8-3 LG 3: Relevant Cash Flow Pattern Fundamentals
a. Year Cash Flow
Initial investment ($120,000)
1-18 $25,000 - $5,000 = $ 20,000
b. Initial investment ($85,000 - $30,000) = ($55,000)
1-5 = $ 20,000
6 $20,000 + $20,000 - $10,000 = $ 30,000
c. Initial investment ($2,000,000)
1-5 $300,000 - $20,000 = $ 280,000
6 $300,000 - $20,000 - $500,000 = ($ 220,000)
7-10 $300,000 - $20,000 = $ 280,000
8-4 LG 3: Expansion versus Replacement Cash Flows
a. Year Relevant Cash Flows
Initial investment ($28,000)
1 4,000
2 6,000
3 8,000
4 10,000
5 4,000
b. An expansion project is simply a replacement decision in which all cash flows from the old asset are zero.
8-5 LG 3: Sunk Costs and Opportunity Costs
a. The $1,000,000 development costs should not be considered part of the decision to go ahead with the new production. This money has already been spent and cannot be retrieved so it is a sunk cost.
b. The $250,000 sale price of the existing line is an incremental cost. If Masters Golf Products does not proceed with the new line of clubs they will not receive the $250,000.
c.
Cash Flows
-$1,800,000 $750,000 $750,000 $750,000 $750,000 $750,000
+ $ 250,000
|—————|—————|—————|————·····———|—————|—>
0 1 2 3 9 10
End of Year
8-6 LG 3: Sunk Costs and Opportunity Costs
a. Sunk cost - Since the funds for the tooling had already been expended and would not change no matter whether the new technology would be acquired or not.
b. Opportunity Cost - The development of the computer programs can be done without additional expenditures on the computers, however, the loss of the cash inflow from the leasing arrangement would be a lost opportunity to the firm.
c. Opportunity Cost - Covol will not have to spend and funds for floor space but the lost cash inflow from the rent would be a cost to the firm.
d. Sunk cost - The money for the storage facility has already been spend and no matter what decision the company makes there is no incremental cash flow generated or lost from the storage building.
e. Opportunity Cost - Foregoing the sale of the crane costs the firm $180,000 of potential cash inflows.
8-7 LG 4: Book Value
Installed Accumulated Book
Asset Cost Depreciation Value
A $ 950,000 $ 674,500 $275,500
B 40,000 13,200 26,800
C 96,000 79,680 16,320
D 350,000 70,000 280,000
E 1,500,000 1,170,000 330,000
8-8 LG 4: Book Value and Taxes on Sale of Assets
a. Book value = $80,000 - (.71 x $80,000)
= $23,200
b. Capital Tax on Depreciation Tax on Total
Sale price gain capital gain recovery recovery tax
$100,000 $20,000 $8,000 $56,800 $22,720 $30,720
56,000 -0- -0- 32,800 13,120 13,120
23,200 -0- -0- -0- -0- -0-
15,000 -0- -0- (8,200) (3,280) (3,280)
8-9 LG 4: Tax Calculations
Current book value = $200,000 - [(.52 x ($200,000)] = $96,000
(a) (b) (c) (d)
Capital gain $ 20,000 -0- -0- -0-
Recaptured depreciation 104,000 54,000 -0- (16,000)
Tax on capital gain $ 8,000 -0- -0-
Tax on depreciation
recovery 41,600 21,600 -0- (6,400)
Total tax $ 49,600 $21,600 $ -0- ($6,400)
8-10 LG 4: Change in Net Working Capital Calculation
a. Current assets Current liabilities
Cash $ + 15,000 Accounts payable $ + 90,000
Accounts receivable + 150,000 Accruals + 40,000
Inventory - 10,000
Net change $ 155,000 $ 130,000
Net working capital = current assets - current liabilities
D NWC = $155,000 - $130,000
D NWC = $ 25,000
b. Analysis of the purchase of a new machine reveals an increase in net working capital. This increase should be treated as an initial outlay and is a cost of acquiring the new machine.
c. Yes, in computing the terminal cash flow, the net working capital increase should be reversed.
