6
Accounting CHAPTER and the Time Value of Money
ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC)
Topics 1. 2. 3. Present value concepts. Use of tables. Present and future value problems: a. Unknown future amount. b. Unknown payments. c. Unknown number of periods. d. Unknown interest rate. e. Unknown present value. 15, 18 8, 19 7, 19 10, 11, 12 1, 5, 13 6, 12, 15, 17 4, 9 3, 11, 16 2, 7, 8, 10, 14 2, 3, 4, 7 8, 16, 17 10, 15 9, 10, 11, 14 3, 4, 5, 6, 8, 12, 17, 18, 19 2, 6 2 2, 7 1, 4, 7, 9, 13, 14 3, 5, 8 Questions 1, 2, 3, 4, 5, 9, 17 13, 14 8 1 Brief Exercises Exercises Problems
4.
Value of a series of irregular deposits; changing interest rates. Valuation of leases, pensions, bonds; choice between projects. Deferred annuity. Expected Cash Flows. 6 15 7, 12, 13, 14, 15
5.
3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15
6. 7.
16 20, 21, 22 13, 14, 15
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-1
ASSIGNMENT CLASSIFICATION TABLE (BY LEARNING OBJECTIVE)
Learning Objectives 1. 2. 3. 4. 5. 6. 7. 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 1 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. 1, 2, 3, 4, 7, 8 5, 6, 9, 13 10, 11, 12, 14, 16, 17 15 2, 3, 6, 9, 10, 15 3, 4, 6, 15, 16 3, 4, 5, 6, 11, 12, 17, 18, 19 7, 8, 13, 14 20, 21, 22 1, 2, 3, 5, 7, 9, 10 2, 7 1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 14 6, 11, 12, 15 13, 14, 15 2 1 Brief Exercises Exercises Problems
8. 9.
6-2
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
ASSIGNMENT CHARACTERISTICS TABLE
Level of Difficulty Simple Simple Simple Moderate Simple Moderate Moderate Simple Moderate Simple Moderate Simple Moderate Moderate Moderate Simple Simple Simple Simple Simple Moderate Moderate Moderate Moderate Moderate Moderate Moderate Moderate Complex Moderate Complex Complex Complex Moderate Moderate Moderate Complex Time (minutes) 510 510 1015 1520 1015 1520 1217 1015 510 1015 1015 1015 1520 1520 1520 1015 1015 1015 1015 510 1520 1520 1520 1520 2030 2030 2025 2530 3035 2030 3035 3035 2530 2025 2025 2025 2025
Item 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 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
Description 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. 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.
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-3
SOLUTIONS TO CODIFICATION EXERCISES
CE6-1
(a) According to the Master Glossary, present value is a tool used to link uncertain future amounts (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. (b) The discount rate adjustment technique is a present value technique that uses a risk-adjusted discount rate and contractual, promised, or most likely cash flows. (c) Other codification references to present value are at (1) FASB ASC 820-10-35-33 and (2) FASB ASC 820-10-55-55-4. Details for these references follow. 1. 820 Fair Value Measurements and Disclosures > 10 Overall > 35 Subsequent Measurement 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) c. The multiperiod excess earnings method, which is used to measure the fair value of certain intangible assets. 2. 820 Fair Value Measurements and Disclosures > 10 Overall > 55 Implementation General, 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 3946, 51, 6271, 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 circumstances 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. (a) Asset reference: 350 Intangibles--Goodwill and Other > 20 Goodwill > 50 Disclosure > Goodwill Impairment Loss > Information for Each Period for Which a Statement of Financial Position Is Presented
6-4
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
CE6-2 (Continued)
50-1 The changes in the carrying amount of goodwill during the period shall be disclosed, including 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 50-2 For each goodwill impairment loss recognized, all of the following information shall be disclosed in the notes to the financial statements that include the period in which the impairment loss is recognized: 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 subsequent periods, the nature and amount of any significant adjustments made to the initial estimate of the impairment loss. (b) Liability reference: 410 Asset Retirement and Environmental Obligations > 20 Asset Retirement Obligations > 30 Initial Measurement Determination of a Reasonable Estimate of Fair Value 30-1 An expected present value technique will usually be the only appropriate technique with which 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).
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-5
CE6-2 (Continued)
(c) Revenue or Expense reference: 720 Other Expenses> 25 Contributions Made> 30 Initial Measurement 30-1 Contributions made shall be measured at the fair values of the assets given or, if made in the form of a settlement or cancellation of a donee's liabilities, at the fair value of the liabilities cancelled. 30-2 Unconditional promises to give that are expected to be paid in less than one year may 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 05-1 05-2 This Subtopic addresses the imputation of interest. Business transactions often involve the exchange of cash or property, goods, or services for a 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. 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.
05-3
6-6
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
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 computed on the amount of the principal plus any accumulated interest. Compound interest involves interest on interest while simple interest does not. 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) (b) (c) (d) Present value of an ordinary annuity at 8% for 10 periods (Table 6-4). Future value of 1 at 8% for 10 periods (Table 6-1). Present value of 1 at 8% for 10 periods (Table 6-2). Future value of an ordinary annuity at 8% for 10 periods (Table 6-3).
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-7
Questions Chapter 6 (Continued) 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. 7. $26,897.80 = $20,000 X 1.34489 (future value of 1 at 21/2 for 12 periods). 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. 10. Amount paid each year = $40,000 3.03735 (present value of an ordinary annuity at 12% for 4 years).
Amount paid each year = $13,169.37. 11. Amount deposited each year = $200,000 (future value of an ordinary annuity at 10% for 4.64100 4 years).
Amount deposited each year = $43,094.16. 12. Amount deposited each year = $200,000 [future value of an annuity due at 10% for 4 years 5.10510 (4.64100 X 1.10)]. 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.
6-8
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
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 = 9.8. $25,000
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: 2.56581 X $20,000 = $51,316.20. 17. (a) (b) (c) (d) Present value of an annuity due. Present value of 1. Future value of an annuity due. Future value of 1.
18. $27,600 = PV of an ordinary annuity of $6,900 for five periods at? percent. $27,600 = PV of an ordinary annuity for five periods at? percent. $6,900 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.
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-9
SOLUTIONS TO BRIEF EXERCISES
BRIEF EXERCISE 6-1 8% annual interest i = 8% PV = $15,000 FV = ?
0
1 n=3
2
3
FV = $15,000 (FVF3, 8%) FV = $15,000 (1.25971) FV = $18,896 8% annual interest, compounded semiannually i = 4% PV = $15,000 FV = ?
0
1
2
3 n=6
4
5
6
FV = $15,000 (FVF6, 4%) FV = $15,000 (1.26532) FV = $18,980
6-10
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
BRIEF EXERCISE 6-2 12% annual interest
i = 12% PV = ? FV = $25,000
0
1
2 n=4
3
4
PV = $25,000 (PVF4, 12%) PV = $25,000 (.63552) PV = $15,888
12% annual interest, compounded quarterly i = 3% PV = ? FV = $25,000
0
1
2 n = 16
14
15
16
PV = $25,000 (PVF16, 3%) PV = $25,000 (.62317) PV = $15,579
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-11
BRIEF EXERCISE 6-3 i=? PV = $30,000 FV = $150,000
0
1
2 n = 21
19
20
21
FV = PV (FVF21, i) OR $150,000 = $30,000 (FVF21, i) FVF21, i = 5.0000 i = 8% BRIEF EXERCISE 6-4 i = 5% PV = $10,000
PV = FV (PVF21, i) $30,000 = $150,000 (PVF21, i) PVF21, i = .20000 i = 8%
FV = $17,100
0 n=? FV = PV (FVFn, 5%) OR $17,100 = $10,000 (FVFn, 5%) FVFn, 5% = 1.71000 n = 11 years
?
