Chapter 8, Problem 42P

1.

To determine

Compute the cost of painting 3,300 square foot house with 14 external openings and 2,400 square foot house with 8 external openings.

Explanation of Solution

Analysis based on square feet:

High point is Home 5 and low point is home 1.

Compute cost equation using square feet as the cost driver.

Variable cost:

$\begin{array}{c}\text{Variable cost}=\frac{\left(\begin{array}{l}\text{Cost of 5th house}\\ -\text{Cost of 1st house}\end{array}\right)}{\left(\begin{array}{l}\text{Square feet of 5th house}\\ -\text{Square feet of 1st house}\end{array}\right)}\\ =\frac{\$4,700-\$2,810}{4,600-2,500}\\ =\$0.90\end{array}$

Fixed cost:

$\begin{array}{c}\text{Cost of 5th house}=\left(\begin{array}{l}\text{Fixed cost}\\ +\left(\begin{array}{l}\text{Variable cost}\\ \times \text{Square feet of 5th house}\end{array}\right)\end{array}\right)\\ \$4,700=\left(\begin{array}{l}\text{Fixed cost}\\ +\left(\$0.90\times 4,600\right)\end{array}\right)\\ \text{Fixed cost}=\$560\end{array}$

Total cost is predicted for 3,300 square foot house with 14 openings using equation for square feet.

Calculate total cost.

$\begin{array}{c}\text{Total cost}=\left(\text{Fixed cost}+\left(\begin{array}{l}\text{Variable cost}\\ \times \text{Number of square feet}\end{array}\right)\right)\\ =\$560+\left(\$0.90\times 3,300\right)\\ =\$3,530\end{array}$

Total cost is predicted for 2,400 square foot house with 8 openings:

Compute total cost.

$\begin{array}{c}\text{Total cost}=\left(\text{Fixed cost}+\left(\begin{array}{l}\text{Variable cost}\\ \times \text{Number of square feet}\end{array}\right)\right)\\ =\$560+\left(\$0.90\times 2,400\right)\\ =\$2,720\end{array}$

2.

To determine

Compute the cost of painting 3,300 square foot house with independent variable and 2,400 square foot house with independent variable.

Explanation of Solution

Analysis is based on external openings as the cost driver.

Compute cost equation using square feet as the cost driver.

$\begin{array}{c}\text{Variable cost}=\frac{\left(\begin{array}{l}\text{Cost of 5th house}\\ -\text{Cost of 9th house}\end{array}\right)}{\left(\begin{array}{l}\text{External openings of 5th house}\\ -\text{External openings of 9th house}\end{array}\right)}\\ =\frac{\$4,700-\$3,242}{19-10}\\ =\$162\end{array}$

Compute cost equation using square feet as the cost driver.

$\begin{array}{c}\text{Cost of 5th house}=\left(\begin{array}{l}\text{Fixed cost}\\ +\left(\begin{array}{l}\text{Variable cost}\\ \times \text{External openings of 5th house}\end{array}\right)\end{array}\right)\\ \$4,700=\left(\begin{array}{l}\text{Fixed cost}\\ +\left(\$162\times 19\right)\end{array}\right)\\ \text{Fixed cost}=\$1,622\end{array}$

Compute total earnings for total cost.

$\begin{array}{c}\text{Total cost}=\left(\begin{array}{l}\text{Fixed cost}\\ +\left(\begin{array}{l}\text{Variable cost}\\ \times \text{Number of external openings}\end{array}\right)\end{array}\right)\\ =\$1,622+\left(\$162\times 14\right)\\ =\$3,890\end{array}$

Total cost is predicted for 3,300 square foot house with 14 external openings:

$\begin{array}{c}\text{Total cost}=\left(\begin{array}{l}\text{Fixed cost}\\ +\left(\begin{array}{l}\text{Variable cost}\\ \times \text{Number of external openings}\end{array}\right)\end{array}\right)\\ =\$1,622+\left(\$162\times 14\right)\\ =\$3,890\end{array}$

Using equation there should be no prediction until 8 external openings are outside the relevant rage, high-low equations were developed in the range.

3.

To determine

Identify the variable that is a better cost driver and give reason.

Explanation of Solution

The graph shown below is the relationship between costs and square feet which is linear and has no significantly outlying points. The same circumstance exists between costs and number of openings. On the whole the home 8 equation is better suitable for the data than the home 9 equation that is removed from the data. As per this view point both variable are good cost drivers.

Figure (1)

Figure (2)

4.

To determine

State the opinion on the statistical reliability and precision of this model.

Explanation of Solution

The t-value and related p-value for independent variable, square feet, are important with p which is less than 0.05. The independent variable, opening is not important with a p-value of 0.3446. Using R-squared of 93% the overall regression is strong and the standard error of the estimate at 171 which is small percentage of the mean of $3,418 the dependent variable.

Summary output:

Regression Statistics
Multiple R	0.96439
R square	0.930048
Adjusted R square	0.914503
Standard error	171.1824
Observation	12

Table (1)

ANOVA
Particulars	df	SS	MS	F	Significance F
Regression	2	3506442	1753221	59.8299	6.33284E-06
Residual	9	263730.8	29303.42
Total	11	3770173

Table (2)

Particulars	Coefficients	Standard error	t-star	P-value	Lower 95%
Intercept	641.7603	270.0336	2.376594	0.041458	30.90182229
X Variable 1	0.706915	0.200038	3.533911	0.006375	0.254398405
X Variable 2	48.34898	48.47343	0.997433	0.344614	-61.30553286

Table (3)

5.

To determine

Identify the sustainability issues for this company and list the role of cost estimation in the regard.

Explanation of Solution

There exists a high probability that MC Company may face multiple sustainability issues in future. Since the company activities involve renovation of older homes, they mostly deal with materials that are hazardous in nature. This may include asbestos that may be used decades ago in sliding and other construction materials.

The present construction codes mandate proper treatment of hazardous materials during renovation process. This implies hazardous materials are treated with special care and even if they are expensive.

The treatment and disposal of materials must be performed by adhering to the regulations mentioned under the local, state, and federal authority.

The sustainability issues tend to create delay in the operations of a project due to additional activities to treat the materials during renovation process.

Ensuring the safety and comfort of the homeowners is a primary concern since handling such toxic materials and environmental protection is a prime concern.