Solution manual engineering economic analysis 9th edition ch12 after tã cash flows

Chapter 12: After-Tax Cash Flows
12-1
(a) Federal Taxes
On the first $35,000
From $35,000 to $70,000

16%
22%

Taxable income $62,000
Non-refundable tax credit=$8,00016%=
Federal taxes payable=

$5,600.00
$5,940.00
$11,540.00
Federal taxes=$11,540
$1,280.00
$10,260.00

(b) Increase in federal taxes after increase of $16,000
On the first $35,000
16%
$5,600.00
From $35,000 to $70,000
22%
$7,700.00
From $70,001 to
$113,804
26%
$2,079.74

$13,300.0
0
Taxable income $78,000
Non-refundable tax credit=$8,00016%=

Federal taxes payable=
Increase in federal taxes=

Federal taxes=$15,380
$1,280.00
$14,100.0
0
$3,840.00

12-2
(a) Alberta resident
Federal Taxes
On the first $35,000

16%

From $35,000 to $70,000

22%

$5,600.0
0
$2,200.0
0
$7,800.0

0

Taxable income $62,000
Non-refundable tax credit=$6,00016%=

Federal taxes=$7,800
$960.00

Federal taxes payable=
Provincial taxes:
Taxable income=$45,000
Non-refundable tax credit=$6,000

$6,840.00

On all income 10%
Total taxes=

$11,340.00

$4,500.0
0


(b) Ontario resident
Federal taxes payable=$6,840
Provincial taxes:
On the first $33,375
6.05%
From $33,375 to $66,752

9.15%

Total taxes=

$2,019.19
$1,063.69
$3,082.88

$9,922.88

12-3
Problem 12.3
Federal Taxes:
On the first $35,000

16%

$1,248.00
$1,248.00

Non-refundable tax credit=$6,00016%

$960.00

Federal taxes payable=
Provincial taxes:
On the first $30,544
10.90%

$288.00

Total taxes=

$1,138.20
$6,661.8
0

Net Income=$7,800-$1,138.2=
Upon increase in income of $2,600
Federal Taxes:
On the first $35,000

$850.20
$850.20

16%

(gross income=$7,800+$2,600=$10,400)
$1,664.0
0
$1,664.0
0

Non-refundable tax credit=$6,00016%

$960.00

Federal taxes payable=
Provincial taxes:
On the first $30,544

10.90%

$704.00
$1,133.60
$1,133.60

Total taxes= $1,837.60
Net Income=$7,800+$2,600-$1,837.60
$8,562.40
Increase in net income=$8,562.40-$6,661.80
$1,900.60


12-4
Federal Taxes:
On the first $35,000

16%

$1,248.00
$1,248.00

Non-refundable tax credit=$6,00016%=

$960.00

Federal taxes payable=
Provincial taxes:
On all income
10.00%

$288.00

Total taxes=

$780.00
$780.00

$1,068.00
$6,732.0
0

Net Income=$7,800 – $1,068.2=
Upon increase in income of $2,600
Federal Taxes:
On the first $35,000

(gross income=$7,800+$2,600=$10,400)

16%

$1,664.0
0
$1,664.0
0

Non-refundable tax credit=$6,00016%=

$960.00

Federal taxes payable=
Provincial taxes:

$704.00

On all income

10.00%

$1,040.0
0
$1,040.0
0

Total taxes= $1,744.00
Net Income=$7,800+$2,600 – $1,837.60
$8,656.00
Increase in net income=$8,656.00 – $6,732.00
$1,924.00


