Chapter 11: Income, Depreciation, and Cash Flow
11-1
Year
1
2
3
4
5
6
Sum
SOYD DDB
$2,400 $3,33
3
$2,000 $2,222
$1,600 $1,482
$1,200 $988
$800
$375*
$400
$0
$8,400 $8,400
*Computed $658 must be reduced to $375 to avoid depreciating the asset below its salvage
value.
11-2
DDB Schedule is:
Year
n
1
2
3
4
5
6
d(n)=(2/n)[P – sum d(n)]
(2/6) ($1,000,000 - $0)
(2/6) ($1,000,000 - $333,333)
(2/6) ($1,000,000 - $555,555)
(2/6) ($1,000,000 - $703,703)
(2/6) ($1,000,000 - $802,469)
See below
DDB
Depreciation
= $333,333
= $222,222
= $148,148
= $98,766
= $65,844
= $56,687
If switch DDB to SL for year 5:
SL
= ($1,000,000 - $802,469 - $75,000)/2
Do not switch.
If switch DDB to SL for year 6:
SL
= ($1,000,000 - $868,313 - $75,000)/1
Do switch.
= $61,266
= $56,687
Sum-of-Years Digits Schedule is:
SOYD in N = [(Remain. useful life at begin. of yr.)/[(N/2)(N+1)]] (P – S)
1st Year:
2nd Year:
3rd Year:
4th Year:
5rd Year:
6th Year:
SOYD = (6/21) ($1 mil - $75,000)
= (5/21) ($1 mil - $75,000)
= (4/21) ($1 mil - $75,000)
= (3/21) ($1 mil - $75,000)
= (2/21) ($1 mil - $75,000)
= (1/21) ($1 mil - $75,000)
= $264,286
= $220,238
= $176,190
= $132,143
= $ 88,095
= $ 44,048
Question: Which method is preferred?
Answer: It depends, on the MARR%, i% used by the firm (individual)
As an example:
If i% is=
0%
2%
10%
25%
PW of DDB is=
$925,000
$881,211
$738,331
$561,631
PW of SOYD is=
$925,000
$877,801
$724,468
$537,130
Preferred is
Equal, same
DDB
DDB
DDB
Thus, if MARR% is > 0%, DDB is best. One can also see this by inspection of the
depreciation schedules above.
11-3
DDB Depreciation
Year
1
2
3
4
(2/5) ($16,000 - $0)
(2/5) ($16,000 - $6,400)
(2/5) ($16,000 $10,240)
(2/5) ($16,000 $13,926)
Sum
DDB Depreciation
= $6,400
= $3,840
= $2,304
= $830
$14,756
Converting to Straight Line Depreciation
If
Switch
for Year
2
3
4
5
Beginning
of Yr
Book
Value
$9,600
$5,760
$3,456
$2,074
Remaining
Life
4 yrs
3 yrs
2 yrs
1 yr
Resulting Depreciation Schedule:
Year
1
2
3
4
5
Sum
DDB with Conversion to
Straight Line
$6,400
$3,840
$2,304
$1,728
$1,728
$16,000
SL = (Book –
Salvage)/Remaining
Life
$2,400
$1,920
$1,728
$2,074
Decision
Do not switch
Do not switch
Switch to SL
11-4
P=$12,000
S=$3,500
N=4
(a) Straight Line Depreciation
SL = -(P-S) / N
$2,125
=($12,000-$3,500) / 4
(b) Sum-of-Years Digits Depreciation
SOYD in yr. N = [(Remain. useful life at begin. of yr.)/[(N/2)(N+1)]] (P – S)
1st Year:
SOYD
= (4/10) ($12,000 - $3,500)=
$3,400
= (3/10) ($12,000 - $3,500)=
$2,550
3 Year:
= (2/10) ($12,000 - $3,500)=
$1,700
4th Year:
= (1/10) ($12,000 - $3,500)=
$850
2nd Year:
rd
(c) Double Declining Balance Depreciation
DDB in any year = 2/N(BookValue)
DDB in any year
Year:
DDB
= 2/N (Book Value)
= (2/4) ($12,000 - $0)
= $6,000
= (2/4) ($12,000 - $6,000)
= $3,000
3 Year:
= (2/4) ($12,000 - $9,000)
= $1,500
4th Year:
= (2/4) ($12,000 - $10,500)
= $750
2nd Year:
rd
(d) CCA
Special handling equipment classifies as a Class 43 asset with a CCA rate of 30%
Year
1
2
3
4
UCC at Start of
Year
$
12,000
$
10,200
$
7,140
$
4,998
Depreciation
Charge for year UCC at end of
CCA Rate
t = dt
year t
15% $
1,800 $
10,200
30% $
3,060 $
7,140
30% $
2,142 $
4,998
30% $
1,499 $
3,499
11-5
The computations for the first three methods (SL, DB, SOYD) are similar to Problem 11-4.
