Intermediate accounting 14e chapter 6 solution manual

Problem 6-2 Time 15–20 minutes Purpose—to present an opportunity for the student to determine solutions to four present and future value situations.. Problem 6-3 Time 20–30 minutes Purpo

CHAPTER 6

Accounting and the Time Value of Money

ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC)

Brief

deposits; changing interest

Learning Objectives

Brief

value of money is relevant.

interest.

2

to deferred annuities and bonds.

value measurement.

ASSIGNMENT CHARACTERISTICS TABLE

Level of Difficulty

Time (minutes)

(cash flows or values) to a present amount using a discount rate (an application of the income approach) that is consistent with value maximizing behavior and capital market equilibrium Present value techniques differ in how they adjust for risk and in the type of cash flows they use.

discount rate and contractual, promised, or most likely cash flows.

ASC 820-10-55-55-4 Details for these references follow.

35-33 Those valuation techniques include the following:

a Present value techniques

b Option-pricing models (which incorporate present value techniques), such as the Black-Scholes-Merton formula (a closed-form model) and a binomial model (a lattice model)

certain intangible assets.

paragraph 55-4 >>> Present Value Techniques

55-4 FASB Concepts Statement No 7, Using Cash Flow Information and Present Value in

Accounting Measurements, provides guidance for using present value techniques to measure fair value That guidance focuses on a traditional or discount rate adjustment technique and an expected cash flow (expected present value) technique This Section clarifies that guidance (That guidance is included or otherwise referred to principally in paragraphs 39–46, 51, 62–71, 114, and 115 of Concepts Statement 7.) This Section neither prescribes the use of one specific present value technique nor limits the use of present value techniques to measure fair value to the techniques discussed herein The present value technique used to measure fair value will depend on facts and cir- cumstances specific to the asset or liability being measured (for example, whether comparable assets or liabilities can be observed in the market) and the availability of sufficient data.

CE6-2

Answers will vary By entering the phrase “present value” in the search window, a list of references to the term is provided The site allows you to narrow the search to assets, liabilities, revenues, and expenses.

Impairment Loss > Information for Each Period for Which a Statement of Financial Position Is Presented

CE6-2 (Continued)

the following (see Example 3 [paragraph 350-20-55-24]):

a The aggregate amount of goodwill acquired.

b The aggregate amount of impairment losses recognized.

c The amount of goodwill included in the gain or loss on disposal of all or a portion of a reporting unit.

Entities that report segment information in accordance with Topic 280 shall provide the above information about goodwill in total and for each reportable segment and shall disclose any significant changes in the allocation of goodwill by reportable segment If any portion of goodwill has not yet been allocated to a reporting unit at the date the financial statements are issued, that unallocated amount and the reasons for not allocating that amount shall be disclosed.

> Goodwill Impairment Loss

dis-closed in the notes to the financial statements that include the period in which the ment loss is recognized:

impair-a A description of the facts and circumstances leading to the impairment.

b The amount of the impairment loss and the method of determining the fair value of the associated reporting unit (whether based on quoted market prices, prices of comparable

businesses, a present value or other valuation technique, or a combination thereof).

c If a recognized impairment loss is an estimate that has not yet been finalized (see paragraphs 350-20-35-18 through 19), that fact and the reasons therefore and, in sub- sequent periods, the nature and amount of any significant adjustments made to the initial estimate of the impairment loss.

Obligations > 30 Initial Measurement

Determination of a Reasonable Estimate of Fair Value

to estimate the fair value of a liability for an asset retirement obligation An entity, when using that technique, shall discount the expected cash flows using a credit-adjusted risk-free rate Thus, the effect of an entity’s credit standing is reflected in the discount rate rather than in the expected cash flows Proper application of a discount rate adjustment technique entails analysis of at least two liabilities—the liability that exists in the marketplace and has

an observable interest rate and the liability being measured The appropriate rate of interest for the cash flows being measured must be inferred from the observable rate of interest of some other liability, and to draw that inference the characteristics of the cash flows must be similar to those of the liability being measured Rarely, if ever, would there be an observable rate of interest for a liability that has cash flows similar to an asset retirement obligation being measured In addition, an asset retirement obligation usually will have uncertainties in both timing and amount In that circumstance, employing a discount rate adjustment technique, where uncertainty is incorporated into the rate, will be difficult, if not impossible See paragraphs 410-20-55-13 through 55-17 and Example 2 (paragraph 410-20-55-35).

