Perform a benefit cost analysis
- In anticipation of the 2010 Winter Olympics, a Vancouver entrepreneur invested $400,000 in equipment to make commemorative trading pins. Half of the price was paid in cash with the remaining $200,000 financed for two years at 10% interest with equal principal payments. The machine will be sold at the end of 2010 for $50,000. The table below is being used to determine the after-tax cash flows for the company. Assume that the company has an effective tax rate of 30% and complete the table to determine the after-tax cash flows. Does the after-tax cash flow beat a MARR of 40%?
(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%.
- The City Council members of Visalia, California, decided to purchase CNG-fueled garbage trucks, as opposed to traditional diesel trucks, at the cost of $260,000 each ($50,000 more than equivalent diesel trucks). The trucks are expected to cost the same in terms of operation, and the city has operated CNG buses before, thus alleviating concerns about maintenance costs. Make the following assumptions: The costs of owning and operating are given in Table 1 and the interest rate is 3.5% per year. (20 points)
- If cost were the only consideration, which technology should be chosen?
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.
- Perform a benefit-cost analysis. Assume that the cleaner air is valued at $15,000 per year. Which technology should be chosen?
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.
- To help pay for the CNG garbage trucks, the city received a $500,000 grant (to be divided among 13 trucks). Does this change the choice from (a)? How should it be incorporated into (b)?
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 |
- Consider the following projects and their cash flows (in millions):
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
- Carol currently pays $4500/yr in heating and cooling bills and is considering spending $15,000 to replace the windows in her house with triple-glazed windows. (15 points)
- If Carol expects the new windows to last 20 years, what is the minimum annual savings she would need to justify buying the windows? You should assume that her MARR is 12% and that heating and cooling costs will remain constant (and not increase due to inflation).
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.
- Suppose Carol thinks that the windows will save $2100/yr, but that she plans on selling the house in 12 years. How much additional value would she need for the windows to add to her house to justify the purchase?
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.
- Nypro is investing $50,000 in a vision system that will inspect molded parts. The system is expected to save $11,000 in rework costs each year. (15 points)
- If Nypro’s MARR is 10% what is the discounted payback period (e.g. payback period with interest)?
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 |
||||
- Besides the fact that the Payback Period does not consider a company’s MARR, state one shortcoming and one benefit of using the Payback Period to evaluate a project.
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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