(20 points)
Year |
||||
Description |
2007 |
2008 |
2009 |
2010 |
Revenues |
||||
Total Revenue |
$400,000 |
$800,000 |
$ 1,500,000 |
|
Expenses |
||||
Production Costs |
($250,000) |
($450,000) |
($700,000) |
|
Interest (10%) |
$ -20,000.00 |
$ -10,000.00 |
||
Depreciation |
$ -1,00,000.00 |
$ -1,00,000.00 |
$ -1,00,000.00 |
$ -1,00,000.00 |
Total Expenses |
||||
Taxable Income |
$ -1,00,000.00 |
$ 30,000.00 |
$ 2,40,000.00 |
$ 7,00,000.00 |
Income Tax (30%) |
$ -30,000.00 |
$ 9,000.00 |
$ 72,000.00 |
$ 2,10,000.00 |
Profit A/T |
$ -70,000.00 |
$ 21,000.00 |
$ 1,68,000.00 |
$ 4,90,000.00 |
CFAT |
$ 1,70,000.00 |
$ 1,21,000.00 |
$ 2,68,000.00 |
$ 5,90,000.00 |
Loan repayment |
$ 1,00,000.00 |
$ 1,00,000.00 |
||
CFAT(Adjusted ) Net |
$ 1,70,000.00 |
$ 21,000.00 |
$ 1,68,000.00 |
$ 5,90,000.00 |
Loan Principal |
$200,000 |
|||
Purchase/Sale |
($400,000) |
|||
Gain/Loss Tax |
||||
Cash Flow A/T |
($200,000) |
|||
Book Value |
$400,000 |
Cash Flows |
PV @ 30% |
NPV |
|
Year 0 |
$ -2,00,000.00 |
1 |
$ -2,00,000.00 |
Year 1 |
$ 1,70,000.00 |
0.769 |
$ 1,30,730.00 |
Year 2 |
$ 21,000.00 |
0.591 |
$ 12,411.00 |
Year 3 |
$ 1,68,000.00 |
0.4547 |
$ 76,389.60 |
Year 4 |
$ 5,90,000.00 |
0.3497 |
$ 2,06,323.00 |
Year4(tv) |
$ 50000 |
0.3497 |
$ 17,485 |
$ 2,43,338.60 |
|||
Cash Flows |
PV @ 60% |
||
Year 0 |
$ -2,00,000.00 |
1 |
$ -2,00,000.00 |
Year 1 |
$ 1,70,000.00 |
0.625 |
$ 1,06,250.00 |
Year 2 |
$ 21,000.00 |
0.391 |
$ 8,211.00 |
Year 3 |
$ 1,68,000.00 |
0.244 |
$ 40,992.00 |
Year 4 |
$ 5,90,000.00 |
0.1526 |
$ 90,034.00 |
Year4(tv) |
$ 50000 |
0.1526 |
$ 7,630 |
$ 53117.00 |
From the above calculation, we can see that the above projects IRR is much more than 60%. hence this project beats the criteria of MARR 40%.
Table 1. Ownership and annual operational costs for
CNG and diesel garbage trucks
Parameter Diesel CNG
Initial Cost $210,000 $260,000
O&M Cost $15,000 $15,000
Annual Increase $1,000 $3,000
Salvage Value $10,000 $30,000
Service Life 8 8
Solution (a).
Diesel |
$ 1 |
$ 2 |
$ 3 |
$ 4 |
$ 5 |
$ 6 |
$ 7 |
$ 8 |
|
Intial Cost |
$ 2,10,000 |
||||||||
O&M Cost |
$ 15,000 |
$ 16,000 |
$ 17,000 |
$ 18,000 |
$ 19,000 |
$ 20,000 |
$ 21,000 |
$ 22,000 |
|
Less: SV |
$ -10,000 |
||||||||
Cash Outflow |
$ 2,25,000 |
$ 16,000 |
$ 17,000 |
$ 18,000 |
$ 19,000 |
$ 20,000 |
$ 21,000 |
$ 12,000 |
|
$ 1.0000 |
$ 0.9662 |
$ 0.9335 |
$ 0.9019 |
$ 0.8714 |
$ 0.8419 |
$ 0.8135 |
$ 0.7860 |
||
NPV(CO) |
$ 2,25,000 |
$ 15,459 |
$ 15,870 |
$ 16,235 |
$ 16,557 |
$ 16,838 |
$ 17,084 |
$ 9,432 |
$ 3,32,474 |
CNG |
|||||||||
$ 1 |
$ 2 |
$ 3 |
$ 4 |
$ 5 |
$ 6 |
$ 7 |
$ 8 |
||
Intial Cost |
$ 2,60,000 |
||||||||
O&M Cost |
$ 15,000 |
$ 18,000 |
$ 21,000 |
$ 24,000 |
$ 27,000 |
$ 30,000 |
$ 33,000 |
$ 36,000 |
|
Less: SV |
$ -30,000 |
||||||||
Cash Outflow |
$ 2,75,000 |
$ 18,000 |
$ 21,000 |
$ 24,000 |
$ 27,000 |
$ 30,000 |
$ 33,000 |
$ 6,000 |
|
$ 1.0000 |
$ 0.9662 |
$ 0.9335 |
$ 0.9019 |
$ 0.8714 |
$ 0.8419 |
$ 0.8135 |
$ 0.7860 |
||
NPV(CO) |
$ 2,75,000 |
$ 17,391 |
$ 19,604 |
$ 21,647 |
$ 23,529 |
$ 25,257 |
$ 26,846 |
$ 4,716 |
$ 4,13,989 |
Hence the Diesel garbage truck cost is less hence it is preferred.
