copyright © 2003 mcgraw hill ryerson limited 12-1 chapter 12 the cost of capital chapter outline ...

copyright © 2003 McGraw Hill Ryerson Limited

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Chapter 12The Cost of Capital

Chapter Outline Geothermal’s Cost of Capital Calculating the Weighted Average Cost of

Capital Measuring Capital Structures Calculating Required Rates of Return Big Oil’s Weighted Average Cost of Capital Interpreting the Weighted Average Cost of

Capital Flotation Costs and the Cost of Capital


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Geothermal’s Cost of Capital• Calculating the Cost of Capital

The choice of the discount rate can be crucial in the capital budgeting decision. The discount rate for a project determines whether

NPV will be positive and if the project acceptable. When the project involves huge capital expenditures

and/or is long-lived, you want to make the correct decision.

Read the Finance In Action box on page 369 of your text to see how important the cost of capital is:

Here the existence of a major investment turned on the choice of the discount rate!


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Geothermal’s Cost of Capital• Calculating the Cost of Capital

If a firm is financed entirely by equity, its cost of capital equals the return required by investors on the company’s stock. You can use the CAPM to estimate this return.

However, very few companies are financed entirely by equity. Instead, they are financed by a mix of securities, each with its

own cost of capital. When there is a mix of securities, the company cost of

capital is no longer the same as the expected return on the common stock. Instead, the expected return reflects the weighted after-tax

cost of the debt financing plus the cost of the equity financing.

The weights are the fractions of debt and equity in the firm’s capital structure.


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Geothermal’s Cost of Capital• Example: Calculating the Cost of Capital

Geothermal is considering an expansion project which will generate $4.5 million annually in perpetuity and costs $30 million.

Geothermal’s return on this proposed investment is 15% ($4.5m / $30m).

But, what is this project’s cost of capital? If it is less than 15%, then the project would be a

good deal and would generate net value for Geothermal’s shareholders.


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Geothermal’s Cost of Capital A firm’s cost of capital will be determined by its capital

structure. Capital structure is the firm’s mix of debt and equity financing. We measure the cost of capital using the market value of the

financing, not the book value. We measure the cost of capital using the market value of the

financing because the book value of the equity reflects past funding and historic rates of return.

But, if investors see the firm as having superior prospects, then the market value of its equity will exceed its book value.

This also means the firm’s debt ratio will be lower than what is recorded on the books.


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Geothermal’s Cost of Capital You are told the following about Geothermal’s capital

structure: It has bonds with a market value of $194 million. The company also has 22.65 million common shares

outstanding, trading at $20 each. This means the market value of the firm’s equity is $453 m. Thus, you know the following about Geothermal’s capital

structure:

Market Value of Debt: $194 (30%) Market Value of Equity: $453 (70%) Total Value of firm: $647 (100%)


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Geothermal’s Cost of Capital If you were to purchase all of the securities issued by

Geothermal, the debt as well as the equity, you would own the entire business. Thus, the expected return on this portfolio of securities is

the firm’s cost of capital. Assume Geothermal’s bonds are yielding 8% and

that its equity returns 14%. To calculate the return on this portfolio, we would:

Get the weighted average of the returns on the debt and the equity.

The weights would depend on the relative market values of the two securities.


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Geothermal’s Cost of Capital• This measure is known as a firm’s weighted average cost of capital (WACC).

• Thus for Geothermal:

(D x rdebt) + (E x requity)

WACC = V

= (D/V x rdebt) + (E/V x requity)

= (0.30 x 8%) + (0.70 x 14%) = 12.2%

Note: WACC is also known as rassets


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Geothermal’s Cost of Capital• Example: Calculating the Cost of Capital

The above calculation of WACC assumes that the firm pays no taxes.

Taxes are important because interest payments are deducted from income before tax is calculated. If Geothermal pays $1 of interest, this will reduce its taxable

income by $1. If it is in a 35% tax bracket, then its tax bill will drop by $0.35.

In a 35% tax bracket, Geothermal’s cost of debt is only $0.65 since the government bears 35% of the cost of the interest payments. The government doesn’t send the firm a cheque for this amount, but

the income tax the firm pays is reduced by 35% of its interest expense.