8-11 LG 4: Calculating Initial Investment
Book Value=(Cost x (1-Sum of the % of depreciation for the number of years old the machine is))
a. Book value = ($325,000 x .48) = $156,000
b. Sales price of old equipment $200,000
Book value of old equipment 156,000
Gain $ 44,000
Taxes on Gain = $44,000 x .40 = $17,600
c. Cost of new machine $325,000
Less sales price of old machine (200,000)
Plus tax on Gain 17,600
Net new investment $142,600
8-12 LG 4: Initial Investment-Basic Calculation
Installed cost of new asset =
Cost of new asset $35,000
+ Installation Costs 5,000
Total installed cost (depreciable value) $40,000
After-tax proceeds from sale of old asset =
Proceeds from sale of old asset ($25,000)
+ Tax on sale of old asset 7,680
Total after-tax proceeds-old asset ($17,320)
Initial investment $22,680
Book value of existing machine = $20,000 x (1 - (.20 + .32 + .19)) = $5,800
Capital gain = $25,000 - $5,800 = $19,200
Tax on capital gain = $ 19,200 x (.40) = 7,680
8-13 LG 4: Initial investment at Various Sale Prices
(a) (b) (c) (d)
Installed cost of new asset:
Cost of new asset $24,000 $24,000 $24,000 $24,000
+ Installation cost 2,000 2,000 2,000 2,000
Total installed-cost $26,000 $26,000 $26,000 $26,000
After-tax proceeds from sale
of old asset
Proceeds from sale
of old asset (11,000) (7,000) (2,900) (1,500)
+ Tax on sale of old asset* 3,240 1,640 0 (560)
Total after-tax proceeds ( 7,760) (5,360) (2,900) (2,060)
Initial investment $18,240 $20,640 $23,100 $23,940
Book value of existing machine = $10,000 x [1 - (.20 -.32 -.19)] = $2,900
Tax Calculations:
a. Recaptured depreciation = $10,000 - $2,900 = $7,100
Capital gain = $11,000 - $10,000 = $1,000
Tax on ordinary gain = $7,100 x (.40) = $2,840
Tax on capital gain = $1,000 x (.40) = 400
Total tax = $3,240
b. Recaptured depreciation = $7,000 - $2,900 = $4,100
Tax on ordinary gain = $4,100 x (.40) = $1,640
c. 0 tax liability
d. Loss on sale of existing asset = $1,500 - $2,900 = ($1,400)
Tax benefit = - $1,400 x (.40) = 560
8-14 LG 4: Calculating Initial Investment
a. Book value = ($61,000 x .31) = $18,600
b. Sales price of old equipment $35,000
Book value of old equipment 18,600
Recapture of depreciation $ 16,400
Taxes on recapture of depreciation = $16,400 x .40 = $6,560
Sale price of old roaster $35,000
Tax on recapture of depreciation (6,560)
After-tax proceeds from sale of old roaster $28,440
c. Changes in current asset accounts
Inventory $ 50,000
Accounts receivable 70,000
Net change $120,000
Changes in current liability accounts
Accruals $ (20,000)
Accounts payable 40,000
Notes payable 15,000
Net change $ 35,000
Change in net working capital $ 85,000
d. Cost of new roaster $130,000
Less After-tax proceeds from sale of old roaster 28,440
Plus change in net working capital 85,000
Initial investment $186,560
8-15 LG 4: Depreciation
Depreciation Schedule
Year Depreciation Expense
1 $68,000 x .20 = $13,600
2 68,000 x .32 = 21,760
3 68,000 x .19 = 12,920
4 68,000 x .12 = 8,160
5 68,000 x .12 = 8,160
6 68,000 x .05 = 3,400
8-16 LG 5: Incremental Operating Cash Inflows
a. Incremental profits before tax and depreciation = $1,200,000 - $480,000
= $720,000 each year.