Solution b :
CNG ( Clean air benefit) |
|||||||||
$ 1 |
$ 2 |
$ 3 |
$ 4 |
$ 5 |
$ 6 |
$ 7 |
$ 8 |
||
Intial Cost |
$ 2,60,000 |
||||||||
O&M Cost |
$ 15,000 |
$ 18,000 |
$ 21,000 |
$ 24,000 |
$ 27,000 |
$ 30,000 |
$ 33,000 |
$ 36,000 |
|
Less: SV |
$ -30,000 |
||||||||
Less: CAB |
$ -15,000 |
$ -15,000 |
$ -15,000 |
$ -15,000 |
$ -15,000 |
$ -15,000 |
$ -15,000 |
$ -15,000 |
|
Cash Outflow |
$ 2,60,000 |
$ 3,000 |
$ 6,000 |
$ 9,000 |
$ 12,000 |
$ 15,000 |
$ 18,000 |
$ 21,000 |
|
$ 1.0000 |
$ 0.9662 |
$ 0.9335 |
$ 0.9019 |
$ 0.8714 |
$ 0.8419 |
$ 0.8135 |
$ 0.7860 |
||
NPV(CO) |
$ 2,60,000 |
$ 2,899 |
$ 5,601 |
$ 8,117 |
$ 10,457 |
$ 12,629 |
$ 14,643 |
$ 16,506 |
$ 3,30,852 |
With clean air benefits, it is better to buy a CNG truck.
Solution c :
CNG ( with grant option a )
CNG ( with grant option a ) |
|||||||||
$ 1 |
$ 2 |
$ 3 |
$ 4 |
$ 5 |
$ 6 |
$ 7 |
$ 8 |
||
Intial Cost |
$ 2,60,000 |
||||||||
O&M Cost |
$ 15,000 |
$ 18,000 |
$ 21,000 |
$ 24,000 |
$ 27,000 |
$ 30,000 |
$ 33,000 |
$ 36,000 |
|
Less: SV/grant |
$ -38,462 |
$ -30,000 |
|||||||
Cash Outflow |
$ 2,36,538 |
$ 18,000 |
$ 21,000 |
$ 24,000 |
$ 27,000 |
$ 30,000 |
$ 33,000 |
$ 6,000 |
|
$ 1.0000 |
$ 0.9662 |
$ 0.9335 |
$ 0.9019 |
$ 0.8714 |
$ 0.8419 |
$ 0.8135 |
$ 0.7860 |
||
NPV(CO) |
$ 2,36,538 |
$ 17,391 |
$ 19,604 |
$ 21,647 |
$ 23,529 |
$ 25,257 |
$ 26,846 |
$ 4,716 |
$ 3,75,527 |
(CNG clean air benefits – with grant option b )
CNG ( Clean air benefit)( with grant option b) |
|||||||||
$ 1 |
$ 2 |
$ 3 |
$ 4 |
$ 5 |
$ 6 |
$ 7 |
$ 8 |
||
Intial Cost |
$ 2,60,000 |
||||||||
O&M Cost |
$ 15,000 |
$ 18,000 |
$ 21,000 |
$ 24,000 |
$ 27,000 |
$ 30,000 |
$ 33,000 |
$ 36,000 |
|
Less: SV/grant |
$ -38,462 |
$ -30,000 |
|||||||
Less: CAB |
$ -15,000 |
$ -15,000 |
$ -15,000 |
$ -15,000 |
$ -15,000 |
$ -15,000 |
$ -15,000 |
$ -15,000 |
|
Cash Outflow |
$ 2,21,538 |
$ 3,000 |
$ 6,000 |
$ 9,000 |
$ 12,000 |
$ 15,000 |
$ 18,000 |
$ 21,000 |
|
$ 1.0000 |
$ 0.9662 |
$ 0.9335 |
$ 0.9019 |
$ 0.8714 |
$ 0.8419 |
$ 0.8135 |
$ 0.7860 |
||
NPV(CO) |
$ 2,21,538 |
$ 2,899 |
$ 5,601 |
$ 8,117 |
$ 10,457 |
$ 12,629 |
$ 14,643 |
$ 16,506 |
$ 2,92,390 |
Project Period
------------------------------------------------------------------------
0 1 2 3 4 5
------------------------------------------------------------------------
1 -$322 $178 $228 $278 $328 $378
2 -$427 $122 $122 $122 $122 $122
3 -$314 $157 $131 $109 $91 $76
4 -$398 $118 $184 $183 $117 $138
Find the best project using any of the analysis methods from this class, assuming a MARR of 18%. (15 points)
