Chapter 5, Problem 45E

Interpretation of Regression Results: Multiple Choice

Cortez Company is planning to introduce a new product that will sell for $96 per unit. The following manufacturing cost estimates have been made on 20,000 units to be produced the first year:

Manufacturing overhead costs have not yet been estimated for the new product, but monthly data on total production and overhead costs for the past 24 months have been analyzed using simple linear regression. The following results were derived from the simple regression and provide the basis for overhead cost estimates for the new product:

Required

1. a.      What percentage of the variation in overhead costs is explained by the independent variable?
   1. (1) 84.8%.
   2. (2) 45.0%.
   3. (3) 92.1%.
   4. (4) 8.48%.
   5. (5) Some other amount.
2. b.      What is the total overhead cost for an estimated activity level of 50,000 direct labor-hours?
   1. (1) $120,000.
   2. (2) $370,000.
   3. (3) $250,000.
   4. (4) $320,000.
   5. (5) Some other amount.
3. c.       How much is the variable manufacturing cost per unit, using the variable overhead estimated by the regression (assuming that direct materials and direct labor are variable costs)?
   1. (1) $88.00.
   2. (2) $82.00.
   3. (3) $86.80.
   4. (4) $72.00.
   5. (5) Some other amount.
4. d.      What is the expected contribution margin per unit to be earned during the first year on 20,000 units of the new product? (Assume that all marketing and administrative costs are fixed.)
   1. (1) $96.00
   2. (2) $24.00
   3. (3) $56.00
   4. (4) $14.00
   5. (5) Some other amount.
5. e.       What is the manufacturing cost equation implied by these results?
   1. (1) Total cost = $640,000 + ($5.00 × Number of units).
   2. (2) Total cost = $120,000 + ($86.80 × Number of units).
   3. (3) Total cost = $120,000 + ($72.00 × Number of units).
   4. (4) Some other equation.

To determine

Identify the appropriate answer for the given statement from the given choices.

Answer to Problem 45E

Option (1) The percentage of the variation in overhead costs is 84.8%.

Explanation of Solution

Regression analysis:

Regression analysis is used to show the relationship between the cost and the activity. It is used to estimate the cost at various level of activity.

The most important step in the calculation of regression analysis is to establish a logical relationship between the cost and the activity. The activity (independent variable) is placed on the right-hand side and the cost (dependent variable) is placed on the left-hand side of the graph.

Percentage of the variation in overhead costs is explained by the independent variable:

The percentage of the variation in overhead costs is 84.8% as per the value of R^2.

Justification for the correct and incorrect answer:

(1)

84.8%: This is the correct figure as the value is equal to the value of R².

(2)

45.0%: This is an incorrect figure as the value is not matching with the value of R².

(3)

92.1%: This is an incorrect figure as the value is not matching with the correct value of 84.8%.

(4)

$14.00: This is an incorrect figure as the value is not matching with the value of R².

(5)

Some other amount: This is an incorrect option as the value is 84.8% is given above in the option.

To determine

Identify the appropriate answer for the given statement from the given choices.

Answer to Problem 45E

Option (2) The total overhead cost is $370,000.

Explanation of Solution

Total overhead cost:

Total overhead cost is the total cost of the given overhead. It consists of fixed cost and variable cost.

Calculate the total overhead cost:

$\begin{array}{c}\text{Total overhead costs = Estimated fixed cost + (Estimated variable cost }\times \text{ labor hours)}\\ \text{= \$120,000 + \$5 }\times \text{ 50,000}\\ \text{= \$370,000}\end{array}$

Thus, the total overhead cost is $370,000.

Justification for the correct and incorrect answer:

(1)

$120,000: This is an incorrect figure as it is not matching with the total overhead cost of $370,000.

(2)

$370,000: This is the correct figure as the total overhead cost is $370,000.

(3)

$250,000: This is an incorrect figure as the value is not matching with the correct value of $370,000.

(4)

$320,000: This is an incorrect figure as the value of total overhead cost is $370,000

(5)

Some other amount:  This is an incorrect option as the value is $370,000 is given in the above options.

To determine

Identify the appropriate answer for the given statement from the given choices.

Answer to Problem 45E

Option (2) The variable manufacturing cost per unit is $82.

