FIN 486 WEEK3

This is the Team Assignement. This Portion of the assignement is mine. Please do in Excel and must be complete by Sunday 11.00PM (Due in 45 hours. I will also post what other member of the team has done... Tomorrow I will be on a flight all day. So cannot respond to email till Sunday morning(24hours from now)

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Resource: Principles of Managerial Finance, Ch. 9

Complete the Spreadsheet Exercise on p. 390, and The Interactive Case 4 Eco Plastics in Ch 9.

Create a spreadsheet with two tabs. Use one tab for the Spreadsheet Exercise on p. 390, and the other tab for The Interactive Case 4 Eco Plastics.

MY PORTION OF THE ASSIGNMENT:

f.

• (1) Assuming that the debt financing costs do not change, what effect would a shift to a more highly leveraged capital structure consisting of 50% long-term debt, 0% preferred stock, and 50% common stock have on the risk premium for Eco's common stock? What would be Eco's new cost of common equity?
• (2) What would be Eco's new weighted average cost of capital?
• (3) Which capital structure--the original one or this one--seems better? Why

CHAPTER 9

• LG 1 Understand the basic concept and sources of capital associated with the cost of capital.
• LG 2 Explain what is meant by the marginal cost of capital.
• LG 3 Determine the cost of long-term debt, and explain why the after-tax cost of debt is the relevant cost of debt.
• LG 4 Determine the cost of preferred stock.
• LG 5 Calculate the cost of common stock equity, and convert it into the cost of retained earnings and the cost of new issues of common stock.
• LG 6 Calculate the weighted average cost of capital (WACC), and discuss alternative weighting schemes.

In your professional life

ACCOUNTING You need to understand the various sources of capital and how their costs are calculated to provide the data necessary to determine the firm’s overall cost of capital.

INFORMATION SYSTEMS You need to understand the various sources of capital and how their costs are calculated to develop systems that will estimate the costs of those sources of capital as well as the overall cost of capital.

MANAGEMENT You need to understand the cost of capital to select long-term investments after assessing their acceptability and relative rankings.

MARKETING You need to understand the firm’s cost of capital because proposed projects must earn returns in excess of it to be acceptable.

OPERATIONS You need to understand the firm’s cost of capital to assess the economic viability of investments in plant and equipment needed to improve or grow the firm’s capacity.

In your personal life

Knowing your personal cost of capital will allow you to make informed decisions about your personal consuming, borrowing, and investing. Managing your personal wealth is a lot like managing the wealth of a business in that you need to understand the trade-offs between consuming wealth and growing wealth and how growing wealth can be accomplished by investing your own monies or borrowed monies. Understanding the cost of capital concepts will allow you to make better long-term decisions and maximize the value of your personal wealth.

Often listed among America’s most admired corporations, Alcoa, Inc., is the world’s largest producer of aluminum, with more than 61,000 employees in 30 countries. A quick glance at its financial statements might suggest that the company has been doing very well in recent years. Alcoa increased its total sales from $18.4 billion in 2009 to $23.7 billion in 2012, an annual growth rate of almost 9 percent, far exceeding overall economic growth over the same period. In each of those years, Alcoa spent more than $1 billion on capital expenditures, expanding and upgrading its manufacturing facilities, entering new joint ventures, and making strategic acquisitions.

During that span, however, Alcoa’s stock underperformed. During the 5-year period ending in May 2013, Alcoa common stock lost almost 80 percent of its value, while the broader stock market (as measured by the Standard & Poor’s 500 Stock Composite Index) rose by about 20 percent. Why did Alcoa perform so poorly? A simple answer is that its business investments failed to earn a return sufficient to meet the expectations of investors. Despite Alcoa’s continued growth, the rate of return that it earned on the assets that it had invested was not sufficient to satisfy investors. When a firm’s operating results disappoint investors, its stock price will fall as investors sell their shares and move to a more attractive investment. According to some estimates, Alcoa’s cost of capital exceeded 12 percent, but its investments were consistently earning returns below 5 percent. That is a recipe for a declining stock price, which is precisely what Alcoa had been experiencing for several years.