PV = FV (PVFn, 5%) $10,000 = $17,100 (PVFn, 5%) PVFn, 5% = .58480 n = 11 years
6-12
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
BRIEF EXERCISE 6-5 First payment today (Annuity Due) i = 12% R= $8,000 $8,000 $8,000 FV AD = $8,000 $8,000 ?
0
1
2 n = 20
18
19
20
FV AD = $8,000 (FVF OA20, 12%) 1.12 FV AD = $8,000 (72.05244) 1.12 FV AD = $645,590
First payment at year-end (Ordinary Annuity) i = 12% FV OA = ? $8,000 $8,000 $8,000
$8,000 $8,000
0
1
2 n = 20
18
19
20
FV OA = $8,000 (FVF OA20, 12%) FV OA = $8,000 (72.05244) FV OA = $576,420
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-13
BRIEF EXERCISE 6-6 i = 11% R=? ? ? FV OA = ? $250,000
0
1
2 n = 10
8
9
10
$250,000 = R (FVF OA10, 11%) $250,000 = R (16.72201) $250,000 16.72201 =R
R = $14,950 BRIEF EXERCISE 6-7 12% annual interest i = 12% PV = ? FV = $300,000
0
1
2 n=5
3
4
5
PV = $300,000 (PVF5, 12%) PV = $300,000 (.56743) PV = $170,229
6-14
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
BRIEF EXERCISE 6-8 With quarterly compounding, there will be 20 quarterly compounding periods, at 1/4 the interest rate: PV = $300,000 (PVF20, 3%) PV = $300,000 (.55368) PV = $166,104
BRIEF EXERCISE 6-9 i = 10% FV OA = R= $16,380 $16,380 $100,000 $16,380
0
1
2 n=?
n
$100,000 = $16,380 (FVF OAn, 10%) FVF OAn, 10% = $100,000 16,380 = 6.10501
Therefore, n = 5 years
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-15
BRIEF EXERCISE 6-10 First withdrawal at year-end i = 8% PV OA = ? R= $30,000 $30,000 $30,000 $30,000 $30,000
0
1
2 n = 10
8
9
10
PV OA = $30,000 (PVF OA10, 8%) PV OA = $30,000 (6.71008) PV OA = $201,302 First withdrawal immediately i = 8% PV AD = ? R= $30,000 $30,000 $30,000 $30,000 $30,000
0
1
2 n = 10
8
9
10
PV AD = $30,000 (PVF AD10, 8%) PV AD = $30,000 (7.24689) PV AD = $217,407
6-16
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
BRIEF EXERCISE 6-11 i=? PV = $793.15 R= $75 $75 $75 $75 $75
0
1
2 n = 12
10
11
12
$793.15 = $75 (PVF OA12, i) $793.15 = 10.57533 PVF12, i = $75 Therefore, i = 2% per month or 24% per year.
BRIEF EXERCISE 6-12 i = 8% PV = $300,000 R = ? ? ? ? ?
0
1
2 n = 20
18
19
20
$300,000 = R (PVF OA20, 8%) $300,000 = R (9.81815) R = $30,556
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-17
BRIEF EXERCISE 6-13 i = 12% R= $30,000 $30,000 $30,000 $30,000 $30,000
12/31/11 12/31/12 12/31/13 n=8
12/31/17 12/31/18 12/31/19
FV OA = $30,000 (FVF OA8, 12%) FV OA = $30,000 (12.29969) FV OA = $368,991
BRIEF EXERCISE 6-14 i = 8% PV OA =
?
R=
$25,000 $25,000 $25,000 $25,000
0
1
2 n=4
3
4
5
6 n=8
11
12
PV OA = $25,000 (PVF OA124, 8%) OR PV OA = $25,000 (7.53608 3.31213)
PV OA = $25,000 (PVF OA8, 8%)(PVF4, 8%) PV OA = $25,000 (5.74664)(.73503)
PV OA = $105,599
PV OA = $105,599
6-18
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
BRIEF EXERCISE 6-15 i = 8% PV = ? PV OA = R = ? $140,000 $140,000 $2,000,000 $140,000 $140,000 $140,000
0
1
2 n = 10
8
9
10
$2,000,000 (PVF10, 8%) = $2,000,000 (.46319) = $ 926,380 $140,000 (PVF OA10, 8%) = $140,000 (6.71008) = 939,411 $1,865,791
BRIEF EXERCISE 6-16 PV OA = $20,000 $4,727.53 $4,727.53
$4,727.53 $4,727.53
0
1 $20,000 (PV OA6, i%) (PV OA6, i%) Therefore, i%
2
5 = $4,727.53 (PV OA6, i%) = $20,000 $4,727.53 = 4.23054 = 11
6
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-19
BRIEF EXERCISE 6-17 PV AD = $20,000 $? $?
$?
$?
0
1
2
5
6
$20,000 = Payment (PV AD6, 11%) $20,000 (PV AD6, 11%) = Payment $20,000 4.6959 = $4,259
6-20
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
SOLUTIONS TO EXERCISES
EXERCISE 6-1 (510 minutes) (a) Rate of Interest 9% 2% 5% 9% 4% 3% (b) Number of Periods 9 20 30 25 30 28
1.
a. b. c. a. b. c.
2.
EXERCISE 6-2 (510 minutes) (a) Simple interest of $2,400 ($30,000 X 8%) per year X 8 ..... Principal ........................................................................................... Total withdrawn .................................................................. Interest compounded annually--Future value of 1 @ 8% for 8 periods ............................................................. Total withdrawn .................................................................. (c) Interest compounded semiannually--Future value of 1 @ 4% for 16 periods .......................................... Total withdrawn .................................................................. EXERCISE 6-3 (1015 minutes) (a) (b) (c) (d) $9,000 X 1.46933 = $13,224. $9,000 X .43393 = $3,905. $9,000 X 31.77248 = $285,952. $9,000 X 12.46221 = $112,160. $19,200 30,000 $49,200
(b)
1.85093 X $30,000 $55,528
1.87298 X $30,000 $56,189
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-21
EXERCISE 6-4 (1520 minutes) (a) Future value of an ordinary annuity of $5,000 a period for 20 periods at 8% $228,809.80 ($5,000 X 45.76196) Factor (1 + .08) X 1.08 Future value of an annuity due of $5,000 a period at 8% $ 247,115 Present value of an ordinary annuity of $2,500 for 30 periods at 10% Factor (1 + .10) Present value of annuity due of $2,500 for 30 periods at 10% Future value of an ordinary annuity of $2,000 a period for 15 periods at 10% Factor (1 + 10) Future value of an annuity due of $2,000 a period for 15 periods at 10% Present value of an ordinary annuity of $3,000 for 6 periods at 9% Factor (1 + .09) Present value of an annuity due of $3,000 for 6 periods at 9%
(b)
$ 23,567.28 ($2,500 X 9.42691) X 1.10
$
25,924 (Or see Table 6-5 which gives $25,924.03)
(c)
$ 63,544.96 ($2,000 X 31.77248) X 1.10
$
69,900
(d)
$ 13,457.76 ($3,000 X 4.48592) X 1.09
$
14,669 (Or see Table 6-5)
EXERCISE 6-5 (1015 minutes) (a) (b) (c) $50,000 X 4.96764 = $248,382. $50,000 X 8.31256 = $415,628. ($50,000 X 3.03735 X .50663) = $76,941. or (5.65022 4.11141) X $50,000 = $76,941 (difference of $.13 due to rounding).
