PLEASE PROVIDE CASH FLOW DIAGRAM AND SHOW ALL WORK! 1. How much would the owner
ID: 2563937 • Letter: P
Question
PLEASE PROVIDE CASH FLOW DIAGRAM AND SHOW ALL WORK!
1. How much would the owner of a pickup truck be justified in paying for the vehicle to be converted to operate on compressed natural gas if the vehicle accumulates 20,000 miles per annum with an average 12 mpg, the savings in fuel costs amounts to $0.50/gallon, the life of the conversion system is 10 years, and the salvage value of the conversion system is 15 percent of its initial cost? Assume that the time value of money is 10 percent Answer $5,434Explanation / Answer
Accumulated Miles per year = 20,000
Millage = 12m/gallon
Required gallon per year = 20,000 /12 = 1666.666667
Saving per year = $ 0.5 x 1666.666667 = $ 833.3333333
Let’s assume the initial cost of conversion be X.
Cash flow from year 1 to 9 = $ 833 per year
Salvage value = 15 % x X = 0.15X
For 10th year cash flow = $ 833 + 0.15 X
Year(n)
Cash flow('C)
PV Factor, F=[1/(1+i)n] @ 16%
PV = C x F
0
X
1/(1+0.1)0
1.0000
X
1
$ 833
1/(1+0.1)1
0.9091
$ 757.57
2
$ 833
1/(1+0.1)2
0.8264
$ 688.70
3
$ 833
1/(1+0.1)3
0.7513
$ 626.09
4
$ 833
1/(1+0.1)4
0.6830
$ 569.18
5
$ 833
1/(1+0.1)5
0.6209
$ 517.43
6
$ 833
1/(1+0.1)6
0.5645
$ 470.39
7
$ 833
1/(1+0.1)7
0.5132
$ 427.63
8
$ 833
1/(1+0.1)8
0.4665
$ 388.75
9
$ 833
1/(1+0.1)9
0.4241
$ 353.41
10
833.33 + 0.15X
1/(1+0.1)10
0.3855
0.3855(833.33+0.15)X
Total PV of cash flows from year 1 to 9
$ 4,799.17
If initial cost of conversion is same as present value of all cash flows, then cost of conversion is justified.
0.3855($ 833.33+0.15X) + $ 4,799.17 = X
$ 321.2860745 + 0.057831X + $ 4,799.17= X
X - 0.057831X = $ 321.2860745 + $ 4,799.17
0.942169 X = $ 5,120.45
X = $ 5,434.75
Year(n)
Cash flow('C)
PV Factor, F=[1/(1+i)n] @ 16%
PV = C x F
0
X
1/(1+0.1)0
1.0000
X
1
$ 833
1/(1+0.1)1
0.9091
$ 757.57
2
$ 833
1/(1+0.1)2
0.8264
$ 688.70
3
$ 833
1/(1+0.1)3
0.7513
$ 626.09
4
$ 833
1/(1+0.1)4
0.6830
$ 569.18
5
$ 833
1/(1+0.1)5
0.6209
$ 517.43
6
$ 833
1/(1+0.1)6
0.5645
$ 470.39
7
$ 833
1/(1+0.1)7
0.5132
$ 427.63
8
$ 833
1/(1+0.1)8
0.4665
$ 388.75
9
$ 833
1/(1+0.1)9
0.4241
$ 353.41
10
833.33 + 0.15X
1/(1+0.1)10
0.3855
0.3855(833.33+0.15)X
Total PV of cash flows from year 1 to 9
$ 4,799.17
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.