mafin chapter 13

8/12/2019 Mafin Chapter 13

1/23

PROBLEM 13-1

A. Purchase price of equipment 9,000,000.00

Additional investment in working capital 3,000,000.00

Initial investment outlay ###########

B.

C.

PROBLEM 13-2

A. Sales revenues ###########

Operating costs ###########

Depreciation ###########

Operating income before taxes 1,000,000.00

Taxes (40%) (400,000.00)

Operating income after taxes 600,000.00

Add back Depreciation 2,000,000.00

First year project cash flow 2,600,000.00

B.

C. Sales revenues ###########

Operating costs ###########

Depreciation ###########

Operating income before taxes 1,000,000.00

Taxes (30%) (300,000.00)

Operating income after taxes 700,000.00

Add back Depreciation 2,000,000.00

First year project cash flow 2,700,000.00

The projects cash flow would increase by $100,000.

PROBLEM 13-3

Original cost of equipment ###########

Depreciation (80%) ###########

Book value 4,000,000.00

Selling price 5,000,000.00

Book value ###########

Gain on sale 1,000,000.00

Selling price 5,000,000.00Tax on gain (1,000,000 x 40%) (400,000.00)

After-tax net salvage value 4,600,000.00

PROBLEM 13-4

Initial outlay (40,000.00)

Present value of cash inflows

1 - (1.10-10

)

0.10

Net present value 15,301.10

Chang should buy the new machine because the project has a positive net present value.

No, lastyears$50,000 expenditure is considered a sunk cost and does not represent an incremental cash flow. Hence, i

included in the analysis.

The potential sale of the building represents an opportunity cost of conducting the project in that building. Therefore, the

tax sale price must be charged against the project as a cost.

The cannibalization of existing sales needs to be considered in this analysis on an after-tax basis, because the cannibalized

sales revenue the firm would realize without the new project but would lose if the new project is accepted. Thus, the

would be to reduce theprojectscash flow by $1,000,000(1 T) = $1,000,000(0.6) = $600,000. Thus, theprojectscash flo

$2,000,000 rather than $2,600,000.

9,000 55,301.10


2/23

PROBLEM 13-5

SYSTEM A



1 - (1.10-6

)

0.10

Net present value of System A 6,131.56

System A's EAA

1 - (1.10-6

)

0.10

SYSTEM B



1 - (1.10-3

)

0.10

Net present value of System B 2,921.11

System B's EAA

1 - (1.10

-3

)0.10

System A should be chosen because it has a higher EAA than System B.

PROBLEM 13-6

A. Straight-line depreciation

Year 1 (800,000 / 4) 200,000.00

Year 2 (800,000 / 4) 200,000.00

Year 3 (800,000 / 4) 200,000.00

Year 4 (800,000 / 4) 200,000.00

MACRS accelerated depreciation

Year 1 (800,000 x 33%) 264,000.00

Year 2 (800,000 x 45%) 360,000.00

Year 3 (800,000 x 15%) 120,000.00

Year 4 (800,000 x 7%) 56,000.00

B. Year Tax % Cash flows

1 40% 25,600.00

2 40% 64,000.00

3 40% (32,000.00)

4 40% (57,600.00)

Year Cash flows PV factor

1 25,600.00 0.909091

2 64,000.00 0.826446

3 (32,000.00) 0.751315

4 (57,600.00) 0.683013

Net present value

PROBLEM 13-8

64,000.00

1,407.85

2,921.11 / 1,174.62

(264,000 - 200,000)

MACRS - SL Difference

52,892.56

(24,042.07)

(39,341.58)

6,000 26,131.56

6,000 14,921.11

6,131.56 /

12,781.64

Ceteris paribus, the accelerated depreciation method will result in a higher NPV (by $12,781.64) than would the use of t

depreciation method.

