Intructor manual intermediate accounting 15th kiesoch06

Solve future value of ordinary and annuity due problems.. Solve present value of ordinary and annuity due problems.. The first category consists of problems that require the computation

CHAPTER 6 Accounting and the Time Value of Money

ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC)

Brief

4 Value of a series of irregular

deposits; changing interest

ASSIGNMENT CLASSIFICATION TABLE (BY LEARNING OBJECTIVE)

Learning Objectives

Brief

1 Identify accounting topics where the time

value of money is relevant.

2 Distinguish between simple and compound

interest.

2

4 Identify variables fundamental to solving

8 Solve present value problems related

to deferred annuities and bonds.

9 Apply expected cash flows to present

value measurement.

ASSIGNMENT CHARACTERISTICS TABLE

Level of Difficulty

Time (minutes)

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 value.These techniques are being used in many areas of financial reporting where the relativevalues of cash inflows and outflows are measured and analyzed The material presented

in Chapter 6 will provide a sufficient background for application of these techniques totopics presented in subsequent chapters

2 (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 beused to measure the relative values of cash inflows and outflows, evaluate alternativeinvestment opportunities, and determine periodic payments necessary to meet futureobligations It is frequently used when market-based fair value information is not readilyavailable 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

3 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

4 (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

5 (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 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 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 interestwill be compounded is calculated by multiplying the number of years involved by thenumber 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 compoundinterest 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 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 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 aspecified 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 be 

deposited 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 deposited 

now 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 These 

concepts 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 be 

equal to or less than a year)

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

d Present Value The value now (present time) of a future sum or sums discounted 

assuming compound interest

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

a Future value of a single sum

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 interestrate 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 inwhich the present value was known and the future value was determined An example ofthe type of question addressed by the present value method is: What amount must beinvested 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 dollaramount 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 lessinterest 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 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 before

the 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 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, bondbuyers determine the present value of these two cash flows using the market rate ofinterest

16 (L.O 9) Concepts Statement No 7 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 aftercomputing 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 financialcalculators, the five most common keys used to solve time value of money problems are:

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)

LECTURE OUTLINE

This chapter can be covered in two to three class sessions Most students have had previousexposure to single sum problems and ordinary annuities, but annuities due and deferredannuities 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 exponentialformulas rather than interest tables to find interest factors Other students with financialcalculators may prefer to “let the calculator do the work.” Remind students that whether theyuse interest tables, exponential formulas, or internal calculator routines, they cannot solveproblems correctly unless they can correctly identify the type of problem, the number ofperiods, and the interest rate involved Students often have no difficulty with problems that areworded: “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 bedeposited 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 upthe problem

The second and third class sessions can be used for determining solutions to more complexproblems, 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. 

1 Discuss the importance of the time value of money.

2 Describe accounting applications of time value concepts: long-term assets, pensions,

leases, long-term notes, stock-based compensation, business combinations,disclosures, and environmental liabilities

3 Describe personal applications of time value concepts: purchasing a home, planning for

retirement, evaluating alternative investments

B (L.O 1) Nature of Interest. 

1 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).

2 Interest rates are stated on an annual basis unless indicated otherwise.

C (L.O 2) Simple Interest. 

T EACHING T IP

Illustration 6-1 can be used to distinguish between simple interest and compound interest.

1 Simple interest is computed on the amount of the principal only.

2 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. 

1 Compound interest is computed on the principal and on any interest earned that has

not been paid or withdrawn

2 The power of time and compounding (E.g., “What do 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)

3 The term period should be used instead of years.

a Interest may be compounded more than once a year:

compounded periods per year

b 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

E (L.O 3) Use of Compound Interest Tables. 

1 The tables contain interest factors that simplify the computation of compound interest.

Example: If $1,000 is deposited today at 9% compound interest, the balance in 3 yearscan be determined:

a By repetitive calculation

First year: $1,000 + ($1,000 × 09) = $1,090

Second year: $1,090 + ($1,090 × 09) = $1,188

Third year: $1,188 + ($1,188 × 09) = $1,295 (rounded)

b By use of exponential formulas

$1,000 X (1.09)3 = $1,295 (rounded)

c By use of financial calculators or spreadsheet programs

d By obtaining the 1.29503 interest factor from Table 6-1 for 3 periods at 9% andperforming the appropriate computation:

$1,000 X 1.29503 = $1,295.03

2 Five interest tables are provided in the text:

a Table 6-1: Future Value of 1

b Table 6-2: Present Value of 1

c Table 6-3: Future Value of an Ordinary Annuity of 1

d Table 6-4: Present Value of an Ordinary Annuity of 1

e Table 6-5: Present Value of an Annuity Due of 1

F (L.O 4) Variables in Compound Interest Problems. 

T EACHING T IP

Illustration 6-2 depicts a time diagram that identifies the four variables that are fundamental

to all compound interest problems Illustration 6-3 can be used to show students how the

four fundamental variables relate to the time value of money concepts

1 The four fundamental variables in compound interest problems are:

a Rate of interest An annual rate, adjusted to reflect the length of the

compounding period

b Number of time periods The number of compounding periods.

c Future value The value at a future date of a given sum(s) invested assuming

Use Illustration 6-4 to discuss the 4-step solution method that can be used to solve any

compound interest problem

1 Emphasize the importance of performing Steps 1 and 2 correctly Whether studentsuse interest tables, exponential formulas, or financial calculators, they cannot solveproblems correctly unless they can correctly identify the type of problem, the number

of periods, and the interest rate involved

H (L.O 5) Single-Sum Problems. 

