Spiceland Solution Manual Intermediate Accounting 7e Ch06
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Question 6-15 Companies frequently acquire the use of assets by leasing rather than purchasing them. Leases
usually require the payment of fixed amounts at regular intervals over the life of the lease. Certain long-term, noncancelable leases are treated in a manner similar to an installment sale by the lessor and an installment purchase by the lessee. In other words, the lessor records a receivable and the lessee records a liability for the several installment payments. For the lessee, this requires that the leased asset and corresponding lease liability be valued at the present value of the lease payments.
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Brief Exercise 6-1 Fran should choose the second investment opportunity. More rapid compounding
has the effect of increasing the actual rate, which is called the effective rate, at which money grows per year. For the second opportunity, there are four, three-month periods paying interest at 2% (one-quarter of the annual rate). $10,000 invested will grow to $10,824 ($10,000 x 1.0824*). The effective annual interest rate, often referred to as the annual yield, is 8.24% ($824 ÷ $10,000), compared to just 8% for the first opportunity.
* Future value of $1: n=4, i=2% (from Table 1)
Brief Exercise 6-2 Bill will not have enough accumulated to take the trip. The future value of his
investment of $23,153 is $347 short of $23,500. FV = $20,000 (1.15763* ) = $23,153
* Future value of $1: n=3, i=5% (from Table 1)
Brief Exercise 6-3
FV factor = $26,600 = 1.33* $20,000 * Future value of $1: n=3, i=? (from Table 1, i = approximately 10%)
Brief Exercise 6-4 John would be willing to invest no more than $12,673 in this opportunity. PV = $16,000 (.79209* ) = $12,673 * Present value of $1: n=4, i=6% (from Table 2)
BRIEF EXERCISES
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2. FV = $20,000 (2.15892* ) = $43,178 * Future value of $1: n=10, i=8% (from Table 1)
3. FV = $30,000 (9.64629* ) = $289,389 * Future value of $1: n=20, i=12% (from Table 1)
4. FV = $50,000 (1.60103* ) = $80,052 * Future value of $1: n=12, i=4% (from Table 1)
Exercise 6-2 1. PV = $20,000 (.50835* ) = $10,167 * Present value of $1: n=10, i=7% (from Table 2)
2. PV = $14,000 (.39711* ) = $5,560 * Present value of $1: n=12, i=8% (from Table 2)
3. PV = $25,000 (.10367* ) = $2,592 * Present value of $1: n=20, i=12% (from Table 2)
4. PV = $40,000 (.46651* ) = $18,660 * Present value of $1: n=8, i=10% (from Table 2)
Exercise 6-3 PV of $1 Payment i=8% PV n First payment: $5,000 x .92593 = $ 4,630 1 Second payment 6,000 x .85734 = 5,144 2 Third payment 8,000 x .73503 = 5,880 4 Fourth payment 9,000 x .63017 = 5,672 6 Total $21,326
EXERCISES
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2. FV = $10,000 (1.80611* ) = $18,061 * Future value of $1: n=20, i=3% (from Table 1)
3. FV = $10,000 (1.81136* ) = $18,114 * Future value of $1: n=30, i=2% (from Table 1)
Exercise 6-5 1. FVA = $2,000 (4.7793* ) = $9,559 * Future value of an ordinary annuity of $1: n=4, i=12% (from Table 3)
2. FVAD = $2,000 (5.3528* ) = $10,706 * Future value of an annuity due of $1: n=4, i=12% (from Table 5) 3. FV of $1 Deposit i=3% FV n First deposit: $2,000 x 1.60471 = $ 3,209 16 Second deposit 2,000 x 1.42576 = 2,852 12 Third deposit 2,000 x 1.26677 = 2,534 8 Fourth deposit 2,000 x 1.12551 = 2,251 4 Total $10,846 4. $2,000 x 4 = $8,000
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Exercise 6-6 1. PVA = $5,000 (3.60478* ) = $18,024 * Present value of an ordinary annuity of $1: n=5, i=12% (from Table 4)
2. PVAD = $5,000 (4.03735* ) = $20,187 * Present value of an annuity due of $1: n=5, i=12% (from Table 6) 3. PV of $1 Payment i = 3% PV n First payment: $5,000 x .88849 = $ 4,442 4 Second payment 5,000 x .78941 = 3,947 8 Third payment 5,000 x .70138 = 3,507 12 Fourth payment 5,000 x .62317 = 3,116 16 Fifth payment 5,000 x .55368 = 2,768 20 Total $17,780
Exercise 6-7 1. PV = $40,000 (.62092* ) = $24,837 * Present value of $1: n=5, i=10% (from Table 2) 2. $36,289 = .55829* $65,000 * Present value of $1: n=10, i=? (from Table 2, i = approximately 6%) 3. $15,884 = .3971* $40,000 * Present value of $1: n=?, i=8% (from Table 2, n = approximately 12 years) 4. $46,651 = .46651* $100,000 * Present value of $1: n=8, i=? (from Table 2, i = approximately 10%) 5. FV = $15,376 (3.86968* ) = $59,500 * Future value of $1: n=20, i=7% (from Table 1)
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Exercise 6-19 List A List B e 1. Interest a. First cash flow occurs one period after agreement begins. m 2. Monetary asset b. The rate at which money will actually grow during a year. j 3. Compound interest c. First cash flow occurs on the first day of the agreement. i 4. Simple interest d. The amount of money that a dollar will grow to. k 5. Annuity e. Amount of money paid/received in excess of amount borrowed/lent. l 6. Present value of a single f. Obligation to pay a sum of cash, the amount of amount which is fixed. c 7. Annuity due g. Money can be invested today and grow to a larger amount. d 8. Future value of a single h. No fixed dollar amount attached. amount a 9. Ordinary annuity i. Computed by multiplying an invested amount by the interest rate. b 10. Effective rate or yield j. Interest calculated on invested amount plus accumulated interest. h 11. Nonmonetary asset k. A series of equal-sized cash flows. g 12. Time value of money l. Amount of money required today that is equivalent to a given future amount. f 13. Monetary liability m. Claim to receive a fixed amount of money.
