Dilution Formula

Dilution Formula (Table of Contents)

• Formula
• Examples
• Calculator

What is the Dilution Formula?

The term “dilution” refers to the situation where the company’s existing shareholder’s ownership percentage reduces due issuance of new shares by that company. In other words, with the increase in the number of new shares issued, the percentage shareholding of the existing shareholders will go down if they don’t buy the new shares. It is also known as equity or stock dilution.

The formula for a diluted shareholding of an existing shareholder (say A) can be expressed as a number of existing shares held by A divided by the sum of the total number of existing shares and the total number of new shares issued. Mathematically, it is represented as,

where,

• N_A = Number of Existing Shares of A
• N_T = Total Number of Existing Shares
• N_N = Total Number of New Shares

Further, the formula for diluted share price can be expressed as a weighted average of a number of existing and new shares as shown below.

where,

• P_T = Current price of existing shares
• P_N = Issue price of new shares

Examples of Dilution Formula (With Excel Template)

Let’s take an example to understand the calculation of Dilution in a better manner.

Dilution Formula – Example #1

Let us take the example of a company named Tuber Inc. wherein the company issued 50,000 stock options to some of its employees. As of now, David, who is one of the non-employee stockholders of the company, has 5,000 shares out of the total outstanding shares of 100,000 shares of the company. Now, calculate the diluted shareholding of David if the employees of the company exercise their stock options.

Solution:

Existing Shareholding is calculated using the formula given below

Existing Shareholding = N_A / N_T

• Existing Shareholding = 5,000 / 100,000
• Existing Shareholding = 5%

Diluted Shareholding is calculated using the formula given below

Diluted Shareholding = N_A / (N_T + N_N)

• Diluted Shareholding = 5,000 / (100,000 + 50,000)
• Diluted Shareholding = 3.33%

Therefore, the shareholding of David is expected to dilute from 5% to 3.33% in case all the stock options are exercised.

Dilution Formula – Example #2

Let us take the example of another company that is scheduled to undertake a capex plan funded through the issuance of additional 100,000 shares. Currently, John holds 20,000 shares out of the total of 150,000 outstanding shares of the company and has no plans to purchase the new shares. Calculate the diluted shareholding of John post new shares issuance. Also, compute the diluted share price if the current price is $75 per share and the new shares are expected to be issued at $80 per share.

Solution:

Existing Shareholding is calculated using the formula given below

Existing Shareholding = N_A / N_T

• Existing Shareholding = 20,000 / 150,000
• Existing Shareholding = 13.33%

Diluted Shareholding is calculated using the formula given below

Diluted Shareholding = N_A / (N_T + N_N)

• Diluted Shareholding = 20,000 / (150,000 + 100,000)
• Diluted Shareholding = 8%

Diluted Share Price is calculated using the formula given below

Diluted Share Price = (P_T * N_T + P_N * N_N) / (N_T + N_N)

• Diluted Share Price = ($75 * 150,000 + $80 * 100,000) / (150,000 + 100,000)
• Diluted Share Price = $77 per share

Therefore, the shareholding of John is expected to dilute from 13.33% to 8%, while the share price is expected to increase from $75 per share to $80 per share with the new issuance.

Explanation

The formula for dilution can be derived by using the following steps:

Step 1: Firstly, determine the number of shares held by the subject shareholder (A in this case) and it is denoted by N_A.

Step 2: Next, determine the total number of shares of the company prior to the issuance of new shares and it is denoted by N_T.

Step 3: Next, determine the number of new shares issued by the company and it is denoted by N_N.

Step 4: Finally, the formula for diluted shareholding of shareholder A can be derived by dividing the number of existing shares held by A (step 1) by the sum of total number of existing shares of the company (step 2) and total number of new shares issued (step 3) as shown below.

Diluted Shareholding of A = N_A / (N_T + N_N)

Relevance and Use of Dilution Formula

The concept of dilution primarily revolves around the stock ownership in a company. The number of outstanding shares available in the stock market is known as the “float”. The concept of dilution comes into play when a company decides to issue additional stock, usually through a secondary offering. The existing shareholders’ ownership stake in the company, who bought the shares during its initial offering, thus becomes smaller.

Dilution Formula Calculator

You can use the following Dilution Formula Calculator