Corporate Governance & Agency Theory
Jensen-Meckling Outside-Equity Agency Cost Formula
Calculate managerial perk extraction F* = (1 - alpha)/k_u, realized equity value, and exact residual agency deadweight loss (1 - alpha)^2 / (2*k_u) under diluted inside ownership.
Prove Jensen & Meckling’s (1976) theorem: rational outside investors make the founder bear 100% of agency DWL!
Michael Jensen and William Meckling (1976) founded modern corporate-governance economics by modeling what happens when an owner-manager sells fraction (1 - alpha) of equity to outside shareholders while retaining inside stake alpha in (0, 1]. If spending F dollars of firm resources on non-pecuniary perquisites (empire-building, plush jets, pet projects) yields private managerial utility U(F) = F - 0.5 * k_u * F^2 (k_u > 0), a 100% owner (alpha = 1) equates marginal utility 1 - k_u * F to 1.00 and wastes F_FB = 0! Once diluted to stake alpha, however, each $1 of firm perks costs the manager only alpha personally, so perk extraction jumps to F* = (1 - alpha) / k_u, firm value drops from V_0 to V_0 - F*, and Residual Agency Cost (Deadweight Loss) equals F* - U(F*) = (1 - alpha)^2 / (2 * k_u)!
Check by hand with Base_Value_V0 = 1,000 (B2), Inside_Equity_alpha = 0.60 (B3), and Utility_Curvature_ku = 0.01 (B4): perk spending jumps to F* = 0.40 / 0.01 = 40.00, realized firm value drops to 1,000 - 40 = 960.00, outside investors pay exact fair value 0.40 * 960 = 384.00, manager private utility of perks is 40 - 0.5 * 0.01 * 1,600 = 32.00, and total founder wealth is 0.60*960 + 384 + 32 = 992.00 — bearing 100% of the exact Agency Deadweight Loss 1,000 - 992 = 8.00!
| Jensen-Meckling Metric (V_0=1,000, alpha=0.60, k_u=0.01) | Formula | Verified Output |
|---|---|---|
| Equilibrium Perk Extraction (F*) | (1 - alpha) / k_u | 40.00 |
| Realized Firm Market Value (V_firm) | V_0 - F* | 960.00 |
| Manager Private Utility of Perks U(F*) | F* - 0.5 * k_u * (F*^2) | 32.00 |
| Residual Agency Cost (Deadweight Loss) | (1 - alpha)^2 / (2 * k_u) | 8.00 (Founder Net = 992.00) |
Diluted-Ownership Managerial Perk Extraction F* & Firm Value Formula
Validate positive base value V_0, inside ownership 0 < alpha <= 1, and curvature k_u > 0 (requiring V_0 >= F*).
=LET(v_0, B2, al_in, B3, ku_p, B4, IF(OR(v_0 <= 0, al_in <= 0, al_in > 1, ku_p <= 0), "Invalid Agency Input", LET(f_pk, (1 - al_in) / ku_p, IF(f_pk > v_0, "Perks Exceed Base Firm Value", ROUND(v_0 - f_pk, 4)))))Exact Jensen-Meckling Residual Agency Deadweight Loss Formula
Notice the quadratic scaling (1 - alpha)^2: cutting outside equity from 40% to 20% (raising alpha from 0.60 to 0.80) slashes agency deadweight loss by 75% (from 8.00 down to 2.00) — motivating management buyouts and performance equity!
=LET(v_0, B2, al_in, B3, ku_p, B4, IF(OR(v_0 <= 0, al_in <= 0, al_in > 1, ku_p <= 0), "Invalid Agency Input", LET(f_pk, (1 - al_in) / ku_p, IF(f_pk > v_0, "Perks Exceed Base Firm Value", ROUND(((1 - al_in)^2) / (2 * ku_p), 4)))))Try the example
Use the original values or change them to test your understanding.