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6 Statement of Changes in Equity

Linking the Income Statement to the Statement of Financial Position

Jacqueline Gagnon

Ratio Analysis

Evaluating Earnings on Contributed Capital

A lightbulb brain in a circle—the 'think' section of the think-see-do approach.

Earnings per share (EPS) is always in the financial press. It’s a popular ratio! EPS lets us know how much income shareholders have earned on each share. Why does EPS matter? Because companies invest the capital contributed by shareholders to create value. EPS gives shareholders feedback on how much value has been created using their shares during the period. Here’s how EPS is calculated:

    \begin{equation*} {{\textbf{Earnings per Share}}\atop (\textbf{EPS})}\;=\;\dfrac{{\text{Income Attributable to}\atop \text{Common Shareholders}}}{{\text{Weighted Average Number of}\atop \text{Common Shares Outstanding}}} \end{equation*}

For EPS, higher is better. Shareholders prefer to make more income on their shares!!

Let’s break this down into two parts: the numerator and denominator.

Income Attributable to Common Shareholders

Sometimes companies have more than one type of shares: common and preferred shares. The issue is that preferred shares get paid their dividends before common shareholders. So any income that is payable as dividends to preferred shareholders, that income is not available to the common shareholders. That’s all you have to know: income attributable to common shareholdersIncome Attributable to Common Shareholders:
Used as the numerator to calculate Earnings per Share (EPS). Any income that is payable as dividends to preferred shareholders, that income is not available to the common shareholders. Calculated as net income less preferred share dividends declared. See also: Earnings per share is simply net income less preferred share dividends.

    \begin{equation*} {\textbf{Income Attributable to}\atop \textbf{Common Shareholders}}\;=\;{\text{Net}\atop \text{Income}}\;-\;{\text{Preferred Share}\atop \text{Dividends}} \end{equation*}

Weighted Average Number of Common Shares Outstanding

Remember the section on issuing and repurchasing common shares? When the number of common shares change during the year, the change in shares has to be proratedProrate:
To make an adjustment for the time an asset was held, or a liability was outstanding. Adjustments for prepaid expenses, depreciation, interest revenue, and interest expense may require proration. Weighted average number of common shares also requires proration for any shares issued and repurchased during the period.. Like this:

Share Issuances

X Co. starts the fiscal year with 10,000 common shares outstanding. Six months later the company issues 5,000 common shares. Calculate the weighted average number of common shares outstandingWeighted Average Common Shares Outstanding:
Calculated as beginning number of common shares outstanding plus prorated common share issuances, less prorated common share repurchases. This is the denominator in Earnings per Share (EPS). for EPS at the fiscal year end.

Weighted Average Number of Common Shares Outstanding:

    \begin{gather*} {10,000\atop \text{shares}}\;+\;\biggl({5,000\atop \text{shares}}\times{{\sfrac{6}{12}}\atop \text{months}}\biggr) \\ \, \\ =\;\mathbf{12,500} \textbf{ shares for EPS calculation} \end{gather*}

There are 15,000 shares outstanding at the end of the year, but the weighted average number of shares outstanding is only 10,250 shares. This is because the 5,000 shares issued are prorated for a half year. In the following year, assuming that there are no shares issued or repurchased, the denominator for EPS will be 15,000 because all shares will be outstanding for the full year.

Share Repurchases

X Co. starts the fiscal year with 10,000 common shares outstanding. Six months later the company repurchases 5,000 common shares. Calculate the weighted average number of common shares outstanding for EPS at the fiscal year end.

Weighted Average Number of Common Shares Outstanding:

    \begin{gather*} {10,000\atop \text{shares}}\;-\;\biggl({5,000\atop \text{shares}}\times{{\sfrac{6}{12}}\atop \text{months}}\biggr) \\ \, \\ =\;\mathbf{7,500} \textbf{ shares for EPS calculation} \end{gather*}

The repurchase calculation is similar to an issuance except that the repurchase is subtracted. This makes sense because there are only 5,000 common shares outstanding at the end of the year. The 5,000 share reduction is simply prorated for the half year.

Let’s practice calculating weighted average number of shares outstanding, then we’ll move on to full EPS calculations.

An eye in a circle—the 'see' section of the think-see-do approach.

My Turn:
Y Co. starts its fiscal year on 01 August, 20X1 with 50,000 common shares outstanding. On 31 December, the company repurchased 10,000 common shares.
Required:
Calculate weighted average number of common shares outstanding for EPS at the fiscal year ended 31 July 20X2.

Weighted Average Number of Common Shares Outstanding:

    \begin{equation*} \begin{aligned} &\;50,000\;-\;\biggl({5,000}\,\times{{\sfrac{6}{12}}\atop \text{months}}\biggr) \\ \, \\ \;=&\;50,000\;-\;5,833 \\ \, \\ \;=&\;\mathbf{44,167}\textbf{ shares for EPS calculation} \\ \end{aligned} \end{equation*}

At the fiscal year ended 31 July 20X2, the company has 40,000 common shares outstanding (50,000 – 10,000). For the EPS calculation, the 10,000 repurchase is prorated for the 7 months remaining after the repurchase. Weighted average number of common shares outstanding is therefore 44,167 shares.

A gear and a pencil in a circle—the 'do' section of the think-see-do approach.

Are you excited to calculate weighted average number of shares outstanding? I knew you were! Take it away…

Your Turn:6—9: Y Co.
Solution:6—9: Solution

And last one. Keep up the great work!

Your Turn:6—10: Z Co.
Solution:6—10: Solution

An eye in a circle—the 'see' section of the think-see-do approach.

Beautiful work! Now let’s put this together. In the following questions there are no preferred shares. You will be given net income to use as the numerator, and you will calculate weighted average number of common shares outstanding as the denominator. Put them together and – presto – you’ve calculated EPS. Let’s give it a try.

My Turn:
HoW Ltd. reported the following for their fiscal years ended 31 December:
20X2 20X1
Net Income 500,000 450,000
Number of Common Shares 15,000 10,000
The only shares outstanding were common shares. There were no issuances or repurchases of common shares in the fiscal year ended 20X1. In 20X2, 5,000 shares were issued on 01 April. These shares were outstanding 9 months in 20X2.
Required:
Calculate EPS for the years ended 31 December 20X1 and 20X2. Comment on the result.

31 December 20X1:

    \begin{equation*} \begin{aligned} \textbf{EPS}\;&=\;\frac{\$\,450,000}{10,000 \text{ shares}} \\ \, \\ &=\;\mathbf{\$\,45} \textbf{ per share} \\ \end{aligned} \end{equation*}

31 December 20X2:

    \begin{equation*} \begin{aligned} \textbf{EPS}\;&=\;\frac{\$\,500,000}{10,000 + ({5,000}\times\sfrac{9}{12})} \\ \, \\ &=\;\frac{\$\,500,000}{13,750 \text{ average shares}} \\ \, \\ &=\;\mathbf{\$\,36.36} \textbf{ per share} \\ \end{aligned} \end{equation*}

Earnings per share was higher in 20X1, which is preferable.

A gear and a pencil in a circle—the 'do' section of the think-see-do approach.

Now it is your turn to calculate EPS. Give it a try!

Your Turn:6—11: WhY
Solution:6—11: Solution

Excellent work. And just one more.

Your Turn:6—12: WhO
Solution:6—12: Solution

Great work!! You have calculated retained earnings, prepared statements of changes in equity, and learned about earnings per share. Great progress!

Starting with the next chapter, we will take a closer look at Statement of Financial Position accounts. Join me as we look at the Cash account. I know I’m looking forward to it 😊

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