For companies to succeed, their investments have to earn a rate of return that exceeds investors’ expectations. How, though, do companies know what investors expect? The answer is that companies have to measure their cost of capital. Read on to learn how firms do that.

LG 1

LG 2

My Finance Lab Video

Chapter 1 established that the goal of the firm is to maximize shareholder wealth. To do so, managers must make investments that are worth more than they cost. In this chapter, you will learn about the cost of capital, which is the rate of return that financial managers use to evaluate all possible investment opportunities to determine which ones add value to the firm. The cost of capital represents the firm’s cost of financing and is the minimum rate of return that a project must earn to increase firm value. In particular, the cost of capital refers to the cost of the next dollar of financing necessary to finance a new investment opportunity. Investments with a rate of return above the cost of capital will increase the value of the firm, because these investments are worth more than they cost. In contrast, projects with a rate of return below the cost of capital will decrease firm value.

cost of capital

Represents the firm’s cost of financing and is the minimum rate of return that a project must earn to increase firm value.

The cost of capital is an extremely important financial concept. It acts as a major link between the firm’s long-term investment decisions and the wealth of the firm’s owners as determined by the market value of their shares. Financial managers are ethically bound to invest only in projects that they expect to exceed the cost of capital; see the Focus on Ethics box for more discussion of this responsibility.

Business Week once referred to Peter Drucker as “The Man Who Invented Management.” In his role as writer and management consultant, Drucker stressed the importance of ethics to business leaders. He believed that it was the ethical responsibility of a business to earn a profit. In his mind, profitable businesses create opportunities, whereas unprofitable ones waste society’s resources. Drucker once said, “Profit is not the explanation, cause, or rationale of business behavior and business decisions, but rather the test of their validity. If archangels instead of businessmen sat in directors’ chairs, they would still have to be concerned with profitability, despite their total lack of personal interest in making profits.”a

But what happens when businesses abandon ethics for profits? Consider Merck’s experience with the drug, Vioxx. Introduced in 1999, Vioxx was an immediate success, quickly reaching $2.5 billion in annual sales. However, a Merck study launched in 1999 eventually found that patients who took Vioxx suffered from an increased risk of heart attacks and strokes. Despite the risks, Merck continued to market and sell Vioxx. By the time Vioxx was withdrawn from the market, an estimated 20 million Americans had taken the drug, 88,000 had suffered Vioxxrelated heart attacks, and 38,000 had died.

News of the 2004 Vioxx withdrawal hit Merck’s stock hard. The company’s shares fell 27 percent on the day of the announcement, slashing $27 billion off the firm’s market capitalization. Moody’s, Standard & Poor’s, and Fitch cut Merck’s credit ratings, costing the firm its coveted AAA rating. The company’s bottom line also suffered as its net income fell 21 percent in the final three months of 2004.

The recall dealt a major blow to Merck’s reputation. The company was criticized for aggressively marketing Vioxx despite the drug’s serious side effects. Questions were also raised about the research reports Merck had submitted in support of the drug. Lawsuits followed. In 2008, Merck agreed to fund a $4.85 billion settlement to resolve approximately 50,000 Vioxxrelated lawsuits. The company had also incurred $1.53 billion in legal costs by the time of the settlement.

The Vioxx recall increased Merck’s cost of capital. What effect would an increased cost of capital have on a firm’s future investments?

aPeter F. Drucker, The Essential Drucker (New York: Collins Business Essentials, 2001).

