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(WACC) Weighted average cost of capital (ra)

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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)

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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)

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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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Gordon model (Constant-Growth Valuation Model)

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The Gordon model is one of the models used in dividend valuation. It is very simple, as long as one knows the formula, which is:

P0=D1/(rs-g)

Also sometimes presented as: P = D/(k-g)

Where:

P0 or P – price of the stock

D1 or D – per share dividend expected at the end of year 1 (at the end of the next financial period)

rs or k – required return for equity investor

g – constant growth rate (expected annual growth of dividends)

Gordon model is usually used for mature companies only since it is assumed that annual growth of dividends remains constant.

It is very important to note that if you are only given the current per share dividend (D0, per share dividend received in this financial period), then you will need to adjust it for the next financial period before you can use it in the Gordon model. To do this you will need to take the current dividend and multiply it by (1 + g). The calculation is as follows:

D1=D0*(1+g)

The original equation of the Gordon model (P0=D1/(rs-g)) calculates the price of the share. However, you are looking for the cost of common stock. Therefore, you need to rearrange equation of the Gordon model as follows:

rs = (D1/Po) + g

Now you just plug in the numbers into the adjusted Gordon equation and you will be able to obtain the cost of common stock. Because common stock is paid out of the after-tax earnings, the tax adjustment is irrelevant.

Sometimes it is necessary to find the growth rate (g) first, before you can calculate the cost of the common stock (rs) with the help of the Gordon model. To do so, you need to find out what was the per share dividends applicable to common stock over the last few years (this information will be given). After obtaining this information, you can calculate the growth rate.

It is best to explain this with an example.

EXAMPLE 1:

Calculating the growth rate, which is necessary for usage of the Gordon model:

The information given below is on per share dividends applicable to common stock over the last few years. You need to find the growth rate of dividends over the given period.

Per share dividends from 2005-2010:

2010 – $4

2009 – $3.96

2008 – $3.76

2007 – $3.27

2006 – $3.25

2005 – $3

Now, by using a financial calculator, you can calculate the growth rate as follows:

PV = -3 (per share dividend in 2005, the first year from which per share dividend information is available)

FV = 4 (per share dividend in 2010, the per share dividend in the current period)

N = 5 (number of periods over which growth occurred)

Find I = it will be 5.92% (this number represents growth of dividends over the given period)

EXAMPLE 2:

Using the growth rate (found above) in the Gordon model:

Now, if we know that the growth of the dividends is expected to be the same into the future and the price of the stock is $55, we can compute the cost of common stock (rs) as follows:

rs=(4*(1+0.0592)/55)+0.0592

rs=0.0770+0.0592

rs=0.1362=0.14%

The cost of common stock also represents the return that investors expect to earn from their shares. If the actual return is less – investors will sell their stock.

Test yourself

The ordinary share is currently sold for $40 each. The growth of shares was 10% over the last 5 years and is expected to be the same in the future. A dividend of $3.5 dollars was paid to shareholders in the current period.

REQUIRED: What is the cost of an ordinary share?

SOLUTION:

We need to use the adjusted Gordon model. In other words, we need to use the formula: rs = (D1/Po) + g

Rs=(3.5*(1+.1)/40) +.1

Rs=(3.85/40) +.1

Rs=19.63%

Note that the dividend is adjusted for growth in the next period by multiplying the current dividend by (1+g).

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

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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)

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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.

Blogbschool.com is powered by www.firmsconsulting.com. Firmsconsulting is a training company that finds and nurtures tomorrow’s leaders in business, government and academia via bespoke online training to develop one’s executive presence, critical thinking abilities, high performance skill-set, and strategy, operations and implementation capabilities. Learn more at www.firmsconsulting.com.

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Cost of long term debt

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The first long term source of finance that we consider is the cost of long term debt, which is usually the cheapest of the long-term sources of finance. The majority of long term debt of large corporations is the result of issuing bonds.

Flotation cost

Companies that issue bonds have to take into account the flotation cost, which is the complete cost the company has to incur to issue and sell a security, such as common stock, preferred stock and bonds. This cost reduces the company’s net proceeds from issuing security.

Flotation cost consists of underwriting and administrative costs. Underwriting costs are payment to investment bankers for their services and administrative costs are costs other than the underwriting costs of issuing bonds.

Finding the before-tax cost of long-term debt (rd)

To find the after-tax cost of long term debt, we first need to find the before-tax cost of long term debt (rd). As mentioned above, the majority of long term debts of large corporations are the result of issuing bonds. By using a financial calculator, we can find the before tax cost of a bond (cost of long-term debt).

THE CALCULATION FOLLOWS:

FV – (future value of the bond which refers to its par value, which is also called the face value, and is usually $1,000)

PV – the value of the bond today at which it is sold (after deducting the flotation cost)

PMT – payment on the bond (for example, at 8% coupon interest rate a bond issuer will have to make annual payments of $80 if the par value is $1,000). Payments can also be made more frequently, such as semi-annually or even monthly, but in such a case we need to adjust the amount of payment and number of periods.

For example, if payment is made semi-annually, we will need to divide $80 by 2 and we will need to multiply number of periods by 2.

