We know that if the firm goes public, the entrepreneur sells a fraction (α_E) of his shares to satisfy his personal liquidity requirements and retains private benefits of control.

However, if the firm is acquired at time t = 0, then he has to give up private benefits of control. Thus, we see that the objective of the entrepreneur in making the exit decision at time t = 0 is to maximize the sum of cash flow received at time t = 0 from selling a fraction of equity (α_E) in the firm, the expected cash flow at time t = 1, and the total estimated value of the private benefits of control accruing to him.

Similarly, if the firm goes public at time t = 0, the PE investor sells a fraction (α_V) of his shares to satisfy personal liquidity requirements but does not gain any private benefits of control as the entrepreneur receives. On the other hand, if the firm is acquired at time t = 0, he receives no private benefits. Thus, we see that the objective of the private equity investor in making the exit decision at time t = 0 is to maximize the sum of cash flow received at time t = 0 from selling a fraction of equity in the firm and the expected cash flow at time t = 1.

It is assumed that there is no information asymmetry between the acquirer and the firm i.e. the acquirer is able to correctly assess the type of the firm. Since the acquirer has considerable bargaining power, he will pay only a fraction (ρ) of the intrinsic net present value of the firm to the target firm’s insiders. After the takeover, the ac-

quirer owns the entire firm, provides the capital I for new investment, and the firm’s management is replaced. For both the firms, there is synergy created due to the acquisition such that the probability of success in competition with incumbent firms increases to p_A, where we assume that 1 > p_A > p_H > p_L. Here Bayar and Chemmanur [10] assume that the increase in the probability of success in product market competition as a result of an acquisition is higher for a L-type firm. Thus, the expected time 1 cash flow for the firms after an acquisition is then given by [I + p_AV_S + (1 − p_A)V_F]. Thus, intrinsic value of the firm pre-acquisition is V_A, where, V_A = p_AV_S + (1 − p_A)V_F. Thus, since the expected value of the firm is V_A and due to bargaining power, acquirer will pay only a fraction (ρ), the acquirer ends up paying a value ρ * V_A to both the firms.

If the firm decides to go for an IPO, a fraction γ of the firm is offered to the public market investors who subscribe for the IPO. To satisfy their liquidity demands, the entrepreneur and the PE investor sell fractions α_V and α_E, respectively, of their remaining shareholdings δ_E(1 − γ) and δ_V(1 − γ), respectively, as part of the IPO. The number of shares outstanding for the firm is normalized to 1, so that the fraction of shares offered in the IPO becomes γ + (δ_Eα_E + δ_Vα_V)(1 − γ). As discussed earlier, price P_ipo is decided by the firm keeping in mind the beliefs of the investors. Also, the prior probability assessment of IPO market investors is and. These probabilities are updated by Bayes’ rule depending on the strategies of the types of firms.

Using the concept of Perfect Bayesian Equilibrium applied to the above model, Bayar and Chemmanur [10] show that for the H-type firms, the payoff from choosing an IPO is always larger than the payoff from choosing an acquisition. However, for L-type firms, it is possible for the payoffs from IPO and acquisition to be equal. Thus, they derive the following semi-separating equilibrium: H-type firms will always choose to go for an IPO i.e. pure strategy and L-type firms will choose to go for an IPO with probability and for acquisition with probability i.e. mixed strategy, where is given by:

There are certain common conditions which Sherman [11] assumes for both the IPO models. The market consists of N investors who have an access to capital and information (informed investors). Since both the IPO models involve a cost of information production, investors much pay C(α) to purchase information which reveals the type of firm (either H-type or L-type) with probability of α and gives a neutral signal M with probability of (1 − α). It is assumed that the probability of receiving a false signal is zero. The mathematical properties of C(α) are: it is twice differentiable, strictly convex and strictly increasing for a value of α Î (0, 1). Apart from the cost of information, each investor faces a “fixed entry cost” of e > 0 if he wishes to participate in the IPO. Although it seems as if investors are carrying the burden of information production, these costs which ultimately reduce the equilibrium IPO price set by the firm, thus signifying that information production costs are actually borne by the issuing firm to reduce information asymmetry.

In the book building method of IPOs, the issuing firm hires an underwriter (investment bank) to help place its shares with different types of investors. The underwriter selects K risk-neutral and potentially informed investors to evaluate the offering in a road show. The model assumes that the underwriter has the flexibility to choose allocation and price for each investor depending on the quality of the signal reported by them and other investors. Given these parameters of the book building process, Sherman [11] calculates the total proceeds (equivalent to P_IPO in Bayar & Chemmanur [10] model) to the issuing firm as:

We can see that this expression is similar to the equilibrium IPO price in the [10] model but includes an extra term “K[C(α) + e]” which represents the cost of information production in the book building process. We will incorporate this in the Bayar & Chemmanur [10] semi-separating equilibrium and derive the relationship between the IPO probability of L-type firm, β and the book building parameters K, C(α) and e. This analysis will help us understand how parameters of the IPO book building process affect the issuing firm’s decision to choose an IPO over an acquisition.