Solution :
Project |
|||||||
Year |
0 |
1 |
2 |
3 |
4 |
5 |
|
Cash Flows |
$ 1 |
$ -322 |
$ 178 |
$ 228 |
$ 278 |
$ 328 |
$ 378 |
PV @ 18% |
1 |
0.8475 |
0.7181 |
0.6086 |
0.5157 |
0.4371 |
|
NPV |
$ -322.00 |
$ 150.86 |
$ 163.73 |
$ 169.19 |
$ 169.15 |
$ 165.22 |
$ 496.15 |
Cash Flows |
$ 2 |
$ -427 |
$ 122 |
$ 122 |
$ 122 |
$ 122 |
$ 122 |
PV @ 18% |
1 |
0.8475 |
0.7181 |
0.6086 |
0.5157 |
0.4371 |
|
NPV |
$ -427.00 |
$ 103.40 |
$ 87.61 |
$ 74.25 |
$ 62.92 |
$ 53.33 |
$ -45.51 |
Cash Flows |
$ 3 |
$ -314 |
$ 157 |
$ 131 |
$ 109 |
$ 91 |
$ 76 |
PV @ 18% |
1 |
0.8475 |
0.7181 |
0.6086 |
0.5157 |
0.4371 |
|
NPV |
$ -314.00 |
$ 133.06 |
$ 94.07 |
$ 66.34 |
$ 46.93 |
$ 33.22 |
$ 59.61 |
Cash Flows |
$ 4 |
$ -398 |
$ 118 |
$ 184 |
$ 183 |
$ 117 |
$ 138 |
PV @ 18% |
1 |
0.8475 |
0.7181 |
0.6086 |
0.5157 |
0.4371 |
|
NPV |
$ -398.00 |
$ 100.01 |
$ 132.13 |
$ 111.37 |
$ 60.34 |
$ 60.32 |
$ 66.17 |
The best investment is in Project 1 as it has got the highest NPV of 496.15
PV = Annual Annuity x (1+r/100)n
$ 15000 = Annual Annuity x ( 1 + 12/100 )20
$ 15000 = Annual Annuity x 9.646
Annual Annuity = $ 15000 / 9.646 = $ 1555 per year savings will be required to justify the investment in the window.
PV = Annual Annuity x (1+r/100)n
$ 15000 = Annual Annuity x ( 1 + 12/100 )12
$ 15000 = Annual Annuity x 3.8960
Annual Annuity( Savings ) = $ 15000 / 3.8960 = $ 3850 per annum.
Additional savings are required per year to justify the investments
= $ 3850 - $ 2100 = $ 1750 per year additional savings is required to justify the investment in 12 years.
Solutions :
PV @ 10% |
PV |
Cumulative PV |
||
Year 0 |
$ -50,000.00 |
|||
Year 1 |
$ 11,000.00 |
0.909 |
$ 9,999.00 |
$ 9,999.00 |
year 2 |
$ 11,000.00 |
0.826 |
$ 9,086.00 |
$ 19,085.00 |
year 3 |
$ 11,000.00 |
0.753 |
$ 8,283.00 |
$ 27,368.00 |
year 4 |
$ 11,000.00 |
0.683 |
$ 7,513.00 |
$ 34,881.00 |
year 5 |
$ 11,000.00 |
0.621 |
$ 6,831.00 |
$ 41,712.00 |
year 6 |
$ 11,000.00 |
0.564 |
$ 6,204.00 |
$ 47,916.00 |
year 7 |
$ 11,000.00 |
0.513 |
$ 5,643.00 |
$ 53,559.00 |
year 8 |
$ 11,000.00 |
0.466 |
$ 5,126.00 |
$ 58,685.00 |
Discounted pay back Period |
= 6.369 years |
|||
6 years & 5 months |
Answer: The payback period does not consider the Inflation factor ( interest cost) this is the biggest shortcoming.
The other shortcoming is that it does not consider post Payback period cash flows.
Benefits: Based on the payback period we select those projects only which recover its investments faster than the other projects.
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