Chapter 10, Problem 66P

a.

To determine

Modify the previously designed cost system for Company CT.

Explanation of Solution

The costs for each season fluctuate on the basis of the excess capacity unused in the winter season. There are two approaches through which the costs could be determined.

Approach 1:

In this approach the excess capacity costs are assigned in the season in which they are incurred, and then to the products.

Compute the product cost for winter:

Compute the overhead rate:

$\begin{array}{c}\text{Overhead rate = }\frac{\text{Capacity cost}}{\text{Number of units}}\\ =\frac{\$13,500}{4,500\text{ gallons}}\\ =\$3.00\text{ per gallon}\end{array}$

Compute the product cost:

$\begin{array}{c}\text{Cost = }\left(\begin{array}{l}\text{Overhead rate}+\\ \text{Rate per gallon}\end{array}\right)\\ =\$3.00+\$1.00\\ =\$4.00\text{ per gallon}\end{array}$

Compute the product cost for summer:

Compute the overhead rate:

$\begin{array}{c}\text{Overhead rate = }\frac{\text{Capacity cost}}{\text{Number of units}}\\ =\frac{\$13,500}{9,000\text{ gallons}}\\ =\$1.50\text{ per gallon}\end{array}$

Compute the product cost:

$\begin{array}{c}\text{Cost = }\left(\begin{array}{l}\text{Overhead rate}+\\ \text{Rate per gallon}\end{array}\right)\\ =\$1.50+\$1.00\\ =\$2.50\text{ per gallon}\end{array}$

Approach 2:

In this approach the excess capacity costs are assigned in the seasons and then to the products.

Compute the product cost for winter:

Compute the overhead rate:

$\begin{array}{c}\text{Overhead rate = }\frac{\left(\text{Capacity cost}\times \text{50\%}\right)}{\text{Number of units}}\\ =\frac{\$13,500\times \text{50\%}}{4,500\text{ gallons}}\\ =\$1.50\text{ per gallon}\end{array}$

Compute the product cost:

$\begin{array}{c}\text{Cost = }\left(\begin{array}{l}\text{Overhead rate}+\\ \text{Rate per gallon}\end{array}\right)\\ =\$1.50+\$1.00\\ =\$2.50\text{ per gallon}\end{array}$

Compute the product cost for summer:

Compute the overhead rate:

$\begin{array}{c}\text{Overhead rate = }\frac{\left[\text{Capacity cost+}\left(\text{Capacity cost}\times \text{50\%}\right)\right]}{\text{Number of units}}\\ =\frac{\left[\$13,500+\left(\$13,500\times \text{50\%}\right)\right]}{9,000\text{ gallons}}\\ =\$2.25\text{ per gallon}\end{array}$

Compute the product cost:

$\begin{array}{c}\text{Cost = }\left(\begin{array}{l}\text{Overhead rate}+\\ \text{Rate per gallon}\end{array}\right)\\ =\$2.25+\$1.00\\ =\$3.25\text{ per gallon}\end{array}$

The price to be paid by Company RCC to Company KC under exclusive contract is $5.62. In case of delay, the price of Company KC must be compared with the price of Company TG, as it offers the next best price to Company

b.

To determine

Identify the maximum price to be considered by Company RCC to offer Company KC, in case of absence of any delay.

Explanation of Solution

Compute the number of loads delayed:

$\begin{array}{c}\text{Load = }\left(\begin{array}{l}\text{Delay }\\ \text{experience}\end{array}\right)\times \left(\begin{array}{l}\text{Number of}\\ \text{deliveries}\end{array}\right)\\ =\left(\frac{\text{80 loads delayed}}{\text{400 loads delivered}}\right)\times \left(\frac{\text{3,000,000 tons}}{\text{500 tons per delivery}}\right)\\ =20\%\times 600\text{ deliveries}\\ \text{=120 delayed deliveries}\end{array}$

Compute the cost of delayed deliveries:

$\begin{array}{c}\text{Cost = }\left(\begin{array}{l}\text{Number of loads delayed}\\ \times \text{ Price per delayed load}\end{array}\right)\\ =120\times \$2,000\\ =\$240,000\end{array}$

Compute the change in price:

$\begin{array}{c}\text{Cost per ton = }\left(\begin{array}{l}\text{Current price}\\ \text{per ton}\end{array}\right)+\left(\begin{array}{l}\text{Change in }\\ \text{price per ton}\end{array}\right)\\ =\$5.62+\frac{\$240,000}{3,000,000}\\ =\$5.62+\$0.08\\ =\$5.70\end{array}$

The price to be paid by Company RCC to Company KC under exclusive contract is $5.70.