12-5
PROBLEM 12-5
Taxable Income
Non-refundable tax
credit
Province

DATA
$

65,000.00
$

8,000.00

2004 Federal Personal rates

Amount
On the first

$
35,000.00
$
70,000.00
$
113,804.00

16.00%

$ 5,600.00

22.00%

$ 7,700.00

26.00%
29.00%

$11,388.78

Total per
Level
$
5,600.00
$
13,300.00
$
24,688.78

from

$ 35,000.00

to

from
above

$ 70,001.00
$ 113,805.00

to

Taxable
Income

$ 65,000.00

Fed tax =

$12,200.00

Fed Avg Tax=

16.80%

x 16% =

$1,280.00

Fed Marg Tax=

22.00%

Total Taxes
Payable =

$10,920.00

Nonrefundable
tax credit

$

8,000.00

2004 Ontario Provincial Tax
On the first
from
above

$ 33,376.00
$ 66,753.00

to
surtax

$
33,375.00
$
66,752.00
Surtax on Prov Tax over

6.05%

$ 2,019.19

9.15%
11.2%

$ 3,053.90

$
2,019.19
$
5,073.09

Tax per Level
$5,600.00
$

6,600.00
$
$

$12,200.00

Tax Amdt.
$
2,019.19
$
2,893.60
$
$
4,912.78

-


Taxable Income
Non-refundable tax
credit
Province

$3,685

20.0%

4864

36.0%

Ontario tax =

$5,175.90

Combined tax =
$
22,000.00

$16,095.90

$

$
245.56
$
17.56
Avg Ont Tax=
Avg Combined
Tax=

7.96%
24.76%

8,000.00

2004 Federal Personal rates

Amount
On the first

$
35,000.00
$
70,000.00
$
113,804.00

16.00%

$ 5,600.00

22.00%

$ 7,700.00

26.00%
29.00%

$11,388.78

Total per
Level
$
5,600.00
$
13,300.00
$
24,688.78

from

$ 35,000.00

to

from
above

$ 70,001.00
$ 113,805.00

to

Taxable
Income

$ 22,000.00

Fed tax =

$3,520.00

Fed Avg Tax=

10.18%

x 16% =

$1,280.00

Fed Marg Tax=

16.00%

Total Taxes
Payable =

$2,240.00

Nonrefundable
tax credit

$

8,000.00

2004 Ontario Provincial Tax
from

$ 33,376.00

On the first
to

$
33,375.00
$

6.05%

9.15%

$ 2,019.19
$ 3,053.90

$
2,019.19
$

Tax per Level
$3,520.00
$
$
$

$3,520.00

Tax Amdt.
$
1,331.00
$

-


66,752.00
above

$ 66,753.00

5,073.09
11.2%

surtax

$
$
1,331.00
$
$

Surtax on Prov Tax over
$3,685
20.0%
4864
36.0%

Ontario tax =

$1,331.00

Combined tax =

$3,571.00

Avg Ont Tax=
Avg Combined
Tax=

Corporate Tax – ($65,000 - $22,000) x 18.6% = $7,998

Jane as an individual=
Jane as corp =

PaysPersonal Tax
$
16,095.90
$
3,571.00

Pays Corp Tax
$
$
7,998.00
65000-22000=43000 @ Ontario Small
Business Rates

Total
$ 16,095.90
$ 11,569.00
18.60%

6.05%
16.23%

-


12-6
(i) As a proprietorship
Federal Taxes:

On the first $35,000
From $35,000 to $70,000

16%
22%

Non-refundable tax credit=$8,00016%=

Provincial taxes:
On all income

Total taxes=

$5,600.00
$6,600.00
$12,200.0
0
$1,280.00

Federal taxes payable=

$10,920.00

10.00%
Provincial taxes payable=

$6,500.00
$6,500.00

$17,420.00

(ii) As a corporation
(ii-1) Personal income (income=$22,000)
Federal Taxes:
On the first $35,000

16%

$3,520.00

Non-refundable tax credit=$8,000*16%=

$1,280.00

Federal taxes payable=

$2,240.00

10.00%

$2,200.00

Taxes payable from personal income=

$4,440.00

Provincial taxes:
On all income

(ii-2) Corporate income (income=$43,000)

Combined tax rate=16.1%
Taxes payable from corporate income=
Total taxes=

$6,923.00

$11,363.00

12-7
Taxable Income
Tax Bill

= Adjustable Gross Income – Allowable Deductions
= ($500,000 - $30,000) - $30,000
= $170,000
= 0.15 ($50,000) + 0.25 ($25,000) + 0.34 ($25,000)
+ 0.39 ($70,000) – tax credits
= $49,550 – 48,000
= $41,550

12-8
Generally all depreciation methods allocated the cost of the equipment (less salvage value)
over some assigned useful life. While the depreciation charges in any year may be different


for different methods, the sum of the depreciation charges will be the same. This will affect
the amount of taxes paid in any year, but with a stable income tax rate, the total taxes paid
will be the same. (The difference is not the amount of the taxes, but their timing.)
12-9
Let ia = annual effective after-tax cost of capital.

XYZ, Inc. is paying:
(100%) (100% - 3%) – 1 = 0.030928
= 3.0928%
for use of the money for:
45 – 5
= 40 days.
Number of 40-day periods in 1 year = 365/40
ia

= [1 + (0.030928) (1 – 0.4)9.125 – 1
= 18.27%

= 9.125

= 0.1827

12-10
A = $5,000 (A/P, 15%, 4)
n=0
Loan
Balance
Interest
Payment
Principal
Payment
Loan
Balance
Sum of
Payments
Additional

“Point”
Interest
BTCF
Tax
BenefitInterest
Deduction
Interest
Tax
Saving
(Interest x
0.40)
ATCF

= $5,000 (0.3503)