N – Number of periods

Calculate I – the cost of the bond (for the bond’s issuer it is the cost to maturity of the cash flows, for the bond’s holders it is the return they earn on buying and holding this bond to maturity). Within the context of our discussion, it is also the before-tax cost of long-term debt.

Note that if the net proceeds from the sale of the bond is the same as the face value of the bond than the before-tax cost of long-term debt will be equal to the coupon interest rate. For example, at 8% coupon interest rate, the par value of $1,000 and net proceeds of $1,000 (no flotation costs), the before-tax cost of long-term debt will equal 8%.

Finding the after-tax cost of long-term debt

After we found the before-tax cost of long term debt, we need to find the after-tax cost of long term debt. To do so all we need to do is to multiply the before-tax cost of long-term debt by (1-T), where T stands for the tax rate.

THEREFORE:

ri = rd * (1-T)

EXAMPLE:

If the before-tax cost of long term debt is 10% and tax rate is 28% then the calculation will be as follows:

Ri =10% * (1-.28)

Ri =10% * .72

Ri = 7.2%

Test yourself

You need to calculate the after-tax cost of a 30-year bond. The coupon interest rate is 10%, the par value is $1,000 and the bond is currently selling at $950.

SOLUTION:

PV: -950

FV: 1,000

PMT: 100

N: 30

I: 10.56%

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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Long term sources of finance

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Here we will focus only on the long term sources of finance because only long-term sources provide permanent financing. Long-term sources of finance (also called long-term sources of capital) refer to long-term debt and equity on the balance sheet. They include long-term debt, preferred stock and common stock equity, which in turn include issues of new common stock and retained earnings.

Permanent financing generally refers to financing long-term fixed assets, such as machinery or factory. If the pay-off from the asset is over the long-term period (longer than 1 year), the long-term sources of finance should be used to ensure it is less risky to finance such assets. For example, if long-term debt (one of the long-term sources of finance) rather than short-term debt is used, business can be more certain money will be available to cover obligations as they come due.

While focusing on the long-term sources of finance, we will need to focus on the specific cost of finance. We will need to obtain the specific cost of each of the long-term sources of finance, which refers to the after-tax cost of using each of the sources today.

Read related article: Cost of Long Term Debt 

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The cost of capital

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What is the cost of capital? It is the required rate of return a business must earn on its investments (capital budgeting projects) to maintain the market value of the firm’s shares and to attract funds.

It is a measure used to determine whether or not certain project will decrease or increase the firm’s value in the market place and, consequently, whether or not it should be recommended.

If NPV is more than zero and IRR is greater than the cost of total capital, then a proposed project will increase the market value of the firm and it should be recommended.

If, however, NPV is less than zero and IRR is lower than the cost of all capital, then a proposed project will decrease the market value of the firm and it should not be recommended.

Therefore, if a firm’s risk is assumed to be constant, than any projects with the rate of return higher than the cost of all capital will increase the market value of the firm and any projects with the rate of return below the cost of capital of the enterprise will decrease market value of the firm.

In the discussions that follow we assume that the cost of all capital is measured on the after-tax basis and that a firm’s acceptance of the project does not affect FINANCIAL and BUSINESS RISKS.

FINANCIAL RISK is the chance that a firm will not be able to meet its financial obligations, which can result in bankruptcy. Financial risk is directly affected by a firm’s capital structure (its mix of debt and equity financing). The more debt the firm uses in its capital structure mix, the higher the financial risk.

BUSINESS RISK is the chance that a firm will not be able to cover its operating costs. There are three factors that affect business risk. These are increases in operating leverage, revenue instability and cost instability.

1 – Increase in operating leverage refers to higher use of fixed operating costs.

2 – Increase in revenue instability (or decrease in revenue stability) refers to deterioration of stability of sales of the firm.

3 – Lastly, increase in cost instability (decrease in cost stability) refers to how predictable are costs of the firm, such as labour and raw materials’ costs.

Business risk must be taken as is and the capital structure mix the firm chooses does not influence it.

Firms usually try to maintain an optimal mix of financing (debt and equity) referred to as the target capital structure. Firms have various sources of capital and the cost of capital may be different for each source of financing. When determining the cost of capital, it is helpful to determine an average cost of all sources of capital, which is called the weighted average cost of capital (WACC).

 

Capital Rationing

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Many firms operate under capital rationing. Firms ration capital because more often than not firms do not have unlimited funds to invest. Therefore, not all acceptable projects can be actually accepted. This is, of course, contradictory with goal of maximizing shareholders value.

We can formally define the rationing of capital as follows: It is a situation when firms do not accept all acceptable projects due to a limited amount of funds or due to limits imposed on investments. The goal is to select portfolio of projects with the highest net present value.

Under situations involving scarce capital, businesses will select a portfolio of projects with the highest NPV and which does not exceed the allocated budget. There are two commonly used techniques to select projects in these situations, the net present value NPV approach and the internal rate of return (IRR) approach.

The IRR approach graphs return against the total investment on the investment opportunities schedule (IOS) and by drawing the budget constraint shows the group of projects that are acceptable to be invested in. The NPV approach ranks projects by IRR and than generates a portfolio of projects with the highest overall present value.

When selecting projects, the net present value (NPV) approach is preferred because it maximizes shareholders’ returns whereas an internal rate of return (IRR) approach just generates a portfolio of acceptable projects.