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Corporate Finance Formulas:Principal-Agent Relationship:
• Agent’s utility: u ( w )−a (risk averse)
• Principal’s payoff: x−w (risk neutral)
Optimal Contract:
• Maximize the Principal’s expected payoff:
PH(xS-wS) +(1- PH)(xF-wF)
s.t.:
• Incentive compatibility constraint (IC) (the manager should be
compensated so as to prefer to exert high effort)
PHu(wS)+(1-PH)u(wF)- aH≧ PLu(wS)+(1-PL)u(wF) – aL
• Individual rationality constraints (IR) (the contract should be
attractive to the manager)
PHu(wS)+(1-PH)u(wF)-aH ≧U
where U is the Agent’s reservation utility (opportunity cost)
Solution:
a H ( 1−P L )−a L ( 1−PH )
u ( w S ) =U +
P H −P L
a L P H −a H P L
u ( w F )=U +
P H −P L
1-year investor:
• For a one-year investor, the potential cash flows include:
, • Dividend
• Sale of stock
Discount rate = cost of equity (rE)
Equity investors’ expected rate of return
We will take it as given, but one could use the Capital Asset Pricing
Model (CAPM) to estimate this rate.
• PV of the potential cash flows:
¿1 + P 1
P0=
1+r E
• If the current stock price < this amount → investors would rush
in and buy it → increasing the stock’s price
• If the current stock price > this amount → investors who
already hold this stock would sell it → lowering the stock’s price
¿1 + P 1 ¿1 P1−P0
• r E=
P0
−1= +
P0 P0
¿1
P0
= Dividend yield
P 1−P0
P0
= Capital Gain rate
• The expected total return of the stock should equal the
expected return of other investments available in the market
with the equivalent risk
A multi-year investor:
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