= $1,751.50

1

2

3

4

$750.00

$599,80

$427.02

$228.35

$1,001.50

$1,151.70

$1,324.48

$1,522.32

$3,998.50

$2,846.80

$1,522.32

$0

$1,751.50

$1,751.50

$1,751.50

$1,751.50

$75.00

$75.00

$75.00

$75.00

-$1,751.50

-$1,751.50

-$1,751.50

-$1,751.50

$825.00
+$330.00

$674.80
+$269.90

$502.02
+$200.80

$303.35
+$121.30

-$1,421.50

-$1,481.60

-$1,550.70

-$1,630.20

$5,000

+$4,700

+$4,700

Solving the After-Tax Cash Flow, the after-tax interest rate is 10.9%.
12-11
Federal Tax

= 22.1% ($150,000)

= $33,150

Provincial Tax

=16.0% ($150,000)

= $24,000


Combined federal and provincial tax

= $57,150

Combined incremental state and federal income tax rate

= 22.1%+16%
= 38.1%

12-12
Combined incremental tax rate
= federal tax rate + provincial tax rate
= 26% + 13.7%
=39.7%
12-13
(a) Bonds plus Loan
Year

Before-Tax Cash
Taxable
Flow
Income
0
-$75,000
+$50,000
1- 5 +$5,000
$0
-$5,000
5
+$100,000
$25,000*
-$50,000
capital gain
* taxed at 20%, the capital gain rate.

Income

Taxes

After-Tax Cash
Flow
-$25,000

$0

$0

-$5,000

+$45,000

After-Tax Rate of Return
$25,000
= $45,00 (P/F, i%, 5)
(P/F, i%, 5)
= 0.5556, thus the Rate of Return = 12.47%
Note: The Tax Reform Act of 1986 permits interest paid on loans to finance investments
to continue to be deductible, but only up to the taxpayer’s investment income.
(b) Bonds but no loan
Year
0
1- 5
5

Before-Tax Cash
Flow
-$75,000

+$5,000
+$100,000

Taxable
Income

Income
Taxes

$5,000
$25,000*
capital gain

-$2,500
-$5,000

* Taxed at 20%
After-Tax Rate of Return
$75,000
= $2,500 (P/A, i%, 5) + $95,000 (P/F, i%, 5)
Try i = 7%,
Try i = 8%,

$2,500 (4.100) + $95,000 (0.7130)
$2,500 (3.993) + $95,000 (0.6806)

Using linear interpolation, Rate of Return = 7.9%

= $77,985
= $74,639

After-Tax Cash
Flow
-$75,000
$2,500
+$95,000


12-14
(a)
Purchase Price
P
Land Purchase
P

DATA
$
84,000.00
$
9,000.00

n

20

SL (yrs)

20

DDB (%)

SOTD (yrs)

10%

CCA rate

10%
$
9,600.00

Revenue Yr 1
ann . Rev
increase
Expense yr 1
ann. Exp inc
Tax Rate
Land Salvage
Selling Price S
MARR

$
600.00
$

38%
$
9,000.00
$
10%

Depreciable Asset Net Salvage
$
UCC(n) = 10,779.80
disposal tax $
effect = 4,096.32
Net Salvage at $
Yr n = 4,096.32

Land Net Salvage
Land Purchase $
P 9,000.00
$
Land Salvage 9,000.00
Capital Gain
(Loss) x Tax
Rate/2 = $
Land Net
Salvage at Yr n $
= 9,000.00
IRR=

NPV=

5.78%

($21,564.22)

5.15%

CCA

Year
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

Outlay or
Expense

Revenue

9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600

84,000
600
600
600
600
600
600
600
600

600
600
600
600
600
600
600
600
600
600
600
600

Before-Tax
Cash Flow
-84,000
9,000
9,000
9,000
9,000
9,000
9,000
9,000
9,000
9,000
9,000
9,000
9,000
9,000
9,000

9,000
9,000
9,000
9,000
9,000
9,000

Taxable
Income

CCA

4,200
7,980
7,182
6,464
5,817
5,236
4,712
4,241
3,817
3,435
3,092
2,782
2,504
2,254
2,028
1,826
1,643
1,479

1,331
1,198

Income Tax

4,800
1,020
1,818
2,536
3,183
3,764
4,288
4,759
5,183
5,565
5,908
6,218
6,496
6,746
6,972
7,174
7,357
7,521
7,669
7,802

1,824
388
691
964

1,209
1,430
1,629
1,808
1,970
2,115
2,245
2,363
2,468
2,564
2,649
2,726
2,796
2,858
2,914
2,965

After-Tax
Cash Flow
-84,000
7,176
8,612
8,309
8,036
7,791
7,570
7,371
7,192
7,030
6,885

6,755
6,637
6,532
6,436
6,351
6,274
6,204
6,142
6,086
6,035

Loans,
Land & WC
-9,000

13,096

Total AfterTax Cash
Flow
$
-93,000
7,176
8,612
8,309
8,036
7,791
7,570
7,371
7,192
7,030

6,885
6,755
6,637
6,532
6,436
6,351
6,274
6,204
6,142
6,086
19,131


(b)
Purchase Price
P
Land Purchase
P

DATA
$
84,000.00
$
9,000.00

n

20

SL (yrs)