Explanation of Solution

Variable manufacturing cost:

Variable manufacturing cost is the cost of production that varies with the change in the volume of the production.

Calculate the variable manufacturing cost per unit:

$\begin{array}{c}\text{Variable cost per unit = Direct material + Variable overhead + labor cost}\\ \text{= (\$800,000}÷\text{20,000) + (\$640,000 }÷\text{ 20,000) + (\$5 }\times \text{ 2 (1))}\\ \text{= \$82}\end{array}$

Thus, the variable manufacturing cost is $82.

Working note 1:

Calculate the labor cost per unit:

$\begin{array}{c}\text{Labor hour per unit = }\frac{\text{Total labor hours}}{\text{Total units}}\\ =\frac{40,000\text{ (2)}}{\$20,000}\\ =\text{ 2 labor hour per unit}\end{array}$

Working note 2:

Calculate the total labor hours:

$\begin{array}{c}\text{Total labor hours = }\frac{\text{Direct labor cost}}{\text{Wage rate}}\\ =\frac{\$640,000}{\$16}\\ =\text{ 40,000 direct labor hours}\end{array}$

Justification for the correct and incorrect answer:

(1)

$88.00: This is incorrect figure is not as per the above calculation of 40,000 direct hours.

(2)

$82.00: This is the correct figure as the figure is matching with the calculated figure of $82

(3)

$86.60: This is an incorrect figure as the value is not matching with the correct value of $82.

(4)

$72.00: This is an incorrect figure as the value is $82.00.

(5)

Some other amount:  This is an incorrect option as the value is $82.00 is given above option.

To determine

Identify the appropriate answer for the given statement from the given choices.

Answer to Problem 45E

Option (4). The expected contribution margin is $14.00.

Explanation of Solution

Contribution margin:

The surplus of sales price over the variable expenses is known as the contribution margin. It is computed by deducting the variable expenses from the sales revenue. The contribution margin income statement is made to record the contribution margin.

Calculate the estimated contribution margin:

$\begin{array}{c}\text{Contribution margin = Sales price - Variable cost}\\ \text{= \$96 - \$82}\\ \text{= \$14}\end{array}$

Thus, the estimated contribution margin is $14.

Justification for the correct and incorrect answer:

(1)

$96.00: This is an incorrect figure as it is not as per the above-calculated value of $14.

(2)

$24.00: This is an incorrect figure as per the figure is not matching the calculated figure of $14.

(3)

$56.00: This is an incorrect figure as the value is not matching with the correct value of above-calculated figure $56.

(4)

$14.00: This is the correct figure as per the above calculation.

(5)

Some other amount:  This is an incorrect option as the value is $14 is given in the above options.

To determine

Identify the appropriate answer for the given statement from the given choices.

Answer to Problem 45E

Option (4) The manufacturing cost equation is:

$\text{Total manufacturing cost}=\text{ \$120,000 + \$82 }\times \text{ Units}$  and it is not given in any of the options.

Explanation of Solution

Cost equation:

Cost equation is a mathematical representation of the cost estimation at various level of activity. It is used by defining the fixed cost, and variable cost per unit. The variable cost per unit is multiplied by the given variable to calculate the relative cost.

Calculate the manufacturing cost equation:

$\begin{array}{c}\text{Total manufacturing cost = Fixed manufacturing cost + Variable manufacturing cost}\\ =\text{ \$120,000 + \$82 }\times \text{ Units}\end{array}$

Thus, the manufacturing cost equation is:

$\text{Total manufacturing cost}=\text{ \$120,000 + \$82 }\times \text{ Units}$

Justification for the correct and incorrect answer:

(1)

$Total\cos t=\$640,000+\left(\$5.00\times Numberofunits\right)$ : This is an incorrect figure as the fixed cost is $120,000.

(2)

$Total\cos t=\$120,000+\left(\$86.80\times Numberofunits\right)$: This is an incorrect figure as the variable cost per unit is $82.

(3)

$Total\cos t=\$120,000+\left(\$72.00\times Numberofunits\right)$ : This is an incorrect figure as the variable cost per unit is $82.

(4)

Some other equation: This is the correct figure as the correct answer is not given in any of the above options.