Variable

Description

p_H

Probability of success in the product market of the H-type firm

p_L

Probability of success in the product market of the L-type firm

δ_E

Fraction of initial equity in the firm held by the entrepreneur

δ_V

Fraction of initial equity in the firm held by the private equity investor

δ_O

Fraction of initial equity in the firm held by the other minority investors

I

Investment needed by the firm at time t = 0

α_E

Fraction of shares sold in the IPO by the entrepreneur for liquidity needs

α_V

Fraction of shares sold in the IPO by the private equity investor for liquidity needs

V

Expected value of the firm at time t = 1

V_S

Value of the firm at time t = 1 if the firms succeeds

V_F

Value of the firm at time t=1 if the firms fails

V_H

Expected value of a H-type firm at time t = 1 if the firm chooses an IPO at time t = 0

V_L

Expected value of a L-type firm at time t = 1 if the firm chooses an IPO at time t = 0

Equilibrium IPO price set by the issuing firm at time t = 0

ρ

Fraction of the intrinsic value of the firm paid by the acquirer i.e. bargaining power of the acquirer

V_A

Value of the firm at time t = 1 if it chooses acquisition at time t = 0

p_A

Probability of success in the product market of a firm after acquisition

γ

Fraction of shares offered to the new shareholders in an IPO

θ

Fraction of H-type firms in the universe of firms as perceived by IPO market investors

β_H

Probability that a H-type firm will choose an IPO at time t = 0

β_L

Probability that a L-type firm will choose an IPO at time t = 0

P_acq

Acquisition price paid by the acquirer

Equilibrium IPO price set by the issuing firm at time t = 0 if the firm is controlled by the entrepreneur

Equilibrium IPO price set by the issuing firm at time t = 0 if the firm is controlled by the PE investor

B

Private benefits of controlled enjoyed by the entrepreneur

C(α)

Cost of acquiring information about the type of firm which has an accuracy of α

e

Fixed cost per investor to participate in the IPO process

K

Number of informed investors which the underwriter selects for a road show in the book building process

p

Probability that a participating investor will actually bid in the IPO auction, called entry probability

N

Number of potential bidders in the IPO auction

X

Number of shares offered in the IPO auction

P_x

Probability that the IPO auction will be unsuccessful i.e. less than X shares sold