Copyright 2011 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 14/e, Solutions Manual (For Instructor Use Only)
6-22
EXERCISE 6-6 (1520 minutes) (a) (b) Future value of $12,000 @ 10% for 10 years ($12,000 X 2.59374) = Future value of an ordinary annuity of $620,000 at 10% for 15 years ($620,000 X 31.77248) Deficiency ($20,000,000 $19,698,937)
$
31,125
$19,698,937 $ 301,063
(c)
$75,000 discounted at 8% for 10 years: $75,000 X .46319 = $ 34,739 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.)
EXERCISE 6-7 (1217 minutes) (a) $100,000 X .31524 + $10,000 X 8.55948 = = $31,524.00 85,594.80 $ 117,119 23,939 76,061 $ 100,000 $
(b)
$100,000 X .23939 + $10,000 X 7.60608
= =
(c)
$100,000 X .18270 + $10,000 X 6.81086
= =
$ $
18,270 68,109 86,379
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-23
EXERCISE 6-8 (1015 minutes) (a) Present value of an ordinary annuity of 1 for 4 periods @ 8% Annual withdrawal Required fund balance on June 30, 2015 Fund balance at June 30, 2015 Future value of an ordinary annuity at 8% for 4 years $82,803.25 4.50611
3.31213 X $25,000 $82,803 = $18,376
(b)
Amount of each of four contributions is $18,376 EXERCISE 6-9 (510 minutes) The rate of interest is determined by dividing the future value by the present value and then finding the factor in the FVF table with n = 2 that approximates that number: $118,810 = $100,000 (FVF2, i%) $118,810 $100,000 = (FVF2, i%) 1.1881 = (FVF2, i%)--reading across the n = 2 row reveals that i = 9%. Note: This problem can also be solved using present value tables. EXERCISE 6-10 (1015 minutes) (a) The number of interest periods is calculated by first dividing the future 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. The unknown interest rate is calculated by first dividing the future value 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.
Copyright 2011 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 14/e, Solutions Manual (For Instructor Use Only)
(b)
6-24
EXERCISE 6-11 (1015 minutes) (a) Total interest = Total payments--Amount owed today $155,820 (10 X $15,582) $100,000 = $55,820. Amos should borrow from the bank, since the 8% rate is lower than the manufacturer's 9% rate determined below. PV OA10, i% = $100,000 $15,582 = 6.41766--Inspection of the 10 period row reveals a rate of 9%.
(b)
EXERCISE 6-12 (1015 minutes) Building A--PV = $610,000. Building B-- Rent X (PV of annuity due of 25 periods at 12%) = PV $70,000 X 8.78432 = PV $614,902 = PV Building C-- Rent X (PV of ordinary annuity of 25 periods at 12%) = PV $6,000 X 7.84314 = PV $47,059 = PV Cash purchase price PV of rental income Net present value $650,000 47,059 $602,941
Answer: Lease Building C since the present value of its net cost is the smallest.
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-25
EXERCISE 6-13 (1520 minutes) Time diagram: PV = ? PV OA = ? Messier, Inc. i = 5%
Principal $3,000,000 interest $165,000 $165,000 $165,000
$165,000
$165,000 $165,000
0
1
2
3 n = 30
28
29
30
Formula for the interest payments: PV OA = R (PVF OAn, i) PV OA = $165,000 (PVF OA30, 5%) PV OA = $165,000 (15.37245) PV OA = $2,536,454 Formula for the principal: PV = FV (PVFn, i) PV = $3,000,000 (PVF30, 5%) PV = $3,000,000 (0.23138) PV = $694,140 The selling price of the bonds = $2,536,454 + $694,140 = $3,230,594.
6-26
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
EXERCISE 6-14 (1520 minutes) Time diagram: i = 8% R= PV OA = ?
$800,000 $800,000 $800,000
0
1
2 n = 15
15
16 n = 10
24
25
Formula: PV OA = R (PVF OAn, i) PV OA = $800,000 (PVF OA2515, 8%) PV OA = $800,000 (10.67478 8.55948) PV OA = $800,000 (2.11530) PV OA = $1,692,240 OR Time diagram: i = 8% R= PV OA = ?
$800,000 $800,000 $800,000
0 1 FV (PVn, i)
2
15 16 (PV OAn, i)
24
25
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-27
EXERCISE 6-14 (Continued) (i) Present value of the expected annual pension payments at the end of the 10th year: PV OA = R (PVF OAn, i) PV OA = $800,000 (PVF OA10, 8%) PV OA = $800,000 (6.71008) PV OA = $5,368,064 (ii) Present value of the expected annual pension payments at the beginning of the current year: PV = FV (PVFn, i) PV = $5,368,064 (PVF15,8%) 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.
6-28
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
EXERCISE 6-15 (1520 minutes) (a) i = 6% PV = $1,000,000 FV = $1,898,000
0
1
2
n=?
FVF(n, 8%) = $1,898,000 $1,000,000 = 1.898 reading down the 6% column, 1.898 corresponds to 11 periods. (b) By setting aside $300,000 now, Lee can gradually build the fund to an amount to establish the foundation. PV = $300,000 FV = ?
0 FV
1
2
8
9
= $300,000 (FVF9, 6%) = $300,000 (1.68948) = $506,844--Thus, the amount needed from the annuity: $1,898,000 $506,844 = $1,391,156. $? $? $? FV = $1,391,156
0
1
2
8
9
Payments = FV (FV OA9, 6%) = $1,391,156 11.49132 = $121,061
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-29
EXERCISE 6-16 (1015 minutes) Amount to be repaid on March 1, 2020. Time diagram: i = 6% per six months
PV = $90,000 FV = ?
3/1/10
3/1/11
3/1/12
3/1/18
3/1/19
3/1/20
n = 20 six-month periods Formula: FV = PV (FVFn, i) FV = $90,000 (FVF20, 6%) FV = $90,000 (3.20714) FV = $288,643 Amount of annual contribution to debt retirement fund. Time diagram: i = 10% R R=? R ? R ? R ? R ? FV AD = $288,643
3/1/15
3/1/16
3/1/17
3/1/18
3/1/19
3/1/20
6-30
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
EXERCISE 6-16 (Continued) 1. 2. 3. 4. Future value of ordinary annuity of 1 for 5 periods at 10%............................................................................................ Factor (1 + .10) ............................................................................... Future value of an annuity due of 1 for 5 periods at 10%............................................................................................ Periodic rent ($288,643 6.71561) ..........................................
6.10510 X 1.10000 6.71561 $42,981
EXERCISE 6-17 (1015 minutes) Time diagram: i = 11% R
PV OA = $421,087
R ?
R ?
?
0
1 n = 25
24
25
Formula:
PV OA = R (PVF OAn, i) $421,087 = R (PVF OA25, 11%) $421,087 = R (8.42174) R = $421,087 8.42174 R = $50,000
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-31
EXERCISE 6-18 (1015 minutes) Time diagram: i = 8%
PV OA = ? $400,000 $400,000 $400,000 $400,000 $400,000
0
1
2 n = 15
13
14
15
Formula:
PV OA = R (PVF OAn, i) PV OA = $400,000 (PVF OA15, 8%) PV OA = $400,000 (8.55948) R = $3,423,792
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.
6-32
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
EXERCISE 6-19 (1015 minutes) Time diagram: i = 8%
PV AD = ? R= $400,000 $400,000 $400,000
$400,000 $400,000
0 Formula: Using Table 6-4
1
2 n = 15
13
14
15
Using Table 6-5 PV AD = R (PVF ADn, i) PV AD = $400,000 (PVF AD15, 8%) PV AD = $400,000 (9.24424) PV AD = $3,697,696
PV AD = R (PVF OAn, i) PV AD = $400,000 (8.55948 X 1.08) PV AD = $400,000 (9.24424) PV AD = $3,697,696
The recommended method of payment would be the immediate cash payment of $3,500,000, since that amount is less than the present value of the 15 annual payments of $400,000 ($3,697,696).
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-33
EXERCISE 6-20 (1520 minutes) Expected Cash Flow Probability Cash Estimate X Assessment = Flow (a) $ 4,800 20% $ 960 6,300 50% 3,150 7,500 30% 2,250 Total Expected Value $ 6,360 (b) $ 5,400 7,200 8,400 30% 50% 20% Total Expected Value 10% 80% 10% Total Expected Value $ 1,620 3,600 1,680 $ 6,900 $ (100) 2,400 500 $ 2,800
(c) $(1,000) 3,000 5,000
EXERCISE 6-21 (1015 minutes) Estimated Cash Probability Expected Outflow X Assessment = Cash Flow $200 10% $ 20 450 30% 135 600 50% 300 750 10% 75 X PV Factor, n = 2, i = 6% $ 530 X 0.89
Present Value $471.70
6-34
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
EXERCISE 6-22 (1520 minutes) (a) This exercise determines the present value of an ordinary annuity or expected cash flows as a fair value estimate. Cash flow Probability Expected Estimate X Assessment = Cash Flow $ 380,000 20% $ 76,000 630,000 50% 315,000 750,000 30% 225,000
X PV Factor, n = 8, I = 8% Present Value $ 616,000 X 5.74664 = $3,539,930
The fair value estimate of the trade name exceeds the carrying value; thus, no impairment is recorded. (b) This fair value is based on unobservable inputs--Killroy's own data on the expected future cash flows associated with the trade name. This fair value estimate is considered Level 3, as discussed in Chapter 2.
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-35
TIME AND PURPOSE OF PROBLEMS
Problem 6-1 (Time 1520 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 1520 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 2030 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 2030 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 2025 minutes) Purpose--to provide the student with an opportunity to determine which of four insurance options results in the largest present The value. 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 2530 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 3035 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 2030 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.
6-36
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
Time and Purpose of Problems (Continued) Problem 6-9 (Time 3035 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 3035 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 2530 minutes) Purpose--to present the student an opportunity to apply present value to retirement funding problems, including deferred annuities. Problem 6-12 (Time 2025 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 2025 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 2025 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 2025 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.
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-37
SOLUTIONS TO PROBLEMS
PROBLEM 6-1
(a)
Given no established value for the building, the fair market value of the note would be estimated to value the building. Time diagram: i = 9% PV = ? FV = $240,000
1/1/12
1/1/13 n=3
1/1/14
1/1/15
Formula: PV = FV (PVFn, i) PV = $240,000 (PVF3, 9%) PV = $240,000 (.77218) PV = $185,323
Cash equivalent price of building ........................................ Less: Book value ($250,000 $100,000) ........................... Gain on disposal of the building.....................................
$185,323.20 150,000.00 $ 35,323.20
6-38
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-1 (Continued) (b) Time diagram: i = 11%
Principal $300,000 Interest $27,000
PV OA = ? $27,000
$27,000
$27,000
1/1/12
1/1/13
1/1/14 n = 10
1/1/21
1/1/22
Present value of the principal FV (PVF10, 11%) = $300,000 (.35218) ......................... Present value of the interest payments R (PVF OA10, 11%) = $27,000 (5.88923)................. Combined present value (purchase price).................... (c) Time diagram: i = 8%
PV OA = ? $4,000 $4,000 $4,000 $4,000 $4,000
= $105,654
= 159,009 $264,663
0
1
2 n = 10
8
9
10
Formula: PV OA = R (PVF OAn,i) PV OA = $4,000 (PVF OA10, 8%) PV OA = $4,000 (6.71008) PV OA = $26,840 (cost of machine)
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-39
PROBLEM 6-1 (Continued) (d) Time diagram: i = 12%
PV OA = ? $20,000 $5,000 $5,000 $5,000 $5,000 $5,000 $5,000 $5,000 $5,000
0
1
2
3
4 n=8
5
6
7
8
Formula: PV OA = R (PVF OAn,i) PV OA = $5,000 (PVF OA8, 12%) PV OA = $5,000 (4.96764) PV OA = $24,838 Cost of tractor = $20,000 + $24,838.20 = $44,838 (e) Time diagram: i = 11%
PV OA = ? $120,000 $120,000 $120,000 $120,000
0
1
2 n=9
8
9
Formula: PV OA = R (PVF OAn, i) PV OA = $120,000 (PVF OA9, 11%) PV OA = $120,000 (5.53705) PV OA = $664,446
6-40
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-2
(a)
Time diagram: i = 8%
R R=? R ? R ? R ? R ? R ?
FV OA = $90,000
R ? R ?
0
1
2
3
4 n=8
5
6
7
8
Formula:
FV OA = R (FVF OAn,i) $90,000 = R (FVF OA8, 8%) $90,000 = R (10.63663) R = $90,000 10.63663 R = $8,461
(b)
Time diagram: i = 12%
R R=? R ? R ? R ? FV AD = 500,000
40
41
42 n = 25
64
65
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-41
PROBLEM 6-2 (Continued) 1. 2. 3. 4. Future value of an ordinary annuity of 1 for 25 periods at 12% ....................................................... Factor (1 + .12) ................................................................ Future value of an annuity due of 1 for 25 periods at 12%............................................................. Periodic rent ($500,000 149.33393)....................... 133.33387 X 1.1200 149.33393 $3,348
(c)
Time diagram: i = 9%
PV = $20,000 FV = $47,347
0
1
2
3
n Present value approach PV = FV (PVFn, i) or $20,000 = $47,347 (PVFn, 9%) PVFn, 9% = $20,000 $47,347 = .42241
Future value approach FV = PV (FVFn, i) $47,347 = $20,000 (FVFn, 9%) FVFn, 9% = $47,347 $20,000 = 2.36735
2.36735 is approximately the value of $1 invested at 9% for 10 years.
.42241 is approximately the present value of $1 discounted at 9% for 10 years.
6-42
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-2 (Continued) (d) Time diagram: i=? PV = $19,553 FV = $27,600
0
1
2 n=4
3
4
Future value approach FV = PV (FVFn, i) or $27,600 = $19,553 (FVF4, i) = $27,600 $19,553 = 1.41155
Present value approach PV = FV (PVFn, i) $19,553 = $27,600 (PVF4, i) = $19,553 $27,600 = .70844
FVF4, i
PVF4, i
1.41155 is the value of $1 invested at 9% for 4 years.
.70844 is the present value of $1 discounted at 9% for 4 years.
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-43
PROBLEM 6-3 Time diagram (Bid A): i = 9%
$69,000 PV OA = R = ? 3,000 3,000 3,000 3,000 69,000 3,000 3,000 3,000 3,000 0
0
1
2
3
4
5 n=9
6
7
8
9
10
Present value of initial cost 12,000 X $5.75 = $69,000 (incurred today)....................... Present value of maintenance cost (years 14) 12,000 X $.25 = $3,000 R (PVF OA4, 9%) = $3,000 (3.23972)................................... Present value of resurfacing FV (PVF5, 9%) = $69,000 (.64993) ........................................... Present value of maintenance cost (years 69) R (PVF OA95, 9%) = $3,000 (5.99525 3.88965) ............ Present value of outflows for Bid A...................................... 6,317 $129,881 44,845 9,719 $ 69,000
6-44
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-3 (Continued) Time diagram (Bid B): i = 9%
$126,000 PV OA = R = ? 1,080 1,080 1,080 1,080 1,080 1,080 1,080 1,080 1,080 0
0
1
2
3
4
5 n=9
6
7
8
9
10
Present value of initial cost 12,000 X $10.50 = $126,000 (incurred today).............. Present value of maintenance cost 12,000 X $.09 = $1,080 R (PV OA9, 9%) = $1,080 (5.99525)................................. Present value of outflows for Bid B ................................. Bid A should be accepted since its present value is lower. 6,475 $132,475 $126,000
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-45
PROBLEM 6-4
Lump sum alternative: Present Value = $500,000 X (1 .46) = $270,000. Annuity alternative: Payments = $36,000 X (1 .25) = $27,000. Present Value = Payments (PV AD20, 8%) = $27,000 (10.60360) = $286,297. Long should choose the annuity payout; its present value is $16,297 greater.
6-46
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-5
(a) (b)
The present value of $55,000 cash paid today is $55,000. Time diagram: i = 21/2% per quarter
PV OA = ? R= $4,000 $4,000 $4,000 $4,000 $4,000
0
1
2 n = 20 quarters
18
19
20
Formula: PV OA = R (PVF OAn, i) PV OA = $4,000 (PVF OA20, 21/2%) PV OA = $4,000 (15.58916) PV OA = $62,357 (c) Time diagram: i = 21/2% per quarter
$18,000 PV AD = R = $1,800 $1,800 $1,800 $1,800 $1,800
0
1
2 n = 40 quarters
38
39
40
Formula: PV AD = R (PVF ADn, i) PV AD = $1,800 (PVF AD40, 21/2%) PV AD = $1,800 (25.73034) PV AD = $46,315 The present value of option (c) is $18,000 + $46,315, or $64,315.
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-47
PROBLEM 6-5 (Continued) (d) Time diagram: i = 21/2% per quarter
PV OA = ? PV OA = R = ? $4,000 R= $1,500 $4,000 $4,000
$1,500
$1,500 $1,500
0
1 11 n = 12 quarters
12
13
14 n = 25 quarters
36
37
Formulas:
PV OA = R (PVF OAn,i) PV OA = $4,000 (10.25776) PV OA = $41,031 PV OA = R (PVF OAn,i) PV OA = $1,500 (23.95732 10.25776) PV OA = $20,549
PV OA = $4,000 (PVF OA12, 21/2%) PV OA = $1,500 (PVF OA3712, 21/2%)
The present value of option (d) is $41,031.04 + $20,549.34, or $61,580.38. Present values: (a) (b) (c) (d) $55,000. $62,357. $64,315. $61,580.
Option (c) is the best option, based upon present values alone.
6-48
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
Time diagram: i = 12%
($39,000) $18,000 $18,000 $68,000 $68,000 $68,000 $68,000 $38,000 $38,000 $38,000
PV OA = ? R = ($39,000)
Copyright 2011 John Wiley & Sons, Inc.
0 n=5
($60,000 $30,000 $12,000) ($110,000 $30,000 $12,000)
1 n=5 n = 20
5
6
10 11
12
29 30 31
39 40 n = 10
($80,000 $30,000 $12,000)
(0 $30,000 $9,000)
Formulas:
PV OA = R (PVF OAn, i)
12%
PV OA = R (PVF OAn, i)
PV OA = R (PVF OAn, i) ) PV OA = $68,000 (PVF OA3010, PV OA = $68,000 (2.40496) PV OA = $163,537
12%
PV OA =R (PVF OAn, i) ) PV OA = $38,000 (PVF OA4030, PV OA = $38,000 (.18860) PV OA = $7,167
12%
PV OA = ($39,000)(PVF OA5, 12%) PV OA = $18,000 (PVF OA10-5, PV OA = $18,000 (2.04544) PV OA = $36,818
)
PV OA = ($39,000)(3.60478)
PV OA = $18,000 (5.65022 3.60478) PV OA = $68,000 (8.05518 5.65022) PV OA = $38,000 (8.24378 8.05518)
PROBLEM 6-6
PV OA = ($140,586.42)
Kieso, Intermediate Accounting, 14/e, Solutions Manual
Present value of future net cash inflows:
$(140,586.42) 36,817.92 163,537.28 7,166.80 $ 66,936
(For Instructor Use Only)
Stacy McGill should accept no less than $66,935.58 for her vineyard business.
6-49
PROBLEM 6-7 (a) Time diagram (alternative one): i=?
PV OA = $600,000 R= $80,000 $80,000 $80,000 $80,000 $80,000
0
1
2 n = 12
10
11
12
Formulas: PV OA = R (PVF OAn, i) $600,000 = $80,000 (PVF OA12, i) PVF OA12, i = $600,000 $80,000 PVF OA12, i = 7.50 7.50 is present value of an annuity of $1 for 12 years discounted at approximately 8%.
Time diagram (alternative two): i=?
PV = $600,000 FV = $1,900,000
0
1
2 n = 12
11
12
6-50
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-7 (Continued) Future value approach FV = PV (FVFn, i) or $1,900,000 = $600,000 (FVF12, i) FVF12, I FVF12, I = $1,900,000 $600,000 = 3.16667 $600,000 = $1,900,000 (PVF12, i) PVF12, i = $600,000 $1,900,000 PVF12, i = .31579 .31579 is the approximate present value of $1 discounted at 10% for 12 years. Present value approach PV = FV (PVFn, i)
3.16667 is the approximate future value of $1 invested at 10% for 12 years.
Dubois should choose alternative two since it provides a higher rate of return. (b) Time diagram: i=?
($824,150 $200,000) PV OA = R = $624,150 $76,952 $76,952 $76,952 $76,952
0
1
8 9 n = 10 six-month periods
10
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-51
PROBLEM 6-7 (Continued) Formulas: PV OA = R (PVF OAn, i) $624,150 = $76,952 (PVF OA10, i) PV OA10, i = $624,150 $76,952 PV OA10, i = 8.11090
8.11090 is the present value of a 10-period annuity of $1 discounted at 4%. The interest rate is 4% semiannually, or 8% annually. (c) Time diagram: i = 5% per six months
PV = ? PV OA = R= ? $32,000 $32,000 $32,000 $32,000 $32,000 ($800,000 X 8% X 6/12)
0
1
2
8 9 10 n = 10 six-month periods [(7 2) X 2]
Formulas: PV OA = R (PVF OAn, i) PV OA = $32,000 (PVF OA10, 5%) PV OA = $32,000 (7.72173) PV OA = $247,095 PV = FV (PVFn, i) PV = $800,000 (PVF10, 5%) PV = $800,000 (.61391) PV = $491,128
Combined present value (amount received on sale of note): $247,095.36 + $491,128 = $738,223
6-52
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-7 (Continued) (d) Time diagram (future value of $200,000 deposit) i = 21/2% per quarter
PV = $200,000 FV = ?
12/31/12
12/31/13
12/31/21
12/31/22
n = 40 quarters Formula: FV = PV (FVFn, i) FV = $200,000 (FVF40, 2 1/2%) FV = $200,000 (2.68506) FV = $537,012 Amount to which quarterly deposits must grow: $1,300,000 $537,012 = $762,988. Time diagram (future value of quarterly deposits) i = 21/2% per quarter
R R=? R ? R ? R ? R ? R ? R ? R ? R ?
