The answer the CFAI gives is that you must first solve for cost of equity (unlevered) with a special formula:

r(0) = [r(e) + r(d) * (1 - t) * D/E] / [1 + (1 - t) * D/E]

and then use that as an input into the MM cost of equity formula (p 106, vol 2).

r(e) = r(0) + (r(0) - r(d)) * (1 - t) * D/E

I’ve searched a while in the textbook as to where the CFAI got this r(0) formula, but it is not found. How was one supposed to deduce the answer? Was one supposed to find the r(0) formula just using algebra with the r(e) formula… is it recommended to memorize the formula the CFAI gives in the answer?