Stock splits and reverse stock splits

Organizations undertake stock splits when it is perceived within the firm that shares of the company are traded at a too high price and this may slow down trading activity. If a stock split is undertaken, the market value of shares can slightly increase. Such increase tends to be maintained as long as dividends after the split also increase.

If a firm undertakes a 2 for 1 split than 2 new shares will be given in exchange for every 1 old share. The stock split does not affect the organizational capital structure.

Organizations can also do reverse stock splits when firm wants to increase the share price. Increase in share price may help to enhance trading of a shares activity. This occurs because unsophisticated investors tend to equate low priced stocks to low quality investments.

If firm undertakes a 1 for 2 split, one new share will be exchanged for 2 old shares.

Book value per share

Book value per share is a value that common stock holders would have received if all assets of the firm were sold for its accounting value and if all liabilities were settled and residual value divided among common stock holders.

In other words, it is a book value of the firm (the net worth of the company, which is assets minus liabilities) divided by the number of shares of common stock outstanding.

The following formula is used to calculate book value per share:

Book value per share = TA-TL/Number of shares of common stock outstanding

Where TA is Total Assets and TL is total liabilities.

Book value per share method is criticized because it relies on historical data and does not take into account the future-expected earnings of the firm. Therefore, it does not reflect the real market value of the firm.

 

Weighted Marginal Cost of Capital (WMCC) and Investment Opportunities Schedule

By finding all break points, we can construct the weighted marginal cost of capital – WMCC – schedule. (WMCC) schedules show the relationship between the level of total new financing and a company’s weighted average cost of capital.

Thereafter, we can construct the investment opportunities schedule (IOS), which is a graph where the business’s investment opportunities are ranked based on their returns and financing required, arranged from the highest returns and all the way to the lowest returns. It is the decreasing function of the level of total financing.

If we combine the weighted marginal cost of capital (WMCC) schedule and investment opportunities schedule (IOS), we can use it to make investment decisions. The rule is to invest in projects up to the point on the graph where marginal return from investment equals its WMCC (where IOS=WMCC).

All projects on the left of the point where IOS=WMCC will maximize shareholders wealth and all points on the right of the point where IOS=WMCC will decrease shareholders’ wealth.

It is important to note that the majority of firms stop investing before the marginal return from investment equals its weighted marginal cost of capital (WMCC). Therefore, the majority of businesses prefer a capital rationing position (the position below the optimal investment budget, which is also called the optimal capital budget).

Test yourself


ABC Company has to make an investment of $1,000,000. The long-term debt weight in the capital structure is 35%. ABC has $700,000 of retained earnings but 50% of it must be paid to common stock shareholders in the form of dividends. Preferred stock is currently not used as a source of finance by ABC.

What are the weights that ABC will have for each source of capital?

SOLUTION:

Firstly, we need to find out how much of retained earnings ABC has left after payment of dividends to shareholders: $700,000*0.5=$350,000.

Therefore, the weight of retained earnings is 35% ($350,000 out of $1,000,000).

$1,000,000-$350,000 (35%, funds available from long-term debt source) – $350,000 (35%, funds available from retained earnings) = $300,000 (30%)

Therefore, the weights are as follows:

Long-term debt – 40%

Retained earnings – 35%

Common stock – 30%

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Weighted Marginal Cost of Capital (WMCC)

Weighted Marginal Cost of Capital – WMCC – is the WACC applicable to the next dollar of the total new financing. Related to the concept is the break point concept. Weighted average cost of capital (WACC) may change over time due to changes in the volume of financing. This occurs as the volume of financing increases, the risk increases and providers of funds require higher return on the funds that they make available.

The WACC of the next dollar of the total financing may be different from the WACC of the last dollar of the total financing.

Related articles: Break Point, Weighted Average Cost of Capital (WACC)

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(WACC) Weighted average cost of capital (ra)

Weighted average cost of capital (WACC) (ra) is a very simple concept. Weighted average cost of capital (WACC) refers to the weighted cost of both debt and equity financing, according to the firm’s specific optimal mix of financing (debt and equity). Knowing the weighted average cost of capital (WACC) enables better decision making about proposed projects.

