Chapter 8, Problem 43P

1.

To determine

Draw a graph for the two brands of machine.

Explanation of Solution

The data of the graph shows no significant outliers but there is nonlinearity as shown below.

Figure (1)

2&3

To determine

Compute cost equation and costs of operating each machine using high-low method.

Explanation of Solution

Machine A:

Calculate unit variable cost.

$\begin{array}{c}\text{Unit variable cost}=\frac{\left(\begin{array}{l}\left(\begin{array}{l}\text{Estimated total costs of }\\ \text{Brand A for output 64,000}\end{array}\right)\\ -\left(\begin{array}{l}\text{Estimated total costs of }\\ \text{Brand A for output 2,000}\end{array}\right)\end{array}\right)}{\left(\begin{array}{l}\left(\begin{array}{l}\text{Output of Estimated total }\\ \text{costs of \$438,000 }\left(\text{Brand A}\right)\end{array}\right)\\ -\left(\begin{array}{l}\text{Output of Estimated total }\\ \text{costs of \$97,000 }\left(\text{Brand A}\right)\end{array}\right)\end{array}\right)}\\ =\frac{\$438,000-\$97,000}{\text{64,000}-\text{2,000}}\\ =\$5.50\end{array}$

$\begin{array}{c}\text{Constant}=\left(\begin{array}{l}\left(\begin{array}{l}\text{Estimated total costs of }\\ \text{Brand A for output 64,000}\end{array}\right)\\ -\left(\begin{array}{l}\text{Unit variable cost}\\ \times \left(\begin{array}{l}\text{Output of Estimated total }\\ \text{costs of \$438,000 }\left(\text{Brand A}\right)\end{array}\right)\end{array}\right)\end{array}\right)\\ =\$438,000-\left(\$5.50\times 64,000\right)\\ =\$86,000\end{array}$

Calculate the total cost at 40,000 square yards.

$\begin{array}{c}\text{Total costs}=\left(\begin{array}{l}\text{Constant }\\ \text{+}\left(\begin{array}{l}\text{Unit variable cost}\\ \times \text{Number of square yards}\end{array}\right)\end{array}\right)\\ =\$86,000+\left(\$5.50\times 40,000\right)\\ =\$306,000\end{array}$

Calculate the total cost at 25,000 square yards.

$\begin{array}{c}\text{Total costs}=\left(\begin{array}{l}\text{Constant }\\ \text{+}\left(\begin{array}{l}\text{Unit variable cost}\\ \times \text{Number of square yards}\end{array}\right)\end{array}\right)\\ =\$86,000+\left(\$5.50\times 25,000\right)\\ =\$223,500\end{array}$

Calculate the total cost at 60,000 square yards.

$\begin{array}{c}\text{Total costs}=\left(\begin{array}{l}\text{Constant }\\ \text{+}\left(\begin{array}{l}\text{Unit variable cost}\\ \times \text{Number of square yards}\end{array}\right)\end{array}\right)\\ =\$86,000+\left(\$5.50\times 60,000\right)\\ =\$416,000\end{array}$

Machine B:

Calculate unit variable cost.

$\begin{array}{c}\text{Unit variable cost}=\frac{\left(\begin{array}{l}\left(\begin{array}{l}\text{Estimated total costs of }\\ \text{Brand B for output 64,000}\end{array}\right)\\ -\left(\begin{array}{l}\text{Estimated total costs of }\\ \text{Brand B for output 2,000}\end{array}\right)\end{array}\right)}{\left(\begin{array}{l}\left(\begin{array}{l}\text{Output of Estimated total }\\ \text{costs of \$368,000 }\left(\text{Brand B}\right)\end{array}\right)\\ -\left(\begin{array}{l}\text{Output of Estimated total }\\ \text{costs of \$120,000 }\left(\text{Brand B}\right)\end{array}\right)\end{array}\right)}\\ =\frac{\$368,000-\$120,000}{\text{64,000}-\text{2,000}}\\ =\$4\end{array}$

$\begin{array}{c}\text{Constant}=\left(\begin{array}{l}\left(\begin{array}{l}\text{Estimated total costs of }\\ \text{Brand B for output 64,000}\end{array}\right)\\ -\left(\begin{array}{l}\text{Unit variable cost}\\ \times \left(\begin{array}{l}\text{Output of Estimated total }\\ \text{costs of \$368,000 }\left(\text{Brand B}\right)\end{array}\right)\end{array}\right)\end{array}\right)\\ =\$368,000-\left(\$4\times 64,000\right)\\ =\$112,000\end{array}$

Calculate the total cost at 40,000 square yards.

$\begin{array}{c}\text{Total costs}=\left(\begin{array}{l}\text{Constant }\\ \text{+}\left(\begin{array}{l}\text{Unit variable cost}\\ \times \text{Number of square yards}\end{array}\right)\end{array}\right)\\ =\$112,000+\left(\$4\times 40,000\right)\\ =\$272,000\end{array}$

Calculate the total cost at 25,000 square yards.

$\begin{array}{c}\text{Total costs}=\left(\begin{array}{l}\text{Constant }\\ \text{+}\left(\begin{array}{l}\text{Unit variable cost}\\ \times \text{Number of square yards}\end{array}\right)\end{array}\right)\\ =\$112,000+\left(\$4\times 25,000\right)\\ =\$212,000\end{array}$

Calculate the total cost at 60,000 square yards.

$\begin{array}{c}\text{Total costs}=\left(\begin{array}{l}\text{Constant }\\ \text{+}\left(\begin{array}{l}\text{Unit variable cost}\\ \times \text{Number of square yards}\end{array}\right)\end{array}\right)\\ =\$112,000+\left(\$4\times 60,000\right)\\ =\$352,000\end{array}$

4.

To determine

Identify the machine to be purchased and the square yard. Describe whether high-low method is useful or not.

Explanation of Solution

The limitations from the preceding analysis and their related conclusion is that the used data models does not present a complete picture on the underlying cost behavior patterns. By observing the inspection of data provided and inspection of the graph, Machine A is preferred to Machine B to an estimated figure of 40,000 units.

The error that is found in the analysis is in using High Low method for the process of cost estimation. The high low method seems to derive a linear relationship from the least to the largest output level whereas the relationship between output and cost is not linear with respect to the graph.

It can be concluded that the application of a cost estimation method must be used with extreme precautions and the graph serves as an essential tool to identify any potential mistakes.

5.

To determine

Comment on the given statement.

Explanation of Solution

In this case, the nature and extent of the effect of the defect on customers and Company H must be considered. The safety of those people is compromised as long as they use the buildings with defective glass. It is the duty of the cost analyst to present a complete report the management regarding the cost associated with each machine. The cost analysis must be in such a manner that the management is able to make an ethical choice in an appropriate manner.

6.

To determine

Explain the additional consideration that are important to Company H.

Explanation of Solution

Company H must be fully aware of the import duties and the restrictions for the purchase of such machines apart from the cost of the machines. The manner in which the restrictions and duties affect the cost and availability of the machine must be properly studied. Moreover, exchange rate policies must be kept in special consideration due to their volatility.