(c) Revenue or Expense reference: 720 Other Expenses> 25 Contributions Made> 30 Initial Measurement

the form of a settlement or cancellation of a donee’s liabilities, at the fair value of the ties cancelled.

be measured at net settlement value because that amount, although not equivalent to the present value of estimated future cash flows, results in a reasonable estimate of fair value.

CE6-3

Interest cost includes interest recognized on obligations having explicit interest rates, interest imputed

on certain types of payables in accordance with Subtopic 835-30, and interest related to a capital lease determined in accordance with Subtopic 840-30 With respect to obligations having explicit interest rates, interest cost includes amounts resulting from periodic amortization of discount or premium and issue costs on debt.

According to the discussion at: 835 Interest> 30 Imputation of Interest

note or similar instrument When a note is exchanged for property, goods, or services in a bargained transaction entered into at arm’s length, there should be a general presumption that the rate of interest stipulated by the parties to the transaction represents fair and adequate compensation to the supplier for the use of the related funds That presumption, however, must not permit the form of the transaction to prevail over its economic substance and thus would not apply if interest is not stated, the stated interest rate is unreasonable, or the stated face amount

of the note is materially different from the current cash sales price for the same or similar items

or from the market value of the note at the date of the transaction The use of an interest rate that varies from prevailing interest rates warrants evaluation of whether the face amount and the stated interest rate of a note or obligation provide reliable evidence for properly recording the exchange and subsequent related interest.

05-3 This Subtopic provides guidance for the appropriate accounting when the face amount of a note

does not reasonably represent the present value of the consideration given or received in the exchange This circumstance may arise if the note is non-interest-bearing or has a stated interest rate that is different from the rate of interest appropriate for the debt at the date of the transaction Unless the note is recorded at its present value in this circumstance, the sales price and profit to a seller in the year of the transaction and the purchase price and cost to the buyer are misstated, and interest income and interest expense in subsequent periods are also misstated.

ANSWERS TO QUESTIONS

1 Money has value because with it one can acquire assets and services and discharge obligations.

The holding, borrowing or lending of money can result in costs or earnings And the longer the time period involved, the greater the costs or the earnings The cost or earning of money as a function of time is the time value of money.

Accountants must have a working knowledge of compound interest, annuities, and present value concepts because of their application to numerous types of business events and transactions which require proper valuation and presentation These concepts are applied in the following areas: (1) sinking funds, (2) installment contracts, (3) pensions, (4) long-term assets, (5) leases, (6) notes receivable and payable, (7) business combinations, (8) amortization of premiums and discounts, and (9) estimation of fair value.

2 Some situations in which present value measures are used in accounting include:

(a) Notes receivable and payable—these involve single sums (the face amounts) and may

involve annuities, if there are periodic interest payments.

(b) Leases—involve measurement of assets and obligations, which are based on the present value

of annuities (lease payments) and single sums (if there are residual values to be paid at the conclusion of the lease).

(c) Pensions and other deferred compensation arrangements—involve discounted future

annuity payments that are estimated to be paid to employees upon retirement.

(d) Bond pricing—the price of bonds payable is comprised of the present value of the principal

or face value of the bond plus the present value of the annuity of interest payments.

(e) Long-term assets—evaluating various long-term investments or assessing whether an asset

is impaired requires determining the present value of the estimated cash flows (may be single sums and/or an annuity).

3 Interest is the payment for the use of money It may represent a cost or earnings depending upon

whether the money is being borrowed or loaned The earning or incurring of interest is a function

of the time, the amount of money, and the risk involved (reflected in the interest rate).

Simple interest is computed on the amount of the principal only, while compound interest is puted on the amount of the principal plus any accumulated interest Compound interest involves interest on interest while simple interest does not.

com-4 The interest rate generally has three components:

(a) Pure rate of interest—This would be the amount a lender would charge if there were no

possibilities of default and no expectation of inflation.

(b) Expected inflation rate of interest—Lenders recognize that in an inflationary economy, they

are being paid back with less valuable dollars As a result, they increase their interest rate to compensate for this loss in purchasing power When inflationary expectations are high, interest rates are high.

(c) Credit risk rate of interest—The government has little or no credit risk (i.e., risk of

nonpayment) when it issues bonds A business enterprise, however, depending upon its financial stability, profitability, etc can have a low or a high credit risk.

Accountants must have knowledge about these components because these components are essential in identifying an appropriate interest rate for a given company or investor at any given moment.

5 (a) Present value of an ordinary annuity at 8% for 10 periods (Table 6-4).

