978-0134730417 Chapter 11 Part 1

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362

Chapter 11

The Cost of Capital

LEARNING OBJECTIVES (Slides 11-2 to 11-3)

1. Understand the different kinds of financing available to a company: debt financing, equity

financing, and hybrid equity financing.

2. Understand the debt and equity components of the weighted average cost of capital

(WACC) and explain the tax implications on debt financing and the adjustment to the WACC.

3. Calculate the weights of the components using book values or market values.

4. Explain how the capital budgeting models use the WACC.

5. Determine a project’s beta and its implications in capital budgeting problems.

6. Select optimal project combinations from a company’s portfolio of acceptable projects.

IN A NUTSHELL…

This chapter clarifies the mystery of the hurdle rate or discount rate that was heretofore

assumed as a given. Companies can finance their capital requirements by issuing different types

of debt, preferred stock and common stock. After describing the salient features of each type of

capital component, the author explains the methodology that can be used to determine a firm’s

weighted average cost of capital (WACC). In particular, the tax implications, weighting

procedures, and methods to calculate component costs are explained with examples. The use of

the WACC as the hurdle rate when doing capital budgeting problems, and the process by which

a firm can use the WACC to form optimal combinations of projects, are covered last.

LECTURE OUTLINE

11.1 The Cost of Capital: A Starting Point (Slides 11-4 to 11-7)

There are primarily three broad sources of financing that companies can use to raise capital:

debt, common stock (equity), and preferred stock (hybrid equity).

Figure 11.1 (shown below) displays the three sources and their main suppliers.

Each capital component has its own risk and return profile and, therefore, its own rate of return

required by investors to provide funds to the firm.

Chapter 11 ◼ The Cost of Capital 363

Firms estimate their weighted average cost of capital (WACC) by multiplying each component

weight by the component cost and summing up the products.

The WACC is essentially the minimum acceptable rate of return that the firm should earn on its

investments of average risk, in order to be profitable.

In other words, the WACC should be used as the discount rate when computing NPV, or as the

criterion that must be exceeded when using IRR for making capital budgeting decisions.

Example 1: Measuring weighted average cost of a mortgage

Jim wants to refinance his home by taking out a single mortgage and paying off all the other

subprime and prime mortgages that he took on while the going was good. Listed below are the

balances and rates owed on each of his outstanding home-equity loans and mortgages:

Lender Balance Rate

First Cut-Throat Bank $ 150,000 7.5%

11.2 Components of the Weighted

Average Cost of Capital (Slides 11-8 to 11-23)

In order to determine a firm’s WACC, we need to know how to calculate the relative weights

and costs of the debt, preferred stock, and common stock of a firm.

Debt Component: The cost of debt (Rd) is the rate that firms have to pay when they borrow

money from banks, finance companies, and other lenders.

It is essentially measured by calculating the yield to maturity (YTM) on a firm’s outstanding

bonds, as covered in Chapter 6.

Although best solved for by using a financial calculator or spreadsheet, the YTM can also be

figured out as follows:

364 Brooks ◼ Financial Management: Core Concepts, 4e

The YTM on outstanding bonds, based on the bonds’ current selling price, tells us what investors

require for lending the firm their money in current market conditions.

However, if a firm were to go ahead and issue new debt, which is what typically happens when

firms expand or grow, it would also have to pay some transactions costs to the investment

bankers, and thereby receive lower net proceeds from each bond. The lower the amount the

firm gets to keep from the sale, the higher its costs are going to be.

Accordingly, to correctly estimate the cost of debt for inclusion in the WACC calculation, we

must adjust the market price by the amount of commissions that would have to be paid when

issuing new debt, and then calculate the YTM.

Chapter 11 ◼ The Cost of Capital 365

Example 2: Calculating the cost of debt

Kellogg’s wants to raise an additional $3,000,000 of debt as part of the capital that would be

needed to expand their operations into the Morning Foods sector. They were informed by their

investment banking consultant that they would have to pay a commission of 3.5% of the selling

price on new issues. Their CFO is in the process of estimating the corporation’s cost of debt for

inclusion into the WACC equation. The company currently has an 8%, AA-rated, noncallable

bond issue outstanding, which pays interest semiannually, will mature in seventeen years, has a

$1,000 face value, and is currently trading at $1,075. Calculate the appropriate cost of debt for

the firm.

Note: It is important to stress the point that it is the net proceeds and not the market price that

determines the appropriate cost of new debt.

