The King Card Company has a return-on-assets (investment) ratio of 12 percent.

a. If the debt-to-total-assets ratio is 40 percent, what is the return on equity?
b. If the firm had no debt, what would the return-on-equity ratio be?

Total Debt to Total assets = short term debt + long term debt / total assets

If that is true and the ratio is known (40%) Would it not become 40% ratio / 12% ratio =

133.3

No. Without knowing actual equity, at the very least, there is no way to answer the questions. Not enough data. With a dollar amout of equity, you you can (based on the information provided) determine Total Assets, Total Liabilities, ROE, etc. But without that crucial bit of data, there isn't enough information to answer the questions. Or, if you had $ total assets, or $ total liabilities, you could use that info to figure out equity, and the rest would be easy.

Elliot