Question 1 (20 points): Consider an investment project that has the life time of
ID: 2781273 • Letter: Q
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Question 1 (20 points): Consider an investment project that has the life time of 10 years and requires the investment of $600,000 at time zero for machinery and equipment to be depreciated over 6 years with half year straight line depreciation method (starting in year 1 to year 7). Annual revenue is estimated to be $200,000 and annual operating costs of $50,000. $150,000 for working capital investment is also needed at time zero and working capital return is expected to equal the initial working capital investment at the end of the project (10h year). Salvage value of the machinery and equipment is expected to be zero. The minimum After Tax Cash Flow ROR is 10% and the effective income tax rate is 35%. Calculate After Tax Cash Flow, NPV, and ROR of the project. Question 2 (20 points): Calculate the depreciation for in question I using Declining Balance Depreciation method and declining balance rate of 180%, and the asset to be depreciated over 6 years. Show your work in detail for depreciation calculations please. Calculate After Tax Cash Flow, NPV, and ROR of the project and compare your results with question 1.Explanation / Answer
1a) Initial Investment=600,000
Depriciation=(Asset Value-Salvage Value)/Number of Years(Lifetime)
= (600,000-0)/10=60,000
Annual Revenue
200,000.00
Less Operating Costs
-50,000.00
Operating Income
150,000.00
Less Depreciation
-60,000.00
Profit Before Tax
90,000.00
Less Tax Charge (35% of 90,000)
-31,500.00
Income After tax
58,500.00
Add Depreciation
60,000.00
After Tax Cash Flow
118,500.00
Cash Inflow/Outflow
Cost of Equipment
Working Capital
After Tax Cash Flow
Return of Working Capital
Net Cash Flow
Discount Factor (1/(1+r)^n)
PV Net Cash Flow(Net Cash Flow *Discount Factor)
Year 0
-600,000.00
-150,000.00
0.00
0.00
-750,000.00
1.0000
-750,000.00
Year 1
0.00
0.00
118,500.00
0.00
118,500.00
0.9091
107,727.27
Year 2
0.00
0.00
118,500.00
0.00
118,500.00
0.8264
97,933.88
Year 3
0.00
0.00
118,500.00
0.00
118,500.00
0.7513
89,030.80
Year 4
0.00
0.00
118,500.00
0.00
118,500.00
0.6830
80,937.09
Year 5
0.00
0.00
118,500.00
0.00
118,500.00
0.6209
73,579.18
Year 6
0.00
0.00
118,500.00
0.00
118,500.00
0.5645
66,890.16
Year 7
0.00
0.00
118,500.00
0.00
118,500.00
0.5132
60,809.24
Year 8
0.00
0.00
0.00
0.00
0.00
0.4665
0.00
Year 9
0.00
0.00
0.00
0.00
0.00
0.4241
0.00
Year 10
0.00
0.00
0.00
150,000.00
150,000.00
0.3855
57,831.49
NPV
-115,260.88
(Note: In the above table r (discount rate) used is 10 %.)
The last part of the question asks us to find ROR. ROR is the discount rate that equates the NPV of the project equal to zero. Since no closed form solution exits for ROR you can use financial calculator or excel to find ROR. I am going to use excel. The syntax in excel for IRR is:
=IRR (values, [guess])
Where values is the array of PV of Net Cash Flow. Guess is an optional command and we can leave it as blank. Finally we get an IRR of -3.77%.
Conclusion: After Tax Cash Flow is $ 118,500, NPV is -$ 115,260.88, and IRR is -3.77%.
1b) with a straight line method depreciation % is expressed as:
1/number of years=1/6=16.67%
With declining balance method depreciation is going to be 1.8 time of 16.67 % which equals 30.01 %.
Depriciation Schedule
Year
Cost
Accumulated Depriciation
Open NBV (B-C)
Rate
Depriciation(D*E)
Accumulated Depc(C+F)
Closing NBV (B-G)
1
600,000
0
600,000
30.01%
180,060.00
180,060.00
419,940.00
2
600,000
180,060.00
419,940.00
30.01%
126,023.99
306,083.99
293,916.01
3
600,000
306,083.99
293,916.01
30.01%
88,204.19
394,288.19
205,711.81
4
600,000
394,288.19
205,711.81
30.01%
61,734.11
456,022.30
143,977.70
5
600,000
456,022.30
143,977.70
30.01%
43,207.71
499,230.01
100,769.99
6
600,000
499,230.01
100,769.99
30.01%
30,241.07
529,471.08
70,528.92
7
600,000
529,471.08
70,528.92
30.01%
21,165.73
550,636.81
49,363.19
So our net income and after tax cash flow will change every year now. Yearly cash flow table is given below:
Revenue
LessOperating Costs
Operating Income
Less Depreciation
Profit Before Tax
Tax Charge
Income After Tax
Add Depreciation
After Tax Cash Flow
Year 1
600,000
50,000
550,000
180,060.00
369,940.00
129,479.00
240,461.00
180,060.00
420,521.00
Year 2
600,000
50,000
550,000
126,023.99
423,976.01
148,391.60
275,584.40
126,023.99
401,608.40
Year 3
600,000
50,000
550,000
88,204.19
461,795.81
161,628.53
300,167.27
88,204.19
388,371.47
Year 4
600,000
50,000
550,000
61,734.11
488,265.89
170,893.06
317,372.83
61,734.11
379,106.94
Year 5
600,000
50,000
550,000
43,207.71
506,792.29
177,377.30
329,414.99
43,207.71
372,622.70
Year 6
600,000
50,000
550,000
30,241.07
519,758.93
181,915.62
337,843.30
30,241.07
368,084.38
Year 7
600,000
50,000
550,000
21,165.73
528,834.27
185,092.00
343,742.28
21,165.73
364,908.00
Cash Inflow/Outflow
Cost of Equipment
Working Capital
After Tax Cash Flow
Return of Working Capital
Net Cash Flow
Discount Factor (1/(1+r)^n)
PV Net Cash Flow(Net Cash Flow *Discount Factor)
Year 0
-600,000.00
-150,000.00
0.00
0.00
-750,000.00
1.0000
-750,000.00
Year 1
0.00
0.00
420,521.00
0.00
420,521.00
0.9091
382,291.82
Year 2
0.00
0.00
401,608.40
0.00
401,608.40
0.8264
331,907.77
Year 3
0.00
0.00
388,371.47
0.00
388,371.47
0.7513
291,789.23
Year 4
0.00
0.00
379,106.94
0.00
379,106.94
0.6830
258,935.14
Year 5
0.00
0.00
372,622.70
0.00
372,622.70
0.6209
231,369.38
Year 6
0.00
0.00
368,084.38
0.00
368,084.38
0.5645
207,774.03
Year 7
0.00
0.00
364,908.00
0.00
364,908.00
0.5132
187,255.51
Year 8
0.00
0.00
0.00
0.00
0.00
0.4665
0.00
Year 9
0.00
0.00
0.00
0.00
0.00
0.4241
0.00
Year 10
0.00
0.00
0.00
150,000.00
150,000.00
0.3855
57,831.49
NPV
1,199,154.37
Therefore, IRR of the project 36.67%.
Conclusion: With declining balance depreciation method our NPV becomes positive $ 1,199,154.37 and the IRR is positive at 36.67%.
Annual Revenue
200,000.00
Less Operating Costs
-50,000.00
Operating Income
150,000.00
Less Depreciation
-60,000.00
Profit Before Tax
90,000.00
Less Tax Charge (35% of 90,000)
-31,500.00
Income After tax
58,500.00
Add Depreciation
60,000.00
After Tax Cash Flow
118,500.00
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