160,000.00

(80,000.00)

(144,000.00)

PV of cash flows

23,272.73

(56,000 - 200,000)

(120,000 - 200,000)

(360,000 - 200,000)


3/23

A. Base price (140,000.00)

Modification (30,000.00)

Increase in working capital (8,000.00)

Net cost of spectometer (178,000.00)

B. Year 1 Year 2 Year 3

After-tax savings 30,000.00 30,000.00 30,000.00

Depreciation tax savings 22,440.00 30,600.00 10,200.00

Salvage value 60,000.00

Tax on salvage value (19,240.00)

Return of working capital 8,000.00Project cash flows 52,440.00 60,600.00 88,960.00

Computations:

Before-tax labor cost 50,000.00

Tax (40%) (20,000.00)

After-tax savings 30,000.00

MACRS Depreciation Tax %

Year 1 (170,000 x 33%) 56,100.00 40%

Year 2 (170,000 x 45%) 76,500.00 40%

Year 3 (170,000 x 15%) 25,500.00 40%

Year 4 (170,000 x 7%) 11,900.00

Tax on salvage value [(60,000 - 11,900) x 40%] 19,240.00

C. Year Cash flows PV factor

0 (178,000.00) 1.000000

1 52,440.00 0.892857

2 60,600.00 0.797194

3 88,960.00 0.711780

Net present value

The spectrometer should not be purchase because the net present value is negative.

PROBLEM 13-9A.

B. Base price (108,000.00)

Shipping and installation costs (12,500.00)


Net cost of machine (126,000.00)

C. Year 1 Year 2 Year 3

After-tax savings 28,600.00 28,600.00 28,600.00

Depreciation tax savings 13,917.75 18,978.75 6,326.25

Salvage value 65,000.00

Tax on salvage value (19,797.75)

Return of working capital 5,500.00

Project cash flows 42,517.75 47,578.75 85,628.50

Computations:

Before-tax labor cost 44,000.00

Tax (35%) (15,400.00)

After-tax savings 28,600.00

MACRS Depreciation Tax %

Year 1 (120,500 x 33%) 39,765.00 35%

Year 2 (120,500 x 45%) 54,225.00 35%

Year 3 (120,500 x 15%) 18,075.00 35%

Depreciation tax savings

22,440.00

(19,548.65)

(178,000.00)


13,917.75

18,978.75

30,600.00

10,200.00

PV of cash flows

46,821.43

48,309.95

63,319.97

The $5,000 spent last year on exploring the feasibility of the project is a sunk cost and should not be included in the

analysis.

6,326.25


4/23

Year 4 (120,500 x 7%) 8,435.00

Tax on salvage value [(65,000 - 8,435) x 35%] 19,797.75

D. Year Cash flows PV factor

0 (126,000.00) 1.000000

1 42,517.75 0.892857

2 47,578.75 0.797194

3 85,628.50 0.711780

Net present value

The machine should be purchase because the net present value is positive.

PROBLEM 13-10

Purchase price (8,000.00)

Sale of old machine 2,500.00

Tax on sale of old machine 160 (160.00)

Change in net working capital (2,000 - 500) (1,500.00)

Total investment (7,160.00)

Selling price 2,500.00

Book value (2,100.00)

Gain on sale 400.00

Tax on gain (2,100 x 40%) 160.00

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

1,500.00 3,000.00 4,500.00 6,000.00 7,500.00 9,000.00

500.00 884.00 468.00 244.00 212.00 52.00

800.00

Tax on SV (800 x 40%) (320.00)

1,500.00

-300

2,000.00 3,884.00 4,968.00 6,244.00 7,712.00 10,732.00

Computations:

Increase in sales 1,000.00

Decrease in cost 1,500.00

Pre-tax revenue increase 2,500.00

Tax (40%) (1,000.00)

After-tax revenue increase 1,500.00

MACRS 7200

Year 1 (8,000 x 20%) 1,600.00

Year 2 (8,000 x 32%) 2,560.00

Year 3 (8,000 x 19%) 1,520.00

Year 4 (8,000 x 12%) 960.00

Year 5 (8,000 x 11%) 880.00

Year 6 (8,000 x 6%) 480.00

Depreciation: Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

New 1,600.00 2,560.00 1,520.00 960.00 880.00 480.00

Old 350.00 350.00 350.00 350.00 350.00 350.00

Change 1,250.00 2,210.00 1,170.00 610.00 530.00 130.00

(126,000.00)