20

DDB (%)
SOTD (yrs)

10%

CCA rate

10%
$
9,600.00

Revenue Yr 1
ann . Rev
increase
Expense yr 1
ann. Exp inc
Tax Rate
Land Salvage
Selling Price S
MARR

$
600.00
$

38%
$

16,000.00
$
84,000.00
10%

Depreciable Asset Net Salvage
$
UCC(n) = 10,779.80
disposal tax $
effect = (27,823.68)
Net Salvage at $
Yr n = 56,176.32

Land Net Salvage
Land Purchase $
P 9,000.00
$
Land Salvage 16,000.00
Capital Gain
(Loss) x Tax $
Rate/2 = 1,330.00
Land Net
Salvage at Yr n $
= 14,670.00
IRR=

NPV=

5.78%

($21,564.22)

7.22%


CCA

Year
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

Outlay or
Expense

Revenue

9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600
9,600

84,000
600
600
600

600
600
600
600
600
600
600
600
600
600
600
600
600
600
600
600
600

Before-Tax
Cash Flow
-84,000
9,000
9,000
9,000
9,000
9,000
9,000
9,000
9,000
9,000

9,000
9,000
9,000
9,000
9,000
9,000
9,000
9,000
9,000
9,000
9,000

Taxable
Income

CCA

4,200
7,980
7,182
6,464
5,817
5,236
4,712
4,241
3,817
3,435
3,092
2,782
2,504

2,254
2,028
1,826
1,643
1,479
1,331
1,198

Income Tax

4,800
1,020
1,818
2,536
3,183
3,764
4,288
4,759
5,183
5,565
5,908
6,218
6,496
6,746
6,972
7,174
7,357
7,521
7,669
7,802

1,824
388
691
964
1,209
1,430
1,629
1,808
1,970
2,115
2,245
2,363
2,468
2,564
2,649
2,726
2,796
2,858
2,914
2,965

After-Tax
Cash Flow
-84,000
7,176
8,612
8,309
8,036
7,791

7,570
7,371
7,192
7,030
6,885
6,755
6,637
6,532
6,436
6,351
6,274
6,204
6,142
6,086
6,035

Loans,
Land & WC
-9,000

70,846

Total AfterTax Cash
Flow
$
-93,000
7,176
8,612
8,309
8,036

7,791
7,570
7,371
7,192
7,030
6,885
6,755
6,637
6,532
6,436
6,351
6,274
6,204
6,142
6,086
76,881


12-15
SOYD Depreciation
N=8
SUM = (N/2) (N + 1) = 36
1st Year Depreciation
Annual Decline
Year
0
1
2
3
4

5
6
7
8

Before-Tax Cash
Flow
-$120,000
+$29,000
+$26,000
+$23,000
+$20,000
+$17,000
+$14,000
+$11,000
+$8,000
+$12,000

Sum

= (8/36) ($120,000 - $12,000)
= (1/36) ($120,000 - $12,000)

= $24,000
= $3,000

SOYD
Deprec.

Taxable

Income

Income Taxes at
48%

$24,000
$21,000
$18,000
$15,000
$12,000
$9,000
$6,000
$3,000

$5,000
$5,000
$5,000
$5,000
$5,000
$5,000
$5,000
$5,000
$0

-$2,300
-$2,300
-$2,300
-$2,300
-$2,300
-$2,300

-$2,300
-$2,300
$0

After-Tax Cash
Flow
-$120,000
+$26,700
+$23,700
+$20,700
+$17,700
+$14,700
+$11,700
+$8,700
+$5,700
+$12,000

$108,000

Will the firm obtain a 6% after tax rate of return?
PW of Cost = PW of Benefits
$120,000 =$26,700(P/A, i%, 8)-$3,000(P/G, i%, 8)+$12,000(P/F, i%, 8)
At i = 6%
PW of Benefits

=$26,700(6.210)-$3,000(19.842)+$12,000(0.6274)
= $113,810
i is too high
Therefore, the firm will not obtain a 6% after-tax rate of return.

Further calculations show actual rate of return to be approximately 4.5%.
12-16
Year
0
1
2
3
4
5
Sum

Before-Tax Cash
Flow
-$50,000
+$20,000
+$17,000
+$14,000
+$11,000
+$8,000
+$5,000 (salvage
val.)

SOYD
Deprec.