T EACHING T IP

Problems 1, 2, and 3 in Illustration 6-5 demonstrate single-sum problem situations.

1 Formula for future value:

Future value = [Present value amount] × [Future value factor for n periods at i %]

FV = PV(FVF n, i)

2 Formula for present value:

Present value = [Future value amount] × [Present value factor for n periods at i %]

PV = FV(PVF n, i)

3 Present value is always a smaller quantity than the future value

4 The process of finding the future value is called accumulation The process of finding the present value is called discounting.

5 The factors in Table 6-2 are the reciprocal of corresponding factors in Table 6-1.Therefore, all single-sum problems can be solved by using either Table 6-1 or 6-2 Forexample, if the future value is known and the present value is to be solved for, thepresent value can be found:

a by multiplying the known future value by the appropriate factor from Table 6-2, or

b by dividing the known future value by the appropriate factor from Table 6-2

H (L.O 6) Future Value of Ordinary and Annuity Due Problems. 

1 Annuity problems involve a series of equal periodic payments or receipts called rents.

a In an ordinary annuity the rents occur at the end of each period The first rent

will occur one period from now

b In an annuity due the rents occur at the beginning of each period The first rent

will occur now

n = the number of semiannual rents paid or received, i = the annual interest rate divided

by 2, and R = the amount of rent paid or received every 6 months.

3 Formula for future value of an ordinary annuity:

Future value of ordinary annuity (FVOA)

= [Periodic rent] × [Future value of ordinary annuity factor for n periods at i %]

FVOA = R (FVF–OA n, i)

4 Formula for future value of annuity due:

Future value of annuity due (FVAD)

= [Periodic rent] × [Future value of ordinary annuity factor for n periods at

i %] × [(1 + i)]

FVAD = R (FVF–OA n, i ) × (1 + i)

a An interest table is not provided for the future value of an annuity due

b Example: At 9%, what is the future value of an annuity due of 7 payments of

$3,000 each?

$3,000 × 9.20044 × 1.09 = $30,085.44

5 The factors in Tables 6-3 and 6-4 are not reciprocals of each other.

6 Some confusion may arise in annuity problems because of two different meanings ofthe word “period.”

a For the purpose of looking up interest factors, n equals the number of “periods”

and is always equal to the number of rents.

b In the phrase “when computing the future value of an ordinary annuity the number

of compounding periods is one less than the number of rents,” the term “periods”refers to “compounding periods” or “interest-bearing periods.” This refers to thenumber of times interest is earned on the principal and any accumulated interest.This usage of the term “period” is useful for distinguishing between ordinary annui-ties and annuities due This usage is intended to explain why the adjustment offactors from Table 6-3 is done the way it is when the problem involves the futurevalue of an annuity due

I (L.O 7) Present Value of Ordinary and Annuity Due Problems. 

T EACHING T IP

Problems 5 and 7 in Illustration 6-5 demonstrate present value of annuity problem

situations

1 Formula for present value of an ordinary annuity:

Present value of ordinary annuity (PVOA)

= [Periodic rent] × [Present value of ordinary annuity factor for n periods at i %]

PVOA = R (PVF–OA n, i)

2 The present value of an ordinary annuity is always smaller than the future value of asimilar annuity

3 Formula for present value of annuity due:

Present value of annuity due (PVAD)

4 Comparison of annuity amounts

a The present value of an annuity due is always smaller than the future value of

a similar annuity due

b The future value (present value) of an annuity due is always larger than the future

value (present value) of a similar ordinary annuity with the same interest rate andnumber of rents

J (L.O 8) Deferred Annuities. 

T EACHING T IP

Problems 9 and 10 in Illustration 6-5 demonstrate deferred annuity problem situations.

1 A deferred annuity does not begin to produce rents until two or more periods haveexpired

2 A deferred annuity problem can occur in either an ordinary annuity situation or an

annuity due situation.

a In order to keep the presentation straightforward, only the ordinary annuity situationhas been illustrated in the text and in Illustration 6-5

b The differences between the two situations are as follows:

Ordinary Annuity Annuity Due of

of n Rents Deferred n Rents Deferred

for y Periods for y Periods

First rent occurs (y + 1) periods y periods from

from now nowLast rent occurs (y + n) periods (y + n – 1) periods

from now from nowFuture value is immediately after one period aftermeasured as of the last rent the last rent

c If a deferred annuity involves solving for a present value, the distinction between

an ordinary annuity and an annuity due has no practical significance

See Problem 10 in Illustration 6-5, which can be set up either as the present value

of an ordinary annuity of 4 rents deferred 3 periods, as was done in Illustration

6-5, or can be set up as the present value of an annuity due of 4 rents deferred 4

periods If the latter is done, different combinations of factors will be used, but thesame answer will be obtained