Chapter 13, Problem 35E

1.

To determine

Calculate the price for the part using a markup of 45% of full manufacturing cost.

Explanation of Solution

Calculate the price for the part using a markup of 45% of full manufacturing cost as follows:

$\begin{array}{c}\text{Price per part = }\frac{\left[\begin{array}{l}\text{Total manufacturing cost (3)}\times \\ \left(1+45\%\right)\end{array}\right]}{\text{Expected sales in units}}\\ =\frac{\$7,385,875\times 1.45}{50,000\text{ units}}\\ =\$214.1904\end{array}$

Working note (1):

Calculate the total variable cost.

$\begin{array}{c}\text{Total variable cost = }\left(\begin{array}{l}\text{Variable manufacturing cost+}\\ \text{Variable selling and administrative cost}\end{array}\right)\\ =\$4,680,000+\$855,650\\ =\$5,535,650\end{array}$

Working note (2):

Calculate the total fixed cost.

$\begin{array}{c}\text{Total fixed costs = }\left(\begin{array}{l}\text{Facility-level fixed overhead}+\\ \text{Fixed selling and administrative+}\\ \text{Batch-level fixed overhead}\end{array}\right)\\ =\left(\begin{array}{l}\$2,345,875+\$675,495+\\ \$360,000\end{array}\right)\\ =\$3,381,370\end{array}$

Working note (3):

Calculate the total manufacturing cost.

$\begin{array}{c}\begin{array}{l}\text{Total manufacturing }\\ \text{cost }\end{array}\}\text{= }\left(\begin{array}{l}\text{Variable manufactuirng+}\\ \text{Facility level fixed overhead+}\\ \text{Batch-level fixed overhead}\end{array}\right)\\ =\left(\begin{array}{l}\$4,680,000+\$2,345,875+\\ \$360,000\end{array}\right)\\ =\$7,385,875\end{array}$

Working note (4):

Calculate the total selling and administrative.

$\begin{array}{c}\begin{array}{l}\text{Total selling and }\\ \text{administrative}\end{array}\}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Variable selling and }\\ \text{administrative}\end{array}\right)+\\ \text{Fixed selling and administrative}\end{array}\right]\\ =\$855,650+\$675,495\\ =\$1,531,145\end{array}$

Working note (5):

Calculate the total life cycle cost.

$\begin{array}{c}\text{Total life cycle cost = }\left(\begin{array}{l}\text{Total manufacturing cost (3)+}\\ \text{Total selling and administrative (4)}\end{array}\right)\\ =\$7,385,875+\$1,531,145\\ =\$8,917,020\end{array}$

Working note (6):

Calculate the manufacturing cost per unit.

$\begin{array}{c}\begin{array}{l}\text{Manufacturing }\\ \text{cost per unit}\end{array}\}\text{ = }\frac{\text{Total manufacturing cost (3)}}{\text{Expected sales in units}}\\ =\frac{\$7,385,875}{50,000\text{ units}}\\ =\$147.72\\ \end{array}$

Working note (7):

Calculate the life cycle cost per unit.

$\begin{array}{c}\begin{array}{l}\text{Life cycle }\\ \text{cost per unit}\end{array}\}\text{ = }\frac{\text{Total life cycle cost (5)}}{\text{Expected sales in units}}\\ =\frac{\$8,917,020}{50,000\text{ units}}\\ =\$178.34\end{array}$

2.

To determine

Calculate the price for the part using a markup of 25% of full life-cycle cost.

Explanation of Solution

Calculate the price for the part using a markup of 25% of full life-cycle cost as follows:

$\begin{array}{c}\text{Price per part = }\frac{\left[\begin{array}{l}\text{Total life-cycle cost (5)}\times \\ \left(1+25\%\right)\end{array}\right]}{\text{Expected sales in units}}\\ =\frac{\$8,917,020\times 1.25}{50,000\text{ units}}\\ =\$222.9250\end{array}$

3.

To determine

Calculate the price for the part using a desired gross margin percentage to sales of 40%.

Explanation of Solution

Calculate the price for the part using a desired gross margin percentage to sales of 40% as follows:

$\begin{array}{c}\text{Price per part = }\frac{\text{Manufacturing cost per unit (6)}}{\left(1-\text{Desired profit percentage}\right)}\\ =\frac{\$147.72}{\left(1-40\%\right)}\\ =\$246.1960\end{array}$

4.

To determine

Calculate the price for the part using a desired life-cycle cost percentage to sales of 25%.

Explanation of Solution

Calculate the price for the part using a desired life-cycle cost percentage to sales of 25% as follows:

$\begin{array}{c}\text{Price per part = }\frac{\text{Life cycle cost per unit (7)}}{\left(1-\text{Desired profit percentage}\right)}\\ =\frac{\$178.34}{\left(1-25\%\right)}\\ =\$237.7867\end{array}$

5.

To determine

Calculate price for the part using a desired before tax return on investment of 15%.

Explanation of Solution

Calculate price for the part using a desired before tax return on investment of 15%t as follows:

$\begin{array}{c}\text{Price per part = }\left(\begin{array}{l}\text{Life cycle cost per unit (7)}\times \\ \left(1+\text{Total investment rate}\right)\end{array}\right)\\ =\$178.34\times \left(1-0.3760\right)\\ =\$245.3905\end{array}$

Working note (8):

Calculate the total investment rate.

$\begin{array}{c}\text{Total investment rate = }\frac{\left(\begin{array}{l}\text{Total investment in product line}\times \\ \text{Desired return on investment}\end{array}\right)}{\left(\begin{array}{l}\text{Expected sales in units}\times \\ \text{Life cycle cost per unit (7)}\end{array}\right)}\\ =\frac{\$22,350,000\times 15\%}{\left(50,000\text{ units}\times \text{\$178}\text{.34}\right)}\\ =0.3760\end{array}$

6.

To determine

Calculate the contribution margin and operation profit for each method and choose the appropriate price.

Explanation of Solution

Calculate the contribution margin and operation profit for each method and choose the appropriate price as follows:

Table (1)

Excel workings:

Table (1)

Price to achieve desired ROA of 15% is better price for the company, because the operating profit from this price is more than the other.