Question

The firm Ragnar has announced an initial public offering of shares (IPO). The shares are being offered in the IPO at a price of $6 each. All potential investors know that at this price the share is either undervalued by $0.50 (probability 60%) or overvalued by $0.30 (probability 40%).

‘Informed’ investors such as banks are able to distinguish whether the share is overvalued or undervalued. ‘Uninformed’ investors are not able to do this. Demand from uninformed investors is sufficient to take up all the shares offered in the IPO.
If the demand for the shares is greater than the number offered, the shares will be rationed.

You are an uninformed investor with $12,000 to invest. If rationing occurs you will only be able to buy 800 of Ragnar’s IPO shares.

(a) By what percentage is the IPO underpriced/overpriced?

(b) What would be your expected profit if you were able to buy 2,000 of the IPO shares? Do you expect to be able to do this? Why/why not?

(c) As an uninformed investor, what is your expected profit from participating in the IPO?

(d) What would your expected profit be if the undervaluation is only $0.20 per share instead of $0.50, and everything else unchanged? What is the underpricing percentage now?

(e) Explain what is meant by the ‘winner’s curse’ in the context of IPOs, with reference to your answers for the previous parts of the question. Briefly discuss one other possible reason for the empirically observed underpricing of IPOs.

Answer 1

The firm Ragnar has announced an initial public offering of shares (IPO). The shares are being offered in the IPO at a price of $6 each. All potential investors know that at this price the share is either undervalued by $0.50 (probability 60%) or overvalued by $0.30 (probability 40%).

a) Percentage is the IPO underpriced/overpriced.

Price of IPO =6

Expected value = 6+(0.5*60%)+(-0.3*40%)

= $6.18

underpriced share = 6.18-6

= 0.18

in % = 0.18/(6.18)*100

= 2.91%

b)Expected profit if you were able to buy 2,000 of the IPO shares

Profit if able to buy all shares = 2000*0.18

= $900

Undervaluation of share prices causes high demand. So, we will not able to get all 2000 shares .we would be able to get 800 shares only.

c)Expected profit from participating in the IPO

Profit of uninformed decision = 800*0.18

= $144

d)Expected profit be if the undervaluation is only $0.20 per share instead of $0.50, and everything else unchanged

expected value = Sum of (Probability*Valuation)

= (0.2*60%)+(-0.3*40%)

= 0

So, there is no under or over pricing of the share. The share is expected to be fairly priced.

Underpricing percentage = 0

Because there is no under or overpriced the IPO is expected to be priced fairly.

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