A firm’s cost of capital reflects the expected average future cost of funds over the long run, and it reflects the entirety of the firm’s financing activities. For example, a firm may raise the money it needs to build a new manufacturing facility by borrowing money (debt), by selling common stock (equity), or by doing both. Managers must take into account respective costs of both forms of capital when they estimate a firm’s cost of capital. In fact, most firms do finance their activities with a blend of equity and debt. In Chapter 13, we will explore the factors that determine what mix of debt and equity is optimal for any particular firm. For now, we will simply say that most firms have a desired mix of financing, and the cost of capital must reflect the cost of each type of financing that a firm uses. To capture all the relevant financing costs, assuming some desired mix of financing, we need to look at the overall cost of capital rather than just the cost of any single source of financing.

My Finance Lab Solution Video

A firm is currently considering two investment opportunities. Two financial analysts, working independently of each other, are evaluating these opportunities. Assume the following information about investments A and B.

Investment A

The analyst studying this investment recalls that the company recently issued bonds paying a 6% rate of return. He reasons that because the investment project earns 7% while the firm can issue debt at 6%, the project must be worth doing, so he recommends that the company undertake this investment.

Investment B

Least costly financing source available

Equity = 14%

The analyst assigned to this project knows that the firm has common stock outstanding and that investors who hold the company’s stock expect a 14% return on their investment. The analyst decides that the firm should not undertake this investment because it only produces a 12% return while the company’s shareholders expect a 14% return.

In this example, each analyst is making a mistake by focusing on one source of financing rather than on the overall financing mix. What if instead the analysts used a combined cost of financing? By weighting the cost of each source of financing by its relative proportion in the firm’s target capital structure, the firm can obtain a weighted average cost of capital. Assuming that this firm desires a 50–50 mix of debt and equity, the weighted average cost here would be 10%[(0.50 × 6% debt) + (0.50 × 14% equity)]. With this average cost of financing, the firm should reject the first opportunity (7% expected return < 10% weighted average cost) and accept the second (12% expected return > 10% weighted average cost).

In this chapter, our concern is only with the long-term sources of capital available to a firm because they are the sources that supply the financing necessary to support the firm’s capital budgeting activities. Capital budgeting is the process of evaluating and selecting long-term investments. This process is intended to achieve the firm’s goal of maximizing shareholders’ wealth. Although the entire capital budgeting process is discussed throughout Part 5, at this point it is sufficient to say that capital budgeting activities are chief among the responsibilities of financial managers and that they cannot be carried out without knowing the appropriate cost of capital with which to judge the firm’s investment opportunities.

There are four basic sources of long-term capital for firms: long-term debt, preferred stock, common stock, and retained earnings. All entries on the right-hand side of the balance sheet, other than current liabilities, represent these sources:

Not every firm will use all of these sources of financing. In particular, preferred stock is relatively uncommon. Even so, most firms will have some mix of funds from these sources in their capital structures. Although a firm’s existing mix of financing sources may reflect its target capital structure, it is ultimately the marginal cost of capital necessary to raise the next marginal dollar of financing that is relevant for evaluating the firm’s future investment opportunities.

What is the cost of capital?

What role does the cost of capital play in the firm’s long-term investment decisions? How does it relate to the firm’s ability to maximize shareholder wealth?

What does the firm’s capital structure represent?

What are the typical sources of long-term capital available to the firm?

LG 3

The cost of long-term debt is the financing cost associated with new funds raised through long-term borrowing. Typically, the funds are raised through the sale of corporate bonds.

cost of long-term debt

The financing cost associated with new funds raised through long-term borrowing.

The net proceeds from the sale of a bond, or any security, are the funds that the firm receives from the sale. The total proceeds are reduced by the flotation costs, which represent the total costs of issuing and selling securities. These costs apply to all public offerings of securities: debt, preferred stock, and common stock. They include two components: (1) underwriting costs, or compensation earned by investment bankers for selling the security; and (2) administrative costs, or issuer expenses such as legal and accounting costs.

net proceeds

Funds actually received by the firm from the sale of a security.

flotation costs

The total costs of issuing and selling a security.

