Corporate Finance & Restructuring
Myers Debt-Overhang Underinvestment NPV Hurdle Formula
Quantify senior-creditor wealth transfer, shareholder net NPV Delta_E, and Stewart Myers’s (1977) debt-overhang hurdle NPV_min = I * (1 - p_G) / p_G.
Audit why distressed shareholders rationally walk away from positive-NPV investments!
Stewart Myers (1977) identified a fundamental agency cost of risky senior debt (face value D_face): suppose existing assets pay V_G >= D_face in survival state G (probability p_G) and V_B < D_face in default state B (probability 1 - p_G). If equityholders fund a safe capex project costing I_inv that adds riskless cash flow Delta_V > I_inv (positive social NPV = Delta_V - I_inv > 0!), default-state cash flow min(Delta_V, D_face - V_B) goes straight to senior bondholders! Whenever V_B + Delta_V <= D_face, equityholders capture only p_G * Delta_V - I_inv, rejecting every positive-NPV project whose NPV sits below hurdle NPV_min* = I_inv * ((1 - p_G) / p_G)!
Verify on senior debt D_face = 100 (B2), Good-state asset value V_G = 140 (B3), Bad-state distress value V_B = 40 (B4), survival probability p_G = 0.60 (B5), equity capex I_inv = 30 (B6), and safe payoff Delta_V = 42 (B7 -> Social NPV = +12.00 > 0!): in the Bad state (40 + 42 = 82 <= 100), creditors capture 100% of Delta_V (expected creditor windfall = 0.40 * 42 = +16.80!), leaving equityholders net Delta_E = 0.60 * 42 - 30 = -4.80 < 0 (Project Rejected despite +12.00 NPV!). Writing down senior debt face value in a consensual restructuring from 100 to 65 flips Delta_E positive to 0.60 * 42 + 0.40 * (82 - 65) - 30 = +2.00, unlocking the investment!
| Debt-Overhang Metric (I=30, dV=42, p_G=60%) | Unrestructured D = 100 | Restructured D = 65 |
|---|---|---|
| Total Firm Social NPV (Delta_V - I) | +12.00 | +12.00 |
| Creditor Wealth Transfer (Delta_Debt) | +16.80 | +10.00 |
| Shareholder Net Gain (Delta_Equity) | -4.80 (Underinvestment!) | +2.00 (Invests!) |
| Unrestructured NPV Hurdle I*(1-p_G)/p_G | +20.00 (Requires dV >= 50) | Resolved by Write-Down |
Exact Two-State Shareholder Incremental Value Delta_E Formula
Use exact call-option payoffs MAX(0, V_state + Delta_V - D_face) - MAX(0, V_state - D_face) in both states so the formula handles partial AND full Bad-state debt recovery seamlessly!
=LET(d_fc, B2, v_gd, B3, v_bd, B4, p_gd, B5, i_cx, B6, dv_pj, B7, IF(OR(d_fc < 0, v_bd < 0, v_gd < v_bd, p_gd <= 0, p_gd >= 1, i_cx <= 0, dv_pj < 0), "Invalid Overhang Input", LET(eg_gn, MAX(0, v_gd + dv_pj - d_fc) - MAX(0, v_gd - d_fc), eb_gn, MAX(0, v_bd + dv_pj - d_fc) - MAX(0, v_bd - d_fc), ROUND(p_gd * eg_gn + (1 - p_gd) * eb_gn - i_cx, 4))))Senior Creditor Wealth Transfer Delta_Debt = Social_NPV + I_inv - (Delta_E + I_inv) Formula
Verify value conservation: Delta_Equity + Delta_Debt = Delta_V - I_inv = Social_NPV across every debt level.
=IF(ISTEXT(E3), E3, ROUND((B7 - B6) - E3, 4))Try the example
Use the original values or change them to test your understanding.