(d) Furniture: Class 8 (CCA rate=20%)
Year
Class
No.
Undep.
capital
cost at
beginning
of year
Cost of
acq.
during the
year
Proceeds
of
disp.
during
the
year
1
8
0
50,000.0
0
0
2
8
45,000.00
0
0
3
8
36,000.00
0
0
4
5
6
7
8
9
10
8
8
8
8
8
8
8
28,800.00
23,040.00
18,432.00
14,745.60
11,796.48
9,437.18
7,549.75
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Undep.
capital
cost
50,000.0
0
45,000.0
0
36,000.0
0
28,800.0
0
23,040.00
18,432.00
14,745.60
11,796.48
9,437.18
7,549.75
Summary of Methods
Year
1
2
3
4
5
6
7
8
9
10
SL
$5,00
0
$5,00
0
$5,00
0
$5,00
0
$5,00
0
$5,00
0
$5,00
0
$5,00
0
$5,00
0
$5,00
0
DDB
SOYD CCA
$10,000 $9,09
1
$5,000.00
$8,000
$8,182
$9,000.00
$6,400
$7,273
$7,200.00
$5,120
$6,364
$5,760.00
$4,096
$5,455
$4,608.00
$3,277
$4,545
$3,686.40
$2,621
$3,636
$2,949.12
$2,097
$2,727
$2,359.30
$1,678
$1,818
$1,887.44
$1,342
$909
$1,509.95
50% rule
Reduced
undep.
capital
cost
CCA
rate
%
Capital
cost
allowance
25,000.00
25,000.00
45,000.0
0
36,000.0
0
28,800.0
0
23,040.00
18,432.00
14,745.60
11,796.48
9,437.18
7,549.75
20
5,000.00
20
9,000.00
20
7,200.00
45,000.0
0
36,000.0
0
28,800.0
0
20
20
20
20
20
20
20
5,760.00
4,608.00
3,686.40
2,949.12
2,359.30
1,887.44
1,509.95
23,040.00
18,432.00
14,745.60
11,796.48
9,437.18
7,549.75
6,039.80
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Undep.
Capital
Cost
at end of
year
11-6
(a)
Year
1
SL
SOYD
$15,200 $25,333 (2/5) ($76,000 - $0)
2
$15,200 $20,267 (2/5) ($76,000 $30,400)
$15,200 $15,200 (2/5) ($76,000 $48,640)
$15,200 $10,133 (2/5) ($76,000 $59,584)
$15,200 $5,067
(2/5) ($76,000 $66,150)
$76,000 $76,000
3
4
5
Sum
(b)
DDB
=
$30,400
= $18,240
= $10,944
= $6,566
= $3,940
$70,090
By looking at the data in Part (a), some students may jump to the conclusion that
one should switch from DDB to Straight Line depreciation at the beginning of Year 3.
This mistaken view is based on the fact that in the table above the Straight Line
depreciation for Year 3 is $15,2000, while the DDB depreciation is only $10,944.
This is not a correct analysis of the situation.
This may be illustrated by computing the Straight Line depreciation for Year 3, if DDB
depreciation had been used in the prior years.
With DDB depreciation for the first two years, the book value at the beginning of Year
3 = $76,000 - $30,400 - $18,240 = $27,360.
SL depreciation for subsequent years = ($27,360 - $0)/3 = $9,120.
Thus, the choice for Year 3 is to use DDB = $10,944 or SL = $9,120. One would
naturally choose to continue with DDB depreciation.
For subsequent years:
If Switch for
Year
4
5
Beginning of
Yr
Book Value
$16,416
$9,850
Remaining
Life
SL = (Book –
Salvage)/Remaining Life
2 yrs
1 yr
$8,208
$9,850
When SL is compared to DDB in Part (a), it is apparent that the switch should take
place at the beginning of Year 4. The resulting depreciation schedule is:
Year
1
2
3
4
5
DDB with Conversion to
Straight Line
$30,400
$18,240
$10,944
$8,208
$8,208
Sum
(c)
$76,000
CCA rate =30%
Year
Class
No.