The formula for weighted average cost of capital (WACC) (ra) is as follows:

WACC=(wd*rd)+(we*re)+(ws*rn or rr)

Where:

wd = a weight for the long-term debt

we = a weight for the preferred stock

we = a weight for the common stock

rd = the cost of long-term debt

re = the cost of preferred stock

rn = the cost of new common stock

rr = the cost of retained earnings

All sources of capital and their weights must be taken into account.

Example


Project Omega was proposed with an expected return of 9% and the firm’s cost of capital for debt financing is 7% and cost of capital for equity financing is 12%. Further, the optimal mix of debt and equity of the firm is 40 percent of debt and 60 percent of equity. Then, the weighted average cost of capital (WACC) is calculated as follows:

weighted average cost of capital (WACC) = 7% * 0.40 + 12% * 0.60

2.8 + 7.2 = 10%

The weighted average cost of capital (WACC) is 10%.

Given the information above, the proposed project with expected return of 9% should be rejected as it is below the firm’s 10% weighted average cost of capital (WACC).

When making investment decisions, business must only choose projects that bring returns higher than the weighted average cost of capital (WACC).

Test yourself


Company ABC has the following sources of capital:

Long-term debt at 7% after-tax cost with weight of 35% in the capital structure.

Preferred stock at 9% after-tax cost with weight of 10% in the capital structure.

Common stock at 14% after-tax cost with weight of 55% in the capital structure.

REQUIRED: Find the weighted average cost of capital (WACC).

SOLUTION:

weighted average cost of capital (WACC) =7%*.35+9%*.10+14%*.55

WACC=2.45+.9+7.7

WACC=11.05%

Calculating weights


As per above, to calculate the weighted average cost of capital (WACC) we need to know the weight of each source of financing. When calculating weights, market values or book values can be used. Market values evaluate the proportion of capital at the market value and book values evaluate the proportion of capital at the book (accounting) value. It is better to use market values, as it is a more realistic value.

Further, when calculating weights, we can use either target or historical proportions. Target proportions refer to the optimal capital mix that a business would like to achieve. Historical proportion refers to the proportion based on the past. The target proportion is preferred.

***

Weighted average cost of capital (WACC) is a VERY important concept to understand. It is one of the central concepts in business and finance. The basic idea of weighted average cost of capital (WACC) concept is that it shows us the expected average cost of funds in the long-term. Make sure you are comfortable with explanations and calculations of the weighted average cost of capital (WACC) before progressing to the next section.

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Finding the after-tax cost of retained earnings (rr)

The cost of retained earnings is the same as the cost of new common stock less flotation costs. Therefore, it is cheaper for businesses to use retained earnings compared to issuing new common stock.

Retained earnings are already earnings after-tax. Therefore, no tax adjustment is required when calculating the cost of retained earnings.

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Using CAPM (Capital Asset Pricing Model)

In addition to Gordon Model, another way to find the cost of common stock is by using Capital Asset Pricing Model (CAPM). CAPM allows us to ascertain the relationship between required return and non-diversifiable risk, which is measured by the beta coefficient (b).

Beta coefficient (b) refers to the index that measures non-diversifiable risk (risk which a company cannot eliminate through diversification). It indicates how an asset’s return will react to the changes in the market return, which in turn shows the return on a portfolio of all securities in the market.

Capital Asset Pricing Model (CAPM) is simple, as long as you know the formula and have the information necessary for the formula. The formula is as follows:

rs= Rf+(b*(rm-Rf))

Where:

rs – required return (return on a portfolio or a security)

Rf – risk free rate (e.g. rate on the U.S. Treasury bill)

b – beta coefficient

rm – market return

EXAMPLE:

If Rf (risk free rate) is 5%, beta is 2 and market return (rm) is 12%, the rs (required return or cost of common stock) can be found as follows:

Rs=5%+(2*(12%-5%)

Rs=19%

Test yourself

Assuming we know that beta (company’s market risk coefficient) is 2, market return is 13%, risk free rate of return is 7%, current dividend is $4 and dividend growth over the past 5 years is 5% and the same growth is expected in the future. With CAPM, find the price of the ordinary share.

SOLUTION:

First, using CAPM, we find rs:

rs= Rf+(b*(rm-Rf))

rs=7+(2*(13-7))

rs=19%

Next, we use the Gordon model (P0=D1/(rs-g)) to find the price of the ordinary share:

Po=(4*(1+.05))/(.19-.05)

Po=4.2/0.14

Po=$30

Test yourself:

ABC’s financial manager prepared the following information. The dividend which were paid in the current year was $5. The growth of dividends over the last 5 years were 7% and the same growth of dividends is expected to be in the future. Risk free rate is 8%, market rate is 14% and beta coefficient is 2.

