9-17 Keep the Defender:
(a)
EOY BTCF Depr TI T (40%) ATCF
0
– $14,000
—
-$4,000
a
$1,600
-$12,400
bLoss on disposal for defender when sold 6 years from now.
Replace with Challenger (and sell the defender):
EOY BTCF Depr TI T (40%) ATCF
0
1
-$80,000
7,000
—
$16,000
—
-$9,000
—
$3,600
– $80,000
10,600
EOY Incremental Cash Flows ∆(Challenger – Defender)
0
1
-$67, 000
10,600
115
(b) ERR Analysis (
ε
= 12%)
$67,600 (F/P, i’ ∆%, 6)= ∑
=
∆
6
1k
ATCF k(F/P, 12%, 6-k)
9-18 Keep the Defender:
EOY BTCF Depr TI T(40%) ATCF
0
-$250,000
—
-$50,000 a
$20,000
-$230,000
Replace with Challenger (and sell the defender):
EOY BTCF Depr TI T (40%) ATCF
0
1
2
-$500,00
-11, 000 a
-11,000
—
$50,000
90,000
—
-$61,000
-101,000
—
$24,400
40,400
-$500,000
13,400
29,400
116
7
-11,000
32,750
-43,750
17,500
6,500
aBTCF 101−= $4,000 – (0.03)($500,000)= -$11,000
Incremental ATCF: ∆(Challenger – Defender)
Year ATCF ∆
0
1
2
-$270,000
17,400
33,400
PW(i’ ∆%)= 0 = ∑
=
10
0k
k
ATCF (P/F, i’ ∆%, k)
PW(0%)= $24,000
117
9-19 Keep the Defender; A
EOY BTCF Depr TI T (40%) ATCF
0
1
-$150,000 a
-578,000 c
—
44,600
-$38,450
-622,600
$15,380
249,040
-$134,620
-328,960
aForegone MV amount; opportunity cost of keeping the defender.
bGain on disposal of $150,000 – $111,550 = $38,450 would occur if defender is sold now.
cTotal annual expenses= -$300,000 – $250,000 –($500,000)(0.04) -$8,000 = -$578,000
8
118
9-20 Keep the Defender:
EOY BTCF Depr TI T(40%) ATCF
0
1—5
5
-$14,000
-14,000
8,000
—
2,800 c
—
8,000 b
-16,800
0d
-$3,000
6,720
0
-$17,200
-7, 280
8,000
aForegone MV amount; an opportunity cost of keeping the defender.
bBV10 = $50,000 – 10($2,800) = $22,000
A loss on disposal of $14,000 – $22,000 = -$8,000, would occur if the defender is sold
EO BTCF Depr TI T(40%) ATCF
0
1
2
3
-$65,000
-9,000
-9,000
-9,000
—
13,000
20,800
12,480
—
-$22,000
-29,800
-21,480
—
8,800
11,920
8,592
-$65,000
-200
2,920
-408
119
9-21 Keep the Defender:
EOY BTCF Depr TI T(40%) ATCF
0
1
-$40,000
-20,000
—
30,000 b
$5,000 a
-50,000
-$2,000
20,000
-$42,000
0
bS.L. amount = $150,000/5 = $30,000
PW(10%) = -$42,000 – $6,000(P/F, 10%,2) – $12,000(P/A, 10%,3)(P/F, 10%,2) + $1200(P/F, 10%,5) = -$70,875
aA half-year of depreciation is taken in year of disposal of the challenger.
bBV 5= $11,520; The loss on disposal is MV 5– BV 5= -$6,520 when the challenger is sold.
5
120
9-22 Assume study period = 6 years.
Keep the Defender: Assume MV = 0 at end of study period.
EOY BTCF Depr TI T(40%) ATCF
0
-$130,000 a
0
-$90,000 b
$36,000
-$94,000
bThe entire $90,000 (gain on disposal) would have been taxable if the defender was sold, since the current BV of the
conveyor system is zero.
PW(10%) = -$94,000 + $520(P/A, 10%, 6) + $1,600(P/A, 10%, 4)(P/F, 10%,1) = -$87,124
71,643 b
aBTCF k= $6,000(1.06) k – $2,750
bMV 6= (0.5)($120,000)(1.03) 6= $71,643. Note that the entire MV amount is taxable since BV 6= 0.
6
121
9-23 Keep the Defender:
EOY BTCF Depr TI T(40%) ATCF
0
-$57,000
—
-$30,000 a
$12,000
-$45,000
aGain (if sold) = $57,000 – $27,000 = $30,000
bMarket value = $18,500(1.032) 5= $21,656
Replace with Challenger (and sell the defender):
EOY BTCF Depr TI T(40%) ATCF
122
9-24 Keep the Defender:
EOY BTCF Depr TI T(40%) ATCF
0
1
-$15,000
-28,600 b
—
$9,216
-$1,176 a
-37,816
$470
15,126
-$14,530
-13,474
aBV 0= $80,000(0.20+0.32+0.192+0.1152)= $13,824
Gain on disposal = $15,000 – $13,824= $1,176
bAnnual Expenses= -$12(8)(250) – $3,000 -0.02($80,000)= -$28,600
=
4
0k
Replace with Challenger (and sell the defender): Let
Ι
= capital investment amount.
EO BTCF Depr TI T(40%) ATCF
0
1
2
-$
Ι
-13,500 – 0.021 a
-13,500 – 0.021
—
0.2001
0.32001
—
-13,500 – 0.22001
-13,500 – 0.34001
—
5,400 + 0.08801
5,400 + 0.13601
-$
Ι
-8,100 + 0.06801
-8,100 + 0.11601
Ι
123
%10
Ι
cd4= $
Ι
(0.1152)(0.5)= $0.0576
Ι
dBV 4= $
Ι
– $
Ι
(0.2 + 0.32 + 0.192 + 0.0576) = $0.2304
Ι
Ι
Ι
Ι
Ι
Ι
Ι
Ι
9-25 Use the capitalized worth method and the repeatability assumption due to the indefinitely long study period. Note
that all market values are completely offset by the removal costs.
Alternative a: Do not relocate existing transformers
Site A: Property tax for existing transformers (years 1-10)
= -($2,100 + $475)(0.02)= -$51.50
Capital investment for replacement transformers (EOY 10 and every 30 years thereafter)
= -$900 – $340= -$1,240
Property tax for replacement transformers (years 11- ∞)
08.0
124
Ι
Alternative b: Relocate existing transformers
Cost to remove existing transformers from site A and reinstall at site B (EOY 0)
=-$110- $475= -$585
Site A: Capital investment for replacing transformers (EOY 0 and every 30 years thereafter)
125