12/31/12
12/31/13
12/31/21
12/31/22
n = 40 quarters
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-53
PROBLEM 6-7 (Continued) Formulas: FV OA = R (FVF OAn, i) $762,988 = R (FVF OA40, 2 1/2%) $762,988 = R (67.40255) R = $762,988 67.40255 R = $11,320
6-54
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-8 Vendor A: $ 18,000 payment X 6.14457 (PV of ordinary annuity 10%, 10 periods) $ 110,602 + 55,000 down payment + 10,000 maintenance contract $ 175,602 total cost from Vendor A $ 9,500 semiannual payment X 18.01704 (PV of annuity due 5%, 40 periods) $ 171,162 $ 1,000 X 3.79079 (PV of ordinary annuity of 5 periods, 10%) $ 3,791 PV of first 5 years of maintenance $ 2,000 [PV of ordinary annuity 15 per., 10% (7.60608) X 3.81529 PV of ordinary annuity 5 per., 10% (3.79079)] $ 7,631 PV of next 10 years of maintenance $ X $ 3,000 [(PV of ordinary annuity 20 per., 10% (8.51356) .90748 PV of ordinary annuity 15 per., 10% (7.60608)] 2,722 PV of last 5 years of maintenance
Vendor B:
Vendor C:
Total cost of press and maintenance Vendor C: $ 150,000 cash purchase price 3,791 maintenance years 15 7,631 maintenance years 615 2,722 maintenance years 1620 $ 164,144 The press should be purchased from Vendor C, since the present value of the cash outflows for this option is the lowest of the three options.
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-55
PROBLEM 6-9 (a) Time diagram for the first ten payments: i = 10%
PVAD = ? R=
$800,000 $800,000 $800,000 $800,000 $800,000 $800,000 $800,000
0
1
2
3
7
8
9
10
n = 10 Formula for the first ten payments: PV AD = R (PVF ADn, i) PV AD = $800,000 (PVF AD10, 10%) PV AD = $800,000 (6.75902) PV AD = $5,407,216
Formula for the last ten payments: PV OA = R (PVF OAn, i) PV OA = $400,000 (PVF OA19 9, 10%) PV OA = $400,000 (8.36492 5.75902) PV OA = $400,000 (2.6059) PV OA = $1,042,360 Note: The present value of an ordinary annuity is used here, not the present value of an annuity due.
6-56
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-9 (Continued) The total cost for leasing the facilities is: $5,407,216 + $1,042,360 = $6,449,576. OR Time diagram for the last ten payments: i = 10%
PV = ? R= $400,000 $400,000 $400,000 $400,000
0
FVF (PVFn, i)
1
2
9
10
17
18
19
R (PVF OAn, i)
Formulas for the last ten payments: (i) Present value of the last ten payments: PV OA = R (PVF OAn, i) PV OA = $400,000 (PVF OA10, 10%) PV OA = $400,000 (6.14457) PV OA = $2,457,828
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-57
PROBLEM 6-9 (Continued) (ii) Present value of the last ten payments at the beginning of current year: PV = FV (PVFn, i) PV = $2,457,828 (PVF9, 10%) PV = $2,457,828 (.42410) PV = $1,042,365* *$5 difference due to rounding. Cost for leasing the facilities $5,407,216 + $1,042,365 = $6,449,581 Since the present value of the cost for leasing the facilities, $6,449,581, is less than the cost for purchasing the facilities, $7,200,000, McDowell Enterprises should lease the facilities. (b) Time diagram: i = 11%
PV OA = ? R= $15,000 $15,000 $15,000
$15,000 $15,000 $15,000 $15,000
0
1
2
3
6
7
8
9
n=9
6-58
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-9 (Continued) Formula: PV OA = R (PVF OAn, i) PV OA = $15,000 (PVF OA9, 11%) PV OA = $15,000 (5.53705) PV OA = $83,056 The fair value of the note is $83,056. (c) Time diagram: Amount paid = $792,000
0
10
30 Amount paid = $800,000
Cash discount = $800,000 (1%) = $8,000 Net payment = $800,000 $8,000 = $792,000 If the company decides not to take the cash discount, then the company can use the $792,000 for an additional 20 days. The implied interest rate for postponing the payment can be calculated as follows: (i) Implied interest for the period from the end of discount period to the due date: Cash discount lost if not paid within the discount period Net payment being postponed = $8,000/$792,000 = 0.010101
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-59
PROBLEM 6-9 (Continued) (ii) Convert the implied interest rate to annual basis: Daily interest = 0.010101/20 = 0.00051 Annual interest = 0.000505 X 365 = 18.43% Since McDowell's cost of funds, 10%, is less than the implied interest rate for cash discount, 18.43%, it should continue the policy of taking the cash discount.
6-60
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-10
1.
Purchase. Time diagrams: Installments i = 10%
PV OA = ? R= $350,000 $350,000 $350,000 $350,000 $350,000
0
1
2
3 n=5
4
5
Property taxes and other costs i = 10%
PV OA = ? R= $56,000 $56,000 $56,000 $56,000 $56,000 $56,000
0
1
2
9
10
11
12
n = 12
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-61
PROBLEM 6-10 (Continued) Insurance i = 10%
PV AD = ? R= $27,000 $27,000 $27,000 $27,000 $27,000 $27,000
0
1
2
9
10
11
12
n = 12
Salvage Value i = 10%
PV = ? FV = $500,000
0
1
2
9
10
11
12
n = 12 Formula for installments: PV OA = R (PVF OAn, i) PV OA = $350,000 (PVF OA5, 10%) PV OA = $350,000 (3.79079) PV OA = $1,326,777
6-62
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-10 (Continued) Formula for property taxes and other costs: PV OA = R (PVF OAn, i) PV OA = $56,000 (PVF OA12, 10%) PV OA = $56,000 (6.81369) PV OA = $381,567 Formula for insurance: PV AD = R (PVF ADn, i) PV AD = $27,000 (PVF AD12, 10%) PV AD = $27,000 (7.49506) PV AD = $202,367 Formula for salvage value: PV = FV (PVFn, i) PV = $500,000 (PVF12, 10%) PV = $500,000 (0.31863) PV = $159,315
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-63
PROBLEM 6-10 (Continued) Present value of net purchase costs: Down payment .................................................................. Installments ....................................................................... Property taxes and other costs................................... Insurance ............................................................................ Total costs.......................................................................... Less: Salvage value ....................................................... Net costs............................................................................. $ 400,000 1,326,777 381,567 202,367 $2,310,711 159,315 $2,151,396
2.
