Chapter 11, Problem 45P

1.

To determine

Calculate the contribution margin of Component Y34 and Model SC67. Also, calculate the contribution margin earned by the division.

Answer to Problem 45P

The contribution margin for Component Y34, Model SC67 and division are $100,000, $760,000 and $860,000 respectively.

Explanation of Solution

Contribution margin can be defined as the amount obtained after deducting the variable expense from sales revenue. It means the amount of sales left after covering the variable expenses.

The following table represents the contribution margin:

	Component Y34 ($)	Model SC67 ($)	Company ($)
Sales1 (A)	260,000	1,680,000	1,940,000
Variable expenses2 (B)	160,000	920,000	1,080,000
Contribution margin $\left(\text{A}-\text{B}\right)$	100,000	760,000	860,000

Table (1)

Therefore, the contribution margin for Component Y34, Model SC67 and division are $100,000, $760,000 and $860,000 respectively.

Working Notes:

1. Calculation of sales under Component Y34:

$\begin{array}{c}\text{Sales}=\text{Number of units}\times \text{Selling price per unit}\\ =40,000\text{ units}\times \$6.5\\ =\$260,000\end{array}$

Hence, the amount of sales under Component Y34 is $260,000.

Calculation of sales under Model SC67:

$\begin{array}{c}\text{Sales}=\text{Number of units}\times \text{Selling price per unit}\\ =40,000\text{ units}\times \$42\\ =\$1,680,000\end{array}$

Hence, the amount of sales under the Model SC67 is $1,680,000.

2. Calculation of variable expense under Component Y34:

$\begin{array}{c}\text{Variable expense}=\text{Number of units}\times \left(\text{Total unit cost}-\text{Fixed overhead}\right)\\ =40,000\text{ units}\times \left(\$6.5-\$2.5\right)\\ =40,000\text{ units}\times \text{\$4}\\ =\$160,000\end{array}$

Hence, the amount of variable expense under Component Y34 is $160,000.

Calculation of variable expense under Model SC67:

$\begin{array}{c}\text{Variable expense}=\text{Number of units}\times \left(\text{Total unit cost}-\text{Fixed overhead}\right)\\ =40,000\text{ units}\times \left(\$38-\$15\right)\\ =40,000\text{ units}\times \text{\$23}\\ =\$920,000\end{array}$

Hence, the amount of variable expense under Model SC67 is $920,000.

2.

To determine

Predict the transfer price of the component division. Also, calculate minimum transfer and maximum transfer.

Answer to Problem 45P

The minimum and maximum transfer price will be $12.

Explanation of Solution

Transfer Price:

The amount of price charged by the selling department for a component to the purchasing department of a similar company is known as transfer price.

The transfer price for the Component division will be $12 per unit. The minimum and maximum transfer price will be equal to $12 per unit because the Component division is selling the units at $12 to the outsiders and the PSF division can purchase the units at $12 from the external suppliers.

3.

To determine

Calculate the number of units that the PSF division manager will purchase either internally or externally.

Explanation of Solution

Use the following formula to calculate the cost per unit after the new transfer pricing policy:

$\text{Cost per unit}=\left(\begin{array}{l}\text{Total unit cost of Model SC67}\\ -\text{Total unit cost of Compnent Y34}\\ +\text{Cost to purchase the part}\end{array}\right)$

Substitute $38 for a total unit cost of Model SC67, $6.50 for a total unit cost of Component Y34 and $12 for the cost to purchase the part in the above formula.

$\begin{array}{c}\text{Cost per unit}=\$38-\$6.50+\$12\\ =43.50\end{array}$

The cost per unit of Model SC67 is $43.50 per unit which is more than the selling price of $42. Therefore, the company should not continue the production and not purchase any number of units.

4.

To determine

Determine the number of units of Component Y34 to be sold externally.

Explanation of Solution

The company should sell all the units of 40,000 of Component Y34 externally with the market price of $12 per unit. The reason behind the sale of 40,000 units is that the division has the capacity to sell all the units of the component.

5.

To determine

Calculate firm-wide contribution margin. Also, describe whether the decision by C was good or bad.

Explanation of Solution

Use the following formula to calculate firm-wide contribution margin:

$\text{Contribution margin}={\text{Sales}}^{\text{1}}-{\text{Variable expenses}}^{\text{2}}$

Substitute $480,000 for sales and $160,000 for the variable expense in the above formula.

$\begin{array}{c}\text{Contribution margin}=\$480,000-\$160,000\\ =\$320,000\end{array}$

The firm-wide contribution margin is $320,000. The decision of C was wrong as the overall contribution margin decreases by $540,000$\left(\$860,000-\$320,000\right)$.

Working Notes:

1. Calculation of sales:

$\begin{array}{c}\text{Sales}=\text{Number of units}\times \text{Selling price per unit}\\ =40,000\text{ units}\times \$12\\ =\$480,000\end{array}$

Hence, the amount of sales is $480,000.

2. Calculation of variable expense:

$\begin{array}{c}\text{Variable expense}=\text{Number of units}\times \left(\text{Total unit cost}-\text{Fixed overhead}\right)\\ =40,000\text{ units}\times \left(\$6.5-\$2.5\right)\\ =40,000\text{ units}\times \text{\$4}\\ =\$160,000\end{array}$

Hence, the amount of variable expense is $160,000.