Undep.
capital
cost at
beginning
of year
Cost of
acq.
during the
year
Proceeds
of
disp.
during
the
year
Undep.
capital
cost
50% rule
Reduced
undep.
capital
cost
CCA
rate
%
Capital
cost
allowance
1
43
0
76,000.0
0
0
76,000.00
38,000.0
0
38,000.00
20
2
43
68,400.00
0
0
68,400.00
0.00
68,400.00
20
3
4
43
43
54,720.00
43,776.00
0
0
0
0
54,720.00
43,776.00
0.00
0.00
54,720.00
43,776.00
20
20
7,600.00
13,680.0
0
10,944.0
0
8,755.20
5
43
35,020.80
0
0
35,020.80
0.00
35,020.80
20
7,004.16
Salvage value=0, therefore loss on disposal=$28,016.64
11-7
(a) Straight Line
SL
depreciation in any year
= ($45,000 - $0)/5
= $9,000
(b) SOYD
sum = (n/2) (n+1) = (5/2) (5)
= 15
Depreciation in Year 1= (5/15) ($45,000 - $0)
= $15,000
Gradient
= (1/15) ($45,000 - $0)
= -$3,000
(c) DDB
Year
1
2
3
4
5
(2/5) ($45,000 - $0)
(2/5) ($45,000 $18,000)
(2/5) ($45,000 $28,800)
(2/5) ($45,000 $35,280)
(2/5) ($45,000 $39,168)
DDB
= $18,000
= $10,800
= $6,480
= $3,888
= $2,333
(d) CCA Class 8 asset (CCA rate=20%)
Undep.
Capital
Cost
at end of
year
68,400.0
0
54,720.00
43,776.00
35,020.80
28,016.6
4
Year
Class
No.
Undep.
capital
cost at
beginning
of year
1
8
2
3
4
8
8
8
0
40,500.0
0
32,400.00
25,920.00
5
8
20,736.00
Cost of
acq.
during the
year
Proceeds
of
disp.
during
the
year
Undep.
capital
cost
45,000.0
0
0
0
0
0
0
0
0
45,000.0
0
40,500.0
0
32,400.00
25,920.00
0
0
20,736.00
50% rule
Reduced
undep.
capital
cost
CCA
rate
%
Capital
cost
allowance
22,500.00
20
4,500.00
0.00
0.00
0.00
22,500.00
40,500.0
0
32,400.00
25,920.00
20
20
20
8,100.00
6,480.00
5,184.00
0.00
20,736.00
20
4,147.20
Undep.
Capital
Cost
at end of
year
40,500.0
0
32,400.00
25,920.00
20,736.00
16,588.8
0
Salvage value=0, therefore loss on disposal=$16,588.80
Summary of Depreciation Schedules
Year
1
2
3
4
5
Sum
SL
$9,000
$9,000
$9,000
$9,000
$9,000
$45,000
DDB
$18,000
$10,800
$6,480
$3,888
$2,333
$41,501
SOYD
CCA
$15,000
$4,500.00
$12,000
$8,100.00
$9,000
$6,480.00
$6,000
$5,184.00
$3,000
$4,147.20
$45,000 $28,411.20
11-8
CCA rate=30%
Year
Class
No.
Undep.
capital
cost at
beginning
of year
1
2
3
4
5
8
8
8
8
8
0
5,525.00
3,867.50
2,707.25
1,895.08
Cost of
acq.
during
the
year
6,500.00
0
0
0
0
Proceeds
of
disp.
during
the
year
0
0
0
0
0
Undep.
capital
cost
50%
rule
Reduced
undep.
capital
cost
CCA
rate
%
6,500.00
5,525.00
3,867.50
2,707.25
1,895.08
3,250.00
0.00
0.00
0.00
0.00
3,250.00
5,525.00
3,867.50
2,707.25
1,895.08
30
30
30
30
30
Capital cost
allowance
Salvage value=$1,200, therefore loss on disposal=$126.55
Year
1
2
SL
$1,060
$1,060
SOYD
$1,767
$1,413
DDB
$2,600
$1,560
UOP*
$707
$1,178
CCA
Year
$975.00 1
$1,657.50 2
975.00
1,657.50
1,160.25
812.18
568.52
Undep.