b. Year (1) (2) (3) (4) (5) (6)
PBDT $720,000 $720,000 $720,000 $720,000 $720,000 $720,000
Depr. 400,000 640,000 380,000 240,000 240,000 100,000
NPBT 320,000 80,000 340,000 480,000 480,000 620,000
Tax 128,000 32,000 136,000 192,000 192,000 248,000
NPAT 192,000 48,000 204,000 288,000 288,000 372,000
c. Cash
flow $592,000 $688,000 $584,000 $528,000 $528,000 $472,000
(NPAT + depreciation)
PBDT = Profits before depreciation and taxes
NPBT = Net profits before taxes
NPAT = Net profits after taxes
8-17 LG 5: Incremental Operating Cash Inflows-Expense Reduction
Year (1) (2) (3) (4) (5) (6)
Incremental
expense savings $16,000 $16,000 $16,000 $16,000 $16,000 $0
Incremental profits
before dep. and taxes* $16,000 $16,000 $16,000 $16,000 $16,000 $0
Depreciation 9,600 15,360 9,120 5,760 5,760 2,400
Net profits
before taxes 6,400 640 6,880 10,240 10,240 -2,400
Taxes 2,560 256 2,752 4,096 4,096 -960
Net profits
after taxes 3,840 384 4,128 6,144 6,144 -1,440
Operating cash
inflows** 13,440 15,744 13,248 11,904 11,904 960
* Incremental profits before depreciation and taxes will increase the same amount as the decrease in expenses.
** Net profits after taxes plus depreciation expense.
8-18 LG 5: Incremental Operating Cash Inflows
a.
Expenses Profits Before Operating
(excluding Depreciation Net Profits Net Profits Cash
Year Revenue depreciation) and Taxes Depreciation Before Taxes Taxes After Tax Inflows
New Lathe
1 $40,000 $30,000 $10,000 $2,000 $8,000 $3,200 $4,800 $6,800
2 41,000 30,000 11,000 3,200 7,800 3,120 4,680 7,880
3 42,000 30,000 12,000 1,900 10,100 4,040 6,060 7,960
4 43,000 30,000 13,000 1,200 11,800 4,720 7,080 8,280
5 44,000 30,000 14,000 1,200 12,800 5,120 7,680 8,880
6 -0- -0- -0- 500 (500) (200) (300) 200
Old Lathe
1-5 $35,000 $25,000 $10,000 -0- $10,000 $4,000 $6,000 $6,000
b. Calculation of Incremental Cash Inflows
Year New Lathe Old Lathe Incremental Cash Flows
1 $ 6,800 $ 6,000 $ 800
2 7,880 6,000 1,880
3 7,960 6,000 1,960
4 8,280 6,000 2,280
5 8,880 6,000 2,880
6 200 -0- 200
c.
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Diagram of Relevant Cash Flows |
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Cash Inflow ($) |
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8-19 LG 5: Determining Operating Cash Flows
a. Year
1 2 3 4 5 6
Revenues:(000)
New buses $1,850 $1,850 $1,830 $1,825 $1,815 $1,800
Old buses 1,800 1,800 1,790 1,785 1,775 1,750
Incremental revenue $ 50 $ 50 $ 40 $ 40 $ 40 $ 50
Expenses: (000)
New buses $ 460 $ 460 $ 468 $ 472 $ 485 $ 500
Old buses 500 510 520 520 530 535
Incremental expense $ (40) $ (50) $ (52) $ (48) $ (45) $ (35)
Depreciation: (000)
New buses $ 600 $ 960 $ 570 $ 360 $ 360 $ 150
Old buses 324 135 0 0 0 0
Incremental depr. $ 276 $ 825 $ 570 $ 360 $ 360 $ 150
Incremental depr. tax
savings @40% 110 330 228 144 144 60
Year
1 2 3 4 5 6
Cash Flows: (000)
Revenues $ 50 $ 50 $ 40 $ 40 $ 40 $ 50
Expenses 40 50 52 48 45 35
Less taxes @40% (36) (40) (37) (35) (34) (34)
Depr. tax savings 110 330 228 144 144 60
Net operating cash
inflows $ 164 $ 390 $ 283 $ 197 $ 195 $ 111
8-20 LG 6: Terminal Cash Flows-Various Lives and Sale Prices
a.