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Exercise 6-20 1. a. An annuity is a series of cash flows or other economic benefits occurring at
fixed intervals, ordinarily as a result of an investment. Present value is the value at a specified time of an amount or amounts to be paid or received later, discounted at some interest rate. In an annuity due, the payments occur at the beginning, rather than at the end, of the periods. Thus, the present value of an annuity due includes the initial payment at its undiscounted amount. This lease should be evaluated using the present value of an annuity due.
2. d. Both future value tables will be used because the $75,000 already in the account will be multiplied times the future value factor of 1.26 to determine the amount 3 years hence, or $94,500. The three payments of $4,000 represent an ordinary annuity. Multiplying the three-period annuity factor (3.25) by the payment amount ($4,000) results in a future value of the annuity of $13,000. Adding the two elements together produces a total account balance of $107,500.
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Problem 6-3 Choose the option with the lowest present value of cash payments. 1. PV = $1,000,000 2. PV = $420,000 + 80,000 (6.71008* ) = $956,806 * Present value of an ordinary annuity of $1: n=10, i=8% (from Table 4) 3. PV = PVAD = $135,000 (7.24689* ) = $978,330 * Present value of an annuity due of $1: n=10, i=8% (from Table 6) 4. PV = $1,500,000 (.68058* ) = $1,020,870 * Present value of $1: n=5, i=8% (from Table 2) Harding should choose option 2.
Problem 6-4 The restaurant should be purchased if the present value of the future cash
flows discounted at 10% rate is greater than $800,000. PV = $80,000 (4.35526* ) + 70,000 (.51316** ) + 60,000 (.46651**) n=7 n=8 + $50,000 (.42410**) + 40,000 (.38554**) + 700,000 (.38554**) n=9 n=10 n=10 * Present value of an ordinary annuity of $1: n=6, i=10% (from Table 4) ** Present value of $1:, i=10% (from Table 2) PV = $718,838 < $800,000
Since the PV is less than $800,000, the restaurant should not be purchased.
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Problem 6-5 The maximum amount that should be paid for the store is the present value of the
estimated cash flows. Years 1-5: PVA = $70,000 x 3.99271* = $279,490
* Present value of an ordinary annuity of $1: n=5, i=8% (from Table 4)
Years 6-10: PVA = $70,000 x 3.79079* = $265,355
* Present value of an ordinary annuity of $1: n=5, i=10% (from Table 4)
PV = $265,355 x .68058* = $180,595 * Present value of $1: n=5, i=8% (from Table 2)
Years 11-20:
PVA = $70,000 x 5.65022* = $395,515 * Present value of an ordinary annuity of $1: n=10, i=12% (from Table 4)
PV = $395,515 x .62092* = $245,583 * Present value of $1: n=5, i=10% (from Table 2)
PV = $245,583 x .68058* = $167,139 * Present value of $1: n=5, i=8% (from Table 2) End of Year 20:
PV = $400,000 x .32197* x .62092 x .68058 = $54,424 * Present value of $1: n=10, i=12% (from Table 2) Total PV = $279,490 + 180,595 + 167,139 + 54,424 = $681,648 The maximum purchase price is $681,648.
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Problem 6-8 Requirement 1 Present value of payments 4-6:
PVA = $40,000 x 2.48685* = $99,474 * Present value of an ordinary annuity of $1: n= 3, i= 10% (from Table 4)
PV = $99,474 x .75131* = $74,736 * Present value $1: n= 3, i= 10% (from Table 2) Present value of all payments: $ 62,171 (PV of payments 1-3: $25,000 x 2.48685* ) 74,736 (PV of payments 4-6 calculated above) $136,907 The note payable and corresponding building should be recorded at $136,907.