(b) Future value of 1 at 8% for 10 periods (Table 6-1).

(c) Present value of 1 at 8% for 10 periods (Table 6-2).

(d) Future value of an ordinary annuity at 8% for 10 periods (Table 6-3).

6 He should choose quarterly compounding, because the balance in the account on which interest

will be earned will be increased more frequently, thereby resulting in more interest earned on the investment This is shown in the following calculation:

Semiannual compounding, assuming the amount is invested for 2 years:

n = 4

$1,500 X 1.16986 = $1,754.79

i = 4 Quarterly compounding, assuming the amount is invested for 2 years:

n = 8

$1,500 X 1.17166 = $1,757.49

i = 2 Thus, with quarterly compounding, Jose could earn $2.70 more.

8 $44,671.20 = $80,000 X 55839 (present value of 1 at 6% for 10 periods).

9 An annuity involves (1) periodic payments or receipts, called rents, (2) of the same amount,

(3) spread over equal intervals, (4) with interest compounded once each interval.

Rents occur at the end of the intervals for ordinary annuities while the rents occur at the beginning

of each of the intervals for annuities due.

$40,000

10 Amount paid each year =

Amount paid each year = $13,169.37.

Amount deposited each year = $39,176.51.

13 The process for computing the future value of an annuity due using the future value of an ordinary

annuity interest table is to multiply the corresponding future value of the ordinary annuity by one plus the interest rate For example, the factor for the future value of an annuity due for 4 years at 12% is equal to the factor for the future value of an ordinary annuity times 1.12.

14 The basis for converting the present value of an ordinary annuity table to the present value of an

annuity due table involves multiplying the present value of an ordinary annuity factor by one plus the interest rate.

Questions Chapter 6 (Continued)

15 Present value = present value of an ordinary annuity of $25,000 for 20 periods at? percent.

$245,000 = present value of an ordinary annuity of $25,000 for 20 periods at? percent.

$245,000 Present value of an ordinary annuity for 20 periods at? percent =

The factor 9.8 is closest to 9.81815 in the 8% column (Table 6-4).

16 4.96764 Present value of ordinary annuity at 12% for eight periods.

2.40183 Present value of ordinary annuity at 12% for three periods.

2.56581 Present value of ordinary annuity at 12% for eight periods, deferred three periods.

The present value of the five rents is computed as follows:

4.0 = PV of an ordinary annuity for five periods at?

4.0 = approximately 8%.

19 The IRS argues that the future reserves should be discounted to present value The result would

be smaller reserves and therefore less of a charge to income As a result, income would be higher and income taxes may therefore be higher as well.

BRIEF EXERCISE 6-8

With quarterly compounding, there will be 20 quarterly compounding periods,

at 1/4 the interest rate:

16,380

= 6.10501 Therefore, n = 5 years

First withdrawal at year-end

value of 1 @ 4% for 16 periods 1.87298

X $30,000 Total withdrawn $56,189

(a) Future value of an ordinary

Present value of annuity

due of $2,500 for 30 periods

Present value of an annuity

due of $3,000 for 6 periods

Accept the bonus of $40,000 now.

(Also, consider whether the 8% is an appropriate discount rate if the president can earn compound interest at a higher rate without too much additional risk.)

(a) Present value of an ordinary annuity of 1

$118,810 = $100,000 (FVF 2, i% )

$118,810 ÷ $100,000 = (FVF 2, i% )

Note: This problem can also be solved using present value tables.

EXERCISE 6-10 (10–15 minutes)

value of $1,000,000 by $148,644, which is 6.72748—the value $1.00 would accumulate to at 10% for the unknown number of interest periods The factor 6.72748 or its approximate is then located in the Future Value of

1 Table by reading down the 10% column to the 20-period line; thus, 20 is the unknown number of years Mark must wait to become a millionaire.

of $1,000,000 by the present investment of $239,392, which is 4.17725— the amount $1.00 would accumulate to in 15 years at an unknown interest rate The factor or its approximate is then located in the Future Value

of 1 Table by reading across the 15-period line to the 10% column; thus, 10% is the interest rate Elvira must earn on her investment to become

a millionaire.

EXERCISE 6-11 (10–15 minutes)

$155,820 (10 X $15,582) – $100,000 = $55,820.

the manufacturer’s 9% rate determined below.

Answer: Lease Building C since the present value of its net cost is the

smallest.