37,962.28

37,929.49

60,948.67

Depreciation tax

savings

Return of workingcapital

After-tax oppor-tunity

cost

Project cash flows

10,840.44

After-tax revenue

increase

Salvage value

PV of cash flows


5/23

Tax (40%) 500.00 884.00 468.00 244.00 212.00 52.00

Depreciation tax-

savings750.00 1,326.00 702.00 366.00 318.00 78.00

Pre-tax opportunity cost of old machine 500.00

Tax (40%) (200.00)

After-tax opportunity cost of old machine 300.00


0 (7,160.00) 1.000000

1 2,000.00 0.869565

2 3,884.00 0.756144

3 4,968.00 0.657516

4 6,244.00 0.571753

5 7,712.00 0.497177

10,732.00 0.432328 4,639.74

Net present value 12826.53

The machine replacement should be made because the net present value is positive.

PROBLEM 13-12

A. Project A

Probability Cash flow

0.20 x 60000.60 x 6750

0.20 x 7500

Expected annual cash flow

Project B

Probability Cash flow

0.20 x 0

0.60 x 6750

0.20 x 18000

Expected annual cash flow

A = SQRT[(6,000 - 6,750)2

x 0.20] + [(6,750 - 6,750)2

x 0.60] + [(7,500 - 6,750)2

x 0.20]A = SQRT[(-750

2x 0.20) + (0

2x 0.60) + (750

2x 0.20)]

A = 474.34

B = SQRT[(0 - 7,650)2 x 0.20] + [(6,750 - 7,650)2 x 0.60] + [(18,000 - 7,650)2 x 0.20]

B = SQRT[(02x 0.20) + (-900

2x 0.60) + (10,350

2x 0.20)]

B = 5797.84

CVA = 474.34 / 6,750

CVA = 0.070273

CVB

= 5,797.84 / 7,650

CVB = 0.757888

B.

Project A



1 - (1.10-3

)

0.10


PV of cash flows

(7,160.00)

1,739.13

2,936.86

3,266.54

12,826.53

3,570.03

3,834.23

3,600.00

7,650.00

Project B is the riskier project because it has the greater variability in its probable cash flows, whether me

standard deviation or the coefficient of variation. Hence, Project B is evaluated at the 12% cost of capital, w

requires only a 10% cost of capital.

1,500.00

6,750.00

Probable cash flow

Probable cash flow

-

4,050.00

1,200.004,050.00

6,750 16,786.25


6/23

Project B



1 - (1.12-3

)

0.12


Project B has the higher NPV; therefore, the firm should accept Project B.

C.

PROBLEM 13-13

A. Project A


0 (10,000.00) 1.000000

1 6,000.00 0.909091

2 8,000.00 0.826446

Net present value

Project B

Initial outlay


1 - (1.10-4

)

0.10

Net present value

Since neither project can be repeated, Project B should be selected because it has a higher NPV than Project A.

B. Project A's Extended NPV

Year 0 Year 1 Year 2 Year 3 Year 4

(10,000.00) 6000 8000

(10,000.00) 6000 8000(10,000.00) 6,000.00 (2,000.00) 6,000.00 8,000.00

Project A


0 (10,000.00) 1.000000

1 6,000.00 0.909091

2 (2,000.00) 0.826446

3 6,000.00 0.751315

4 8,000.00 0.683013

Net present value

Project BInitial outlay


1 - (1.10-4

)

0.10

Net present value

Since Project As extended NPV = $3,773.65, it should be selected over Project B with an NPV = $2,679.46.

C. Project A's EAA

1 - (1.10-4

)

0.10

(10,000.00)

2,066.12

PV of cash flows

(10,000.00)

5,454.55

6,611.57

7,650 18,374.01

The portfolio effects from Project B would tend to make it less risky than otherwise. This would tend to reinforce the dec

Project B. Again, if Project B were negatively correlated with the GDP (Project B is profitable when the economy is down)

risky and Project B's acceptance is reinforced.

