Financial Leverage and trailing P/E relationship

This was from the Schweser q-bank which states that "an increase in financial leverage will cause the trailing P/E multiple to increase:

An increase in financial leverage will cause the required rate of return to increase, thereby decreasing the P/E. This is clear in the expression for trailing P/E:

P0 / E0 = [(1 – b)(1 + g)] / (r – g) (Note: the topic review does not allow for any interactive relationship between leverage, return on equity (ROE), and growth. Thus, no explicit consideration is given to whether the increase in leverage would increase ROE and therefore growth through the g = (ROE × retention) relationship.)

I thought the answer was “increase” due to the g=PRAT relationship. Maybe I am a dummy compared to the question writer, but I don’t see how the trailing P/E is clearly related to financial leverage via required return. I guess I get that if leverage was higher, you would need a higher return, but it doesn’t seem intuitive to me. Would appreciate any color on how to think about this more cogently. Thanks

If you increase the financial leverage portion of PRAT which is “T”, g will increase, making your denominator (r-g) smaller, and your P/E multiple larger.

in theory, ‘r’ will increase as leverage does, but, i think it’s more intuitive to think of it in an “all else constant” state, where g increases, everything else constant, P/E increases…

Sorry, I made a typo (just edited the original post). On the quiz, I actually answered “increase,” using your same logic (g increases as leverage increases, therefore P/E increases). Schweser said I was wrong and that the P/E decreases because leverage increases reqd rate of return.

I just don’t know why they cherry-picked that part of the equation because the readings I’ve done seem to spell out the relationship between g and leverage a lot more clearly than leverage and required return.

I believe that you’re not a dummy compared to the author of the question.

I agree with you then. It’s a terrible question. I would’ve chosen increase as well.