Capital
Cost
at end of
year
5,525.00
3,867.50
2,707.25
1,895.08
1,326.55
3
4
5
Sum
$1,060
$1,060
$1,060
$5,300
$1,060
$707
$353
$5,300
$936
$204
$0
$5,300
$1,160.25 3
$812.18 4
$568.52 5
$5,174.45
*UOP Depreciation is based on actual production.
11-9
Class 9 asset (CCA rate=25%)
Year
1
2
3
4
5
Class
No.
9
9
9
9
9
Undep.
capital
cost at
beginning
of year
($1,000)
Cost of
acq.
during
the
year
($1,000)
0
1,312.50
984.38
738.28
553.71
1,500.00
0
0
0
0
Proceeds
of
disp.
during
the
year
($1,000)
0
0
0
0
0
Undep.
capital
cost
($1,000)
50%
rule
($1,000)
Reduced
undep.
capital
cost
($1,000)
CCA
rate
%
Capital
cost
allowance
($1,000)
Undep.
Capital
Cost
at end of
year
($1,000)
1,500.00
1,312.50
984.38
738.28
553.71
750.00
0.00
0.00
0.00
0.00
750.00
1,312.50
984.38
738.28
553.71
25
25
25
25
25
187.50
328.13
246.09
184.57
138.43
1,312.50
984.38
738.28
553.71
415.28
50%
rule
Reduced
undep.
capital
cost
CCA
rate
%
Capital
cost
allowance
Undep.
Capital
Cost
at end of
year
11-10
CCA class 8 (CCA rate 20%)
Year
Class
No.
Undep.
capital
cost at
beginning
of year
Cost of
acq.
during the
year
Proceeds
of
disp.
during
the
year
Undep.
capital
cost
1
2
3
8
8
8
0
9,000.00
7,200.00
10,000.0
0
0
0
0
0
0
10,000.0
0
9,000.00
7,200.00
5,000.00
0.00
0.00
5,000.00
9,000.00
7,200.00
20
20
20
1,000.00
1,800.00
1,440.00
4
5
6
7
8
9
10
8
8
8
8
8
8
8
5,760.00
4,608.00
3,686.40
2,949.12
2,359.30
1,887.44
1,509.95
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5,760.00
4,608.00
3,686.40
2,949.12
2,359.30
1,887.44
1,509.95
0.00
0.00
0.00
0.00
0.00
0.00
0.00
5,760.00
4,608.00
3,686.40
2,949.12
2,359.30
1,887.44
1,509.95
20
20
20
20
20
20
20
1,152.00
921.60
737.28
589.82
471.86
377.49
301.99
9,000.0
0
7,200.00
5,760.00
4,608.0
0
3,686.40
2,949.12
2,359.30
1,887.44
1,509.95
1,207.96
11-11
Class 43 asset (CCA rate=30%)
Year
Class
No.
Undep.
capital
cost at
beginning
of year
Cost of
acq.
during the
year
1
2
3
4
5
43
43
43
43
43
0
63,750.00
44,625.00
31,237.50
21,866.25
75,000.00
0
0
0
0
Proceeds
of
disp.
during
the
year
0
0
0
0
0
6
43
0
0
7
8
9
10
43
43
43
43
15,306.38
10,714.4
6
7,500.12
5,250.09
3,675.06
0
0
0
0
0
0
0
0
Undep.
capital
cost
50% rule
Reduced
undep.
capital
cost
CCA
rate
%
Capital
cost
allowance
Undep.
Capital
Cost
at end of
year
75,000.00
63,750.00
44,625.00
31,237.50
21,866.25
37,500.00
0.00
0.00
0.00
0.00
37,500.00
63,750.00
44,625.00
31,237.50
21,866.25
30
30
30
30
30
11,250.00
19,125.00
13,387.50
9,371.25
6,559.88
15,306.38
10,714.4
6
7,500.12
5,250.09
3,675.06
0.00
15,306.38
10,714.4
6
7,500.12
5,250.09
3,675.06
30
4,591.91
63,750.00
44,625.00
31,237.50
21,866.25
15,306.38
10,714.4
6
30
30
30
30
3,214.34
2,250.04
1,575.03
1,102.52
7,500.12
5,250.09
3,675.06
2,572.54
0.00
0.00
0.00
0.00
11-12
Initial Cost
Useful Life
Salvage Value
CCA Rate
145
5
10
0.3
Year
1
2
3
4
5
6
7
SV-UCC
SL
$27.00
$27.00
$ 27.00
$27.00
$27.00
$--$--$---
SOYD
$45.00
$36.00
$27.00
$18.00
$9.00
$--$--$---
150%DB
$43.50
$30.45
$21.32
$14.92
$10.44
$--$--$14.37
DDB
$58.00
$34.80
$20.88
$12.53
$7.52
$--$--$1.28
CCA
$21.75
$36.98
$25.88
$18.12
$12.68
$--$--$19.59
TOTAL
$135.00
$135.00
$120.63
$133.72
$115.41
Column B is probably a unit of production.
