6-41
PROBLEM 6-2
(a) Time diagram:
i = 8% FV – OA = $90,000
R R R R R R R R
R = ? ? ? ? ? ? ? ?
0 1 2 3 4 5 6 7 8
n = 8
(b) Time diagram:
i = 12%
FV – AD =
R R R R 500,000
R = ? ? ? ?
PROBLEM 6-2 (Continued)
1.
Future value of an ordinary annuity of 1 for
(c) Time diagram:
i = 9%
PV = $20,000 FV = $47,347
Future value approach
Present value approach
FV = PV (FVFn, i)
PV = FV (PVFn, i)
$47,347 = $20,000 (FVFn, 9%)
$20,000 = $47,347 (PVFn, 9%)
FVFn,
9%
= $47,347 ÷ $20,000
PVFn, 9%
= $20,000 ÷ $47,347
= 2.36735
= .42241
6-43
PROBLEM 6-2 (Continued)
(d) Time diagram:
Future value approach
Present value approach
FV = PV (FVFn, i)
PV = FV (PVFn, i)
or
$27,600 = $19,553 (FVF4, i)
$19,553 = $27,600 (PVF4, i)
= $27,600 ÷ $19,553
= $19,553 ÷ $27,600
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
Present value of initial cost
12,000 X $5.75 = $69,000 (incurred today) ………………
Present value of maintenance cost (years 1–4)
12,000 X $.25 = $3,000
R (PVF – OA4, 9%) = $3,000 (3.23972) ……………………….
9,719
Present value of resurfacing
FV (PVF5, 9%) = $69,000 (.64993)………………………………
44,845
Present value of maintenance cost (years 6–9)
R (PVF – OA9–5, 9%) = $3,000 (5.99525 – 3.88965) ………
6-45
PROBLEM 6-3 (Continued)
Time diagram (Bid B):
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 (PV – 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.
6-47
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
(c) Time diagram:
i = 21/2% per quarter
$18,000
PV – AD =
R = $1,800 $1,800 $1,800 $1,800 $1,800
6-48
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
The present value of option (d) is $41,031.04 + $20,549.34, or
$61,580.38.
Present values:
(a) $55,000.
Formulas:
PV – OA = R (PVF – OAn, i)
PV – OA = R (PVF – OAn, i)
PV – OA = R (PVF – OAn, i)
PV – OA =R (PVF – OAn, i)
PV – OA = ($39,000)(PVF – OA5, 12%)
PV – OA = $18,000 (PVF – OA10-5, 12%)
PV – OA = $68,000 (PVF – OA30–10, 12%)
PV – OA = $38,000 (PVF – OA40–30, 12%)
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)
PV – OA = ($140,586.42)
PV – OA = $18,000 (2.04544)
PV – OA = $68,000 (2.40496)
PV – OA = $38,000 (.18860)
PV – OA = $36,818
PV – OA = $163,537
PV – OA = $7,167
Copyright © 2011 John Wiley & Sons, Inc. Kieso, Intermediate Accounting, 14/e, Solutions Manual (For Instructor Use Only) 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
7.50 is present value of an annuity of $1 for 12 years discounted at
approximately 8%.
PROBLEM 6-7 (Continued)
Future value approach
Present value approach
FV = PV (FVFn, i)
PV = FV (PVFn, i)
$1,900,000 = $600,000 (FVF12, i)
$600,000 = $1,900,000 (PVF12, i)
3.16667 is the approximate future
value of $1 invested at 10%
for 12 years.
.31579 is the approximate present
value of $1 discounted at 10%
for 12 years.
Dubois should choose alternative two since it provides a higher rate
of return.
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
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]
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
Amount to which quarterly deposits must grow:
$1,300,000 – $537,012 = $762,988.
Time diagram (future value of quarterly deposits)
PROBLEM 6-7 (Continued)
Formulas: FV – OA = R (FVF – OAn, i)
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
Vendor B:
$ 9,500
semiannual payment
$ 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)]
$ 7,631
PV of next 10 years of maintenance
$ 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
3,791
maintenance years 1–5
7,631
maintenance years 6–15
2,722
maintenance years 16–20
$ 164,144
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
0 1 2 3 7 8 9 10
n = 10
Formula for the first ten payments:
Formula for the last ten payments:
PV – OA = R (PVF – OAn, i)
PV – OA = $400,000 (PVF – OA19 – 9, 10%)
Note: The present value of an ordinary annuity is used here, not the
present value of an annuity due.
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%
PROBLEM 6-9 (Continued)
(ii) Present value of the last ten payments at the beginning of current
year:
PV = FV (PVFn, i)
(b) Time diagram:
i = 11%
PV – OA = ?
R =
PROBLEM 6-9 (Continued)
Formula: PV – OA = R (PVF – OAn, i)
The fair value of the note is $83,056.
(c) Time diagram:
Amount paid =
$792,000
0 10 30
Amount paid =
$800,000
PROBLEM 6-9 (Continued)
(ii) Convert the implied interest rate to annual basis: