROBLEMS

PROBLEMS

SOLUTIONS



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ILLUSTRATION 6-5 (continued)



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LLUSTRATION 6-5 (continued)



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LLUSTRATION 6-5 (continued)



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LLUSTRATION 6-6BOND VALUATION



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ILLUSTRATION 6-7EXPECTED CASH FLOWS AND PRESENT VALUE


ACCT550 Ch 6 Summary for Students

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