11-13
Initial Cost
Useful Life
Salvage Value
CCA Rate
1060
5
90
40%
Year
1
2
3
4
5
6
7
SV-UCC
TOTAL
SL
$194.00
$194.00
$194.00
$194.00
$194.00
$--$--$--$970.00
SOYD
$323.33
$258.67
$194.00
$129.33
$ 64.67
$--$--$--$970.00
150%DB
$318.00
$222.60
$155.82
$109.07
$ 76.35
$--$--$ 88.15
$881.85
DDB
$424.00
$254.40
$152.64
$ 91.58
$ 54.95
$--$--$ (7.57)
$977.57
CCA
$212.00
$339.20
$203.52
$122.11
$ 73.27
$--$--$ 19.90
$950.10
150%DB
$2,000
$1,500
$1,125
$ 844
$ 633
$ 475
$--$ 824
$6,576
DDB
$2,667
$1,778
$1,185
$ 790
$ 527
$ 351
$--$ 102
$7,298
CCA
$1,600
$2,560
$1,536
$ 922
$ 553
$ 332
$--$ (102)
$7,502
Column E is probably a unit of production.
11-14
Initial Cost
Useful Life
Salvage Value
CCA Rate
Year
1
2
3
4
5
6
7
SV-UCC
TOTAL
SL
$1,233
$1,233
$1,233
$1,233
$1,233
$1,233
$--$0
$7,400
$8,000
6
$600
40%
SOYD
$2,114
$1,762
$1,410
$1,057
$ 705
$ 352
$--$--$7,400
11-15
Comparison Worksheet
Initial Cost
$ 250,000
Useful Life
15
Salvage Value
0
CCA Rate
0.1
Year
SL
SOYD
1
$16,667
$31,250
2
$16,667
$29,167
3
$16,667
$27,083
4
$16,667
$25,000
5
$16,667
$22,917
6
$16,667
$20,833
7
$16,667
$18,750
8
$16,667
$16,667
9
$16,667
$14,583
10
$16,667
$12,500
11
$16,667
$10,417
12
$16,667
$ 8,333
13
$16,667
$ 6,250
14
$16,667
$ 4,167
15
$16,667
$ 2,083
16
$--$--17
$--$--18
$--$--19
$--$--20
$--$--SV-UCC
$0
$--TOTAL
$250,000
$250,000
i=
NPW of
deprec=
NPW of
balance
Total
NPW
$
0.2
$
97,456.2
$
0.0
$
97,456.2
depreciable amount= $250,000
150%DB
$25,000
$22,500
$20,250
$18,225
$16,403
$14,762
$13,286
$11,957
$10,762
$ 9,686
$ 8,717
$ 7,845
$ 7,061
$ 6,355
$ 5,719
$--$--$--$--$--$51,473
$198,527
DDB
$33,333
$28,889
$25,037
$21,699
$18,806
$16,298
$14,125
$12,242
$10,610
$ 9,195
$ 7,969
$ 6,906
$ 5,986
$ 5,187
$ 4,496
$--$--$--$--$--$29,223
$220,777
CCA
$12,500
$23,750
$21,375
$19,238
$17,314
$15,582
$14,024
$12,622
$11,360
$10,224
$ 9,201
$ 8,281
$ 7,453
$ 6,708
$ 6,037
$--$--$--$--$--$ 54,332
$195,668
$ 127,119.9
$
97,469.7 $ 115,957.0
$ 90,807.4
$
$
6,325.7 $
$
-
$ 127,119.9
$
3,591.3
103,795.4 $ 119,548.3
Book Values
SL
$ 233,333
$ 216,667
$ 200,000
$ 183,333
$ 166,667
$ 150,000
$ 133,333
$ 116,667
$ 100,000
$ 83,333
$ 66,667
$ 50,000
$ 33,333
$ 16,667
$
0
$
0
$
0
$
0
$
0
$
0
SOYD
$218,750
$189,583
$162,500
$137,500
$114,583
$ 93,750
$ 75,000
$ 58,333
$ 43,750
$ 31,250
$ 20,833
$ 12,500
$ 6,250
$ 2,083
$
(0)
$
(0)
$
(0)
$
(0)
$
(0)
$
(0)
150%DB
$ 225,000
$ 202,500
$ 182,250
$ 164,025
$ 147,623
$ 132,860
$ 119,574
$ 107,617
$ 96,855
$ 87,170
$ 78,453