Or alternatively: PV = $25,000 (2.48685* ) + 40,000 (1.86841** ) = $136,907 * Present value of an ordinary annuity of $1: n=3, i=10% (from Table 4)
Problem 6-9 Choose the alternative with the highest present value. Alternative 1: PV = $180,000 Alternative 2: PV = PVAD = $16,000 (11.33560* ) = $181,370 * Present value of an annuity due of $1: n=20, i=7% (from Table 6) Alternative 3: PVA = $50,000 x 7.02358* = $351,179 * Present value of an ordinary annuity of $1: n=10, i=7% (from Table 4) PV = $351,179 x .54393* = $191,017 * Present value of $1: n=9, i=7% (from Table 2) John should choose alternative 3.
Or, alternatively (for 3): PV = $50,000 (3.82037* ) = $191,019 (difference due to rounding)
Problem 6-13 Choose the option with the lowest present value of cash outflows, net of the
present value of any cash inflows. (Cash outflows are shown as negative amounts; cash inflows as positive amounts)
1. Buy option: PV = - $160,000 - 5,000 (5.65022* ) + 10,000 (.32197** ) * Present value of an ordinary annuity of $1: n=10, i=12% (from Table 4) ** Present value of $1: n=10, i=12% (from Table 2) PV = - $160,000 - 28,251 + 3,220 PV = - $185,031
2. Lease option: PVAD = - $25,000 (6.32825* ) = - $158,206 * Present value of an annuity due of $1: n=10, i=12% (from Table 6) Kiddy Toy should lease the machine.
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Problem 6-14 (concluded) Present value of pension obligations: Tinkers: $20,000 x 5.83627 = $116,725 Evers: $25,000 x 5.25791 = $131,448* Chance: $30,000 x 4.73684 = $142,105 *rounding difference
Requirement 2 Present value of pension obligations as of December 31, 2009:
Employee PV as of 12/31/06 x FV of $1 factor, = PV as of 12/31/09
n=3, i=11% Tinkers $116,725 x 1.36763 = $159,637 Evers 131,448 x 1.36763 = 179,772 Chance 142,105 x 1.36763 = 194,347 Total present value $533,756
Amount of annual contribution: FVAD = Annuity amount x Annuity factor
Annuity amount = FVAD
Annuity factor
Annuity amount = $533,756 = $143,881 3.7097* * Future value of an annuity due of $1: n=3, i=11% (from Table 5)
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The settlement was determined by calculating the present value of lost future income ($200,000 per year)1 discounted at a rate which is expected to approximate the time value of money. In this case, the discount rate, i, apparently is 7% and the number of periods, n, is 25 (the number of years to John’s retirement). John’s settlement was calculated as follows: $200,000 x 11.65358* = $2,330,716 annuity amount * Present value of an ordinary annuity of $1: n=25, i=7% (from Table 4) Note: In the actual case, John’s present salary was increased by 3% per year to reflect future salary increases.
1In the actual case, John’s present salary was increased by 3% per year to reflect future salary increases.
CASES
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Analysis Case 6-2 Sally should choose the alternative with the highest present value. Alternative 1: PV = $50,000 Alternative 2: PV = PVAD = $10,000 (5.21236* ) = $52,124 * Present value of an annuity due of $1: n=6, i=6% (from Table 6) Alternative 3: PVA = $22,000 x 2.67301* = $58,806 * Present value of an ordinary annuity of $1: n=3, i=6% (from Table 4) PV = $58,806 x .89000* = $52,337 * Present value of $1: n=2, i=6% (from Table 2) Sally should choose alternative 3.
Writing (35%) ______ 5 Proper letter format. ______ 6 Terminology and tone appropriate to the audience of a player's agent.
______ 12 Organization permits ease of understanding. _____ Introduction that states purpose. _____ Paragraphs that separate main points.
______ 12 English _____ Sentences grammatically clear and well organized, concise. _____ Word selection. _____ Spelling. _____ Grammar and punctuation. ____
______ 35 points
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Ethics Case 6-4 The ethical issue is that the 21% return implies an annual return of 21% on an
investment and misrepresents the fund’s performance to all current and future stakeholders. Interest rates are usually assumed to represent an annual rate, unless otherwise stated. Interested investors may assume that the return for $100 would be $21 per year, not $21 over two years. The Damon Investment Company ad should explain that the 21% rate represented appreciation over two years.
Judgment Case 6-5 Purchase price of new machine $150,000 Sales price of old machine (100,000) Incremental cash outflow required $ 50,000 The new machine should be purchased if the present value of the savings in
operating costs of $8,000 ($18,000 - 10,000) plus the present value of the salvage value of the new machine exceeds $50,000. PV = ($8,000 x 3.99271* ) + ($25,000 x .68058** ) PV = $31,942 + 17,015 PV = $48,957 * Present value of an ordinary annuity of $1: n=5, i=8% (from Table 4) ** Present value of $1: n=5, i=8% (from Table 2) The new machine should not be purchased.
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The effective interest rate can be determined by solving for the unknown present value of $1 factor (40 semiannual periods):
PV of $1 factor = $751.8 = .45289* $1,660
* Present value of $1: n= 40, i= ? (from Table 2, i = 2%) The effective, semiannual interest rate is 2% We could also solve for the annual rate using the increase in the carrying value of