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Assume that you are considering to buy a Toyota Corolla automobile
Assume that you are considering to buy a Toyota Corolla automobile. You need to select one of the Diesel and Gasoline option. The related information is given in the following table. The car will be used for 5 years and then it will be sold. What is the annual average distance that makes Diesel and Gasoline option equivalent (1=10%). Price (TL) Insurance (TL/year) Fuel cost (LTL) Fuel consumption (Lt/km) Salvage value after 5 years. (TL) Diesel 94000 700 4.44 0.042 70000 Gasoline 78000 700 5.16 0.058 58000 Select one: O a. 27000 - O b. 17000 O c. 12000 O d. 7000 O e. 37000 O f. 19992
Expert Solution
Price of diesel car is 16,000 more than gasoline car.
Present value of salvage of diesel car after 5 years = [70,000 / 1.1^5] = 43,464.49
Present value of salvage of gasoline car after 5 years = [58,000 / 1.1^5] = 36,013.43
It means that you tend to pay 16,000 - 43,464.49 + 36,013,42 = 8,548.94 extra for diesel car.
Let say you drive X km every year.
Annual fuel cost of diesel car = X * 0.042 * 4.44 = 0.186X. Likewise, annuam fuel cost of gasoline car is X * 058 * 5.16 = 0.299X. Difference of present value of annual fuel cost (0.299X - 0.186X = 0.113X)would be equal to 8,548.94 to make both alternative equally feasible.
Present value is calculated as: [Annual Cost / (1 + Rate of Interest)^Year]
Present value of first year of difference of these annual cost is [0.113X / 1.1] = 0.103X
Present value of second year of difference of these annual cost is [0.113X / 1.1^2] = 0.093X
Present value of third year of difference of these annual cost is [0.113X / 1.1^3] = 0.085X
Present value of forth year of difference of these annual cost is [0.113X / 1.1^4] = 0.077X
Present value of fifth yearof difference of these annual cost is [0.113X / 1.1^5] = 0.070X
Sum of present value = 0.428X which is equal to 8,548.94
Thus, X = 19,992
Option F is correct.
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