How will the exercise of the underwriters’ option affect the total shares outstanding and EPS?

Short answer:

When the underwriters exercise their “over‑allotment” (or “greenshoe”) option, the company issues additional shares that were not part of the original offering. Those extra shares are added to the company’s share‑count, so the total shares outstanding increase by the exact number of shares the underwriters purchase. Because the denominator of the earnings‑per‑share (EPS) calculation grows, the EPS will be diluted (i.e., reduced) unless the company’s net earnings increase by at least the same proportion.

Below is a detailed, step‑by‑step explanation of why and how this happens, plus a simple “what‑if” illustration to make the impact concrete.

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1. What is the underwriters’ option (over‑allotment)?

Feature	Description
Purpose	Gives the lead underwriter a right (usually up to 15 % of the original offering size) to buy extra shares at the offering price after the IPO/seasoned equity offering (SEO) is priced.
Why it exists	It stabilizes the market after the offering (the underwriter can “cover” any excess demand and prevent price volatility).
Typical size	Up to 15 % of the total shares sold in the primary offering (some agreements allow more).
Result	The company receives extra cash (the proceeds of the additional shares) and the share‑count expands by the same amount of shares the underwriter purchases.

In the Aura announcement (the only information supplied is that the underwriters have exercised the option), the company will now have “original shares + additional shares” outstanding.

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2. Direct effect on total shares outstanding

1. Original shares = the number of shares that were outstanding immediately before the offering (including any shares already sold in the current offering).
   
2. Option‑shares = the number of shares the underwriters elect to purchase (the “over‑allotment”).
   

New total shares outstanding =

[
\text{Original shares} + \text{Option‑shares}
]

The exact numeric increase can’t be derived from the headline alone, but the principle is:

• If the underwriters purchase 10 million shares, the total share count rises by 10 million.
  
• If they purchase the full 15 % of a 50‑million‑share offering, that adds 7.5 million shares.

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3. Effect on Earnings‑Per‑Share (EPS)

EPS definition (basic):

[
\text{EPS} = \frac{\text{Net income (or earnings)}}{\text{Shares outstanding}}
]

All else being equal (same net income), adding more shares reduces the denominator, thereby reducing the EPS.

3.1 Simple formula for the “post‑option” EPS

If we denote:

• NI = net income (or the portion of net income that will be used in the EPS calculation, typically GAAP or adjusted earnings)
  
• S₀ = shares outstanding before the option is exercised
  
• ΔS = the number of shares bought under the option

Then:

[
\text{New EPS} = \frac{NI}{S₀ + \Delta S}
]

3.2 “Dilution” concept

• Dilution percentage = (\frac{ΔS}{S₀ + ΔS})
  
  This is the proportionate increase in the share base.

• EPS impact (assuming net income unchanged):

[
\text{% change in EPS} = -\frac{ΔS}{S₀ + ΔS}
]

• Example: If the company originally had 100 million shares and the underwriters purchase 10 million more:

  • New shares = 110 million
    
  • Dilution = 10 / 110 = 9.09 %
    
  • If prior EPS was $3.00, new EPS (with unchanged earnings) would be:
    

[
\text{New EPS} = \frac{3.00 \times 100\ \text{M}}{110\ \text{M}} \approx \$2.73
]

That’s a 9 % reduction in EPS.

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4. Why the EPS might not fall as much in reality

1. Use of proceeds:

   • The cash raised can be used for growth (e.g., acquisitions, R&D, debt reduction).
     
   • If the investment generates additional earnings that offset the share‑dilution, EPS may stay flat or even increase over time.
     

2. Operating leverage:

   • If the newly financed assets have high operating leverage (high profit margins), the incremental earnings may exceed the incremental share count, producing accretive EPS.

3. Timing:

   • Immediately after the transaction, the static EPS will drop (pure dilution).
     
   • Over the medium‑ to long‑term, the net effect depends on the incremental earnings generated by the capital raised.

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5. Practical takeaway for investors and analysts

Step	What to look for
1. Size of the over‑allotment	Usually disclosed in the prospectus/press release (e.g., “up to 15 % of the offering”).
2. Number of shares issued	Multiply the percentage (e.g., 15 %) by the total number of shares sold in the offering.
3. New total share count	Add that number to the pre‑offering shares outstanding (which can be found in the latest 10‑K or 10‑Q).
4. Immediate EPS impact	Compute the dilution factor and apply it to the most recent EPS to gauge the “raw” dilution.
5. Potential earnings lift	Examine the company’s use‑of‑proceeds description: product launch, acquisition, debt payoff, etc., and model potential earnings growth to see if the EPS dilution is likely to be temporary or permanent.
6. Analyst commentary	Look for management’s guidance on expected revenue/EBITDA/Net‑income increases that could offset the share increase.

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6. Summary answer to the question

How will the exercise of the underwriters’ option affect the total shares outstanding and EPS?

• Total shares outstanding will increase by the exact number of shares the underwriters purchase under the over‑allotment (typically up to 15 % of the offering size).
  
• EPS will be diluted (i.e., it will decline) because the same level of net earnings will be spread over a larger number of shares. The magnitude of the decline equals the percentage increase in the share count (e.g., a 10 % increase in shares ≈ a 9‑10 % drop in EPS if earnings stay flat).
  
• Any eventual offsetting earnings increase—from the use of the proceeds—could partially or fully neutralize the dilution over time, but the immediate accounting effect is a higher share count and a lower EPS.

If you have the exact numbers (the size of the original offering and the exact over‑allotment amount), plug them into the formulas above to compute the precise post‑exercise share count and the resulting EPS.