PhD Course in Corporate Finance

Transcription

1 Initial Public Offerings 1 Revised March 8, Professor of Corporate Finance, University of Mannheim; Homepage: Tel: +49 (621) , maug@uni-mannheim.de. This note is made publicly available subject to the condition that any user notifies the author of its use. Please bring any errors and omissions to the attention of the author.

2 The Model Based on Rock (1986) A company offers 1 share of its common stock for the first time in an initial public offering (IPO). Value of company is uncertain: { V with probability p V = V with probability 1 p The share is offered at an initial offering price P 0 ; the price cannot be revised.

3 There are two groups of investors: Informed investors acuire information about the company. They apply for 0 < Q I 1 shares if and only if they expect to break at least even, otherwise they do not apply for shares. Uninformed investors do not acuire any information and only know the probability distribution for firm values. They apply for Q U 1 shares if and only if they expect to break at least even, otherwise they do not apply for shares. Note: If uninformed investors and informed investors apply for shares, then demand exceeds supply. Assume also that the number of shares cannot be increased in this case (no Greenshoe option ).

4 We also assume: Investors cannot short sell the shares. The information acuired by informed investors is of the form of a binary signal σ {σ; σ} where: Pr (σ = σ V = V ) = Pr ( σ = σ V = V ) = 1 ɛ. Hence ɛ is the error of the signal. Assume for now that ɛ = 0, i. e. informed investors receive a perfect signal. If demand exceeds supply, shares are rationed pro rata, i. e. 1 every investor receives a proportion Q U +Q I per share ordered.

5 From these assumptions it is easy to derive the decision rule of informed investors: Apply if P 0 V, Do not apply if P 0 > V. It is clear that the issuer will never issue shares below V, and no investor will ever buy shares if P 0 > V. Hence P 0 [ V, V ] and the policy of the informed investor can be rewritten as: Apply if V = V, Do not apply if V = V.

6 Then we can write the incentive compatibility constraint for the uninformed investors as follows: Q U ( ) p V P 0 + (1 p) (V P0 ) 0. Q U + Q I This implies that the offering price is bounded from above. Define α Q U Q U +Q I. Then: P 0 αp V + (1 p) V 1 (1 α) p. Uninformed investors will not participate if this constraint is violated.

7 This shows immediately that the offer is underpriced. The average price in secondary trading is: P 1 = p V + (1 p) V. Then the average IPO discount is: IPO = P 1 P 0 = p V + (1 p) V ( 1 ( 1 ) α 1 (1 α) p ) 1 1 (1 α) p = p (1 p) ( V V ) 1 α 1 (1 α) p.

8 Note that: Exercise The variance of a Bernoulli random variable like firm value is p (1 p) ( V V ) 2, hence the IPO discount is closely related to the uncertainty or volatility of the share price. The IPO discount is zero only if α = 1 as long as volatility is not zero. Hence, 1 α is a parameter for the degree of adverse selection. Generalize the model above for the case where ɛ > 0 and informed investors information is only imperfect. Derive new expressions for P 0 and IPO.

9 Exercise Extend the model of Rock (1986) to include underwriter price support in the secondary market as follows. Assume the firm hires an underwriter who is committed to buy all shares from the firm at the price P F. The underwriter sells the shares in the IPO for P 0 and agrees to buy shares back in the secondary market for some support price P. Only investors who bought shares in the IPO can sell them back at the support price.

10 Solve the model using the following steps: Assume that P [ V, V ]. Rewrite the condition for the uninformed investors to participate in the IPO. Show that P 0 becomes a function of P. Derive this function and show whether it is decreasing or increasing. Write down the payoff of the underwriter. This must include the payoff from buying shares from the firm and selling them to investors, and the expected cost of price support, i. e. the cost of buying shares above their intrinsic value. (Hint: assume the underwriter buys these shares from investors and immediately sells them in the secondary market for the intrinsic value P 1 ). From this, what is the price P F the underwriter can offer the firm and still make a positive profit?

11 Assume many banks compete for underwriting the issue, so the underwriter makes zero profits in euilibrium and the underwriter who buys the shares from the firm at the highest price P F conducts the offering. Which level of price support P is offered in euilibrium? Verify the initial assumption that P [ V, V ]. Hence, what is the euilibrium solution for P 0 and P F? Show that the euilibrium has the following properties: (1) the adverse selection problem is eliminated completely, and the firm receives a fair price of the stock, and (2) the IPO is overpriced. Comment on this solution. Note: Models of IPO price support were published by Chowdhry and Nanda (1996) and Benveniste, BuSaba and Wilhelm (1996).

