# Solution manual engineering economic analysis 9th edition ch11 incme depreciation and cash fowl

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
= (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

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