9 A suburban taxi company is considering buying taxis with diesel engines instea
ID: 1111351 • Letter: 9
Question
9 A suburban taxi company is considering buying taxis with diesel engines instead of gasoline engines. The cars average 50,000 kilometers a year, with a useful life of three years for the taxi with the gasoline engine, and four years for the diesel taxi. Other comparative information is as follows: Description Fuel cost per liter Mileage in km/liter Diesel $13,000 481 Gasoline $12,000 511 200 500 3,000 Annual repairs Annual Insurance 300 500 2,000 Salvage value Determine the more economical choice if interest is 6%.Explanation / Answer
Answer:
(1) Annual fuel cost = (Number of KM per year / mileage) x Fuel cost per liter
Diesel car: (50,000 / 35) x $0.48 = $686
Gasoline car: (50,000 / 28) x $0.51 = $911
(2)
Total annual cost = Fuel + Repairs + Insurance
Diesel: $(686 + 300 + 500) = $1,486
Gasoline: $(911 + 200 + 500) = $1,611
(3) For both cars, Terminal year annual cost = Total Annual cost - Salvage value
Diesel: $(1,486 - 2,000) = - $514
Gasoline: $(1,611 - 3,000) = - $1,389
We perform Present Worth (PW) analysis as follows.
Diesel
Year
Initial Cost ($)
Annual Total Cost ($)
Annual Cash Outflow
Discount Factor @6%
Discounted Cash Flow
(1)
(2)
(3) = (1) + (2)
(4)
(3) x (4)
0
13,000
13,000
1.0000
13,000
1
1,486
1,486
0.9434
1,402
2
1,486
1,486
0.8900
1,323
3
-514
-514
0.8396
-432
PW =
15,293
Gasoline
Year
Initial Cost ($)
Annual Total Cost ($)
Annual Cash Outflow
Discount Factor @6%
Discounted Cash Flow
(1)
(2)
(3) = (1) + (2)
(4)
(3) x (4)
0
12,000
12,000
1.0000
12,000
1
1,611
1,611
0.9434
1,520
2
1,611
1,611
0.8900
1,434
3
1,611
1,611
0.8396
1,353
4
-1,389
-1,389
0.7921
-1,100
PW =
15,206
Since PW of costs for gasoline cars is lower, this is the better choice.
Diesel
Year
Initial Cost ($)
Annual Total Cost ($)
Annual Cash Outflow
Discount Factor @6%
Discounted Cash Flow
(1)
(2)
(3) = (1) + (2)
(4)
(3) x (4)
0
13,000
13,000
1.0000
13,000
1
1,486
1,486
0.9434
1,402
2
1,486
1,486
0.8900
1,323
3
-514
-514
0.8396
-432
PW =
15,293
Gasoline
Year
Initial Cost ($)
Annual Total Cost ($)
Annual Cash Outflow
Discount Factor @6%
Discounted Cash Flow
(1)
(2)
(3) = (1) + (2)
(4)
(3) x (4)
0
12,000
12,000
1.0000
12,000
1
1,611
1,611
0.9434
1,520
2
1,611
1,611
0.8900
1,434
3
1,611
1,611
0.8396
1,353
4
-1,389
-1,389
0.7921
-1,100
PW =
15,206
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