After-tax proceeds from sale of new asset =
Proceeds from sale of proposed asset $10,000 $10,000 $10,000
± Tax on sale of proposed asset* + 16,880 - 400 - 4,000
Total after-tax proceeds-new $26,880 $ 9,600 $ 6,000
+ Change in net working capital + 30,000 + 30,000 + 30,000
Terminal cash flow $ 56,800 $ 39,600 $ 36,000
* (1) Book value of asset = [1- (.20 +.32 +.19) x ($180,000)] = $52,200
Proceeds from sale = $10,000
$10,000 - $52,200 = ($42,200) loss
$42,200 x (.40) = $16,880 tax benefit
(2) Book value of asset = [1 - (.20 +.32 +.19 +.12 +.12) x ($180,000)]
= $9,000
$10,000 - $9,000 = $1,000 recaptured depreciation
$1,000 x (.40) = $400 tax liability
(3) Book value of asset = $0
$10,000 - $0 = $10,000 recaptured depreciation
$10,000 x (.40) = $4,000 tax liability
b. If the usable life is less than the normal recovery period, the asset has not been depreciated fully and a tax benefit may be taken on the loss, therefore the terminal cash flow is higher.
c. (1) (2)
After-tax proceeds from sale of new asset =
Proceeds from sale of new asset $ 9,000 $170,000
+ Tax on sale of proposed asset* 0 (64,400)
+ Change in net working capital + 30,000 + 30,000
Terminal cash flow $ 39,000 $135,600
* (1) Book value of the asset = $180,000 x .05 = $9,000; no taxes are due
(2) Tax = ($170,000 - $9,000) x 0.4 = $64,400.
d. The higher the sale price, the higher the terminal cash flow.
8-21 LG 6: Terminal Cash Flow-Replacement Decision
After-tax proceeds from sale of new asset =
Proceeds from sale of new machine $75,000
- Tax on sale of new machine l (14,360)
Total after-tax proceeds-new asset $60,640 - After-tax proceeds from sale of old asset
Proceeds from sale of old machine (15,000)
+ Tax on sale of old machine 2 6,000
Total after-tax proceeds-old asset ( 9,000)
+ Change in net working capital 25,000
Terminal cash flow $76,640
l Book value of new machine at end of year.4:
[1 - (.20 + .32+.19 + .12) x ($230,000)] = $39,100
$75,000 - $39,100 = $35,900 Gain
$35,900 x (.40) = $14,360 tax liability
2 Book value of old machine at end of year 4:
$0
$15,000 - $0 = $15,000 gain
$15,000 x (.40) = $ 6,000 tax benefit
8-22 LG 5: Relevant Cash Flows for a Marketing Campaign
Marcus Tube
Calculation of Relevant Cash Flow
($000)
Calculation of Net Profits after Taxes and Operating Cash Flow:
With Marketing Campaign
2001 2002 2003 2004 2005
Sales $20,500 $21,000 $21,500 $22,500 $23,500
CGS (@ 80%) 16,400 16,800 17,200 18,000 18,800
Gross Profit $ 4,100 $ 4,200 $ 4,300 $ 4,500 $ 4,700
Less: Operating Expenses
General and
Administrative
(10% of sales) $ 2,050 $ 2,100 $ 2,150 $ 2,250 $ 2,350
Marketing Campaign 150 150 150 150 150
Depreciation 500 500 500 500 500
Total operating
expenses 2,700 2,750 2,800 2,900 3,000
Net profit
before taxes $1,400 $1,450 $1,500 $1,600 $1,700
Less: Taxes 40% 560 580 600 640 680
Net profit
after taxes $ 840 $ 870 $ 900 $ 960 $1,020
+Depreciation 500 500 500 500 500
Operating CF $1,340 $1,370 $1,400 $1,460 $1,520
Without Marketing Campaign
Years 2001 - 2005
Net profit after taxes $ 900
+Depreciation 500
Operating cash flow $ 1,400
Relevant Cash Flow
($000)
With Without Incremental
Year Marketing Campaign Marketing Campaign Cash Flow
2001 $1,340 $1,400 $(60)
2002 1,370 1,400 (30)
2003 1,400 1,400 -0-
2004 1,460 1,400 60
2005 1,520 1,400 120
8-23 LG 5: Relevant Cash Flows-No Terminal Value
a. Installed cost of new asset
Cost of new asset $76,000
+ Installation costs 4,000
Total cost of new asset $80,000