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Geothermal’s Cost of Capital Thus, the cost of the firm’s debt is not 8%, but:

8% x (1- tax rate) = 8% x (1 - 0.35) = 5.2%

Thus if Geothermal is in a 35% tax bracket, its WACC would be calculated as follows:

rassets = [D/V x (1-Tc)rdebt] + (E/V x requity)

= [0.30 x (1-0.35)x8%) + (0.70 x 14%)

= (0.3 x 5.2%) + 9.8%

= 11.4%


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Calculating the WACC• The Steps for Calculating the WACC:

1. Calculate the market value of each of the firm’s securities.

2. Calculate the market weight of each security as a proportion of the firm’s total financing.

3. Determine the required rate of return on each security.

4. Calculate the weighted average of these required returns. Do not forget to adjust the cost of debt for taxes.


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Calculating the WACC • The Steps for Calculating WACC

If there are three (or more) sources of financing, the general approach to calculating WACC is unchanged!

Just calculate the weighted average after-tax return for each security.

For example, if the firm had preferred shares:

WACC = [D/V x (1-Tc)rdebt] + (P/V x rpreferred)+ (E/V x requity)

Practice: Try example 11.1


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Calculating the WACC • What WACC Means

If you discount the expected cash flows from a project at the WACC and you find: The project has a zero NPV.

Then the project’s cash flows are just enough to give each of the security holders the returns they require.

The project has a positive NPV. Then it will provide each of the security holders with the

return they require and it will increase the value of the shareholder’s equity if accepted.

The project has a negative NPV. Then the projects cash flows are insufficient to provide the

required return to all of the security holders and accepting it will decrease the value of the firm.


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Measuring Capital Structure• Practical Problems in Applying WACC

Section 12.3 shows you how to calculate the WACC for a company called Big Oil.

Notice that the first place to start is the company’s accounts and the book value of its securities.

Using judgment, research and some work, you convert from book value to market value.

If you look at Table 12.1, you will see that at book, the firm’s capital structure is:

50% debt and 50% equity However, if you look at Table 12.2, you will see that at

market, the firm’s capital structure is:

25% debt and 75% equity


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Measuring Capital Structure• Practical Problems in Applying WACC

Thus, if you had used the book values in the calculation of Big Oil’s WACC, rather than the market value, your results would have been highly inaccurate!

REMEMBER … WACC usesmarket value not book value!


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Measuring Capital Structure• Calculating Market Value of Debt

Most financial managers accept the book value of bank debt as a fair approximation of market value.

This debt is usually issued at floating rates and if rates change, the payment Big Oil makes will change so as to maintain the loan’s value.

Long term bonds, though, are usually issued at a fixed rate. Thus their market value fluctuates over time.

The market value of a company’s bonds is the PV of all coupons, and the par value, discounted at the current interest rate.

Thus, Big Oil has $200 million in face value of bonds issued at 8%. Payments are $16 million per year.

There are 12 years until maturity. Interest rates are currently 9%.

You should be able to calculate that these bonds have a market value of $185.7 million.


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Measuring Capital Structure• Calculating Market Value of Equity

The market value of a company’s equity is simply the market price per share multiplied by the number of shares outstanding.

Big Oil has 100 million common shares outstanding. Each share has a market value of $12.

You should be able to calculate that the firm’s equity has a market value of $1,200 million.

• You have completed the first two steps for calculating the WACC:

1. Calculate the market value of each of the firm’s securities.2. Calculate the market weight of each security as a proportion of the

firm’s total financing.• Now you want to:

3. Determine the required rate of return on each security.


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Calculating Required Rates of Return

• The Expected Return on Bonds For most large, healthy firms, financial

managers use the yield to maturity on the bonds as the expected return. But, if a firm is in financial difficulty, beware of

assuming that the yield offered by the bonds is the return that investors expect to receive.

Big Oil’s bonds have a yield to maturity of 9%.


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• The Expected Return on Common Stock You may use the CAPM or the Dividend Discount

Model (DDM) to estimate the required rate of return on a firm’s common equity.

• CAPM: Expected Return = risk-free rate + risk premium

requity = rf + (rm - rf)

• DDM: Expected Return = dividend yield + growth

requity = DIV1/P0 + g


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Big Oil’s beta is 0.85 and the market risk premium is 9%.