Lease. Time diagrams: Lease payments i = 10%
PV AD = ? R= $270,000 $270,000 $270,000 $270,000 $270,000
0
1
2
10
11
12
n = 12 Interest lost on the deposit i = 10%
PV OA = ? R= $10,000 $10,000 $10,000 $10,000 $10,000
0
1
2
10
11
12
n = 12
6-64
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-10 (Continued) Formula for lease payments: PV AD = R (PVF ADn, i) PV AD = $270,000 (PVF AD12, 10%) PV AD = $270,000 (7.49506) PV AD = $2,023,666 Formula for interest lost on the deposit: Interest lost on the deposit per year = $100,000 (10%) = $10,000 PV OA = R (PVF OAn, i) PV OA = $10,000 (PVF OA12, 10%) PV OA = $10,000 (6.81369) PV OA = $68,137* Cost for leasing the facilities = $2,023,666 + $68,137 = $2,091,803 Dunn Inc. should lease the facilities because the present value of the costs for leasing the facilities, $2,091,803, is less than the present value of the costs for purchasing the facilities, $2,151,396. *OR: $100,000 ($100,000 X .31863) = $68,137
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-65
PROBLEM 6-11 (a) Annual retirement benefits. $ 48,000 X 2.56330 (future value of 1, 24 periods, 4%) 123,038 annual salary during last year of work X .50 retirement benefit % $ 61,519 annual retirement benefit $ 36,000 X 3.11865 (future value of 1, 29 periods, 4%) 112,271 annual salary during last year of work X .40 retirement benefit % $ 44,909 annual retirement benefit $ 18,000 X 2.10685 (future value of 1, 19 periods, 4%) 37,923 annual salary during last year of work X .40 retirement benefit % $ 15,169 annual retirement benefit $ 15,000 X 1.73168 (future value of 1, 14 periods, 4%) 25,975 annual salary during last year of work X .40 retirement benefit % $ 10,390 annual retirement benefit
Jeancurrent salary
Colincurrent salary
Anitacurrent salary
Gavincurrent salary
6-66
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-11 (Continued) (b) Fund requirements after 15 years of deposits at 12%. Jean will retire 10 years after deposits stop. $ 61,519 annual plan benefit [PV of an annuity due for 30 periods PV of an X 2.69356 annuity due for 10 periods (9.02181 6.32825)] $ 165,705
Colin will retire 15 years after deposits stop. $ 44,909 annual plan benefit X 1.52839 [PV of an annuity due for 35 periods PV of an annuity due for 15 periods (9.15656 7.62817)] $ 68,638
Anita will retire 5 years after deposits stop. $ 15,169 annual plan benefit X 4.74697 [PV of an annuity due for 25 periods PV of an annuity due for 5 periods (8.78432 4.03735)] $ 72,007
Gavin will retire the beginning of the year after deposits stop. $ 10,390 annual plan benefit X 8.36578 (PV of an annuity due for 20 periods) $ 86,920
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-67
PROBLEM 6-11 (Continued) $165,705 Jean 68,638 Colin 72,007 Anita 86,920 Gavin $393,270 Required fund balance at the end of the 15 years of deposits. (c) Required annual beginning-of-the-year deposits at 12%: Deposit X (future value of an annuity due for 15 periods at 12%) = FV Deposit X (37.27972 X 1.12) = $393,270.00 Deposit = $393,270.00 41.75329 Deposit = $9,419.
6-68
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-12 (a) The time value of money would suggest that NET Life's discount rate was substantially higher than First Security's. The actuaries at NET Life are making different assumptions about inflation, employee turnover, life expectancy of the work force, future salary and wage levels, return on pension fund assets, etc. NET Life may operate at lower gross and net margins and it may provide fewer services. As the controller of STL, Brokaw assumes a fiduciary responsibility to the present and future retirees of the corporation. As a result, he is responsible for ensuring that the pension assets are adequately funded and are adequately protected from most controllable risks. At the same time, Brokaw is responsible for the financial condition of STL. In other words, he is obligated to find ethical ways of increasing the profits of STL, even if it means switching pension funds to a less costly plan. At times, Brokaw's role to retirees and his role to the corporation can be in conflict, especially if Brokaw is a member of a professional group such as CPAs or CMAs. If STL switched to NET Life The primary beneficiaries of Brokaw's decision would be the corporation and its many stockholders by virtue of reducing 8 million dollars of annual pension costs. The present and future retirees of STL may be negatively affected by Brokaw's decision because the chance of losing a future benefit may be increased by virtue of higher risks (as reflected in the discount rate and NET Life's weaker reputation). If STL stayed with First Security In the short run, the primary beneficiaries of Brokaw's decision would be the employees and retirees of STL given the lower risk pension asset plan. STL and its many stakeholders could be negatively affected by Brokaw's decision to stay with First Security because of the company's inability to trim 8 million dollars from its operating expenses.
(b)
(c)
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-69
PROBLEM 6-13
Cash Flow Probability Estimate X Assessment = Expected Cash Flow 2013 $2,500 20% $ 500 4,000 60% 2,400 5,000 20% 1,000 X PV Factor, n = 1, I = 5% Present Value $3,900 X 0.95238 = $ 3,714 2014 $3,000 5,000 6,000 30% 50% 20% $ 900 2,500 1,200
X PV Factor, n = 2, I = 5% Present Value $4,600 X 0.90703 = $ 4,172
2015
$4,000 6,000 7,000
30% 40% 30%
X PV Factor, n = 3, I = 5% Present Value $5,700 X 0.86384 = $ 4,924 Total Estimated Liability $12,810
$1,200 2,400 2,100
6-70
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROBLEM 6-14
Cash Flow Probability Estimate X Assessment = Expected Cash Flow 2013 $6,000 40% $2,400 9,000 60% 5,400 X PV Factor, n = 1, I = 6% Present Value $ 7,800 X 0.9434 = $ 7,359 2014 $ (500) 2,000 4,000 20% 60% 20% $ (100) 1,200 800
$1,900
Scrap Value Received at the End of 2014
X PV Factor, n = 2, I = 6% Present Value X 0.89 = $ 1,691
$ 500 900
50% 50%
X PV Factor, n = 2, I = 6% Present Value $ 700 X 0.89 = $ 623 Estimated Fair Value $9,672
$ 250 450
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-71
PROBLEM 6-15 (a) The expected cash flows to meet the asset retirement obligation represent a deferred annuity. Developing a fair value estimate requires determining the present value of the annuity of expected cash flows to be paid in three years and then determine the present value of that amount today. Cash Flow Probability Estimate X Assessment = Expected Cash Flow $15,000 10% $ 1,500 22,000 30% 6,600 25,000 50% 12,500 30,000 10% 3,000 X PV Factor, n = 3, I = 5% Present Value (deferred 10 yrs) $ 23,600 X 2.72325 = $64,269 The value today of the annuity payments to commence in ten years is: $ 64,269 Present value of annuity X .61391 PV of a lump sum to be paid in 10 periods. $ 39,455 Alternatively, the present value of the deferred annuity can be computed as follows: $ 23,600 Expected cash outflows X 1.67184 [PV of an ordinary annuity for 13 periods PV of an annuity due for 10 periods (9.39357 7.72173)] $ 39,455 (b) This fair value estimate is based on unobservable inputs--Murphy's own data on the expected future cash flows associated with the obligation to restore the site. This fair value estimate is considered Level 3, as discussed in Chapter 2.
Copyright 2011 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 14/e, Solutions Manual (For Instructor Use Only)
6-72
FINANCIAL REPORTING PROBLEM
(a)
1.
Long-lived assets, goodwill
For impairment of goodwill and long-lived assets, fair value is determined using a discounted cash flow analysis. 2. 3. 4. (b) Short-term and long-term debt Postretirement benefit plans Employee stock ownership plans
(1) The following rates are disclosed in the accompanying notes: Debt Weighted-Average Effective Interest Rate At December 31 Short-Term Long-Term 2009 2.0% 4.9% 2008 2.7% 4.5%
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-73
FINANCIAL REPORTING PROBLEM (Continued) Benefit Plans Pension Benefits United States 2008 2009 Assumptions used to determine net periodic benefit cost. Discount rate Expected return on assets Other Retiree Benefits 2009 2008
6.5% 7.4%
5.5% 7.4%
6.9% 9.3%
6.3% 9.3%
Stock-Based Compensation Assumptions Weighted average interest rate used in Stock Option Valuation 2009 3.6% 2008 3.4% 2007 4.5%
(2) There are different rates for various reasons: 1. The maturity dates--short-term vs. long-term. 2. The security or lack of security for debts--mortgages and collateral vs. unsecured loans. 3. Fixed rates and variable rates. 4. Issuances of securities at different dates when differing market rates were in effect. 5. Different risks involved or assumed. 6. Foreign currency differences--some investments and payables are denominated in different currencies.