Sherman [11] introduces two types of multi-unit, sealed-bid auctions: a uniform price auction and a discriminatory auction. He goes on to show that the expected IPO proceeds in both types of auctions are the same, thus we will only discuss the uniform price auctions in this paper. The issuing firm wants to auction X number of shares and the lowest bid possible is the price of shares of a L-type firm. This is equivalent to a reserve price which is typically set in auctions. There are N potential bidders such that N > X. Each of the bidders chooses p, which is that probability that he will enter the auction and α, which is the accuracy of the information purchased. There are two basic rules of a uniform price auction: (i) if there are (X + 1) or more bids, all X bidding winners will pay the (X + 1)^st bid, else, (ii) if there are less than (X + 1) bids, all bidders pay the reservation price which is the value of L-type shares. Since it is not necessary that each potential bidder will actually bid, there is a probability that the auction will be incomplete i.e. fewer that X shares will be sold. This uncertainty is a significant disadvantage of using auctions instead of book building. Given these parameters of the uniform price auction process, Sherman [11] calculates the total proceeds (equivalent to P_IPO in Bayar & Chemmanur [10] model) to the issuing firm as:

where, P_x is the probability that the auction will be unsuccessful i.e. lower than X shares will be sold (due to less than optimal bidders bidding) and is given by:

where P (entry = i) is the entry probability of the i^th bidder

Once again, we see that this IPO price is similar to Bayar & Chemmanur [10] with the addition of two terms: (i) “” which is the cost of information production and (ii) “(1 − P_x)” which is the probability that

the auction with be successful. We will incorporate this in the Bayar & Chemmanur [10] semi-separating equilibrium and derive the relationship between the IPO probability of L-type firm, β and the auction parameters p, N, (1 − P_x), C(α) and e. This analysis will help us understand how parameters of the IPO auction process affect the issuing firm’s decision to choose an IPO over an acquisition.

In this section, we incorporate the IPO book building process in the Bayar & Chemmanur [10] and analyse the semi-separating equilibrium which they derive. In the semi-separating equilibrium, we know that H-type firms always choose to go public whereas L-type firms choose IPO with probability β_L and acquisition with probability (1 − β_L). We will derive the equilibrium in the presence of book building and analyse the effect of the book building parameters on β_L. The introduction of book building only affects the equilibrium IPO price set by the firms, does not affect the indifference conditions and hence does not affect the equilibrium derived by Bayar & Chemmanur [10] .

Proposition 1: Choice between IPO and Acquisition in an entrepreneur-controlled firm in the presence of book building

In the presence of book building process for IPOs:

1) The entrepreneur takes the H-type firm public with probability 1.

2) The L-type firm goes public with probability β_L and for an acquisition with probability (1 − β_L) such that,

The equilibrium IPO price is given by Equation (10)

Proof.

From Equation (2), we see that

Since the investors’ beliefs are updated using Bayes’ rule, we get,

Using Equations (2), (6) and (7), we get,

Rearranging Equation (8), we derive the probability of a L-type firm choosing an IPO as mentioned in proposition 1.

Next, we analyse the available payoffs to the L-type firm and derive the equilibrium indifference condition. Since L-type firms use a mixed strategy in equilibrium, the indifference condition in Equation (9) holds.

Solving Equation (9) which is quadratic in the equilibrium IPO price, we derive the expression for in an entrepreneur-controlled firm.

where,

Proposition 2: Statics of the exit choice between IPO and Acquisition in an entrepreneur controlled firm in the presence of book building

The probability of a L-type firm choosing an IPO (β_L): (a) decreases when the number of informed investors (K) in the road show increases; (b) decreases when the cost of acquiring information (C(α)) increases; (c) decreases when the fixed entry cost per investor (e) increases.

Proof.

To derive the relationship between probability of choosing IPO (β_L) and the parameters of the book building process, we partially differentiate β_L in Equation (5) with respect to K, C(α) and e. Proposition 2(a) signifies the effect of the road show on the exit decision. An increase in number of road show investors signifies increase in time and cost required for the book building process to be successful. Thus, if an entrepreneur knows ex-ante, that a large number of road show investors are necessary to make the IPO successful, the IPO option becomes less attractive to him. Proposition 2(b) discusses the effect of cost of information acquisition on the exit choice. The cost of acquiring information (C) will increase as the desired level of information accuracy (α) increases. Thus, if the entrepreneur and investors desire a high level of information and pricing accuracy, the cost of information production will increase, thus making IPO a less attractive option. This result signifies that in an IPO market with severe information asymmetry, the attractiveness of an IPO as compared to an acquisition reduces significantly. Proposition 2(c) purely reflects the effect of the fixed cost of participating in an IPO on the exit choice. If the fixed cost of participation per investor is high, IPO becomes less attractive than acquisition.