Big Oil’s expected return on its stock is about 13.5%:

WARNINGS: Beware of false precision! Do not expect estimates of

the cost equity to be precise. Remember that the constant-growth formula in the DDM

will give you poor results if it is applied to firms with unsustainably high current growth rates.

requity = 6% + 0.85(9%) 13.5%


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• The Expected Return on Preferred Stock A preferred stock pays a fixed annual dividend in

perpetuity. Thus, you may use the perpetuity formula to estimate

the required rate of return on a firm’s preferred equity:

Expected Return = dividend yield

rpreferred = Dividend Ppreferred


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Big Oil’s Cost of Capital• Calculating WACC

If Big Oil is in a 35% tax bracket, its WACC would be calculated as follows:


= [0.243 x (1-0.35)x9%) + (0.757 x 13.5%)

= 11.6%


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Interpreting WACC• When You Can and Can’t Use WACC

WACC allows us to measure the cost of capital for companies which issue different types of securities.

WACC also adjusts the cost of capital for the tax-deductibility of interest payments.

However, its use is restricted to certain types of projects. The WACC is the rate of return that the firm must expect to earn

on its average-risk investments if it is to fairly compensate all its security holders.

As such, WACC may be used to value new assets that: Have the same risk as the old ones. Will support the same ratio of debt as the firm itself.

In other words, the WACC is an appropriate discount rate if and only if the project is a carbon copy of the firm’s existing business.

You should know, however, that WACC is sometimes used as a company-wide benchmark discount rate.

This benchmark will be adjusted upward for unusually risky projects and downwards for unusually safe ones.


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Interpreting WACC• Some Common Mistakes

You calculated Big Oil’s WACC is 11.6% because the firm uses so little debt (about 25%).

But, debt is much less expensive than equity. Could you lower WACC by issuing more debt and raising its

proportion in the firm’s capital structure? For example, if you use Big Oil’s required returns on

debt and equity, but change the weights, you can reduce its WACC to 9.7%:


= [0.50 x (1-0.35)x9%) + (0.50 x 13.5%)

= 9.7%


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Interpreting WACC Do you see what is wrong with the logic? As the firm borrows more, its risk goes up. The consequence:

The cost of both the company’s debt and its equity will go up as investors demand a higher return to compensate them for the increased risk.

When you thought you could reduce Big Oil’s WACC by borrowing more, you were recognizing only the explicit cost of the debt.

However, there is also an implicit cost of using more debt. Increased borrowing increases risk, leading security holders to

demand a higher rate of return. However, despite the increased cost of capital for the company’s

securities, the overall WACC will remain the same as the fractions of debt and equity change. This happens because more weight is put on the debt which costs

less than the equity. That is, a change in capital structure must affect the return on the

individual securities; however, the return on the package of debt and equity securities is unaffected.


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Interpreting WACC• Revisiting the Project Cost of Capital

In Chapter 11, you learned that the required rate of return on a project depends on that project’s risk level and not the source of funds.

Since it will be rare for a project to be financed entirely with equity, we now need to consider ways of calculating a project’s WACC.

The project’s WACC should reflect the project’s overall risk and the best securities mix for the project.

Thus, calculating a project’s cost of capital has two components:1. Assess the risks of the project by determining its beta.2. Determine the best financing mix for the project.


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Floatation Costs and the Cost of Capital Often a firm needs to issue securities to raise the necessary

cash for a project. There is a cost associated with issuing securities.

These costs, when added to the others of the project, can make the project less attractive.

For example, you are looking at a project for your firm which costs $900,000 and generates $90,000 per year in perpetuity.

If the opportunity cost of capital on this project is 10%, it is barely acceptable, having a NPV of zero ($90,000/10% - $900,0000).

Now suppose your firm has to issue equity at a cost of $100,000 to finance the project.

The project would now have a cost of $1 million and a negative NPV, making it unacceptable.

Some companies attempt to account for floatation costs by increasing the discount rate.

A better way of handling these costs is to recognize that they are just another cost of undertaking the project.

Thus, they should be treated as a negative incremental cash flow when determining the project’s NPV.

copyright © 2003 mcgraw hill ryerson limited 12-1 chapter 12 the cost of capital chapter outline ...

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