$ 70,607
$ 63,547
$ 57,192
$ 51,473
$ 51,473
$ 51,473
$ 51,473
$ 51,473
$ 51,473
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
DDB
216,667
187,778
162,741
141,042
122,236
105,938
91,813
79,571
68,962
59,767
51,798
44,892
38,906
33,719
29,223
29,223
29,223
29,223
29,223
29,223
6,677.2
$ 97,484.6
CCA gives greater NPW than SL
CCA
$237,500
$213,750
$192,375
$173,138
$155,824
$140,241
$126,217
$113,596
$102,236
$ 92,012
$ 82,811
$ 74,530
$ 67,077
$ 60,369
$ 54,332
$ 54,332
$ 54,332
$ 54,332
$ 54,332
$ 54,332
11-16
Comparison Worksheet
Initial Cost
$100,000
Useful Life
5
Salvage Value
$20,000
CCA Rate
30%
Year
1
2
3
4
5
SV-UCC
TOTAL
SL
$16,000
$16,000
$16,000
$16,000
$16,000
$--$80,000
SOYD
$26,667
$21,333
$16,000
$10,667
$ 5,333
$--$80,000
DDB
$40,000
$24,000
$14,400
$ 8,640
$ 1,600
i=
NPW of deprec=
NPW of balance
Total NPW
10%
$60,653
$--$60,653
$64,491
$--$64,491
$73,912
$80,000
$73,912
CCA
$15,000
$25,500
$17,850
$12,495
$ 8,747
$ 409
$80,000
$62,087
$ 254
$62,341
The DDB method gives the highest NPW
11-17
SOYD Depreciation
Sum = (5/2) (5 + 1) = 15
Year
1
2
3
4
5
Sum
(5/15)
($120,000)
(4/15)
($120,000)
(3/15)
($120,000)
(2/15)
($120,000)
(1/15)
($120,000)
SOYD
= $40,000
PW at Yr 0 at 8%
$37,036
= $32,000
$27,434
= $24,000
$19,051
= $16,000
$11,760
= $8,000
$5,445
= $120,000 = $100,726
Unit of Production Depreciation
Year
1
2
3
4
($15,000/$40,000)
($120,000)
($11,000/$40,000) ($120,000)
($4,000/$40,000) ($120,000)
($6,000/$40,000) ($120,000)
UOP
= $45,000
PW at Yr 0 at 8%
$41,666
= $33,000
= $12,000
= $18,000
$28,291
$9,526
$13,230
5
Sum
($4,000/$40,000) ($120,000)
= $12,000
$8,167
= $120,000 = $100,880
To maximize PW at Year 0, choose UOP depreciation.
11-18
(a) DDB
Year
1
2
(2.4)($10,000 - $0)
(2/4)($10,000 - $5,000)
DDB
= $5,000
= $2,500
2nd year depreciation - $2,500
(b) SOYD
2nd year SOYD = (3/10) = $3,000
(c) CCA – Class 12 Assets are at 100% rate
Because of ½ year rule, this is really 50% per year
2nd year CCA = 50% x ($10,000) = $5,000
11-19
See solution to 11-8.
11-20
See solution to 11-15.
11-21
(1) Use Table 11-1 to find the MACRS GDS Property Class for each asset:
(a) CCA class 10 asset
(b) CCA class 43 asset
(c) CCA class 1 asset
(2) Depreciation in year 3
(a) Dep3=$3,034.50
(b) Dep3=$5,355.00
(c) Dep3=$4,892.16
(3) Book Value
= Cost Basis – Sum of Depreciation Charges
(a)
$17,000 - $14,571.39 = $2,428.61
(b)
$30,000 - $25,714.22 = $4,285.78
(c)
$130,000 - $26,121.52
= $103,878.48
11-22
Year
Class
No.