12,679.46

12,679.46

(10,000.00)

4,000

2,679.46

3,733.65 / 1,190.48

(10,000.00)

5,454.55

(1,652.89)

3,773.65

4,507.89

5,464.11

4,000

2,679.46

PV of cash flows


7/23

Project B's EAA

1 - (1.10-4

)

0.10

Since Project As EAA = $1,190.48, it should be selected over Project B with an EAA = $845.29.

PROBLEM 13-14

Machine 190-3

Initial outlay


1 - (1.14-3

)

0.14

Net present value

Machine 190-3's Extended NPV

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

(190,000.00) 87,000.00 87,000.00 87,000.00

(190,000.00) 87,000.00 87,000.00 87,000.00

(190,000.00) 87,000.00 87,000.00 (103,000.00) 87,000.00 87,000.00 87,000.00


0 (190,000.00) 1.000000

1 87,000.00 0.877193

2 87,000.00 0.769468

3 (103,000.00) 0.674972

4 87,000.00 0.592080

5 87,000.00 0.519369

6 87,000.00 0.455587

Extended net present value

Machine 190-3's EAA

1 - (1.14-6

)

0.14

Machine 360-6

Initial outlay


1 - (1.14-6

)

0.14

Net present value

Machine 360-6's EAA

1 - (1.14-6

)

0.14

PROBLEM 13-17

Project X's NPV

Year Cash flow PV factor PV of CF

0 (100,000.00) 1.000000 (100,000.00)

1 30,000.00 0.892857 26,785.71

2 50,000.00 0.797194 39,859.69

3 70,000.00 0.711780 49,824.62

2,679.46 / 845.29

(190,000.00)

66,943.67

(69,522.07)

39,636.03

20,069.49

51,510.98

45,185.07

201,981.9987,000

11,981.99

PV of cash flows

(190,000.00)

76,315.79

22,256.02 / 5,723.30

Both new machines have positive NPVs; hence the old machine should be replaced. Further, since its NPV is gr

replacement chain approach and its EAA is higher than Model 190-3, choose Model 360-6.

11,981.99 / 5,161.02

(360,000.00)

382,256.0298,300

22,256.02


8/23


9/23

305,061.70 566,470.78

Year Cash flow Balance

- (270,000.00) (270,000.00)

1.00 97,800.00 (172,200.00)

2.00 109,800.00 (62,400.00)

3.00 79,800.00 17,400.004.00 71,800.00 89,200.00

5.00 101,600.00 190,800.00

0.35 -7663.52 (2,682.23) (42,463.72) 631,108,645.55

0.35 37035.13 12,962.30 2,234.93 1,748,218.45

0.3 81733.79 24,520.14 46,933.59 660,828,547.01

34,800.20 1,293,685,411.01

35,967.84

1.033553


10/23

should not be

possible after-

ales represent

fter-tax effect

would now be


11/23

e straight-line


12/23


13/23


14/23

2500 5000 7500 10000 12500 15000

1000 2000 3000 4000 5000 6000

sured by the

hile Project A


15/23

ision to accept

, then it is less


16/23

ater with the


17/23

Year 5

108,000.00

108,000.00

(43,200.00)

64,800.00

64,800.00

20,000.00

28,000.00

(11,200.00)101,600.00

15.97%


18/23

PROBLEM 13-10

Purchase price (8,000.00)

Sale of old machine 2,500.00

Tax on sale of old machine 160 (160.00)

Change in net working capital (2,000 - 500) (1,500.00)

Total investment (7,160.00)

Selling price 2,500.00

Book value (2,100.00)

Gain on sale 400.00

Tax on gain (2,100 x 40%) 160.00

Year 1 Year 2 Year 3 Year 4 Year 5

1,500.00 3,000.00 4,500.00 6,000.00 7,500.00

500.00 884.00 468.00 244.00 212.00

2,000.00 3,884.00 4,968.00 6,244.00 7,712.00

800.00

Tax on SV (800 x 40%) (128.00)