Duchess Corporation, a major hardware manufacturer, is contemplating selling $10 million worth of 20-year, 9% coupon (stated annual interest rate) bonds, each with a par value of $1,000. Because bonds with similar risk earn returns greater than 9%, the firm must sell the bonds for $980 to compensate for the lower coupon interest rate. The flotation costs are 2% of the par value of the bond (0.02 × $1,000), or $20. The net proceeds to the firm from the sale of each bond are therefore $960 ($980 minus $20).

The before-tax cost of debt, rd, is simply the rate of return the firm must pay on new borrowing. A firm’s before-tax cost of debt for bonds can be found in any of three ways: quotation, calculation, or approximation.

A relatively quick method for finding the before-tax cost of debt is to observe the yield to maturity (YTM) on the firm’s existing bonds or bonds of similar risk issued by other companies. The YTM of existing bonds reflects the rate of return required by the market. For example, if the market requires a YTM of 9.7 percent for a similar-risk bond, this value can be used as the before-tax cost of debt, rd, for new bonds. Bond yields are widely reported by sources such as the Wall Street Journal.

This approach finds the before-tax cost of debt by calculating the YTM generated by the bond’s cash flows, given the net proceeds that the firm receives when it issues the bonds. From the issuer’s point of view, this value is the cost to maturity of the cash flows associated with the debt. The YTM can be calculated by using a financial calculator or an electronic spreadsheet. It represents the annual before-tax percentage cost of the debt.

In the preceding example, $960 were the net proceeds of a 20-year bond with a $1,000 par value and 9% coupon interest rate. The calculation of the annual cost is quite simple. The cash flow pattern associated with this bond’s sales consists of an initial inflow (the net proceeds) followed by a series of annual outlays (the interest payments). In the final year, when the debt is retired, an outlay representing the repayment of the principal also occurs. The cash flows associated with Duchess Corporation’s bond issue are as follows:

End of year(s)

Cash flow

      0

 $  960

   1–20

−$   90

     20

− $1,000

The initial $960 inflow is followed by annual interest outflows of $90 (9% coupon interest rate × $1,000 par value) over the 20-year life of the bond. In year 20, an outflow of $1,000 (the repayment of the principal) occurs. We can determine the cost of debt by finding the YTM, which is the discount rate that equates the present value of the bond outflows to the initial inflow.

My Finance Lab Financial Calculator

Calculator use (Note: Most calculators require either the present value [net proceeds] or the future value [annual interest payments and repayment of principal] to be input as negative numbers when we calculate yield to maturity. That approach is used here.) Using the calculator and the inputs shown at the left, you should find the before-tax cost of debt (yield to maturity) to be 9.452%.

Spreadsheet use The before-tax cost of debt on the Duchess Corporation bond can be calculated using an Excel spreadsheet. The following Excel spreadsheet shows that by referencing the cells containing the bond’s net proceeds, coupon payment, years to maturity, and par value as part of Excel’s RATE function, you can quickly determine that the appropriate before-tax cost of debt for Duchess Corporation’s bond is 9.452%.

Although you may not recognize it, both the calculator and the Excel function are using trial-and-error to find the bond’s YTM, they just do it faster than you can.

Although not as precise as using a calculator, there is a method for quickly approximating the before-tax cost of debt. The before-tax cost of debt, rd, for a bond with a $1,000 par value can be approximated by

(9.1)

Where

Substituting the appropriate values from the Duchess Corporation example into the approximation formula given in Equation 9.1, we get

This approximate value of before-tax cost of debt is close to the 9.452%, but it lacks the precision of the value derived using the calculator or spreadsheet.