1
2
3
4
5
1
1
1
1
1
Undep.
capital
cost at
beginning
of year
($1,000)
Cost of
acq.
during
the
year
($1,000)
0
588.00
564.48
541.90
520.22
600.00
0
0
0
0
Proceeds
of
disp.
during
the
year
($1,000)
0
0
0
0
0
Undep.
capital
cost
($1,000)
50%
rule
($1,000)
Reduced
undep.
capital
cost
($1,000)
600.00
588.00
564.48
541.90
520.22
300.00
0.00
0.00
0.00
0.00
300.00
588.00
564.48
541.90
520.22
CCA
rate
%
Capital
cost
allowance
($1,000)
Undep.
Capital
Cost
at end
of year
($1,000)
12.00
23.52
22.58
21.68
20.81
588.00
564.48
541.90
520.22
499.42
Capital
cost
allowance
($1,000)
Undep.
Capital
Cost
at end
of year
($1,000)
17.00
33.32
31.99
30.71
833.00
799.68
767.69
736.99
4
4
4
4
4
UCC at end of 5 years=$600,000-100,584.22=$499,416
Gain on disposal=$100,584
11-23
Year
Class
No.
1
2
3
4
1
1
1
1
Undep.
capital
cost at
beginning
of year
($1,000)
Cost of
acq.
during
the
year
($1,000)
0
833.00
799.68
767.69
850.00
0
0
0
Proceeds
of
disp.
during
the
year
($1,000)
0
0
0
0
Undep.
capital
cost
($1,000)
50%
rule
($1,000)
Reduced
undep.
capital
cost
($1,000)
850.00
833.00
799.68
767.69
425.00
0.00
0.00
0.00
425.00
833.00
799.68
767.69
CCA
rate
%
4
4
4
4
UCC at end of year 4=$850,000-113,015 = $736,985
11-24
Same as above.
11-25
(a) EUACI = (P – S) (A/P, i%, n) + Si + Annual operating cost
= ($80,000 - $20,000) (A/P, 10%, 20) + $20,000 (0.10) + $18,000
= $60,000 (0.1175) + $2,000 + $18,000
= $27,050
EUACII = ($100,000 - $25,000) (A/P, 10%, 25) + $25,000 (0.10) + $20,000
- $5,000 (P/A, 10%, 10) (A/P, 10%, 25)
= $75,000 (0.1102) + $2,500 + $20,000 - $5,000 (6.145) (0.1102)
= $27,380
To minimize EUAC, select Machine II.
(b) Capitalized Cost of Machine I= PW of an infinite life = EUAC/i
In part (a), EUAC = $27,050, so:
Capitalized Cost
= $27,050/0.10
= $270,500
(c) Fund to replace Machine I
Required future sum F
Annual Deposit
= $80,000 - $20,000 = $60,000
A
= $60,000 (A/P, 10%, 20)
= $60,000 (0.0175) = $1,050
(d)
Year
0
1- 20
20
$80,000
Cash
Flow
-$80,000
+$28,000
-$18,000
+$20,000
= ($28,000 - $18,000) (P/A, i%, 20) + $20,000 (P/F, i%, 20)
Solve by trial and error:
Try i = 10%
($10,000) (8.514) + $20,000 (0.1486)
= $88,112
≠ $80,000
Try i = 12%
($10,000) (7.469) + $20,000 (0.1037)
= $76,764
≠ $80,000
Rate of Return = 10% + (2%) [($88,112 - $80,000)/($88,112 - $76,764)]
= 11.4%
(e) SOYD depreciation
Book value of Machine I after two periods
Dep. Charge in any year = (Remain. useful life at beginning of yr/SOYD
for total useful life)(P – S)
Sum of years digits
= (n/2) (n + 1) = 20/2 (20 + 1) = 210
1st Year depreciation = (20/210) ($80,000 - $20,000)
2nd Year depreciation = (19/210) ($80,000 - $20,000)
Book value
= Cost – depreciation to date
= $80,000 - $11,143
= $68,857
(f) DDB Depreciation
Book value of Machine II after three years
= $5,714
= $5,429
Sum = $11,143
Depreciation charge in any year
= (2/n) (P – Depreciation charge to date)
1st Year Depreciation = (2/25) ($100,000 - $0)
= $8,000
2nd Year Depreciation = (2/25) ($100,000 - $8,000) = $7,360
3rd Year Depreciation = (2/25) ($100,000 - $15,360)
= $6,771
Sum = $22,131
Book Value
= Cost – Depreciation to date
= $100,000 - $22,131
= $77,869
(g) CCA depreciation (class 43 asset)
Year
1
2
3
Class
No.
