A car-leasing agency purchases new cars each year for use in the agency. The cars
cost $15, 000 new. They are used for 3 years, after which they are sold for $3, 600.
The owner of the agency estimates that the variable costs of operating cars, exclusive
of gasoline, are $0. 16 per mile. Cars are leased at a flat rate of $0. 33 per mile
(gasoline not included).
a) What is the break-even mileage for the 3 −year period?
b) What are the total revenue, total cost, and total profit for the 3 −year period
if a car is leased for 50, 000 miles?
c) What price per mile must be charged in order to break-even if a car is leased for
50, 000 miles over a period of 3 years?
d) What price per mile must be charged in order to earn a profit of $5, 000 per car
over its 3 −year lifetime if it is leased for a total of 50, 000 miles?
Answers
Step-by-step explanation:
(a)new car cost = $ 15,00
selling price = $ 3,600
total fixed cost involved = 15000 - 3600
= $ 11,400
variable cost per miles =$ 0.16
revenue per mile = $ 0.33
contribution per mile = revenue per mile - variable cost per miles
= 0.33 - 0.16
=$ 0.17
\text{break\: even\: mileage} = \dfrac{\text{ fixed \: cost }}{\text{contribution \: per \: unit} }breakevenmileage=
contribution per unit
fixed cost
\text{ break\: even\: mileage } = \dfrac{11400 }{0.17 } breakevenmileage =
0.17
11400
=67058.82
(b) total number of miles = 50,000
total profit = contribution per miles x total miles - fixed cost
= 0.17 x 50,000 - 11400
= $ 8500 - 11400
= - $ 3100 (loss)
total cost = fixed cost + variable cost x total miles
= 11400 + 0.16 x 50,000
= 11400 + 8000
= $ 19400
total revenue = revenue per unit x total miles
= 0.33 x 50000
= $ 16500
(c)
if break even miles = 50,000
\text{ break\: even\: mileage }= \dfrac{\text{ fixed \: cost } }{\text{contribution \: per \: unit} } breakevenmileage =
contribution per unit
fixed cost
50,000 = \dfrac{11400 }{\text{contribution \: per \: mile }}50,000=
contribution per mile
11400
\text{ contribution \: per \: mile }= \dfrac{11400 }{50,000 } contribution per mile =
50,000
11400
contribution per miles = 0.228
(d)
profit = 5000
total revenue = profit + TC
= 5000 + 19400
= 24,400
\text{revenue per unit} = \dfrac{\text{total revenue} }{ \text{total miles}}=\dfrac{24400}{50000}=0.488revenue per unit=
total miles
total revenue
=
50000
24400
=0.488
(e) Level of output to earn zero profit-
total profit = contribution per miles x total miles - fixed cost
\Rightarrow 0= x\times 50,000 - 11400 \\ \Rightarrow x=\dfrac{11400}{50000}=0.228⇒0=x×50,000−11400
⇒x=
50000
11400
=0.228
Answer:
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