In this section, we incorporate the uniform price auction process in the Bayar & Chemmanur [10] and analyse the semi-separating equilibrium which they derive. In the semi-separating equilibrium, we know that H-type firms always choose to go public whereas L-type firms choose IPO with probability β_L and acquisition with probability (1 − β_L). We will derive the equilibrium in the presence of uniform price auction and analyse the effect of the auction parameters on β_L. The introduction of book building only affects the equilibrium IPO price set by the firms, does not affect the indifference conditions and hence does not affect the equilibrium derived by Bayar & Chemmanur [10] .

Proposition 3: Choice between IPO and acquisition in an entrepreneur-controlled firm in the presence of uniform price auctions

In the presence of uniform price auction for IPOs:

1) The entrepreneur takes the H-type firm public with probability 1.

2) The L-type firm goes public with probability β_L and for an acquisition with probability (1 − β_L) such that,

The equilibrium IPO price is given by Equation (10)

Proof.

From Equation (2), we see that

Since the investors’ beliefs are updated using Bayes’ rule, we get from Equations (6) and (7),

Using Equations (3), (6) and (7), we get,

Rearranging Equation (16), we derive the probability of a L-type firm choosing an IPO as mentioned in proposition 3.

Next, we analyse the available payoffs to the L-type firm and derive the equilibrium indifference condition. Since L-type firms use a mixed strategy in equilibrium, the indifference condition in Equation (9) holds. Following that, we see that the equilibrium IPO price is given by Equation (10).

Proposition 4: Statics of the exit choice between IPO and acquisition in an entrepreneur controlled firm in the presence of uniform price auction

The probability of a L-type firm choosing an IPO (β_L): (a) decreases when the number of potential bidders (N) in the auction increases; (b) increases when the certainty of the auction being successful (1 − P_x) increases; (c) decreases when the cost of acquiring information (C(α)) increases; (d) decreases when the fixed entry cost per investor (e) increases.

Proof.

Proposition 4(a) signifies the effect of the number of potential bidders on the exit decision. We know that each participating bidder has to pay a fixed fee of “e”. Thus, if more bidders participate, the total fixed cost “N*e” increases, thus reducing the IPO price which can be set by the firm. Also, Sherman [11] mentions that in the uniform price auctions, the increase in number of potential bidders (N) causes either the increase in variance in the number of entrants or decrease in the expected number of entrants, or both. This adversely affects the total expected proceeds from the IPO. Proposition 4(b) analyses the effect of uncertainty of the success of the auction on the exit decision. If the certainty that the auction will be successful i.e. the IPO offering is fully subscribed by the bidders, is high, then the entrepreneur is more likely to prefer an IPO over acquisition. Proposition 4(c) discusses the effect of cost of information acquisition on the exit choice and proposition 4(d) purely reflects the effect of the fixed cost of participating in an IPO on the exit choice. If the fixed cost of participation per investor is high, IPO becomes less attractive than acquisition.

To derive the relationship between probability of choosing IPO (β_L) and the parameters of the book building process, we partially differentiate β_L in Equation (15) with respect to K, C(α) and e.

Thus, we see that the sign of each partial derivative is consistent with the relationships mentioned in propositions 4(a) to 4(d).

In the presence of IPO methods like book building and auctions, we observe that the probability of choosing IPOs reduces as the cost of information production increases. Thus, we predict that the ratio of IPOs to acquisitions should be greater in markets where the information asymmetry problem is severe. We know that developed markets such as USA have many transparent market mechanisms to reduce information asymmetry whereas the information asymmetry problem is severe in an emerging market like India. Thus, our model predicts that the ratio of IPOs to acquisitions should be greater in USA than in India. This prediction of our model is supported by data. We see from Bayar & Chemmanur [9] that the ratio is IPOs to acquisitions in USA from 2004 to 2007 is close to 1, whereas, the ratio of IPOs to acquisitions in India from 2004 to 2007 is always less than 0.5². The Wall Street Journal³ has also reported that the quantum of IPOs in USA has reduced since the introduction of the Sarbanes-Oxley Act of 2002, which has increased the cost of going public due to increased governance and disclosure requirements.

In the presence of book building, we see that the probability of choosing IPOs reduces as the number of road show investors increases. If a large number of investors are necessary to make a road show successful, it increases the cost of going public. Thus, our model predicts that the ratio of IPOs to acquisitions should be lower in markets where the size and scale of the road show are large. We know that firms going public in developed markets like USA will typically conduct their road shows only in USA and other developed markets like UK and Europe. However, firms going public in emerging markets like India will typically conduct their road shows in India, other emerging markets like China and in developed markets like USA, UK and Europe. Thus, we see that road shows of emerging market firms need to be on a larger scale than those in developed markets. Thus, our model predicts that ratio of IPOs to acquisitions in developed markets should be higher than that in emerging markets.