Undep.
capital
cost at
beginning
of year
($1,000)
Cost of
acq.
during
the
year
($1,000)
0
85.00
59.50
100.00
0
0
43
43
43
Proceeds
of
disp.
during
the
year
($1,000)
0
0
0
Undep.
capital
cost
($1,000)
50%
rule
($1,000)
Reduced
undep.
capital
cost
($1,000)
100.00
85.00
59.50
50.00
0.00
0.00
50.00
85.00
59.50
CCA
rate
%
Capital
cost
allowance
($1,000)
Undep.
Capital
Cost
at end
of year
($1,000)
15.00
25.50
17.85
85.00
59.50
41.65
30
30
30
11-26
Year
Undep.
capital
cost at
beginning
of year
Cost of
acq.
during the
year
Proceeds
of
disp.
during
the
year
1
0
20,000.0
0
0
2
17,000.00
0
0
Undep.
capital
cost
20,000.0
0
17,000.0
0
50% rule
10,000.0
0
0.00
Reduced
undep.
capital
cost
10,000.0
0
17,000.0
0
CCA
rate
%
Capital
cost
allowance
30
3,000.00
17,000.0
0
30
5,100.00
11,900.00
Loss on disposal = 17,000-14,000 = $3,000
11-27
CCA
P= $50,000
dep yr 1 $ 7,500
dep yr 2 $ 12,750
UCC at end of 3 rd year (before 3rd yr CCA taken) = $29,750
selling price
recapture (loss)
15000 $(14,750)
25000 $(4,750)
60000 $20,250
SL
$50,000
$6,250
$6,250
$37,500
$(22,500)
$(12,500)
$12,500
Undep.
Capital
Cost
at end of
year
11-28
Gross income from sand and gravel
$0.65/m3 (45,000 m4) = $29,250
To engineering student
- $2,500
Taxable Income inc. depletion
= $26,750
Percentage depletion = 5% ($29,250) = $1,462.50
Therefore, allowable depletion is $1,462.50.
11-29
Mr. Salt’s cost of depletion
Percentage depletion
= $45,000 (1,000 Bbl/15,000Bbl)
= 15% ($12,000) = $1,800, but limited to 50% of
taxable income before depletion or
= 50% ($12,000 - $3,000)
= $4,500
Therefore, allowable depletion = $3,000.00.
11-30
(a) SOYD Depreciation
N=8
SUM = (N/2) (N+1) = 36
1st Year SOYD Depreciation = (8/36) ($600,000 - $60,000)
= $120,000
Subsequent years are a declining gradient:
G
= (1/36) ($600,000 - $60,000)
= $15,000
Year
1
2
3
4
5
6
7
8
Sum
SOYD Depreciation
$120,000
$105,000
$90,000
$75,000
$60,000
$45,000
$30,000
$15,000
$540,000
(b) Unit of Production (UOP) Depreciation
Depreciation/hour
= $3,000
= $540,000/21,600 hours
= $25/hr
Year
1
2
3
4
5
6
7
8
Sum
11-31
11-32
Utilization hrs/yr
6,000
4,000
4,000
1,600
800
800
2,200
2,200
UOP Depreciation
$150,000
$100,000
$100,000
$40,000
$20,000
$20,000
$55,000
$55,000
$540,000
11-33
See solution to problem 11.16
11-34
Comparison Worksheet
Initial Cost
Useful Life
Salvage Value
CCA Rate
Year
1
2
3
4
5
6
SL
$15,000
$15,000
$15,000
$15,000
$15,000
$15,000
100000
6
10000
20%
BV
$85,000
$70,000
$55,000
$40,000
$25,000
$10,000
Sum Of Year
$25,714
$21,429
$17,143
$12,857
$ 8,571
$ 4,286
11-35
Year
1
2
3
4
5
6
7
8
9
10
CCA
$175,000
$315,000
$252,000
$201,600
$161,280
$129,024
$103,219
$ 82,575
$ 66,060
$ 52,848
BV
$74,286
$52,857
$35,714
$22,857
$14,286
$10,000
CCA
$10,000
$18,000
$14,400
$11,520
$ 9,216
$ 7,373
UCC
$90,000
$72,000
$57,600
$46,080
$36,864
$29,491