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 6 7 8 9 10
n = 9
44,845
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
Present value of initial cost
12,000 X $10.50 = $126,000 (incurred today) ………
$126,000
Present value of maintenance cost
12,000 X $.09 = $1,080
R (PVF – OA9, 9%) = $1,080 (5.99525) …………………..
6,475
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.
PROBLEM 6.5
(a) The present value of $55,000 cash paid today is $55,000.
(b) Time diagram:
i = 21/2% per quarter
PV – OA = R =
? $4,000 $4,000 $4,000 $4,000 $4,000
PV – OA = $62,357
(c) Time diagram:
i = 21/2% per quarter
$18,000
PV – AD =
PROBLEM 6.5 (Continued)
(d) Time diagram:
i = 21/2% per quarter
PV – OA = R =
? $1,500 $1,500 $1,500 $1,500
PV – OA = R =
? $4,000 $4,000 $4,000
Formulas:
PV – OA = R (PVF – OAn,i) PV – OA = R (PVF – OAn,i)
The present value of option (d) is $41,031* + $20,549**, or
$61,580.
Present values:
(a) $55,000.
435,522
48,697
$ 376,596
Stacy McGill should accept no less than $376,596 for her vineyard business.
LO: 5, Bloom: AP, Difficulty: Moderate, Time: 25-30, AACSB: Analytic, AICPA BB: None, AICPA FC: Measurement, AICPA PC: None
6-46 Copyright © 2019 WILEY Kieso, Intermediate Accounting, 17/e, Solutions Manual (For Instructor Use Only)
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 10 11 12
n = 12
7.50 is the approximate present value of an annuity factor of $1 for 12
years discounted at approximately 8%.
Time diagram (alternative two):
i = ?
PROBLEM 6.7 (Continued)
Future value approach
Present value approach
FV = PV (FVFn, i)
PV = FV (PVFn, i)
or
$1,900,000 = $600,000 (FVF12, i)
$600,000 = $1,900,000 (PVF12, i)
Dubois should choose alternative two since it provides a higher rate
of return.
(b) Time diagram:
i = ?
PROBLEM 6.7 (Continued)
Formulas: PV – OA = R (PVF – OAn, i)
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 (.10 ÷ 2)
PV = ?
PV – OA = R =
? $32,000 $32,000 $32,000 $32,000 $32,000 ($800,000 X 8% X 6/12)
PROBLEM 6.7 (Continued)
(d) Time diagram (future value of $200,000 deposit)
i = 21/2% per quarter (.10 ÷ 4)
PV =
$200,000 FV = ?
12/31/20 12/31/21 12/31/29 12/31/30
n = 40 quarters (10 x 4)
Formula: FV = PV (FVFn, i)
Time diagram (future value of quarterly deposits)
i = 21/2% per quarter
R R R R R R R R R
R = ? ? ? ? ? ? ? ? ?
PROBLEM 6.7 (Continued)
Formulas: FV – OA = R (FVF – OAn, i)
PROBLEM 6.8
Vendor A:
$ 18,000
payment
X 6.14457
$ 110,602
+ 55,000
down payment
+ 10,000
maintenance contract
$ 175,602
total cost from Vendor A
Vendor B:
$ 9,500
semiannual payment
X 18.01704
(PV of annuity due 5% (.10 ÷ 2), 40 periods)
$ 171,162
Vendor C:
$ 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)]
$ 3,000
[(PV of ordinary annuity 20 per., 10% (8.51356) –
X .90748
PV of ordinary annuity 15 per., 10% (7.60608)]
$ 2,722
PV of last 5 years of maintenance
Total cost of press and maintenance Vendor C:
$ 150,000
cash purchase price
maintenance years 1–5
maintenance years 6–15
2,722
maintenance years 16–20
$ 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.
PROBLEM 6.9
(a) Time diagram for the first ten payments:
i = 10%
PV–AD = ?
R =
$800,000 $800,000 $800,000 $800,000 $800,000 $800,000 $800,000
Formula for the first ten payments:
Formula for the last ten payments:
or
Note: The present value of an ordinary annuity is used here, not the
present value of an annuity due.
PROBLEM 6.9 (Continued)
OR
Time diagram for the last ten payments:
i = 10%
Formulas for the last ten payments:
(i) Present value of the last ten payments:
PROBLEM 6.9 (Continued)
(ii) Present value of the last ten payments at the beginning of current
year:
(b) Time diagram:
i = 11%
PV – OA = ?
R =
PROBLEM 6.9 (Continued)
(c) Time diagram:
Amount paid =
$792,000
(i) Implied interest for the period from the end of the discount period
to the due date:
PROBLEM 6.9 (Continued)
(ii) Convert the implied interest rate to annual basis:
PROBLEM 6.10
1. Purchase.
Time diagrams:
Installments
i = 10%
PV – OA = ?
R =
$350,000 $350,000 $350,000 $350,000 $350,000
Property taxes and other costs
i = 10%
PV – OA = ?
R =
PROBLEM 6.10 (Continued)
Insurance
i = 10%
PV – AD = ?
R =
Salvage Value
i = 10%
PV = ? FV = $500,000
0 1 2 9 10 11 12
n = 12
Formula for installments:
PROBLEM 6.10 (Continued)
Formula for property taxes and other costs:
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: