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The following Information applies to the questions displayed below.) Bargain Rental Car offers rental cars in an off-airport location near a major tourist destination in California. Management would like to better understand the variable and fixed portions of It car washing costs. The company operates its own car wash facility in which each rental car that is returned is thoroughly cleaned before being released for rental to another customer. Management belleves that the variable portion of its car washing costs relates to the number of rental returns. Accordingly, the following data have been compiled:
Month Rental Returns Car Wash Costs
January 2,380 $ 10,825
February 2,421 $ 11,865
March 2,586 $ 11,332
April 2725 $ 12422
May 2968 $ 13850
June 3281 $ 14419
July 3,353 $ 14,935
August 3,489 $ 15,738
September 3,057 $ 13,563
October 2,876 $ 11,889
November 2,735 $ 12,683
December 2,983 $ 13,796
Using least-squares regression, estimate the variable cost per rental return and the monthly fixed cost Incurred to wash cars. (Round Fixed cost to the nearest whole dollar amount and the Varlable cost per unit to 2 decimal places.)

Answer :

Answer:

a. The variable cost per rental return is $4.04.

b. The monthly fixed cost Incurred to wash cars is $1,376.

Explanation:

Note: See the attached excel file for the calculations of Rental Returns (x), Car Wash Costs (y), xy, and x^2.

Since Σ = Total of or summation of, we can therefore obtain the following from the attached excel file:

Σx = 34,854

Σy = 157,317

Σxy = 462,541,971

Σx^2 = 102,623,516

N = Number of months = 12

a. calculation of variable cost per rental return

To calculate the variable cost per rental return, the following formula is used:

Variable cost per rental return = (NΣxy − ΣxΣy) /((NΣx²) − (Σx)²) ……………… (1)

Substituting the relevant values into equation (1), we have:

Variable cost per rental return = ((12 * 462,541,971) - (34,854 * 157,317)) / (((12 * 102,623,516) - 34,854^2)

Variable cost per rental return = 4.03917240317595

Rounding to 2 decimal places as required, we have:

Variable cost per rental return = $4.04

Therefore, the variable cost per rental return is $4.04.

b. Calculation of monthly fixed cost Incurred to wash cars

To calculate the monthly fixed cost Incurred to wash cars, the following formula is used:

Fixed Cost per month =  {Σy - (Variable cost per rental return * Σx) / N ....... (2)

Substituting the relevant values into equation (2), we have:

Fixed Cost per month = (157,317 - (4.04 * 34,854)) / 12

Fixed Cost per month = $1,375.57

Rounding to the nearest whole dollar amount as required, we have:

Fixed Cost per month = $1,376

Therefore, the monthly fixed cost Incurred to wash cars is $1,376.

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The variable cost per rental return is $4.04 and the fixed cost per month is $1378.

The following can be depicted from the question

Σx = 34,854

Σy = 157,317

Σxy = 462,541,971

Σx² = 102,623,516

N = number of months = 12

Variable cost per rental return will be:

= ( N Σxy − Σx Σy)/{(N Σx²) − (Σx)²}

= {( 12 × 462,541,971) - (34,854 × 157,317) } / {(12 ×102,623,516) - (34,854)²}

= (5,550,503,652 - 5,483,126,718) / (1231482192 - 1214801316)

= 67,376,934 / 16680876

= $4.04

Fixed Cost per month will be:

=  {Σy - ( Variable cost per rental return × Σx )/N

= {157,317 - (4.04 × 34,854)} /12

= ( 157,317 - 140,810.16) /12

= $1378

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