Corporate Finance & Capital Structure
Myers-Majluf Equity Issuance & Pecking Order Formula
Calculate Stewart Myers and Nicholas Majluf’s (1984) pooled equity-issuance dilution loss on undervalued high-state firms and prove why internal cash and riskless debt beat seasoned equity.
Prove why rational managers forfeit a +$20M positive-NPV project rather than issue undervalued stock!
Textbook frictionless finance says a firm should fund EVERY project with NPV > 0 regardless of financing source. Stewart Myers and Nicholas Majluf (1984) overturned that rule under asymmetric information! Suppose insiders know whether existing assets-in-place are High-State A_H or Low-State A_L (< A_H), whereas outside equity investors only know prior probability p_H (Expected Assets A_bar = p_H * A_H + (1 - p_H) * A_L). To fund a project requiring investment I > 0 with known positive NPV > 0 via seasoned equity, pooling prices total post-issue firm equity at V_pool = A_bar + I + NPV, leaving existing shareholders Retention Fraction s_old = (A_bar + NPV) / (A_bar + I + NPV)! For a High-State firm, Old Shareholders’ True Post-Issue Wealth is W_old_H = s_old * (A_H + I + NPV) — whenever W_old_H < A_H, dilution of undervalued existing assets exceeds the entire project NPV, forcing High-State firms to PASS UP the positive-NPV project unless funded via internal cash or riskless debt (the Pecking Order)!
Verify on High_Assets A_H = 150.00 ($M, B2), Low_Assets A_L = 50.00 ($M, B3), High_Prior p_H = 0.50 (B4 -> A_bar = 100.00 $M), Required_Issue I = 100.00 ($M, B5), and Project_NPV = 20.00 ($M, B6): Pooled Valuation is 100 + 100 + 20 = 220.00 ($M), Old-Shareholder Retention Share is 120 / 220 = 0.5455 (54.55%), High-State Old Shareholders’ Post-Issue Wealth is (120 / 220) * (150 + 100 + 20) = 147.27 ($M), and Net Gain vs Walking Away (150.00 $M) is -2.73 ($M -> "Forfeit Project: Equity Dilution Exceeds NPV"!) — whereas funding via internal cash or riskless debt captures the full +20.00 ($M -> 170.00 $M)!
| Myers-Majluf Metric (A_H=150, A_L=50, p_H=0.5, I=100, NPV=20) | Formula | Verified Output |
|---|---|---|
| Pooled Market Asset Expectation (A_bar) | p_H * A_H + (1 - p_H) * A_L | 100.00 ($M) |
| Old-Shareholder Pooled Retention (s_old) | (A_bar + NPV) / (A_bar + I + NPV) | 0.5455 (6 / 11) |
| High-Type Old-Shareholder Wealth | s_old * (A_H + I + NPV) | 147.27 ($M vs 150 Walk-Away!) |
| High-Type Net Equity-Issue Gain | W_old_H - A_H | -2.73 ($M — Underinvestment!) |
High-State Old-Shareholder Pooled Equity-Issue Net Gain Formula
Validate A_H > A_L >= 0, 0 < p_H < 1, required financing I > 0, and NPV >= 0.
=LET(a_hi, B2, a_lo, B3, p_hi, B4, inv_i, B5, npv_p, B6, IF(OR(a_lo < 0, a_hi <= a_lo, p_hi <= 0, p_hi >= 1, inv_i <= 0, npv_p < 0), "Invalid Pecking-Order Input", LET(a_br, p_hi * a_hi + (1 - p_hi) * a_lo, s_ol, (a_br + npv_p) / (a_br + inv_i + npv_p), ROUND(s_ol * (a_hi + inv_i + npv_p) - a_hi, 2))))Myers-Majluf Pooling vs Separating Equilibrium Verdict Formula
Test raising Project_NPV from 20 to 30 ($M): High-Type Old-Shareholder Net Gain flips from -2.73 to +8.26 ($M), restoring "Pooling Equity Issue Survives"!
=IF(ISTEXT(E4), E4, IF(E4 >= 0, "Pooling Equity Issue Survives", "Underinvestment: Reject Equity (Use Cash/Debt)"))Try the example
Use the original values or change them to test your understanding.