Question

In: Economics

Two alternative machines will produce the same​ product, but one is capable of​ higher-quality work, which...

Two alternative machines will produce the same​ product, but one is capable of​ higher-quality work, which can be expected to return greater revenue. The following are relevant data. Determine which is the better​ alternative, assuming repeatability and using SL​ depreciation, an​ income-tax rate of 23%, and an​ after-tax MARR of 8%.

Machine A Machine B
Capital Investment $20,000 $29,000
Life 12 Years 6 Years
Terminal BV (and MV) $4,500 $500
Annual Receipts $158,000 $188,000
Annual Expenses $129,000 $174,000

1) Calculate the AW value for the Machine A.

2)Calculate the AW value for the Machine B.

Solutions

Expert Solution

For machine A

SL dep per year = (P-S)/N = (20000-4500) / 12 = 1291.67

BTCF = 158000 - 129000 = 29000

taxable income = 29000 - 1291.67 = 27708.33

tax = 0.23 * 27708.33 = 6372.92

ATCF = BTCF - tax = 29000 - 6372.92 = 22627.08

AW of machine A = -20000*(A/P,8%,12) + 22627.08 + 4500*(A/F,8%,12)

= -20000*0.132695 + 22627.08 + 4500*0.052695

= 20210.31

For machine B

SL dep per year = (P-S)/N = (29000-500) / 6 = 4750

BTCF = 188000 - 174000 = 14000

taxable income = 14000 - 4750 = 9250

tax = 0.23 * 9250 = 2127.50

ATCF = BTCF - tax = 14000 - 2127.50 = 11872.50

AW of machine B = -29000*(A/P,8%,6) + 11872.50+ 500*(A/F,8%,6)

= -29000*0.216315 + 11872.50+ 500*0.136315

= 5667.53

As AW of machine A is more, it should be selected

Using Excel

Alternative A
Yrs BTCF Depreciation Taxable income Tax ATCF
0 -20000 -20000
1 29000 1291.67 27708 6373 22627
2 29000 1291.67 27708 6373 22627
3 29000 1291.67 27708 6373 22627
4 29000 1291.67 27708 6373 22627
5 29000 1291.67 27708 6373 22627
6 29000 1291.67 27708 6373 22627
7 29000 1291.67 27708 6373 22627
8 29000 1291.67 27708 6373 22627
9 29000 1291.67 27708 6373 22627
10 29000 1291.67 27708 6373 22627
11 29000 1291.67 27708 6373 22627
12 29000 1291.67 27708 6373 27127
12 4500 0 0
NPW 152306
AW 20210
Alternative B
Yrs BTCF of B Depreciation of B Taxable income Tax of B ATCF of B
0 -29000 -29000
1 14000 4750 9250 2127.5 11872.5
2 14000 4750 9250 2127.5 11872.5
3 14000 4750 9250 2127.5 11872.5
4 14000 4750 9250 2127.5 11872.5
5 14000 4750 9250 2127.5 11872.5
6 14000 4750 9250 2127.5 12372.5
6 500 0 0 0
NPW 25641 NPW 26200
AW 5668

Showing formula in excel

Alternative A
Yrs BTCF Depreciation Taxable income Tax ATCF
0 -20000 =B31
1 =158000-129000 =(20000-4500)/12 =B32-C32 =D32*0.23 =B32-E32
2 =158000-129000 =(20000-4500)/12 =B33-C33 =D33*0.23 =B33-E33
3 =158000-129000 =(20000-4500)/12 =B34-C34 =D34*0.23 =B34-E34
4 =158000-129000 =(20000-4500)/12 =B35-C35 =D35*0.23 =B35-E35
5 =158000-129000 =(20000-4500)/12 =B36-C36 =D36*0.23 =B36-E36
6 =158000-129000 =(20000-4500)/12 =B37-C37 =D37*0.23 =B37-E37
7 =158000-129000 =(20000-4500)/12 =B38-C38 =D38*0.23 =B38-E38
8 =158000-129000 =(20000-4500)/12 =B39-C39 =D39*0.23 =B39-E39
9 =158000-129000 =(20000-4500)/12 =B40-C40 =D40*0.23 =B40-E40
10 =158000-129000 =(20000-4500)/12 =B41-C41 =D41*0.23 =B41-E41
11 =158000-129000 =(20000-4500)/12 =B42-C42 =D42*0.23 =B42-E42
12 =158000-129000 =(20000-4500)/12 =B43-C43 =D43*0.23 =B43-E43+B44
12 4500 0 0
NPW =NPV(8%,F32:F44)+F31
AW =PMT(8%,12,-F45)
Alternative B
Yrs BTCF of B Depreciation of B Taxable income Tax of B ATCF of B
0 -29000 =B49
1 =188000-174000 =(29000-500)/6 =B50-C50 =D50*0.23 =B50-E50
2 =188000-174000 =(29000-500)/6 =B51-C51 =D51*0.23 =B51-E51
3 =188000-174000 =(29000-500)/6 =B52-C52 =D52*0.23 =B52-E52
4 =188000-174000 =(29000-500)/6 =B53-C53 =D53*0.23 =B53-E53
5 =188000-174000 =(29000-500)/6 =B54-C54 =D54*0.23 =B54-E54
6 =188000-174000 =(29000-500)/6 =B55-C55 =D55*0.23 =B55-E55+500
6 500 0 0 =D56*0.5
NPW =NPV(14%,B50:B56)+B49 NPW =NPV(8%,F50:F56)+F49
AW =PMT(8%,6,-F57)

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