6-74
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
FINANCIAL STATEMENT ANALYSIS CASE
(a)
Cash inflows of $375,000 less cash outflows of $125,000 = Net cash flows of $250,000. $250,000 X 2.48685 (PVF OA3, 10%) = $621,713
(b)
Cash inflows of $275,000 less cash outflows of $155,000 = Net cash flows of $120,000. $120,000 X 2.48685 (PVF OA3,10%) = $298,422
(c)
The estimate of future cash flows is very useful. It provides an understanding of whether the value of gas and oil properties is increasing or decreasing from year to year. Although it is an estimate, it does provide an understanding of the direction of change in value. Also, it can provide useful information to record a write-down of the assets.
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-75
ACCOUNTING, ANALYSIS, AND PRINCIPLES Accounting (a) The present value of the note is presumably equal to the fair-value of the inventory. The note has 20 semi-annual periods to maturity. $670,591.65 = $50,000 X PVF-OA20,i PVF-OA20,i = $670,591.65 $50,000 PVF-OA20,i = 13.59033 Searching across the interest rate columns on the 20-period row reveals that the interest rate is 4% semi-annually or 8 percent annually. (b) Johnson should initially record the note at its fair-value, $670,591.65.
Analysis If interest rates increase, the fair-value of the note will decline. This is because the remaining cash flows are being discounted at a higher rate. That is, the present value of the future cash flows is less at a higher discount rate. Principles Fair-value versus historical cost potentially involves a trade-off between the primary qualities of relevance and reliability. The fair-values of various assets (and liabilities) is potentially more relevant to financial statement readers. However, it is often a more subjective measure than historical cost. Thus, fair-value may not be as reliable as historical cost. Fair-value is more subjective because it often must be estimated, requiring assumptions about discount rates and, as later chapters illustrate, about the amounts and timing of future cash flows.
6-76
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROFESSIONAL RESEARCH
Search strings: "present value", present and value, Present value $, "best estimate", "estimated cash flow", "expected cash flow", "fresh-start measurement", "interest methods of allocation" (a) Statement of Financial Accounting Concepts No. 7, "Using Cash Flow Information and Present Value in Accounting Measurements (FASB 2000). (b) See Appendix B: APPLICATIONS OF PRESENT VALUE IN FASB STATEMENTS AND APB OPINIONS, CON7, Par. 119 119. . . . The accompanying table is presented to assist readers in understanding the differences between the conclusions reached in this Statement and those found in FASB Statements and APB Opinions that employ present value techniques in recognition, measurement, or amortization (period-to-period allocation) of assets and liabilities in the statement of financial position. Some examples are: Debt payable and related premium or discount Asset acquired by incurring liabilities in a business combination--"An asset acquired by incurring liabilities is recorded at cost--that is, at the present value of the amounts to be paid" (paragraph 67(b)). APB Opinion No. 21, Interest on Receivables and Payables--Note exchanged for property, goods, or services. Capital lease or operating lease-- . . . The lessee's incremental borrowing rate is used unless (a) the lessor's implicit rate can be determined and (b) the implicit rate is less than the incremental borrowing rate. FASB Statement No. 91, Accounting for Nonrefundable Fees and Costs Associated with Originating or Acquiring Loans and Initial Direct Costs of Lease . . . Origination fees and costs are reflected over the life of the loan as an adjustment of the yield on the net investment in the loan.
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-77
PROFESSIONAL RESEARCH (Continued) FASB Statement No. 106, Employers' Accounting for Postretirement Benefits Other Than Pensions . . . Effective settlement rate--". . . as opposed to `settling' the obligation, which incorporates the insurer's risk factor, `effectively settling' the obligation focuses only on the time value of money and ignores the insurer's cost for assuming the risk of experience losses" (paragraph 188). FASB Statement No. 121, Accounting for the Impairment of LongLived Assets and for Long-Lived Assets to Be Disposed Of . . . The objective is to estimate the fair value of the impaired asset. . . . (c) 1. CON7, Glossary of terms: Best estimate: The single most-likely amount in a range of possible estimated amounts; in statistics, the estimated mode. In the past, accounting pronouncements have used the term best estimate in a variety of contexts that range in meaning from "unbiased" to "most likely." This Statement uses best estimate in the latter meaning, as distinguished from the expected amounts described below. 2. CON7, Glossary of terms: Estimated Cash Flow and Expected Cash Flow: In the past, accounting pronouncements have used the terms estimated cash flow and expected cash flow interchangeably. In this Statement: Estimated cash flow refers to a single amount to be received or paid in the future. Expected cash flow refers to the sum of probability-weighted amounts in a range of possible estimated amounts; the estimated mean or average. 3. CON7, Glossary of terms: Fresh-Start Measurements: Measurements in periods following initial recognition that establishes a new carrying amount unrelated to previous amounts and accounting conventions. Some fresh-start measurements are used every period, as in the reporting of some marketable securities at fair value under FASB Statement No.115, Accounting for Certain Investments in Debt and Equity Securities. In other situations, fresh-start measurements are prompted by an exception or "trigger," as in a remeasurement of assets under FASB Statement No. 121, Accounting for the Impairment of Long-Lived Assets and for Long-Lived Assets to Be Disposed Of.
6-78
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROFESSIONAL RESEARCH (Continued) 4. CON7, Glossary of terms: Interest Methods of Allocation: Reporting conventions that use present value techniques in the absence of a fresh-start measurement to compute changes in the carrying amount of an asset or liability from one period to the next. Like depreciation and amortization conventions, interest methods are grounded in notions of historical cost. The term interest methods of allocation refers both to the convention for periodic reporting and to the several approaches to dealing with changes in estimated future cash flows. Note to instructor: The concepts statements are not in the codification. Thus, the references to previous FASB standards above do not have codification sections indicated. A good extension of this research case would have students track down codification references for the items above.
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-79
PROFESSIONAL SIMULATION
Measurement i = 12%
Principal $100,000 Interest $10,000
PV OA = ?
$10,000
$10,000
$10,000
$10,000
0
1
2
3 n=5
4
5
Present value of the principal FV (PVF5, 12%) = $100,000 (.56743) Present value of the interest payments R (PVF OA5, 12%) = $10,000 (3.60478) Combined present value (purchase price) i = 8%
Principal $100,000 Interest $10,000
= $56,743
= 36,048 $92,791
PV OA = ? $10,000
$10,000
$10,000
$10,000
0
1
2
3 n=5
4
5
Present value of the principal FV (PVF5, 8%) = $100,000 (.68058) Present value of the interest payments R (PVF OA5, 8%) = $10,000 (3.99271) Combined present value (Proceeds) = 39,927 $107,985 = $ 68,058
6-80
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
PROFESSIONAL SIMULATION (Continued) 12% Inputs:
5
12
?
10,000
10,000
N Answer: 8% Inputs: 5
I
PV 92,790.45
PMT
FV
8
?
10,000
10,000
N Answer: Valuation
A 1 2 3 Bond Amortization Schedule B
I
PV 107,985.42
PMT
FV
Note: Calculators generally round to the nearest cent.
C
D
E
F
G
Carrying Interest 4 5 6 7 8 9 10 11 12 13 14 15
The following formula is entered in the cells in this column: =+E5*0.12.
Bond Discount Amortization
Value of Bonds $92,790.45
The following formula is entered in the cells in this column: =+C6-B6.
Date Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Cash Interest
Expense
10,000.00 10,000.00 10,000.00 10,000.00 10,000.00
$11,134.85 11,271.04 11,423.56 11,594.39 11,785.71
$1,134.85 1,271.04 1.423.56 1,594.39 1,785.71
93,925.30 95,196.34 96,619.90 98,214.29 100,000.00
The following formula is entered in the cells in this column: =+E5+D6
Copyright 2011 John Wiley & Sons, Inc.
Kieso, Intermediate Accounting, 14/e, Solutions Manual
(For Instructor Use Only)
6-81