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CHAPTER 6
Accounting and the Time Value of Money
ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC)
Topics Questions
Brief Exercises Exercises Problems
- Present value concepts. 1, 2, 3, 4, 5, 9, 17
- Use of tables. 13, 14 8 1
- Present and future value problems: a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 7 b. Unknown payments. 10, 11, 12 6, 12, 15, 17
8, 16, 17 2, 6
c. Unknown number of periods.
4, 9 10, 15 2
d. Unknown interest rate. 15, 18 3, 11, 16 9, 10, 11, 14 2, 7 e. Unknown present value. 8, 19 2, 7, 8, 10, 14
3, 4, 5, 6, 8, 12, 17, 18, 19
1, 4, 7, 9, 13, 14
- Value of a series of irregular deposits; changing interest rates.
3, 5, 8
- Valuation of leases, pensions, bonds; choice between projects.
6 15 7, 12, 13, 14, 15
3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15
- Deferred annuity. 16
- Expected Cash Flows. 20, 21, 22 13, 14, 15
ASSIGNMENT CLASSIFICATION TABLE (BY LEARNING OBJECTIVE)
Learning Objectives Questions^ BriefExercises Exercises Problems
- Describe the accounting concepts and fundamental concepts related to the time value of money.
1, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 17, 18
1, 2
- Solve future and present value of 1 problems.
2, 7, 8, 10, 11, 12
1, 2, 3, 4, 7, 8
2, 3, 6, 9, 10, 15
1, 2, 3, 5, 7, 9, 10
- Solve future value of ordinary and annuity due problems.
8, 9, 10, 11, 13
5, 6, 9, 13 3, 4, 6, 15, 16
2, 7
- Solve present value of ordinary and annuity due problems.
12, 14 10, 11, 12, 14, 16, 17
3, 4, 5, 6, 11, 12, 17, 18, 19
1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 14
- Solve present value problems related to deferred annuities, bonds, and expected cash flows.
2, 12, 15, 16, 19
15 7, 8, 13, 14, 20, 21, 22
6, 11, 12, 13, 14, 15
ANSWERS TO QUESTIONS
- 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. LO: 1, Bloom: K, Difficulty: Simple, Time: 3-5, AACSB: Communication, AICPA BB: None, AICPA FC: Reporting, AICPA PC: Communication
- 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 and/or bargain purchase options 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 associated with an investment or long-term asset (may be single sums and/or an annuity). LO: 1, 5, Bloom: K, Difficulty: Simple, Time: 3-5, AACSB: Communication, AICPA BB: None, AICPA FC: Reporting, AICPA PC: Communication
- 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, as well as the amount of money, and the risk involved (risk may be reflected in the interest rate). Simple interest is computed on the amount of the principal only, while compound interest is com- puted on the amount of the principal plus any accumulated interest. Compound interest involves interest on interest while simple interest does not. LO: 1, Bloom: K, Difficulty: Simple, Time: 3-5, AACSB: Communication, AICPA BB: None, AICPA FC: Reporting, AICPA PC: Communication
- 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 (future) 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 U.S. 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. LO: 1, Bloom: K, Difficulty: Simple, Time: 3-5, AACSB: Communication, AICPA BB: None, AICPA FC: Reporting, AICPA PC: Communication
Questions Chapter 6 (Continued)
- (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). LO: 1, Bloom: C, Difficulty: Simple, Time: 3-5, AACSB: Communication, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
- 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, i = 4 Quarterly compounding, assuming the amount is invested for 2 years: n = 8 $1,500 X 1.17166 = $1, i = 2 Thus, with quarterly compounding, Jose could earn $3 more. LO: 1, Bloom: AP, Difficulty: Simple, Time: 3-5, AACSB: Analytic , AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
- $26,898 = $20,000 X 1.34489 (future value of 1 at 2 1 / 2 % for 12 periods). LO: 2, Bloom: AP, Difficulty: Simple, Time: 3-5, AACSB: Analytic , AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
- $44,671 = $80,000 X .55839 (present value of 1 at 6% for 10 periods). LO: 2, Bloom: AP, Difficulty: Simple, Time: 3-5, AACSB: Analytic , AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
- 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. LO: 3, Bloom: C, Difficulty: Simple, Time: 3-5, AACSB: Communication, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
- 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. LO: 4, Bloom: AP, Difficulty: Simple, Time: 3-5, AACSB: Analytic , AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
- Amount deposited each year = $200,0004.64100^ (future 4 years).^ value^ of^ an^ ordinary^ annuity^ at^ 10%^ for
Amount deposited each year = $43,094.16. LO: 3, Bloom: AP, Difficulty: Simple, Time: 3-5, AACSB: Analytic , AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
- Amount deposited each year = $200,0005.10510^ [future value of an annuity due at 10% for 4 years (4.64100 X 1.10)].