Preferred Stock Component: Because preferred stock holders receive a constant dividend

with no maturity point, its cost (Rp) can be estimated by dividing the annual dividend by the net

proceeds (after floatation cost) per share of preferred stock

Rp = Dp/Net price

Example 3: Cost of Preferred Stock

Kellogg’s will also be issuing new preferred stock worth $1 million. They will pay a dividend

of $4 per share, which has a market price of $40. The floatation cost on preferred will amount

to $2 per share. What is their cost of preferred stock?

Equity Component: The cost of equity (Re) is essentially the rate of return that investors are

demanding or expecting to make on money invested in a company’s common stock.

366 Brooks ◼ Financial Management: Core Concepts, 4e

The cost of equity can be estimated by using either the SML approach (covered in Chapter 8) or

the Dividend Growth Model (covered in Chapter 7).

The security market line approach to Re calculates the cost of equity as a function of the risk–

free rate (rf) the market risk-premium [E(rm) – rf], and beta (βi). That is,

Chapter 11 ◼ The Cost of Capital 367

Example 4: Calculating Cost of Equity with the SML equation

Remember Kellogg’s from the two earlier examples? Well, to reach their desired capital

structure, the CEO has decided to utilize all of the company’s expected retained earnings in the

coming quarter. Kellogg’s beta is estimated at 0.65 by Value Line. The risk-free rate is currently

4%, and the expected return on the market is 15%. How much should the CEO put down as one

estimate of the company’s cost of equity?

The dividend growth approach to Re: The Gordon Model, introduced in Chapter 7, is used to

calculate the price of a constant growth stock.

However, with some algebraic manipulation it can be transformed into Equation 11.6, which

calculates the cost of equity, as shown below:

where Div0 = last paid dividend per share;

Po = Current market price per share; and

g = constant growth rate of dividend.

For newly issued common stock, the price must be adjusted for floatation cost (commission paid

to investment banker) as shown in Equation 11.7 below:

Where F is the floatation cost in percent.

Example 5: Applying the Dividend Growth Model to calculate Re

Kellogg’s common stock is trading at $45.57, and its dividends are expected to grow at a

constant rate of 6%. The company paid a dividend last year of $2.27. If the company issues

stock, they will have to pay a floatation cost per share equal to 5% of selling price. Calculate

Kellogg’s cost of equity with and without floatation costs.

Cost of equity without floatation cost:

368 Brooks ◼ Financial Management: Core Concepts, 4e

Re = (Div0*(1 + g)/Po) + g ➔ ($2.27*(1.06)/$45.57) + 0.06➔11.28%

Cost of equity with floatation cost:

Re = [$2.27*(1.06)/(45.57*(1 – 0.05)] + 0.06 ➔11.56%

Depending on the availability of data, either of the two models, or both, can be used to estimate

Re.

With two values, the average can be used as the cost of equity. For example, in Kellogg’s case

we have (11.15% + 11.28%)/2➔11.22% (without floatation costs)

or (11.15% + 11.56%)/2 ➔ 11.36%

Retained Earnings, although housed within a firm, does have a cost, i.e., the opportunity cost

for the shareholders not being able to invest the money themselves.

Note: Remind students that it is the addition to or change in retained earnings between this

year and last year that represents the amount of equity capital that has been added to the

capital base via a reinvestment of part or all of the income earned that year.

The cost of retained earnings can be calculated by using either of the previous two approaches,

without including floatation cost.

The Debt Component and Taxes. Because interest expenses are tax deductible, the cost of

debt, must be adjusted for taxes, as shown below, prior to including it in the WACC calculation:

After-tax cost of debt = Rd*(1 – Tc)

11.3 Weighting the Components:

Book Value or Market Value? (Slides 11-24 to 11-30)

As explained earlier, in order to calculate the WACC of a firm, each component’s cost is

multiplied by its proportion in the capital mix and then summed up.

There are two ways to determine the proportion or weights of each capital component, using

book value, or using market values.

Book Value: Weights can be determined by taking the balance sheet values for debt, preferred

stock, and common stock, adding them up, and dividing each by the total.

Adjusted Weighted Average Cost of Capital: Equation 11.9 can be used to combine all the

weights and component costs into a single average cost, which can be used as the firm’s

discount or hurdle rate:

Chapter 11 ◼ The Cost of Capital 369

( )

adj ps d c

E PS D

WACC R R T

V V V

=  +  +   −

11.9

Market Value: Weights are determined by taking the current market prices of the firm’s

outstanding securities and multiplying them by the number outstanding, to get the total value;

and then dividing each by the total market value to get the proportion or weight of each

370 Brooks ◼ Financial Management: Core Concepts, 4e

Example 6: Calculating capital component weights

Kellogg’s CFO is in the process of determining the firm’s WACC and needs to figure out the

weights of the various types of capital sources. Accordingly, he starts by collecting information

from the balance sheet and the capital markets, and makes up the following table:

Component

Balance Sheet

Value

Number

outstanding

Current Market

Price

Market Value

Debt

$ 150,000,000

150,000

$1,075

$161,250,000

Preferred Stock

$ 45,000,000

1,500,000

$40

$ 60,000,000

Common Stock

$ 180,000,000

4,500,000

$45.57

$205,065,000

What should he do next?

Example 7: Calculating Adjusted WACC

Using the market value weights and the component costs determined earlier, calculate Kellogg’s

adjusted WACC.

374 Brooks ◼ Financial Management: Core Concepts, 4e

With a WACC of 9.5%, only Projects 3 and 4, with IRRs of 10% and 11%, respectively, would be

accepted.

However, Projects 1 and 2 could have been profitable lower risk projects that are being rejected

in favor of higher risk projects, merely because the risk levels have not been adequately

adjusted for.

To adjust for risk, we would need to get individual project discount rates based on each project’s

beta.

Using a risk-free rate of 3%, a market risk premium of 9%, a before-tax cost of 10%, a tax rate of

30%, equally-weighted debt and equity levels, and varying project betas, we can compute each

project’s hurdle rate as follows:

Table 11.2 summarizes how the decisions made with and without adjusting for varying project

risk could lead to incorrect decisions.

376 Brooks ◼ Financial Management: Core Concepts, 4e

1,3,4,5 2m + 1.75m + 0.75m + 0.5m = $5m 0.95m

2,3,4,5 2.25m + 1.75m + 0.75m + 0.5m = $5.25m 0.85m

All other combinations would either exceed the $5.75m limit or underutilize the funds.

2) Select the combination which has the highest NPV, i.e., Combination 1 including projects

1,2,4, and 5 with a total NPV of $1.5m.

Chapter 11 ◼ The Cost of Capital 377

Questions

1. From what sources can a company raise capital? Do these different sources of capital all

charge the same rate? Why or why not?

2. Why is the yield to maturity on a bond the appropriate cost of debt financing?

3. What are the two different ways to estimate the cost of equity for a firm?

4. Should retained earnings reinvested in the company have a zero cost of capital because it

generates the funds internally and the company does not need to pay itself for borrowing

money? If not, why?

5. When calculating the cost of capital, why is it that the company only adjusts the cost of

debt for taxes?

6. What are the two ways to estimate the percentage (weights) of funds that a company has

received from lenders and owners? Which is more appropriate?

7. Why not use a single WACC for all company projects?

8. What are the types of errors a manager can make if he or she does not assign individual

WACCs to each potential project?

9. Why is selecting a beta for a project more of an art than a science?

10. If the capital budget is constrained by the amount of funds available for potential projects,

what mistake might a manager make if he or she just lists the potential projects by highest

to lowest NPV and picks the projects moving down the list until the funds are exhausted?

Prepping for Exams

1. d

2. a

10. d

Problems

1. WACC. Eric has another get-rich-quick idea but needs funding to support it. He chooses an all-

debt funding scenario. Eric will borrow $2,000 from Wendy, who will charge him 6% on the

loan. He will also borrow $1,500 from Bebe, who will charge 8% on the loan, and $800 from

Shelly, who will charge 14% on the loan. What is the weighted average cost of capital for Eric?

ANSWER

Chapter 11 ◼ The Cost of Capital 381

And solving via a calculator we have: set P/Y = 2; C/Y = 2

c. If the bond sells for $1,080 we have:

d. If the bond sells for $1,173 we have:

4. Cost of debt. Dunder-Mifflin, Inc. (DMI) is selling 600,000 bonds to raise money for the

publication of new magazines in the coming year. The bonds will pay a coupon rate of 12%

on semiannual payments and will mature in thirty years. Its par value is $100. What is the

cost of debt to DMI if the bonds raise

a. $45,000,000?

b. $54,000,000?

c. $66,000,000?

d. $75,000,000?

ANSWER