- After-tax proceeds from sale of old asset
Proceeds from sale of old asset (55,000)
+ Tax on sale of old asset* 16,200
Total proceeds, sale of old asset (38,800)
Initial investment $41,200
* Book value of old machine:
[1 - (.20 + .32 + .19)] x $50,000 = $14,500
$55,000 - $14,500 = $40,500 gain on asset
$35,500 recaptured depreciation x.40 = $14,200
$ 5,000 capital gain x .40 = 2,000
Total tax on sale of asset = $16,200
b. Calculation of Operating Cash Flow
Old Machine
Year (1) (2) (3) (4) (5) (6)
PBDT $14,000 $16,000 $20,000 $18,000 $14,000 $ 0
Depreciation 6,000 6,000 2,500 0 0 0
NPBT $ 8,000 $10,000 $17,500 $18,000 $14,000 0
Taxes 3,200 4,000 7,000 7,200 5,600 0
NPAT $4,800 $ 6,000 $10,500 $10,800 $ 8,400 $ 0
Depreciation 6,000 6,000 2,500 0 0 0
Cash flow $10,800 $12,000 $13,000 $10,800 $ 8,400 $ 0
New Machine
Year (1) (2) (3) (4) (5) (6)
PBDT $30,000 $30,000 $30,000 $30,000 $30,000 $ 0
Depreciation 16,000 25,600 15,200 9,600 9,600 4,000
NPBT $14,000 $ 4,400 $14,800 $20,400 $20,400 -$4,000
Taxes 5,600 1,760 5,920 8,160 8,160 -1,600
NPAT $ 8,400 $ 2,640 $ 8,880 $12,240 $12,240 -$2,400
Depreciation 16,000 25,600 15,200 9,600 9,600 4,000
Cash flow $24,400 $28,240 $24,080 $21,840 $21,840 $1,600
Year (1) (2) (3) (4) (5) (6)
Incremental
After-tax
Cash flows $13,600 $16,240 $11,080 $11,040 $13,440 $ 1,600
c.
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Diagram Relevant Cash Flows |
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Cash Flow ($) |
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8-24 LG 4, 5, 6: Integrative-Determining Relevant Cash Flows
a. Initial investment:
Installed cost of new asset =
Cost of new asset $105,000
+ Installation costs 5,000
Total cost of new asset $110,000
- After-tax proceeds from sale of old asset =
Proceeds from sale of old asset (70,000)
+ Tax on sale of old asset* 16,480
Total proceeds from sale of old asset (53,520)
+ Change in working capital 12,000
Initial investment $68,480
* Book value of old asset:
[1 - (.20 + .32)] x $60,000 = $28,800
$70,000 - $28,800 = $41,200 gain on sale of asset
$41,200 Gain x .40 = $16,480 tax
b.
Calculation of Operating Cash Inflows
Profits Before Operating
Depreciation Depre- Net Profits Net Profits Cash
Year and Taxes ciation Before Taxes Taxes After Taxes Inflows
New Grinder
1 $43,000 $22,000 $21,000 $ 8,400 $12,600 $34,600
2 43,000 35,200 7,800 3,120 4,680 39,880
3 43,000 20,900 22,100 8,840 13,260 34,160
4 43,000 13,200 29,800 11,920 17,880 31,080
5 43,000 13,200 29,800 11,920 17,880 31,080
6 --0- 5,500 -5,500 -2,200 -3,300 2,200
Existing Grinder
1 $26,000 $11,400 $14,600 $5,840 $ 8,760 $20,160
2 24,000 7,200 16,800 6,720 10,080 17,280
3 22,000 7,200 14,800 5,920 8,880 16,080
4 20,000 3,000 17,000 6,800 10,200 13,200
5 18,000 -0- 18,000 7,200 10,800 10,800
6 -0- -0- -0- -0- -0- -0-
Calculation of Incremental Cash Inflows
Incremental Operating
Year New Grinder Existing Grinder Cash Flow
1 $34,600 $20,160 $14,440
2 39,880 17,280 22,600
3 34,160 16,080 18,080
4 31,080 13,200 17,880
5 31,080 10,800 20,280
6 2,200 -0- 2,200
c. Terminal Cash Flow:
After-tax proceeds from sale of new asset =
Proceeds from sale of new asset $29,000
- Tax on sale of new asset* ( 9,400)
Total proceeds from sale of new asset 19,600
- After-tax proceeds from sale of old asset =
Proceeds from sale of old asset 0
+ Tax on sale of old asset 0
Total proceeds from sale of old asset 0
+ Change in net working capital 12,000
Terminal cash flow $31,600