1,500.00

2,000.00 3,884.00 4,968.00 6,244.00 9,884.00

MACRS 7200

Year 1 (8,000 x 20%) 1,600.00

Year 2 (8,000 x 32%) 2,560.00

Year 3 (8,000 x 19%) 1,520.00

Year 4 (8,000 x 12%) 960.00

Year 5 (8,000 x 11%) 880.00

Year 6 (8,000 x 6%) 480.00

Depreciation: Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

New 1,600.00 2,560.00 1,520.00 960.00 880.00 480.00

Old 350.00 350.00 350.00 350.00 350.00 350.00

Change 1,250.00 2,210.00 1,170.00 610.00 530.00 130.00

Tax (40%) 500.00 884.00 468.00 244.00 212.00 52.00

Pre-tax opportunity cost of old machine 500.00

Tax (40%) (200.00)

After-tax opportunity cost of old machine 300.00


0 (7,160.00) 1.000000

1 2,000.00 0.869565

2 3,884.00 0.756144

3 4,968.00 0.657516

PV of cash flows

(7,160.00)

1,739.13

2,936.86

3,266.54

Project cash flows

After-tax revenue increase


Salvage value

Return of working capital

After-tax oppor-tunity cost


19/23

4 6,244.00 0.571753

5 9,884.00 0.497177

Net present value

4,914.09

9,266.66

3,570.03


20/23

PROBLEM 13-19

Year 0 Year 1 Year 2

Cost of the new machine (250,000.00)


Pre-tax cost savings 108,000.00 108,000.00

Depreciation (82,500.00) (112,500.00)Operating income before tax 25,500.00 (4,500.00)

Tax (40%) (10,200.00) 1,800.00

Operating income after tax 15,300.00 (2,700.00)

Depreciation 82,500.00 112,500.00

Operating cash flow 97,800.00 109,800.00

Return of net working capital

Sale of machine

Tax on sale (40% x 17,500)

Operating cash flows (270,000.00) 97,800.00 109,800.00

MACRS depreciation

1 250,000.00 X 33% 82,500.00

2 250,000.00 X 45% 112,500.00

3 250,000.00 X 15% 37,500.00

4 250,000.00 X 7% 17,500.00

5 250,000.00

Year Cash flow PV factor PV of CF

0 (270,000.00) 1.000000 (270,000.00) 0.10

1 97,800.00 0.909091 88,909.09 0.15

2 109,800.00 0.826446 90,743.80 0.203 120,800.00 0.751315 90,758.83

NPV 411.72

0.16

1 97,800.00 1 97,800.00 1.464100

2 109,800.00 1 109,800.00 1.331000

3 120,800.00 1 120,800.00 1.210000

328,400.00

0.1

1.00 97800 0.91 88,909.09

2.00 109800 0.27 30,126.53

3.00 120800 0.48 58,367.86

177,403.48

Year - Cash flow Balance

- - (270,000.00) (270,000.00)

1.00 - 97,800.00 (172,200.00)

2.00 - 109,800.00 (62,400.00)

3.00 - 120,800.00 58,400.00


21/23

#REF! #REF! #REF! #REF!

#REF! #REF! #REF! #REF!

0.35 -7663.52 (2,682.23) (7,663.52)

0.35 37035.13 12,962.30 37,035.130.3 81733.79 24,520.14 81,733.79

34,800.20


22/23

Year 3

108,000.00

(37,500.00)70,500.00

(28,200.00)

42,300.00

37,500.00

79,800.00

20,000.00

28,000.00

(7,000.00)

120,800.00

312,035.13

276,893.97

247,892.23

143,188.98 MIRR 17.28%

146,143.80

146,168.00

435,500.78


23/23

20,555,338.58

480,060,298.942,004,123,728.33

2,504,739,365.85

50,047.37

1.438135

mafin chapter 13

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