Well then you need to estimate the distribution of those results. If it's uniform between those numbers then it's an expected loss, and whether it's worth spending a significant amount of money on information depends on whether the company can afford it. If, say, the value of information was 200k in expectation, that doesn't imply that the company should spend anywhere near that amount on information, because they should be somewhat risk averse if they can't spread the risk over many such decisions.
Information isn't useless in this example. For some unexplained reason you have already obtained information for no cost which doesn't make any sense.
The real scenario is: cost overrun by $250k to $1 million over x months, profit increase between $50k to $100k per year. How much are you willing to spend to obtain 100% certainty?