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1 Produced with a Trial Version of PDF Annotator - Agency Problems Jensen and Meckling (1976): Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure Agency Costs of Outside Equity In this paper managerial behavior, agency costs and the ownership structure are modelled. The manager who is also the (part) owner of the firm can choose the amount/value of perks (fringe benefits) F he/she wants to consume paid by the company. Think of the fringe value F as the market value of the manager s consumption 1

2 Produced with a Trial Version of PDF Annotator - of perks like plush office, jets, thick carpets, golf memberships, etc paid by the company [keep the pecuniary compensation, salaries, fixed]. Say that V is the firm value if the manager consumes no perks, and let V F be the market value given that the manager consumes F fringe benefits (we assume that 0 F V ). The owner-manager initially owns all shares. Suppose the manager sells a fraction 1 α of the firm s shares (0 1 α 1). Say the the manager utility for "money" and fringe benefits is given by U(m, F ). So the manager s utility is U(αV + S, F ), whereα is his stake in the firm valued at V, plus the value of the stake sold to outside investors S, andf are his fringe benefits. V value of the firm S the selling price (1 α)v F value of perks 2

3 Assumptions: 1. U : R 2 R fulfills the usual technical conditions U C 2,U 1 > 0,U 2 > 0 and U is concave, i.e. D 2 U is negative definite. 2. Manager (owner) maintains control Consider for now a fixed level of α. An equilibrium is a level of F and a selling price S such that: 1. F argmax F U(α( V F )+S,F) 2. S =(1 α)( V F ) 3

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5 Remarks: "For a claim on the firm of (1 α) the outsider will pay only (1 α) times the value he expects the firm to have given the induced change in the behavior of the owner-manager." D is chosen if α =1. A is maximum if α < 1 and the outsider buy the stake at V. A is to the right of D. Equilibrium is the point B. Note that from the equilibrium condition 2 follows α( V F )+S = α( V F )+(1 α)( V F )= V F which means that the manager ultimately internalizes the loss in market value associated with fringe benefits. α fixed slopes are fixedinequilibrium.lineshavetointersectandbe tangent to utility. 5

6 Produced with a Trial Version of PDF Annotator - Agency costs: Manager can consume more perks (F ) but has to pay the price in a loss of utility. max U(α( V F )+S,F) F Assume interior solution: FOC : αu 1 (α( V F )+S, F )+U 2 (α( V F )+S, F )=0 α = U 2(α( V F )+S, F ) U 1 (α( V F )+S, F ) SOC: α 2 U 11 (α( V F )+S, F ) αu 12 (α( V F )+S, F ) αu 21 (α( V F )+S, F )+U 22 (α( V F )+S, F )=0 The SOC is equivalent to µ U11 U ( α, 1) 12 U 21 U {z 22 } negative definite µ α 1 6 < 0: : max

7 Produced with a Trial Version of PDF Annotator - Comparative statics analysis The FOC in equilibrium (S =(1 α)( V F )): H(α,F ):= αu 1 (( V F ),F )+U 2 (( V F ),F )=0 That is, for each α the equilibrium fringe benefits is given implicity by αu 1 (( V F ),F )+U 2 (( V F ),F )=0. df dα using the implicit function theorem ( H(α,F ) F 6= 0) df H(α,F ) dα = α H(α,F ) F = >0 z } { U 1 ( V F,F ) 2 U F 2 {z } <0 If α then F. (the more shares the manager retains the less consumption of fringe benefits). 7

8 Let ξ(α) be the equilibrium utility level of the manager given α. ξ(α) =U( V F (α),f (α)) ξ 0 (α) =U 1 ( V F (α),f (α)) <0 indirect utility à df! (α) + U 2 ( dα V F (α),f (α)) df (α) dα = df (α) U1 ( dα V F (α),f (α)) + U 2 ( V F (α),f (α)) {z } {z } <0 α =1is maximizing ξ(α). Results: 1. df (α) < 0 dα The higher is α the lower are the perks. 2. dξ(α) > 0 dα The higher is α the higher is the manager s utility. The manager pays the price in equilibrium. He can not distribute the costs to 8 > 0

9 the buyer of the firm. In equilibrium U( V F,F ). This is the agency costs of outside equity. Agency costs for debt: Asset Substitution - Risk Shifting Intuition: Consider a risk neutral economy with r f =0. Case 1: The firm is equity only. The manager has a riskless project that is worth 70. There is another risky project that pays ½ 100 with prob 0.5 0withprob0.5 The manager will not replace the original project with the risky project with lower NPV of 50. Case 2: The firm has debt with face value of 50. The original riskless project has NPV =20for shareholders. The alternative project pays to shareholders 50 in good state, and 0 in bad state with equal probability, 9

10 so has NPV =25. Manager chooses second project even though it had a lower NPV than the first project. More risky projects more volatility call value higher equity is higher. More generally consider a risk neutral manager that can undertake a riskless project with return x 0. The manager can also undertake a project x with another uncertain project with returns distributed over [0,H] according to a c.d.f. G and density g>0. Thefirm has debt with face value F [0,H). We assume that the manager represents the shareholders. The return to shareholders in the case that the original project is kept is x 0 for sure. If the project is replaced they get: Y 2 = Y 1 =max(x 0 F, 0) Z H F (x F )g(x)dx > 0 10

11 Produced with a Trial Version of PDF Annotator - which is the expected value of the risky project x. If x 0 F (Y 1 =0) there will be replacement because y 2 > 0. If x 0 >F the project will be replaced if R H F (x F )g(x) :dx > x 0 F. Therefore, the project will be replaced iff: x 0 <x c (F )=F + = F + Z H F Z H 0 = F + x F = x + (x F )g(x)dx (x F )g(x)dx Z F Z F 0 Z F 0 (x F )g(x)dx (F x)g(x)dx 0 {z } risk premium (expected loss to debtholders) (x F )g(x)dx 11

