She smiled. "I had a good tutor."
Problem 17.9: The trick here is the personal tax rate on equity vs. debt. Most solutions online ignore τ_e. Don't. Use the Miller model: V_L = V_U + [1 - ((1-τ_c)(1-τ_e))/(1-τ_d)] * D. If τ_e = 0.15, τ_d = 0.35, τ_c = 0.21, the bracket term becomes 1 - ((0.79*0.85)/0.65) = 1 - (0.6715/0.65) = 1 - 1.033 = -0.033. So debt actually *destroys* value here. Most people miss this. Priya sat back. Her professor had hinted at this in lecture, but no one in class had understood. The official solutions manual (she'd borrowed a friend's older edition) just said "See equation 17.8" and gave $0.00 change.
Then she found it.
But fin_hermit_99 had explained why .
It was 2:47 AM, and the only light in Priya’s dorm room came from the pale blue glow of her laptop. The spreadsheet on her screen had stopped making sense two hours ago. Chapter 17 of Principles of Corporate Finance, 14th Edition —"Does Debt Policy Matter?"—lay open, its Modigliani-Miller theorem propositions staring back at her like a smug mathematical riddle. Principles Of Corporate Finance 14th Edition Solutions
Beneath the title, she wrote: "Based on fin_hermit_99's approach. Let's keep this going."
She had tried. She really had. But the difference between Proposition I (with taxes) and Proposition II (the cost of equity) had dissolved into a blur of algebraic spaghetti. Her problem set was due in six hours. The "Solutions" section in the back of the book only gave final answers, not the path to get there. She smiled
Priya clicked.
The page loaded in raw markdown. It wasn't official. It was better. Each problem was annotated with not just the numeric solution, but a short, handwritten-style note in ASCII: Most solutions online ignore τ_e