(i) Present value of the expected annual pension payments at the end of

begin-ning of the current year:

PV = FV (PVF n, i )

PV = $5,368,064 (PVF 15,8% )

PV = $5,368,064 (0.31524)

PV = $1,692,228*

*$12 difference due to rounding.

The company’s pension obligation (liability) is $1,692,228.

amount to establish the foundation.

Amount to be repaid on March 1, 2020.

The recommended method of payment would be the 15 annual payments of

$400,000, since the present value of those payments ($3,423,792) is less than the alternative immediate cash payment of $3,500,000.

Estimate X Assessment = Flow

Outflow X Assessment = Cash Flow

EXERCISE 6-22 (15–20 minutes)

expected cash flows as a fair value estimate.

Estimate X Assessment = Cash Flow

the expected future cash flows associated with the trade name This fair value estimate is considered Level 3, as discussed in Chapter 2.

Problem 6-1 (Time 15–20 minutes)

Purpose—to present an opportunity for the student to determine how to use the present value tables in various situations Each of the situations presented emphasizes either a present value of 1 or a present value of an ordinary annuity situation Two of the situations will be more difficult for the student because

a noninterest-bearing note and bonds are involved.

Problem 6-2 (Time 15–20 minutes)

Purpose—to present an opportunity for the student to determine solutions to four present and future value situations The student is required to determine the number of years over which certain amounts will accumulate, the rate of interest required to accumulate a given amount, and the unknown amount

of periodic payments The problem develops the student’s ability to set up present and future value equations and solve for unknown quantities.

Problem 6-3 (Time 20–30 minutes)

Purpose—to present the student with an opportunity to determine the present value of the costs of competing contracts The student is required to decide which contract to accept.

Problem 6-4 (Time 20–30 minutes)

Purpose—to present the student with an opportunity to determine the present value of two lottery payout alternatives The student is required to decide which payout option to choose.

Problem 6-5 (Time 20–25 minutes)

Purpose—to provide the student with an opportunity to determine which of four insurance options results

in the largest present value The student is required to determine the present value of options which include the immediate receipt of cash, an ordinary annuity, an annuity due, and an annuity of changing amounts The student must also deal with interest compounded quarterly This problem is a good summary of the application of present value techniques.

Problem 6-6 (Time 25–30 minutes)

Purpose—to present an opportunity for the student to determine the present value of a series of deferred annuities The student must deal with both cash inflows and outflows to arrive at a present value of net cash inflows A good problem to develop the student’s ability to manipulate the present value table factors to efficiently solve the problem.

Problem 6-7 (Time 30–35 minutes)

Purpose—to present the student an opportunity to use time value concepts in business situations Some of the situations are fairly complex and will require the student to think a great deal before answering the question For example, in one situation a student must discount a note and in another must find the proper interest rate to use in a purchase transaction.

Problem 6-8 (Time 20–30 minutes)

Purpose—to present the student with an opportunity to determine the present value of an ordinary annuity and annuity due for three different cash payment situations The student must then decide which cash payment plan should be undertaken.

Time and Purpose of Problems (Continued)

Problem 6-9 (Time 30–35 minutes)

Purpose—to present the student with the opportunity to work three different problems related to time value concepts: purchase versus lease, determination of fair value of a note, and appropriateness of taking a cash discount.

Problem 6-10 (Time 30–35 minutes)

Purpose—to present the student with the opportunity to assess whether a company should purchase or lease The computations for this problem are relatively complicated.

Problem 6-11 (Time 25–30 minutes)

Purpose—to present the student an opportunity to apply present value to retirement funding problems, including deferred annuities.

Problem 6-12 (Time 20–25 minutes)

Purpose—to provide the student an opportunity to explore the ethical issues inherent in applying time value of money concepts to retirement plan decisions.

Problem 6-13 (Time 20–25 minutes)

Purpose—to present the student an opportunity to compute expected cash flows and then apply present value techniques to determine a warranty liability.

Problem 6-14 (Time 20–25 minutes)

Purpose—to present the student an opportunity to compute expected cash flows and then apply present value techniques to determine the fair value of an asset.

Problems 6-15 (Time 20–25 minutes)

Purpose—to present the student an opportunity to estimate fair value by computing expected cash flows and then applying present value techniques to value an asset retirement obligation.

PROBLEM 6-1

the note would be estimated to value the building.

PV – OA = ? $27,000 $27,000 $27,000 $27,000

1/1/12 1/1/13 1/1/14 1/1/21 1/1/22

n = 10 Present value of the principal

FV (PVF 10, 11% ) = $300,000 (.35218) = $105,654 Present value of the interest payments