Solution
CHAPTER 12 - INCOME TAXES IN ECONOMIC ANALYSrc
Viachint A
Before tax
Year
0
I
2
3
4
5
6
6*
cash flow
-$30,000
- 3,000
- 3,000
- 3.000
- 3,000
- 3,000
- 3,000
0
-3,000
-6,000
-6,000
-6,000
-6,000
-3,000
-6.000
-9,000
-9,000
-9,000
-9,000
-6,000
6,000*"
**Capital gain
Before tax
cash flow
I
$40,000
-2,500
2
_2.500
J
o
-2,500
-2,500
-2,500
-2,500
1
4
tncome
6,000
*Salvage value'
Machine B
End of
Year
I axaDle
Depreciation
Deoreciation
Taxable
income
cash flow
-$30.000
i
o00
4.500
4,500
4,500
4,500
3,000
-2,100
0
i,500
1,500
r,500
1,500
0
3,900
After-tax
Taxes
cash flow
-$40,000
-8,000
-12,800
-7.680
-4,608
-4,608
-10"500
-r
5.300
-10,t80
-7, i08
-2,304
-7,108
-4,804
-2,500
0
-7,500
8
_2,500
Q*
4,000
0
0
-2,500
4.000
5
After-tax
Taxes
2,750
5, r50
2,590
5,750
1,650
5 0go
3.554
3,554
2,402
t,250
l,250
-1,400
I,054
r,054
-98
-1,250
-
r,250
2.600
Study period of 8 years
AE(10)A =
-$5,390 AE(i0)B :
-$5,622
2L. (a) Alternative A
Year
end
Before tax
cash flow
Depreciation
Taxable
income
$0
Taxes
0
-$ 10,000
I
7,000
-J,3
2
6,+oo
-4,444
r,956
- t 6L
3
5,800
5,200
5,400
- 1,481
4.319
- 74r
4,459
-t,128
-t,184
5,400
-2.160
4
5
$0
57
Alternative B:
Year Before tax
end
0
I
7
3
4
5
cash flow
-$5,000
5,200
5,200
5,200
5,700
5,200
PW(6)4 = $8,766
PW(6)8 = $9.874
Depreriation
$0
- 833
3,667
Taxable
income
$0
4,367
$0
-1,461
After tax
cash flow
-$10,000
5,533
5,618
4,072
3,416
3,240
Taxes
After tax
cash flow
$0
-$5,000
-t,141
3,453
-r.661
3,5 33
-1,4t3
-t,661
3,553
4,361
5.200
-1,413
3.181
3,187
-t,14'l
3.453
-2,080
3,r20
oa?
0
Select B
CHAPTER 12 - Ii.{COMtr TAXES IN BCONOMIC ANALYSIS
22- (a) Retained earnings
Before tax
Taxable
cash flow
Year
Depreciation
-$20,000
6,000
6,000
6.000
0
l
L-J
6
Pw(s):
After-iax
income
$0
-2,000
Taxes
$0
$0
1,600
- 800
- 1,600
4,000
2,000
4.000
-4,000
-2.000
cash flow
-$20,000
4,400
5,200
-
4.400
$5,035
(b) Borrowing
Before tax
Loan
cash flow
Year
cash
-$20,000
6,000
6,000
6,000
6,000
0
I
z-4
5
D
Cash flow
flow
after ]oan
$20,000
-2,000
-2,000
22,000
After-tax
Depreciation
$o
Tax
$0
-2,000
-4,000
-4,000
-2,000
4,000
4,000
-16,000
6.000
PW(5) = $4,169
23
(c) PW(9)1u) = $2,116,
Pw(9)G) = $4,450
(a) Retained earnings
Before tax
Year cash flow
Deoreciation
Taxable
Income
Taxes
$0
4O7o
$o
-800
0
4,000
0
-i6,000
-1,600
4,400
-$40,000
$0
$0
1
15,000
-13J32
-oo /
-$40,000
14,333
2
r5,000
1,1 10
16, r i0
3
15,000
15,000
15,000
-11,116
-5,9?4
1,668
-7,17 6
9,07 6
-3,630
I
i.370
i4
I
0.1 86
5
-2.964
r5,000
4,000
6
6+
PW(10) =
12,036
15,000
-4,8
r5,000
4,000
$14,002,
-6,000
-6,000
9.000
9,000
60
2.640
- 1.3
$0
3,200
After-tax
CF
0
4
cash flow
AE(IS) = $3,215
(b) Loan at 77Vo (Pay principal and interesr)
Year
Before tax
End
Lr
0
I
2
-$40,000
3
-Q 7?O
4
i5,000
I5,000
o 110
-4,800
-4,209
-3,546
-2.804
5
r5,000
_Q 7?O
-t,913
5,711
6
i5,000
-9.179
-t "D42
5,2T1
4.000
6+
15,000
15,000
4,000
PW(i0) = $17,323,
Loan
CF
$40,000
-9,129
-g ])q
Interest
on Loan
$0
CF after
loan
$0
5,211
5,711
Taxable
income
$0
-t3,332
-11
L
,116
-5,924
5,21r
-2.964
< a?I
),L
AE(r0) = $1,e77
r36
r
Taxes
(lOVo)
$0
$4,000
1,253
-? I??