12 where x c (F ) is the critical value. The case of equity only would lead to x c (0) = x. In this case the risk premium would be 0. The risk comes from asset shifting Capital Structure Risk. Using Leibneitz s Rule (see below) Z f2 (x) d f(x)dx = dx f 1 (x) we get the following: Z F Z f2 (x) f 1 (x) f 0 (x)dx + f 0 2(x)f(f 2 (x)) f 0 1(x)f(f 1 (x)) d (F x)g(x)dx = g(x)dx = G(F ) > 0 df 0 0 the risk premium is increasing in F. The higher the F the less efficient is the replacement rule. Z F How does the inefficiency effect the value of the firm? The higher the debt the lower the value of the firm because of the project substitution. 12

13 Produced with a Trial Version of PDF Annotator - Debt Overhang Problem: Myers (1977): Determinants of Corporate Borrowing. How does the debt of the past effect your current decision? M & M: capital structure does not change investment decisions. Assumptions: No taxes, no bankruptcy costs, risk free rate of 0. The real state of nature s will be realized in period 1. Let q(s) > 0 on [0, ) be the equilibrium price of a dollar delivered in period 1. The manager acts on behalf of the current shareholders. At t =0the capital structure is determined. The manager decides whether or not to invest I in a project that delivers V (s) in period 1. 13

14 The manager knows the state before he invests, so it knows the project has a positive NPV project or not. For simplicity assume that the firm has no assets in place, only grwoth opportunities. Consider first the case of no debt: V g is an option on assets in place and V E is spent, for example, on R & D (opportunity). 14

15 Produced with a Trial Version of PDF Annotator - If the manager wishes to invest he must issue new shares to raise I dollars and the value of the firm will be The manager will take the project iff V (s) I. Let sassumethatv increases in s so V (s a )=I Z V = (V (s) I)q(s) :ds s a 15

16 Produced with a Trial Version of PDF Annotator - Now consider the case in which it is possible to issue risky debt with face value P>0. The firm cannot issue safe debe (because the firm is worth nothing is states s<s a ). 16

17 Produced with a Trial Version of PDF Annotator - The maturity of the debt is important here. The following two cases are considered (in all cases the state of nature s is observed before the maturity of debt and the investment decision needs to be made). Case 1: The debt matures before the investment decision is made. Case 2: The debt matures after the investment decision is made. Case 1: The manager will undertake the project iff V (s) I + P. 17

18 Produced with a Trial Version of PDF Annotator - On the other hand, if V (s) <I+ P then the debt holders take over the firm. They will issue and invest iff V (s) I. M&Mholds. Case 2: V D = V E = Z Zs a s a V = V D + V E = min{v (s) I,P}q(s)ds max{v (s) I P, 0}q(s)ds Z s a {V (s) I}q(s)ds If the firm raises the amount I ans exercises its investment option, its balance sheet wtill be: 18

19 The manager will undertake the project iff V (s) I +F (Let V (sb) =I +F ). 19 Produced with a Trial Version of PDF Annotator -

20 Produced with a Trial Version of PDF Annotator - Therefore, V L = V U = V D = Z Zs b Zs a s b {V (s) I}q(s)ds {V (s) I}q(s)ds Pq(s)ds V L <V U, M & M does not hold. There is an inefficiency because the debtholders can not discipline the managers. (there are no bankruptcy costs). 20

21 The reason is Debt Overhang. The debt of the past effects the financing decision of the managers. 21

22 Produced with a Trial Version of PDF Annotator - Moral hazard Follow Tirole s basic model Risk neutrality Entrepreneur has assets A Needs to invest amount I Project pays R in success state, 0 in failure state Entrepreneur can choose to work or shirk if work, Pr(success) =p H if shirk, Pr(success) =p L non-pecuniary gain of shirking is B (interpretations: B is private benefit of taking another inferior project) 22

23 Assume project is positive NPV: p H R I>0 shirking is negative NPV: 0 >p L R I + B So need to give entrepreneur incentive to work As usual, if no limited liability, no problem entrepreneur pays lender I in both states With limited liability: state Contract is just payment R l to lender in success 23

24 (given risk neutrality, nothing gained by having lender pay borrower in failure state) So IC constraint is p H (R R l ) p L (R R l )+B i.e. R l R B p So maximum expected pledegeable income is µ p H R B p Note: Less than project income p H R so potential for distortion away from first-best Project is financed iff µ I A p H R B p 24

25 i.e. Observe A Ā I p H µ R B p if A<Ā, credit rationing: Entrepreneur would like to borrower at rate 1, but cannot. the critical value Ā is increasing in B decreasing in p/p H cannot distinguish between debt and equity here. 25

26 RISK SHIFTING Next, consider a closely related variant Entrepreneur choose between projects 1 and 2 project 2 is riskier: p 2 <p 1 lower expected value: p 2 R 2 <p 1 R 1 higher success payoff: R 2 >R 1 Suppose moreover that contract consists only of payment made in success state, R b why can t R b differ between R 1 and R 2? Precise success payoff may be unobservable, non-verifiable, or impossible to appropriate Entrepreneur chooses project 1 iff (R 1 R b ) p 1 (R 2 R b ) p 2 26

27 i.e. So pleageable income is R b p 1R 1 p 2 R 2 p p 1 µ p1 R 1 p 2 R 2 p <p 1 R 1 Problem is that debt-like contract induces entrepreneur to choose highrisk projects If we could make R b depend on R, easy to avoid problem could set R b (R 2 )=0 or just R b (R) =αr 27