Questions:
What are the differences between: a Private Offering, a Best Effort Offering, Firm Committment Underwriting or All or None Underwriting.

Let's say we want to go with a best effort offering. Last year, we issued 50,000 shares and our desired price was $150 but we ended up selling only 35,000 shares. We lowered the price to $120 to sell the additional ones, but 5000 remained. We had to sell these at $100.

Our company is planning to issue 1,000,000 shares in the stock market. Our desired price is $250. 

If we sell the same portions of shares at the same percentage discounts, what could we expect to raise?

Reference answers:
There are different types of offerings in which investment banks assist including private offering, best effort offering, firm commitment and all or none. The following is the expected amount of capital that can be generated in each of the cases.

# Private Offering

In the private offering, the shares are sold only to a selected list of investors that the investment banks identify. The market is not brought into the transaction due to which there is no volatility in the share price. However, it can be the case the investors might not agree to the offered price and they would negotiate for a lower price.
# Best effort offering

In this offering, the underwriter commits in good faith to sell as much of the issue at the agreed price as possible, there is no financial or legal responsibility imposed on the underwriter for any unsold shares or deal performance.

In the best-effort offering, you can expect to raise capital based on the price established through the supply and demand in the market.

# Firm commitment

In the case of a firm commitment, the underwriter agrees to buy the entire issue at a certain price. If the underwriter fails to sell the entire issue, the underwriter must take full financial responsibility for any unsold shares.

In the firm commitment offering, the investment bank will guarantee that the shares will be sold at the agreed price. If they are unable to sell, they will buy them themselves. So you can be sure that all the shares will be sold at the desired price

# All or none

With an all or none underwriting, the issuer determines it must receive the proceeds from the sale of all of the securities. Investors’ funds are held in escrow until all of the securities are sold. If all of the securities are sold, the proceeds are released to the issuer. If all of the securities are not sold, the issue is cancelled and the investors’ funds are returned to them.

Based on your previous experience, you can expect the following amount of capital offering calculated using the expected value

Last time you were able to generate the following 
35000 shares (70%) at $150 (full price)
10000 shares (20%) at $120 (20% discount)
5000 shares (10%) at $100 (33% discount)

We can use these values to establish an expected value for the current offering

70% shares at full price
shares: 70% of 1000000 = 700000 
price: $250 
total = 700000 * $250 = $175000000

20% shares at 20% discount
shares: 20% of 1000000 = 200000
price: $250 - 20% ($50) = $ 200
total: 200000 * $200 = $ 40000000

10% shares at a 33% discount 
shares: 10% of 1000000 = 100000
price: $250 - 33% ($83.33) = $ 166.66
total: $100000 * $166.66 = $ 16660000

Total capital raised = $175000000 + $ 40000000 + $ 6660000 = $221.66 Million

Therefore, you could expect to raise around $220 Million.