Problem 6–11
Requirement 1
PVAD = Annuity amount x Annuity factor
Annuity amount = PVAD
Annuity factor
Requirement 2
Annuity amount = $800,000
Requirement 3
PVAD = (Annuity amount x Annuity factor) + PV of residual
6–36 Intermediate Accounting, 8/e
Problem 6–12
Requirement 1
PVA = Annuity amount x Annuity factor
Requirement 2
Annuity amount = $800,000
Requirement 3
Annuity amount = $800,000
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** )
2. Lease option:
6–38 Intermediate Accounting, 8/e
Problem 6–14
Requirement 1
Tinkers:
PVA = $20,000 x 7.19087* = $143,817
* Present value of an ordinary annuity of $1: n = 15, i = 11% (from Table 4)
Evers:
PVA = $25,000 x 7.19087* = $179,772
* Present value of an ordinary annuity of $1: n = 15, i = 11% (from Table 4)
Chance:
PVA = $30,000 x 7.19087* = $215,726
* Present value of an ordinary annuity of $1: n = 15, i = 11% (from Table 4)
Problem 6–14 (concluded)
Or, alternatively:
Deferred annuity
Employee
PVA factor, i = 11%
–
PVA factor, i = 11%
=
factor
Tinkers
7.54879 (n = 17)
–
1.71252 (n = 2)
=
5.83627
Evers
Chance
7.83929 (n = 19)
3.10245 (n = 4)
=
4.73684
Present value of pension obligations at 12/31/16:
Tinkers: $20,000 x 5.83627 = $116,725
Requirement 2
Present value of pension obligations as of December 31, 2019:
Employee
PV as of 12/31/16
x
FV of $1 factor,
=
FV as of 12/31/16
n = 3, i = 11%
Tinkers
$116,725
x
1.36763
=
$159,637
Evers
Chance
Amount of annual contribution:
FVAD = Annuity amount x Annuity factor
Annuity amount = FVAD
Annuity factor
6–40 Intermediate Accounting, 8/e
Problem 6–15
Bond liability:
PV = $4,000,0001 (18.40158* ) + $100,000,000 (.17193** )
Lease liability:
Lease A:
PVAD = $200,000 (9.36492* ) = $1,872,984 = Liability
Lease B:
PVAD = $220,000 x 8.82371* = $1,941,216
Or, alternatively for Lease B:
PVA = $220,000 x 8.02155* = $1,764,741
Or, alternatively for Lease B:
PV = $220,000 (6.62938* ) = $1,458,464 (difference due to rounding)
From Table 4,
Ethics Case 6–1
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
CASES
6–42 Intermediate Accounting, 8/e
Analysis Case 6–2
Sally should choose the alternative with the highest present value.
Alternative 1:
Alternative 2:
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)
Or, alternatively (for 3):
PV = $22,000 (2.37897* ) = $52,337
Communication Case 6–3
Suggested Grading Concepts and Grading Scheme:
Content (65%)
_____ 25 Explanation of the method used (present value) to
compare the two contracts.
_____ 30 Presentation of the calculations.
49ers PV = $6,989,065
Cowboys PV = $6,492,710
_____ 10 Correct conclusion.
____
_____ 65 points
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
6–44 Intermediate Accounting, 8/e
Analysis Case 6–4
The settlement was determined by calculating the present value of lost future
income ($200,000 per year) discounted at a rate that 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:
Judgment Case 6–5
Purchase price of new machine $150,000
Sales price of old machine (100,000)
Incremental cash outflow required $ 50,000
6–46 Intermediate Accounting, 8/e
Real World Case 6–6
Requirement 1
The maturity value (face amount) can be determined by dividing the present
value by the present value of $1 factor for 15 semiannual periods (end of 2016 –
beginning of 2023) at the semiannual rate of 1.5%:
Requirement 2
Using a 1.5% effective semiannual rate and 40 periods:
Real World Case 6–7
Requirement 1
The effective interest rate can be determined by solving for the unknown present
value of an ordinary annuity of $1 factor for seven periods:
Requirement 2
The effective interest rate can be determined by solving for the unknown present
value of an annuity due $1 factor for 15 periods: