Understanding Beopt Economic Analysis

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I'm not entirely sure what you're asking or confused about...

The Min Cost point of your optimization shows a reduction in annualized energy costs of 200 USD/year, as you indicated. If you look at the utility bills alone (right-click on bottom-left graph and choose Graph Type > Utility Bills), you can see that there are savings of 1321 USD/yr. So approximately 1121 USD/yr is being spent towards efficiency improvements, which over the course of a 30 year analysis period, is indeed tens of thousands of dollars.

(I had to use "USD" instead of "$" because Unmet Hours kept messing up the formatting.)

The built-in help provides extensive details on this; at least it does in v2.8

Roughly-speaking, present value is what you could sell the home for, and AERC is utility bills plus excess mortgage over the reference condition. They are apples and oranges.