Required: What is the market price of ABC’s ordinary shares?

Solution:

Firstly we need to find required return (rs) with the help of the capital asset pricing model (CAPM).

rs= Rf+(b*(rm-Rf))

rs=8+(2*(14-8))

rs=20

Next, we need to use Gordon model:

Po=D1/(rs-g)

Po=5*(1+0.07)/(0.20-0.07)

Po=5.35/0.13

Po=41.15

The price of the ABC’s ordinary share is $41.15. Note that we determined D1 (dividend within the next period) by taking known D0 (last dividend) and multiplying it by (1+ growth rate).

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Finding the specific after-tax cost of common stock (rp)

Our next concern is to find the after-tax cost of common stock, after attending to finding the after-tax cost of long-term debt and after-tax cost of preferred stock.

Common stock


Common stock, which is also called common shares or ordinary shares, refers to the category of ownership of the enterprise. Common shares generally have voting rights and better potential for appreciation of shares compared to preferred stock.

However, holders of common stock generally do not have fixed dividends and cannot receive dividends until dividends are paid out to preferred stock holders. Moreover, in case of liquidation, holders of common stock only have claim on company’s assets if claims of all creditors as well as holders of preferred stock are satisfied. Therefore, common stock is more risky than preferred stock.

Cost of common stock (rp)

To determine the specific after-tax costs of common stock (rp), you can use two techniques: Gordon model or the CAPM (Capital Asset Pricing Model)

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Finding the after-tax cost of preferred stock (rp)

After discussing the cost of long-term debt, we must now find the cost of preferred stock (after-tax). Preferred stock, which is also called preferred shares or preference shares, refers to the category of ownership that has preferential claim on earnings and assets of the firm, compared to common stock ownership.

The preferential claim is generally manifested in the fact that dividends cannot be distributed to common stockholders until it is distributed to holders of preferred stock first. Further, in case of liquidation, holders of the preferred stock also have preferential claim on assets of the firm, compared to the holders of common stock.

Preferred stock is a hybrid instrument as it has characteristics of both debt and equity. The drawback of preferred shares, compared to the common stock, is lower potential for appreciation of shares as well as absence of voting rights.

Calculating the cost of preferred stock


To calculate the specific after-tax cost-of-preferred-stock all we need to do is to take the preferred stock dividend and divide it by the net proceeds from the sale of the preferred stock (funds received minus flotation cost).

Cost-of-preferred-stock (rp) = Preferred stock dividend/(Funds received – Flotation costs)

Because preferred stock is paid out of the after-tax earnings, the cost-of-preferred-stock is already after-tax.

EXAMPLE:

If Company A issued 9% preferred stock at $100 and the flotation cost is $8, then the calculation will be as follows:

rp = 100*9%/100-8

rp =9/92

rp =9.8%

Test yourself


A corporation is issuing 10% preferred stock that should be sold for $15 each. The business will incur flotation costs of $2 per share.

REQUIRED: What is the cost-of-preferred-stock?

SOLUTION:

10%*15/15-2

1.5/13

The answer is 11.54%

Note: If you struggle with a calculation, read using a financial calculator article for some simple tips on using a financial calculator.

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How to calculate EPS (Earnings per Share)?

Calculating earnings per share (EPS) allows us to understand how much dollars were earned on each outstanding share of common stock.

In summary, in order to find earnings per share (EPS), we need to take earnings available for common stockholders (the bottom line of the income statement ) and divide it by number of shares of common stock outstanding.

Earnings per Share (EPS) = Earnings Available for Common Stockholders/ Number of Shares of Common Stock Outstanding

Therefore, in order to determine EPS (earnings per share), we need to know earnings available for common stockholders. Earnings available for common stockholders are calculated as follows:

Sales revenue

LESS: Cost of goods sold

= Gross profit

LESS: Operating expenses

= EBIT (earnings before interest and tax/operating profit)

LESS: Interest

= Net profit before tax

LESS: Taxes

= Net profit after tax

LESS: Preferred stock dividends

= Earnings available for common stockholders

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