* Book value of asset at end of year 5 = $ 5,500
$29,000 - $5,500 = $23,500 gain
$23,500 x .40 = $ 9,400 tax
d. Year 5 Relevant Cash Flow:
Operating cash flow $20,280
Terminal cash flow 31,600
Total inflow $51,880
8-25 LG 4, 5, 6: Integrative-Determining Relevant Cash Flows
a. Initial investment: A B
Installed cost of new asset
Cost of new asset $40,000 $54,000
+ Installation costs 8,000 6,000
Total proceeds, sale of new asset 48,000 60,000
- After-tax proceeds from sale of old asset
Proceeds from sale of old asset (18,000) (18,000)
+ Tax on sale of old asset * 3,488 3,488
Total proceeds, sale of old asset (14,512) (14,512)
+ Change in working capital 4,000 6,000
Initial investment $37,488 $51,488
* Book value of old asset:
[1 - (.20 + .32 + .19)] x ($32,000) = $9,280
b. Calculation of Operating Cash Inflows
Profits Before Operating
Depreciation Depre- Net Profits Net Profits Cash
Year and Taxes ciation Before Taxes Taxes After Taxes Inflows
Hoist A
1 $21,000 $ 9,600 $11,400 $4,560 $6,840 $16,440
2 21,000 15,360 5,640 2,256 3,384 18,744
3 21,000 9,120 11,880 4,752 7,128 16,248
4 21,000 5,760 15,240 6,096 9,144 14,904
5 21,000 5,760 15,240 6,096 9,144 14,904
6 -0- 2,400 -2,400 -960 -1,440 960
Hoist B
1 $22,000 $12,000 $10,000 $4,000 $6,000 18,000
2 24,000 19,200 4,800 1,920 2,880 22,080
3 26,000 11,400 14,600 5,840 8,760 20,160
4 26,000 7,200 18,800 7,520 11,280 18,480
5 26,000 7,200 18,800 7,520 11,280 18,480
6 -0- 3,000 -3,000 -1,200 -1,800 1,200
Existing Hoist
1 $14,000 $3,840 $10,160 $4,064 $6,096 $9,936
2 14,000 3,840 10,160 4,064 6,096 9,936
3 14,000 1,600 12,400 4,960 7,440 9,040
4 14,000 -0- 14,000 5,600 8,400 8,400
5 14,000 --0- 14,000 5,600 8,400 8,400
6 -0- -0- -0- -0- -0- -0-
Calculation of Incremental Cash Inflows
Incremental Cash Flow
Year Hoist A Hoist B Existing Hoist Hoist A Hoist B
1 $16,440 $18,000 $9,936 $6,504 $ 8,064
2 18,744 22,080 9,936 8,808 12,144
3 16,248 20,160 9,040 7,208 11,120
4 14,904 18,480 8,400 6,504 10,080
5 14,904 18,480 8,400 6,504 10,080
6 960 1,200 -0- 960 1,200
c. Terminal Cash Flow:
(A) (B)
After-tax proceeds form sale of new asset
Proceeds from sale of new asset $12,000 $20,000
- Tax on sale of new asset l (3,840) (6,800)
Total proceeds-new asset 8,160 13,200
- After-tax proceeds from sale of old asset
Proceeds from sale of old asset (1,000) (1,000)
+ Tax on sale of old asset 2 400 400
Total proceeds-old asset (600) (600)
+ Change in net working capital 4,000 6,000
Terminal cash flow $11,560 18,600
1 Book value of Hoist A at end of year 5 = $2,400
$12,000 - $2,400 = $9,600 recaptured depreciation
$9,600 x .40 = $3,840 tax
Book value of Hoist B at end of year 5 = $3,000
$20,000 - $3,000 = $17,000 recaptured depreciation
$17,000 x .40 = $6,800 tax
2 Book value of Existing Hoist at end of year 5 = $0
$1,000 - $0 = $1,000 recaptured depreciation
$1,000 x .40 = $400 tax
d. Year 5 Relevant Cash Flow - Hoist A:
Operating cash flow $ 6,504
Terminal cash flow 11,560
Total inflow $18,064
Year 5 Relevant Cash Flow - Hoist B:
Operating cash flow $ 10,080
Terminal cash flow 18,600
Total inflow $28,680
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Diagram Relevant Cash Flows-Hoist A |
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Cash Flow ($) |
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Diagram Relevant Cash Flows-Hoist B |
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Cash Flow ($) |
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