Amount deposited each year = $39,176.51. LO: 3, Bloom: AP, Difficulty: Simple, Time: 3-5, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: Communication
SOLUTIONS TO BRIEF EXERCISES
BRIEF EXERCISE 6-
8% annual interest
i = 8% PV = $15,000 FV =?
n = 3
FV = $15,000 (FVF3, 8%)
FV = $15,000 (1.25971)
FV = $18,
8% annual interest, compounded semiannually
i = 4% PV = $15,000 FV =?
n = 6
FV = $15,000 (FVF6, 4%)
FV = $15,000 (1.26532)
FV = $18,
LO: 2, Bloom: AP, Difficulty: Simple, Time: 5-10, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
BRIEF EXERCISE 6-
12% annual interest
i = 12% PV =? FV = $25,
n = 4
PV = $25,000 (PVF4, 12%)
PV = $25,000 (.63552)
PV = $15,
12% annual interest, compounded quarterly
i = 3% PV =? FV = $25,
n = 16
PV = $25,000 (PVF16, 3%)
PV = $25,000 (.62317)
PV = $15,
LO: 2, Bloom: AP, Difficulty: Simple, Time: 5-10, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
BRIEF EXERCISE 6-
First payment today (Annuity Due)
i = 6% R = FV – AD = $8,000 $8,000 $8,000 $8,000 $8,000?
n = 20
FV – AD = $8,000 (FVF – OA20, 6%) 1. FV – AD = $8,000 (36.78559) 1. FV – AD = $311,
First payment at year-end (Ordinary Annuity)
i = 6% FV – OA = ? $8,000 $8,000 $8,000 $8,000 $8,
n = 20
FV – OA = $8,000 (FVF – OA20, 6%) FV – OA = $8,000 (36.78559) FV – OA = $294, LO: 3, Bloom: AP, Difficulty: Simple, Time: 5-10, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
BRIEF EXERCISE 6-
i = 5% FV – OA = R =???? $250,
n = 10
$250,000 = R (FVF – OA10, 5%)
$250,000 = R (12.57789)
= R
R = $19,
LO: 3, Bloom: AP, Difficulty: Moderate, Time: 5-10, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
BRIEF EXERCISE 6-
8% annual interest
i = 8% PV =? FV = $300,
n = 5
PV = $300,000 (PVF5, 8%)
PV = $300,000 (.68058)
PV = $204,
LO: 2, Bloom: AP, Difficulty: Simple, Time: 3-5, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
BRIEF EXERCISE 6-
First withdrawal at year-end
i = 8% PV – OA = R = ? $30,000 $30,000 $30,000 $30,000 $30,
n = 10
PV – OA = $30,000 (PVF – OA10, 8%)
PV – OA = $30,000 (6.71008)
PV – OA = $201,
First withdrawal immediately
i = 8% PV – AD = ? R = $30,000 $30,000 $30,000 $30,000 $30,
n = 10
PV – AD = $30,000 (PVF – AD10, 8%)
PV – AD = $30,000 (7.24689)
PV – AD = $217,
LO: 4, Bloom: AP, Difficulty: Moderate, Time: 5-10, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
BRIEF EXERCISE 6-
i =? PV = R = $793.15 $75 $75 $75 $75 $
n = 12
$793.15 = $75 (PVF – OA12, i )
PVF12, i =
Therefore, i = 2% per month or 24% per year. LO: 4, Bloom: AP, Difficulty: Simple, Time: 3-5, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
BRIEF EXERCISE 6-
i = 4% PV = $300,000 R =?????
n = 20
$300,000 = R (PVF – OA20, 4%)
$300,000 = R (13.59033)
R = $22,
LO: 4, Bloom: AP, Difficulty: Simple, Time: 3-5, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
BRIEF EXERCISE 6-
i = 8% PV =? PV – OA = R = $2,000, ? $140,000 $140,000 $140,000 $140,000 $140,
n = 10
$2,000,000 (PVF10, 8%) = $2,000,000 (.46319) = $ 926,
$140,000 (PVF – OA10, 8%) = $140,000 (6.71008) = 939,
LO: 5, Bloom: AP, Difficulty: Moderate, Time: 5-10, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
BRIEF EXERCISE 6-
PV – OA = $20,
$20,000 = $4,727.53 (PV – OA6, i%) (PV – OA6, i%) = $20,000 ÷ $4,727. (PV – OA6, i%) = 4. Therefore, i% = 11 LO: 4, Bloom: AP, Difficulty: Simple, Time: 3-5, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
BRIEF EXERCISE 6-
PV – AD = $20,
$20,000 = Payment (PV – AD6, 11%) $20,000 ÷ (PV – AD6, 11%) = Payment $20,000 ÷ 4.6959 = $4, LO: 4, Bloom: AP, Difficulty: Simple, Time: 3-5, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
EXERCISE 6-4 (15–20 minutes)
(a) Future value of an ordinary annuity of $4,000 a period for 20 periods at 8% $183,047.84 ($4,000 X 45.76196) Factor (1 + .08) X 1. Future value of an annuity due of $4,000 a period at 8% $197,
(b) Present value of an ordinary annuity of $2,500 for 30 periods at 5% $38,431 ($2,500 X 15.37245) Factor (1 + .05) X 1. Present value of annuity due of $2,500 for 30 periods at .05% $40,353 (Or see Table 6-5 which gives $40,356.68) (c) Future value of an ordinary annuity of $2,000 a period for 15 periods at 10% $63,544.96 ($2,000 X 31.77248) Factor (1 + 10) X 1. Future value of an annuity due of $2,000 a period for 15 periods at 10% $69,
(d) Present value of an ordinary annuity of $1,000 for 6 periods at 9% $4,485.92 ($1,000 X 4.48592) Factor (1 + .09) X 1. Present value of an annuity date of $1,000 for 6 periods at 9% $4,890 (Or see Table 6-5)
LO: 3, 4, Bloom: AP, Difficulty: Moderate, Time: 15-20, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
EXERCISE 6-5 (10–15 minutes)
(a) $30,000 X 4.96764 = $149,029.
(b) $30,000 X 8.31256 = $249,377.
(c) ($30,000 X 3.03735 X .50663) = $46,164. or (5.65022 – 4.11141) X $30,000 = $46,164.
LO: 4, Bloom: AP, Difficulty: Simple, Time: 10-15, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
EXERCISE 6-6 (15–20 minutes)
(a) Future value of $12,000 @ 5% for 10 years ($12,000 X 1.62889) = $19, (b) Future value of an ordinary annuity of $600, at 10% for 15 years ($600,000 X 31.77248) $19,063, Deficiency ($20,000,000 – $19,063,488) $936,
(c) $70,000 discounted at 4% for 10 years: $70,000 X .67556 = $47, Accept the bonus of $55,000 now. LO: 2, 3, 4, Bloom: AP, Difficulty: Moderate, Time: 15-20, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
EXERCISE 6-7 (12–17 minutes)
(a) $100,000 X .55526 = $55,
- $5,000 X 11.11839 = 55, $111,
(b) $100,000 X .48102 = $48,
- $5,000 X 10.37966 = 51, $100,
(c) $100,000 X .41727 = $41,
- $5,000 X 9.71225 = 48, $90,
LO: 5, Bloom: AP, Difficulty: Moderate, Time: 15-20, AACSB: Analytic, AICPA BB: None, AICPA FC: Reporting, AICPA PC: None