12 Based on Benveniste and Wilhelm (1990) Entrepreneur wants to take his firm public and sell one share to two investors. Each investor observes a signal that is either good (g) with probability p or bad (b) with probability 1 p. Once listed, shares are trading at a price P s where s {0, 1, 2}, the number of good signals: P s = P (2 s) α.

13 The entrepreneur hires an investment bank that sells the shares at offering prices PO s to the public and elicits the information of the two investors by way of a mechanism through direct revelation (the revelation principle applies). The investment bank can choose the allocation s g, s b as a function of the information investors reveal to the bank during bookbuilding. Let φ 1 be the minimum number of shares the entrepreneur wishes to sell in the issue. Let f φ/2 be the maximum each investor is willing to buy.

14 The objective of the bank and the entrepreneur is to choose an allocation and offering prices to maximize expected proceeds. Shares not sold in the IPO will be sold in an SEO later: Π = E (P s ) p 2 ( P 2 PO) g 2p (1 p) ( P 1 PO) 1 ( 1 g + b 1 ) (1 p) 2 ( P 0 PO) b subject to the following constraints. 1 Sell at least φ and at most one share: 1 2g 2 φ 1 g 1 + b 1 φ (1) 1 2b 0 φ

15 2 Investors are willing to buy at most f shares each: 0 g s, b s f s = 0, 1, 2. (2) 3 It must be incentive compatible for the investor with good information to reveal her information truthfully: p ( P 2 P 2 O) 2 g + (1 p) ( P 1 P 1 O) 1 g (3) p ( P 2 P 1 O) 1 b + (1 p) ( P 1 P 0 O) 0 b (4) = p ( P 1 + α P 1 O) 1 b + (1 p) ( P 0 + α P 0 O) 0 b.(5)

16 4 It must be incentive compatible for the investor with bad information to reveal her information truthfully: p ( P 1 P 1 O) 1 b + (1 p) ( P 0 P 0 O) 0 b p ( P 1 P 2 O) 2 g + (1 p) ( P 0 P 1 O) 1 g (6) = p ( P 2 α P 2 O) 1 b + (1 p) ( P 1 α P 1 O) 0 b. 5 Investors are not willing to pay more for shares than they are worth (participation constraint): P s P s 0 s = 0, 1, 2. (7)

17 Analysis Rewrite Π as: Π = E (P s ) 2p [ p ( P 2 PO) 2 2 g + (1 p) ( P 1 PO 1 ) ] 1 g 2 (1 p) [ p ( P 1 PO) 1 1 b + (1 p) ( P 0 PO 0 ) ] 0 b Assume that only (4) is binding and that (6) is not binding. Then substitute (4) into the first suare brackets: Π = E (P s ) 2p [ p ( P 1 + α PO) 1 1 b + (1 p) ( P 0 + α PO 0 ) ] 0 b 2 (1 p) [ p ( P 1 PO) 1 1 b + (1 p) ( P 0 PO 0 ) ] 0 b = E (P s ) 2 [ p ( P 1 PO) 1 1 b + (1 p) ( P 0 PO 0 ) ] 0 b 2pα [ pb 1 + (1 p) b] 0.

18 Now choose the allocation and prices as follows: 1 Π is increasing in P 1 O and P0 O. Hence, choose P1 O = P1 and P 0 O = P0, so (7) is binding for s = 0, 1. Then the first term in suare bracket vanishes. 2 Π is decreasing in b 0 and 1 b, so choose these as small as possible, so from (1), b 0 = φ/2, 1 b = f and 1 g = φ f.

19 3 Rewrite (4) and choose ( P 2 P 2 O) 2 g so that (4) is just satisfied: p ( P 2 P 2 O) 2 g = α (pf + (1 p) φ/2). Solving for P0 2 gives: [ f PO 2 = P2 α g 2 + ] (1 p) φ 2pg 2 Clearly, an admissable solution is 2 g = f and Note that [ PO 2 = P2 α 1 + ] (1 p) φ 2pf. (8) P 2 α P 2 O = α (1 p) φ 2pf > 0. (9)

20 4 With this, PO 2 < P1 = P 2 α. Note that the left hand side of (6) euals zero because the offering prices eual the aftermarket prices from the first step. The right hand side of (6) can be rewritten using (9): ( ) α (1 p) φ 0 p f + (1 p) ( α) φ 2pf 2 = 0, where we have used that P 1 O = P1, 0 b = φ/2, and 1 b = f, hence (6) is also satisfied.

