# Firmsconsulting

## WMCC and Investment Opportunities Schedule

In Cost of Capital, Finance, MBA on October 27, 2010 at 6:52 pm

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%

## Weighted Marginal Cost of Capital – WMCC – and the Break Point

In Cost of Capital, Finance, MBA on October 27, 2010 at 6:49 pm

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. Weighted Marginal Cost of Capital (WMCC) is the WACC applicable to the next dollar of the total new financing.

### Breakpoint

Related to the Weighted Marginal Cost of Capital (WMCC) concept is the break point concept. Break point is the amount of total financing at which the cost of one of the components of total financing escalates. At such point WMCC also increases. Calculation of the break point is required for calculation of the weighted marginal cost of capital (WMCC).

For example, if a business used up all retained earnings to issue common stock and it still requires more financing, it may issue new common stock. The cost of new common stock is higher due to under pricing and flotation costs. Therefore, the cost of one of the financing components rises and consequently WACC also rises and WMCC also escalates. The point at which the cost of one of the components rises is called the break point.

To find a break point for a particular financing source, we need to take the amount of funds available from the financing source at a given cost and divide it by the capital structure weight for the financing source.

Break Point = funds from the financing source/capital structure weight.

### Example

Assume that when the business uses up \$100,000 of its long-term debt at a cost of 7%, it can only use long-term debt at a cost of 10%. The weight of a long-term debt as a source of capital in the company’s capital structure is 40%. To find the break point we take \$100,000 and divide it by 0.4. We end up with \$250,000, which is a break point.

### Test yourself

ABC Corporation has a long-term debt weight of 35% and the equity weight of 65% in the capital structure. The business has \$400,000 of retained earnings left at a cost of 12%. Thereafter, they can issue new common stock at a cost of 17%. ABC can use long-term debt as a source of financing up to the amount of \$200,000 at 8% and thereafter at 10%.

REQUIRED: What are the break points for debt and equity?

SOLUTION:

Debt break point

200,000/.35=\$571,428.65

Equity break point

400,000/.65=\$615,384.6

Therefore, at total new funding levels of \$571,428.65 and \$615,384.6 the WMCC will shift upward.

## (WACC) Weighted average cost of capital (ra)

In Cost of Capital, Finance, MBA on October 27, 2010 at 6:48 pm

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:

Ra=(wi*ri)+(wp*rp)+(ws*rn or rr).

Where:

wi = a weight for the long-term debt

wp = a weight for the preferred stock

ws = a weight for the common stock

ri = the cost of long-term debt

rp = 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.

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

In Cost of Capital, Finance, MBA on October 27, 2010 at 6:47 pm

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.

## Using CAPM (Capital Asset Pricing Model)

In Cost of Capital, Finance, MBA on October 27, 2010 at 6:46 pm

Another way to find the cost of common stock is by using 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.

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

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

b – beta coefficient

rm – market return

EXAMPLE:

If Rf 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 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

## Gordon model (Constant-Growth Valuation Model)

In Cost of Capital, Finance, MBA on October 27, 2010 at 6:45 pm

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

Where:

P0

price of the stock

D1

per share dividend expected at the end of year 1 (at the end of the next financial period)

rs

required return

g

constant growth rate

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 the help of the 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).

TEST YOURSELF:

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

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

SOLUTION

Firstly you need to find the 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, you need to use the 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 you had to adjust the current dividend for the dividend in the future period by the growth rate (by multiplying current dividend by (1+g)).

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

In Cost of Capital, Finance, MBA on October 27, 2010 at 6:44 pm

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-taxcost 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.

COSTs 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)

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

In Cost of Capital, Finance, MBA on October 27, 2010 at 6:43 pm

After discussing the cost of long-term debt , we must not 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

## Cost of long term debt

In Cost of Capital, Finance, MBA on October 27, 2010 at 6:42 pm

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%

## Long term sources of finance

In Cost of Capital, Finance, MBA on October 27, 2010 at 6:40 pm

Here we will focus only on the long term sources of finance because only long-term sources provide permanent financing. Long-term sources refer to long-term debt and equity on the balance sheet (the left side or the bottom half of 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.