Final answer:
The capital intensity ratio for Martha's Fabric House is found by using the debt-equity ratio to first calculate total assets and then dividing by sales. The calculated ratio is approximately 0.786, indicating that around 78.6 cents of capital are needed for every dollar of sales.
Step-by-step explanation:
The question is asking to calculate the capital intensity ratio, which is a measure of how much capital is needed for a business to generate one dollar of sales. This ratio is determined by taking the total assets of a company and dividing them by total sales. The total assets can be found using the debt-equity ratio and total equity (TE).
To determine total assets (TA), we first need to use the debt-equity ratio formula:
Debt-Equity Ratio = Total Debt / Total Equity
Given the debt-equity ratio (0.45), we can rearrange the formula to solve for total debt:
Total Debt = Total Equity * Debt-Equity Ratio
We then add total equity and total debt to find total assets:
Total Assets = Total Equity + Total Debt
Finally, the capital intensity ratio is calculated by:
Capital Intensity Ratio = Total Assets / Sales
Without the value for total debt directly provided, we calculate total debt as follows:
Total Debt = $74,400 * 0.45 = $33,480
Now we can calculate total assets:
Total Assets = $74,400 (total equity) + $33,480 (total debt) = $107,880
With this value, we can determine the capital intensity ratio:
Capital Intensity Ratio = $107,880 / $137,200 ≈ 0.786
This ratio implies that Martha's Fabric House requires approximately 78.6 cents of capital to generate every dollar of sales.