logit model without constant: which statistics for evaluating?

My logistic model has a dependent variable responses (1) if an investment’s cost/benefit ratio≥1 and (0) if c/b ratio<1.
Independents are region(0-1), type of investment (0-1), investment sector(3 categories, one is base)
When constant term included, the model cannot be estimated because of endless iterations. When constant excluded, all parameters are significant at %5 and %10, prob>chi2=0.0082 wald(4)=13.74.
It’s clear that constant term is not good for my model. As far as i understand, cost/benefit ratio may not exist under the assumption all independents equal to zero. But how i could interpret the coefficients and Which statistics or goodness of fit measure should i use for evaluating the significance of model the model without constant term? And what happens to logit model without constant?
Thanks for now.


Not a robit
So the constant provides the log odds for the base case, as you said the reference groups. I did not follow what 0-1 would mean. Do these represent any value within 0-1 or do they mean either 0 or 1?
these are happening in stata. i cant run the model with constant. and it comes up very good results without constant. i cannot find any references about this problem.
dependent variable: cost/benefit ratio. it takes value ''1'' if c/b ratio>=1 and ''0'' if ratio<1. independents are REGION (takes value ''1'' if investment includes one region, and ''0'' if two or more regions), TYPE (''1'' if its new investment and ''0'' otherwise) SECTOR (manufacturing, agriculture and serving -serving is base category). i just need help..