z;t94
-6,985
5,530
q )7)
_) )1)
After-tax
CF
$0
6.524
8,065
3,059
-3,693
-5,211
13,021
-5,583
r
3,95 8
'-312
4,000
-
1,360
2.640
r,578
60
,.1,
i
1
1
CHAPTER 12 - TNCOME TAXES IN ECONOMIC AT,IALYSIS
I
I
?,'a { lnitilirell.
(c) Loan at 14Vo (pay interest only)
Year
Before tax
I-,oan cash
End
cash flow
flow
0
1
2
3
4
5
6
6'F
Loan
$0
-5,600
-5,600
-5,600
-5,600
-5,600
-5,600
$40,000
-5,600
-5,600
-5,600
-5.600
-5,600
-45,600
-$40.000
15,000
15;000
15,000
15,000
i5,000
15,000
CF after
Interest on
loan
Taxes
CF
$0
$0
r0,97
After-tax
$0
9,400
-13332
-3,937
1,513
9,400
-11
,716
-8,316
-5,924
3,416
6,416
9,400
9.400
4.000
3,350
-1,390
-7.514
-3,760
-3,7 60
9,400
9,400
$0
-2.964
9,400
-30,600
4.000
4,000
Taxable
income
$0
-
r,360
3
12,750
8,0i0
6.826
5.640
-3436A
2,640
AE(i0) = $3,855
PW(10) = $i6,789,
Select the alternative in part b. Note that even though the beiore-tax borrowing rate is greater than the
after-tax MARR, it is more desirable to borrow tian use retained earnings. This situation occurs
because the after-tax borrowing rate is less than the after-tax MARR.
24.
(a)
Year
End
0
I
Before tax
cash
flow
-$ 15,000
-800
-800
-800
-800
2- 10
1l
t2
-
After-tax
r,500
Taxable
income
$o
-1,550
-2,300
_750
r,550
$0
620
920
670
-800
3ZO
Depreciation
$0
-150
-
cash flow
Taxes
-$ r 5,000
-
180
t20
-180
-480
/^iP,IZ,IZ
AE(12):
$14,765( 0.1614 ) = -$2,383
(b)
Loan
Before tax
CF
payment
-$ i5,000
$ 15,000
-7,235
-2.735
6
-800
-800
-800
-800
-800
,800
7
-800
-7,235
800
-7,235
-2,235
-) )2,\
Year
End
0
I
2
J
4
5
6
9
10
II
IZ
-800
-800
-800
-800
PlF,T2,I
LVo
Intercst
After
Loan
Loan
on
CF
Depr.
$0
-150
$0
$o
1.200 -3,035
I,1l7 -3,035 -r,500
-r,021 -3,035 - 1,500
-931 -3,035 -i.500
-827 -3.035 - 1,500
-714 -3,035 -1,500
-593 -3,035 - 1.500
-461 -3,035 -1,500
-3.035 - I,500
-3 l9
-r66 -3,035 -I,500
-800 -750
-800
-
-
)1<
-) )75
_1
-2,235
-2,235
NP,I2.IZ
AE(i2) = -$10,500( 0.1614 ) = -$I,695
Taxcs
income
(4OEo)
$o
$0
-2,150
-
r,935
-
1,668
_7'1,)'7
r,100
r,361
1,31I
-3,23t
1.792
-r,143
-3,127
-3,014
1,25I
-1,784
1,206
-1,829
-2,893
-2.161
-2,6T9
1.151
-
I,104
- 1,93
r,048
986
-
-3,411
-2,466
-
1,550
-800
PlF,I2,l2
PlF,12,2
Pw(12) = -[$1,935( 0.8929 ) + $1,668( 0.7912) +
Taxable
.
+ $480( O.3270
)l = -$10,500
620
320
After-tax
CF
$0
-1,704
1,878
I
1,987
)
o4q
-
180
-480
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