21 Discussion Underpricing is the expected difference between market price and offering price: Underpricing is therefore: Increasing in α, Increasing in φ, Decreasing in f. E (P s PO s ) = ( p2 P 2 PO 2 ) = p 2 α [ 1 + (1 p) φ pf ].

22 Expected proceeds are: E (P s ) 2pα [pf + (1 p) φ/2] The second expression represents the rents extracted by informed investors. The offering price is not monotonic (P 2 O < P1 O = P1 ). If that would be reuired, then choose P 1 O < P1 and underpricing increases.

23 Regular investors Assume the bank can extract some of the rents of regular investors and induce them to accept a loss L > 0. Then (7) becomes P s + L P s 0 s = 0, 1, 2. (10) Clearly, the bank will then overprice some IPOs and increase the offering amount.

24 Motivation Based on Khanna, Noe and Sonti (2008) Puzzling observations about IPOs: Hot issue markets: why do many firms suddenly decide to go public? What is the window of opportunity? Underpricing is higher in hot markets than in cold markets. Why do firms not shift to markets where they have to leave less money on the table? Why does competition not eliminate banks rents in hot markets? Why are firms during hot markets younger, less profitable, and with less insider ownership?

25 The Model Economy has N entrepreneurs who may go public. Each is matched with one of a continuum of underwriters: A fraction ρ of projects is good ( G ) with payoff X = 1, 1 ρ is bad ( B ) with payoff X = 0. Going public has an opportunity cost w. Each firm bargains with the underwriter it is matched with who sets the offer price p s. Firms capture a fraction β of the issue price, underwriters 1 β. Underwriters benefit from higher prices through higher fees; they are penalized for overpricing IPOs. Underwriters hire a uantity η [0, 1] of bankers who cost θ and screen projects. With probability 1 η they receive an uninformed signal U. With probability η they become perfectly informed so that Pr (H 1) = Pr (L 0) = η.

26 Timing of Events

27 Solution ρ 1 Average uality of the IPO pool is π = ρ+α(1 ρ), assuming that all G projects and α of the B projects go public ( single crossing ). This is the fundamental value of the shares. 2 There is no underpricing for s = L, H. There is underpricing for s = U : p U < π. 3 The difference in issue prices between G and B firms is βη. G entrepreneurs issue with probability 1.

28 A seuentially rational euilibrium is a triple (π, η, θ) such that: 1 B firms play a mixed strategy: β (1 η) p U = w. 2 The market for bankers clears: Nη (ρ + α (1 ρ)) = Nη ρ π 1. 3 Underwriters hire screening labor ( bankers ) such that V = θ. 4 Underpricing: p U < π.

29 Proposition The larger the pool of potential IPOs (N ) in an overheated euilibrium, the lower the average uality of firms that want to go public (π ). The higher the average uality of IPOs issued, the higher the benefit for B firms to go public. The higher the probability of screening, the lower the benefit for B firms to go public. Hence, B s indifference condition implies that a higher π has to be compensated by a higher η. A higher N (or ρ) shifts the indifference curve in π η space to the right and euilibrium π down. Fixed supply of bankers reduces π: A higher uality ρ or a larger size N of the IPO pool reduces the uality of IPO applicants.

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31 Hot and Cold Markets Proposition If the number of good projects ρn is below β w, there exists an euilibrium in which only good projects try to obtain funding. If ρn is above this cut-off, some bad firms apply for funding. Implications: There is a discontinuous shift at some point such that above the threshold, there are more firms apply for funds. Such a shock is more likely to come from market-wide shocks than from industry-specific IPO waves. β

32 Discussion The story in a nutshell: Hot markets are ignited for neoclassical reasons: The number of good firms that want to go public crosses a critical threshold. Once sufficiently many investment bankers are too busy screening projects, the uality of screening declines, which opens a window of opportunity for bad firms. Bad firms are drawn into the market, which becomes even more crowded, deteriorating the uality of screening further. The uality of IPOs declines and the uncertainty about uality increases, leading to more underpricing.