Taxable
Income

Income Taxes at
20%

$15,000
$12,000
$9,000
$6,000
$3,000

$5,000
$5,000
$5,000
$5,000
$5,000
$0

-$1,000
-$1,000
-$1,000
-$1,000
-$1,000
$0

$45,000

PW of Benefits – PW of Cost
=0
$19,000 (P/A, i%, 5) - $3,000 (P/G, i%, 5)
+ $5,000 (P/F, i%, 5) - $50,000

=0

After-Tax Cash
Flow
-$50,000
+$19,000
+$16,000
+$13,000
+$10,000
+$7,000
+$5,000


Try i = 15%
$19,000 (3.352) - $3,000 (5.775) + $5,000 (0.4972) - $50,000 = -$1,151
Try i = 12%
$19,000 (3.605) - $3,000 (6.397) + $5,000 (0.5674) - $50,000 = +$2,141
Using linear interpolation, find that i = 14%.
12-17
Year
0
1- 8
Sum

Before-Tax Cash
Flow
-$20,000
+$5,000

SL
Deprec.

Taxable
Income

Income Taxes at
40%

$2,500
$20,000

$2,500
$20,000

-$1,000
-$8,000

After-Tax Cash
Flow
-$20,000
+$4,000

(a) Before Tax Rate of Return
$20,000
= $5,000 (P/A, i%, 8)
(P/A, i%, 8) = $20,000/$5,000
=4
i*
= 18.6%
(b) After Tax Rate of Return
$20,000
= $4,000 (P/A, i%, 8)

(P/A, i%, 8) = $20,000/$4,000
=5
i*
= 11.8%
(c)
Year
Before-Tax SL
Taxable
Cash Flow
Deprec.
Income
0
-$20,000
1- 8
+$5,000
$1,000
$4,000
9- 20
$0
$1,000
-$1,000
Sum
$20,000
$20,000

Income Taxes
at 40%

After-Tax Cash
Flow

-$20,000
+$3,400
+$400

-$1,600
+$400
-$8,000

Note that the changed depreciable life does not change Total Depreciation, Total Taxable
Income, or Total Income Taxes. It does change the timing of these items.
After-Tax Rate of Return
PW of Benefits – PW of Cost = 0
$400 (P/A, i%, 20) + $3,000 (P/A, i%, 8) - $20,000 = 0
Try i = 9%
$400 (9.129) + $3,000 (5.535) - $20,000
Try i = 10%
$400 (8.514) + $3,000 (5.335) - $20,000

= +$256.60
= -$589.40

Using linear interpolation, i* = 9.3%.
12-18
Year

Before-Tax
Cash Flow

DDB
Deprec.

Taxable
Income

Income
Taxes at
34%

0
1

-$1,000
+$500

$400

$100

-$34

After-Tax
Cash Flow

NPW at
10%

-$1,000
+$466

-$1,000

$423.6


2
3
4
5

+$340
+$244
+$100
+$100
+$125

$240
$144
$86.4
$4.6*

Sum

$100
$100
$13.6
$95.4

-$34
-$34
-$4.6
-$32.4

+$306
+$210
+$95.4
+$192.6

$875

$252.9
$157.8
$65.2
$119.6
+$19.1

* Reduced to $4.60 so book value not less than salvage value.
At 10%, NPW = +$19.1
Thus the rate of return exceeds 10%. (Calculator solution is 10.94%)
The project should be undertaken.
12-19
Year

