Chapter 2A, Problem 2A.2E

1.

To determine

Introduction:

Variable costs and Fixed costs:

Variable costs are those that increase or decrease with the general volume of work. Some of the examples of variable costs are sales commissions, labor costs, raw material costs, etc. Fixed costs are those costs that remain fixed irrespective of the volume of work. Some of the examples of fixed costs are office rent, administrative expenses, depreciation, etc.

Least square regression method:

The least-square regression method uses the regression line to classify the total cost into variable and fixed cost and thus minimizing the sum of squares of the errors and hence we can get the best line of fit with minimum variances. The least-square regression can be expressed as Y = a + bx

Where Y is Total cost

A is the total fixed cost

B is the variable cost

X is the activity level

To prepare: a scatter plot graph.

Answer to Problem 2A.2E

This is the scatterplot graph for the B rental car.

  

Explanation of Solution

According to the given information the rental returns and car wash costs of B rental cars have been given and we have to prepare a scatter graph plot where the car wash cost should be on the vertical axis and the rental returns on the horizontal axis. To prepare the scatter graph first we have to go to insert option and select scatter graph from charts. The next step is to enter the X values and Y values and then we will get the graph. Now we can add trend line and axis title by clicking on the + symbol next to the graph. After adding the trend line we can click on the arrow button next to the trend line and select more options and then in that we have to checkmark display equation and display R squared value on the chart. The following is the data for plotting the graph:

Rental returns	Car wash costs ($)
2380	10825
2421	11865
2586	11332
2725	12422
2968	13850
3281	14419
3353	14935
3489	15738
3057	13563
2876	11889
2735	12683
2983	13796

2.

To determine

Introduction:

Variable costs are those that increase or decrease with the general volume of work. Some of the examples of variable costs are sales commissions, labor costs, raw material costs, etc. Fixed costs are those costs that remain fixed irrespective of the volume of work. Some of the examples of fixed costs are office rent, administrative expenses, depreciation, etc.

Least square regression method:

The least-square regression method uses the regression line to classify the total cost into variable and fixed cost and thus minimizing the sum of squares of the errors and hence we can get the best line of fit with minimum variances. The least-square regression can be expressed as Y = a + bx

Where Y is Total cost

A is the total fixed cost

B is the variable cost

X is the activity level

To calculate: the variable cost per rental return and the monthly fixed washing cars using least square regression method.

Answer to Problem 2A.2E

Thus, the variable cost per unit is $4.04 and the fixed cost per unit is $145583 for Bargain rental car.

Explanation of Solution

To calculate the variable cost per rental return and the monthly fixed washing cars using the least square regression method first we have to calculate the X, Y, X² and XY. In the given data the rental return is taken as X and car wash costs is taken as Y, let us now calculate the X² and XY:

Months	X	Y	X2	XY
January	2380	10825	5664400	25763500
February	2421	11865	5861241	28725165
March	2586	11332	6687396	29304552
April	2725	12422	7425625	33849950
May	2968	13850	8809024	41106800
June	3281	14419	10764961	47308739
July	3353	14935	11242609	50077055
August	3489	15738	12173121	54909882
September	3057	13563	9345249	41462091
October	2876	11889	8271376	34192764
November	2735	12683	7480225	34688005
December	2983	13796	8898289	41153468
Total	34854	157317	102623516	462541971

Now let us calculate the variable cost using following formula:

Variable cost per unit

  $\begin{array}{l}\begin{array}{l}=\frac{\left(n\sum XY-\sum X\times \sum Y\right)}{(n\sum X^2-{(\sum X)}^2)}\\ =\frac{\left(12\times 462541971–\left(34854\times 157317\right)\right)}{\left(12\times 102623516–{\left(34854\right)}^2\right)}\end{array}\hfill \\ =\frac{(5550503652-5483126718}{(1231482192-1214801316}\hfill \\ \hfill \\ =67376934/16680876=\$4.04\hfill \end{array}$

Now, let us calculate the fixed cost per unit using following formula:

Fixed cost per unit

  $\begin{array}{l}\begin{array}{l}=\frac{\sum Y–\left(variablecostperunit\times \sum X\right)}{n}\\ =\frac{157317-\left(4.04\times 34854\right)}{12}\end{array}\hfill \\ \hfill \\ =157317–11734.18=\$145583\hfill \end{array}$