Bn-1
$100,000.00
$85,000.00
$59,500.00
$41,650.00
$29,155.00

1
2

3
4
5

Calculation of net Salvage

Year

0

CCA Dep.
$15,000.00
$25,500.00
$17,850.00
$12,495.00
$8,746.50

Bn
$85,000.00
$59,500.00
$41,650.00
$29,155.00
$20,408.50

UCC at year 5=
Proceed S=
Gain on disp.=
Tax effect G=
Net S=

$20,408.50
$35,000.00
$14,591.50
$4,961.11
$30,038.89

1

2

OR

$30,000.00

$30,000.00

CCA

$15,000.00

$25,500.00

BTCF
Taxes
Net Profit

$15,000.00
$5,100.00
$9,900.00

$4,500.00
$1,530.00
$2,970.00

$15,000.00

CCA
Investment
Salvage

$25,500.00

3
$30,000.0
0
$17,850.0
0
$12,150.0
0
$4,131.00
$8,019.00
$17,850.0
0

4
$30,000.0
0
$12,495.0
0
$17,505.0

0
$5,951.70
$11,553.30
$12,495.0
0

$28,470.00

$25,869.0
0

$24,048.3
0

$30,000.00
$8,746.50
$21,253.50
$7,226.19
$14,027.31
$8,746.50

-100,000
$30,038.89

Net ATCF

-100,000

IRR=

$24,900.00

15.07%

12-20
SOYD= 15
Year
1

5

Bn-1
$120,000.00

Factor
0.33

Dep.
$40,000.00

Bn
$80,000.00

$52,812.70


2
3
4
5

$80,000.00
$48,000.00
$24,000.00
$8,000.00

0.27
0.20
0.13
0.07

Calculation of net Salvage

Year
OR
Dep.
BTCF
Taxes
Net Profit
Dep.
Investment
Salvage
Net ATCF

0

$32,000.00
$24,000.00
$16,000.00
$8,000.00

$48,000.00
$24,000.00
$8,000.00
$0.00

UCC at year 5=
Proceed S=
Gain on disp.=
Tax effect G=
Net S=

$0.00
$40,000.00
$40,000.00
$13,600.00
$26,400.00

1
$32,000.00
$40,000.00
-$8,000.00
-$2,720.00
-$5,280.00
$40,000.00

2
$32,000.00
$32,000.00
$0.00

$0.00
$0.00
$32,000.00

3
$32,000.00
$24,000.00
$8,000.00
$2,720.00
$5,280.00
$24,000.00

$34,720.00

$32,000.00

$26,400.00
$29,280.00 $26,560.00 $50,240.00

4
5
$32,000.00 $32,000.00
$16,000.00 $8,000.00
$16,000.00 $24,000.00
$5,440.00 $8,160.00
$10,560.00 $15,840.00
$16,000.00 $8,000.00

-$120,000
-$120,000

IRR>MARR, therefore it was a good investment

IRR= 12.88%

12-21
Double Declining Balance Depreciation
Year
1
2
3
4

Bn-1
$100,000.00
$50,000.00
$25,000.00
$12,500.00

Dn
$50,000.00
$25,000.00
$12,500.00
$6,250.00

Bn
$50,000.00
$25,000.00
$12,500.00
$6,250.00

0

1

2

OR

$30,000.00

$30,000.00

Dep.

$50,000.00

$25,000.00

BTCF

-$20,000.00

$5,000.00

Taxes

-$9,200.00

$2,300.00

-$10,800.00

$2,700.00

$50,000.00

$39,200.00

Year

Net Profit
Dep.
Investment
Salvage
Net ATCF

4
$40,000.0
0

5
$10,000.0
0

6
$10,000.0
0

$6,250.00

$33,750.0
0
$15,525.0
0
$18,225.0
0

$0.00
$10,000.0
0

$0.00
$10,000.0
0

$4,600.00

$4,600.00

$5,400.00

$5,400.00

$25,000.00

3
$35,000.0
0
$12,500.0
0

$22,500.0
0
$10,350.0
0
$12,150.0
0
$12,500.0
0

$6,250.00

$0.00

$0.00

$27,700.00

$24,650.0

$24,475.0

$5,400.00

$6,250.00
$11,650.00

-$100,000
-$100,000

0
IRR=

11.61%

0

After tax rate of return=11.61%

12-22
$25,240*
Loan Payment
Loan Repayment
Year
Payment
1
$25,240.00
2
$25,240.00
3
$25,240.00
4
$25,240.00
Year

0

IRR=

(a)

(b)

Interest
$8,000.00
$6,276.00
$4,379.60
$2,293.56

Principal Red.
$17,240.00
$18,964.00
$20,860.40
$22,946.44

Balance
$62,760.00
$43,796.00
$22,935.60
-$10.84

1

2

3

4

$30,000.00
$50,000.00

$8,000.00

$30,000.00
$25,000.00
$6,276.00

$35,000.00
$12,500.00
$4,379.60

$40,000.00
$6,250.00
$2,293.56

-$20,000

-$28,000.00
-$12,880.00
-$15,120.00
$50,000.00
-$17,240.00

-$1,276.00
-$586.96
-$689.04
$25,000.00
-$18,964.00

$18,120.40
$8,335.38

$9,785.02
$12,500.00
-$20,860.40

$31,456.44
$14,469.96
$16,986.48
$6,250.00
-$22,946.44

5
$10,000.0
0
$0.00
$0.00
$10,000.0
0
$4,600.00
$5,400.00
$0.00
0

-$20,000

$17,640.00

$5,346.96

$1,424.62

$290.04

$5,400.00

OR
Dep.
Interest
BTCF
Taxes
Net Profit
Dep.
Investment
Salvage
Net ATCF

Bn-1
$80,000.00
$62,760.00
$43,796.00
$22,935.60

6
$10,000.0
0
$0.00
$0.00
$10,000.0
0
$4,600.00
$5,400.00

$0.00
0
$6,250.00
$11,650.00

34.29%

After-Tax Rate of Return = 34.3%
The purchase of the special tools for $20,000 cash plus an $80,000 loan represents
a leveraged situation.
Under the tax laws all the interest paid is deductible when computing taxable
income, so the after-tax cost of the loan is not 10%, but 5.4%. The resulting rate of
return on the $20,000 cash is therefore much higher in this situation.
Note, however, that the investment now is not just $20,000, but really $20,000 plus
the obligation to repay the $80,000 loan.


12-23
SOYD Depreciation
SOYD=36
Year
Bn-1
1

$108,000.00

0.22

2

$84,000.00

0.19

3

$63,000.00

0.17

4

$45,000.00

0.14

5
6
7
8

$30,000.00
$18,000.00
$9,000.00
$3,000.00

0.11
0.08
0.06
0.03

Dep.
$24,000.0
0
$21,000.0
0
$18,000.0
0
$15,000.0
0
$12,000.0
0
$9,000.00
$6,000.00
$3,000.00

Initial investment=$108,000+$25000=

$133,000

Year

Factor

0

1

OR

$24,000.00

Dep.
BTCF
Taxes
Net Profit

$24,000.00
$0.00
$0.00
$0.00

Dep.
Investment
Salvage
Net ATCF

$24,000.00

2
$24,000.0
0
$21,000.0
0
$3,000.00
$1,020.00
$1,980.00
$21,000.0
0

Bn
$84,000.00
$63,000.00
$45,000.00
$30,000.00
$18,000.00
$9,000.00
$3,000.00
$0.00

3

4

5

6

7

8

$24,000.00

$24,000.00

$24,000.00

$24,000.00

$24,000.00

$24,000.00

$18,000.00
$6,000.00
$2,040.00
$3,960.00

$15,000.00
$9,000.00
$3,060.00
$5,940.00

$12,000.00
$12,000.00
$4,080.00
$7,920.00

$9,000.00
$15,000.00
$5,100.00
$9,900.00

$6,000.00
$18,000.00
$6,120.00
$11,880.00

$3,000.00

$21,000.00
$7,140.00
$13,860.00

$18,000.00

$15,000.00

$12,000.00

$9,000.00

$6,000.00

$3,000.00

$17,880.00

$25,000.00
$41,860.00

-$133,000
-$133,000

$24,000.00

$22,980.00

$21,960.00

$20,940.00

$19,920.00

NPW at 15% is negative (-$29,862). Therefore the project should not be undertaken.

$18,900.00


(Calculator solution: i = 8.05%)


12-24
Year
1
2
3
4
5
6

Bn-1
$12,000.00
$10,500.00
$7,875.00
$5,906.25
$4,429.69
$3,322.27

CCA Dep.

$1,500.00
$2,625.00
$1,968.75
$1,476.56
$1,107.42
$830.57

Calculation of net Salvage

Year
OR
Dep.
BTCF
Taxes
Net Profit
Dep.
Investment
Salvage
Net ATCF

0

Bn
$10,500.00
$7,875.00
$5,906.25
$4,429.69
$3,322.27
$2,491.70

UCC at year 6=
Proceed S=
Gain on disp.=
Tax effect G=
Net S=

$2,491.70
$1,000.00
-$1,491.70
-$507.18
$1,507.18

1
$1,727.00
$1,500.00
$227.00
$77.18
$149.82
$1,500.00

2
$2,414.00
$2,625.00
-$211.00
-$71.74
-$139.26
$2,625.00

3
$2,872.00

$1,968.75
$903.25
$307.11
$596.15
$1,968.75

4
$3,177.00
$1,476.56
$1,700.44
$578.15
$1,122.29
$1,476.56

5
$3,358.00
$1,107.42
$2,250.58
$765.20
$1,485.38
$1,107.42

6
$1,997.00
$830.57
$1,166.43
$396.59
$769.85
$830.57

$1,649.82

$2,485.74

$2,564.90

$2,598.85

$2,592.80

$1,507.18
$3,107.59

-$12,000
-$12,000

AW=-$230.58
Since AW<0, the investment is not desirable.
12-25
(a) Payback

= $500,000/($12,000,000 x (0.05 – 0.03))

= 2.08 years

(b) After-Tax Payback:
SOYD=
Year
1
2

3
4
5

Year
OR
Dep.
BTCF
Taxes

15
Bn-1
$500,000.00
$333,333.33
$301,333.33
$277,333.33
$261,333.33

0

Factor
0.33
0.27
0.20
0.13
0.07

Dep.
$166,666.67
$32,000.00

$24,000.00
$16,000.00
$8,000.00

Bn
$333,333.33
$301,333.33
$277,333.33
$261,333.33
$253,333.33

1
$240,000.00
$166,666.67
$73,333.33
$29,333.33

2
$240,000.00
$32,000.00
$208,000.00
$83,200.00

3
$240,000.00
$24,000.00
$216,000.00
$86,400.00

4

$240,000.00
$16,000.00
$224,000.00
$89,600.00

5
$240,000.00
$8,000.00
$232,000.00
$92,800.00


Net Profit
Dep.
Investment
Net ATCF

-$500,000.00
-$500,000.00

$44,000.00
$166,666.67

$124,800.00
$32,000.00

$129,600.00
$24,000.00

$134,400.00

$16,000.00

$139,200.00
$8,000.00

$210,666.67

$156,800.00

$153,600.00

$150,400.00

$147,200.00

Payback period=2.86 years
IRR= 20.49%

12-26
SOYD=
Year
1
2
3
4
5
6
7
Year
OR

Dep.
BTCF
Taxes
Net Profit
Dep.
Investment
Net ATCF
IRR=

28
Bn-1
$14,000.00
$10,500.00
$7,500.00
$5,000.00
$3,000.00
$1,500.00
$500.00
0

-$14,000
-$14,000
10.71%

Factor
0.25
0.21
0.18
0.14
0.11

0.07
0.04

Dep.
$3,500.00
$3,000.00
$2,500.00
$2,000.00
$1,500.00
$1,000.00
$500.00

Bn
$10,500.00
$7,500.00
$5,000.00
$3,000.00
$1,500.00
$500.00
$0.00

1
$3,600
$3,500
$100
$47
$53
$3,500

2

$3,600
$3,000
$600
$282
$318
$3,000

3
$3,600
$2,500
$1,100
$517
$583
$2,500

4
$3,600
$2,000
$1,600
$752
$848
$2,000

5
$3,600
$1,500
$2,100
$987
$1,113
$1,500

6
$3,600
$1,000
$2,600
$1,222
$1,378
$1,000

7
$3,600
$500
$3,100
$1,457
$1,643
$500

$3,553

$3,318

$3,083

$2,848

$2,613

$2,378

$2,143

12-27
GIVEN:

First Cost
= $18,600
Annual Cost = $16,000
Salvage Value = $3,600
Depreciation = S/L with n = 10, S = $3,600
Savings/bag = $0.030
Cartons/year = 200,000
Savings bag/carton = 3.5
Annual Savings
= ($0.03) (3.5) (200,000)
SL Depreciation
= ($18,000 - $3,600)/10

Initial investment=$18,600-$1,860=
Year
OR
Dep.
BTCF
Taxes
Net Profit
Dep.
Investment
Salvage
Net ATCF

(a) PW

0

1
$5,000
$1,500
$3,500
$1,750
$1,750
$1,500

$16,74
0
2
$5,000
$1,500
$3,500
$1,750
$1,750
$1,500

= $21,000
= $1,500/year

(10% tax credit)
3
$5,000
$1,500
$3,500

$1,750
$1,750
$1,500

4
$5,000
$1,500
$3,500
$1,750
$1,750
$1,500

5
$5,000
$1,500
$3,500
$1,750
$1,750
$1,500

6
$5,000
$1,500
$3,500
$1,750
$1,750
$1,500

7
$5,000

$1,500
$3,500
$1,750
$1,750
$1,500

8
$5,000
$1,500
$3,500
$1,750
$1,750
$1,500

9
$5,000
$1,500
$3,500
$1,750
$1,750
$1,500

10
$5,000
$1,500
$3,500
$1,750
$1,750
$1,500

$3,250

$3,600
$6,850

$16,740
$16,740

$3,250

$3,250

$3,250

$3,250

$3,250

= -$16,740 + $3,250 (P/A, 20%, 10) + $3,600 (P/F, 20%, 10)
= -$2,535

(b) Set PW = 0 at i* and solve for i*:
$0 = -$16,740 + $3,250 (P/A, i*, 10) + $3,600 (P/F, i*, 10)
by trial and error method, i* = 16% per year.

$3,250

$3,250

$3,250

12-28
Fed + Alta rate = 29+ 10 = 39%
DATA
Purchase Price
P
Land Purchase
P

n

$
82,000.00
$
30,000.00

5

SL (yrs)

DDB (%)
SOTD (yrs)
CCA rate
Revenue Yr 1
ann . Rev
increase

4%
$

9,000.00

Expense yr 1
ann. Exp inc
Tax Rate
Land Salvage
Selling Price S
MARR

39%
$
30,000.00
$
90,000.00
10%

Depreciable Asset Net Salvage
$
68,2
53.4
UCC(n) = 9
$
(6,92
disposal tax effect = 1.14)
$
83,0
Net Salvage at Yr n 78.8
= 6

Land Net Salvage

Land $
Purchase P 30,000.00
$
Land Salvage 30,000.00
Capital Gain
(Loss) x Tax
Rate/2 = $
Land Net
Salvage at Yr $
n = 30,000.00
IRR=

NPV=

-24.28%

($57,189.11)

9.98%

($167.58)


Year

Revenue

Outlay or
Expense

0
1
2
3
4
5

9,000
9,000
9,000
9,000
9,000

82,000
0
0
0
0
0

Before-Tax
Cash Flow
-82,000
9,000
9,000
9,000
9,000
9,000

CCA

Taxable
Income

Income Tax

After-Tax
Cash Flow

1,640
3,214
3,086
2,962
2,844

7,360
5,786
5,914
6,038
6,156

2,870
2,256
2,307
2,355
2,401

-82,000
6,130
6,744

6,693
6,645
6,599

Loans,
Land &
WC
-30,000

113,079

Total After-Tax
Cash Flow
$
-112,000
6,130
6,744
6,693
6,645
119,678