Unlike the dividends paid to equityholders, the interest payments paid to bond-holders are tax deductable for the firm, so the interest expense on debt reduces the firm’s taxable income and, therefore, the firm’s tax liability. To find the firm’s net cost of debt, we must account for the tax savings created by debt and solve for the cost of long-term debt on an after-tax basis. The after-tax cost of debt, ri, can be found by multiplying the before-tax cost, rd, by 1 minus the tax rate, T:

ri = rd × (1 − T)

(9.2)

My Finance Lab Solution Video

Duchess Corporation has a 40% tax rate. Using the 9.452% before-tax debt cost calculated above and applying Equation 9.2, we find an after-tax cost of debt of 5.67%[9.452% × (1 − 0.40)]. Typically, the cost of long-term debt for a given firm is less than the cost of preferred or common stock, partly because of the tax deductibility of interest.

My Finance Lab Solution Video

Kait and Kasim Sullivan, a married couple in the 28% federal income-tax bracket, wish to borrow $60,000 to pay for a new luxury car. To finance the purchase, they can either borrow the $60,000 through the auto dealer at an annual interest rate of 6.0%, or they can take a $60,000 second mortgage on their home. The best annual rate they can get on the second mortgage is 7.2%. They already have qualified for both of the loans being considered.

If they borrow from the auto dealer, the interest on this “consumer loan” will not be deductible for federal tax purposes. However, the interest on the second mortgage would be tax deductible because the tax law allows individuals to deduct interest paid on a home mortgage. To choose the least-cost financing, the Sullivans calculated the after-tax cost of both sources of long-term debt. Because interest on the auto loan is not tax deductible, its after-tax cost equals its stated cost of 6.0%. Because the interest on the second mortgage is tax deductible, its after-tax cost can be found using Equation 9.2:

Because the 5.2% after-tax cost of the second mortgage is less than the 6.0% cost of the auto loan, the Sullivans may decide to use the second mortgage to finance the auto purchase.

What are the net proceeds from the sale of a bond? What are flotation costs, and how do they affect a bond’s net proceeds?

What methods can be used to find the before-tax cost of debt?

How is the before-tax cost of debt converted into the after-tax cost?

My Finance Lab

The interest expense on debt provides a tax deduction for the issuer so any calculation of a firm’s net cost of debt should reflect this benefit. Based on the information provided at MFL, compute a firm’s after-tax cost of debt using a spreadsheet model.

LG 4

Preferred stock represents a special type of ownership interest in the firm. It gives preferred stockholders the right to receive their stated dividends before the firm can distribute any earnings to common stockholders. The key characteristics of preferred stock were described in Chapter 7. However, the one aspect of preferred stock that requires review is dividends.

When dividends are stated as “preferred stock dividends,” the stock is often referred to as “x-dollar preferred stock.” Thus, a “$4 preferred stock” is expected to pay preferred stockholders $4 in dividends each year on each share of preferred stock owned.

Sometimes preferred stock dividends are stated as an annual percentage rate. This rate represents the percentage of the stock’s par, or face, value that equals the annual dividend. For instance, an 8 percent preferred stock with a $50 par value would be expected to pay an annual dividend of $4 per share (0.08 × $50 par = $4). Before the cost of preferred stock is calculated, any dividends stated as percentages should be converted to annual dollar dividends.

The cost of preferred stock, rp, is the ratio of the preferred stock dividend to the firm’s net proceeds from the sale of the preferred stock. The net proceeds represent the amount of money to be received minus any flotation costs. The following equation gives the cost of preferred stock, rp, in terms of the annual dollar dividend, Dp, and the net proceeds from the sale of the stock, Np:

cost of preferred stock, rp

The ratio of the preferred stock dividend to the firm’s net proceeds from the sale of preferred stock.

(9.3)

Duchess Corporation is contemplating issuance of a 10% preferred stock that they expect to sell for $87 per share. The cost of issuing and selling the stock will be $5 per share. The first step in finding the cost of the stock is to calculate the dollar amount of the annual preferred dividend, which is $8.70 (0.10 × $87). The net proceeds per share from the proposed sale of stock equals the sale price minus the flotation costs ($87 − $5 = $82). Substituting the annual dividend, Dp, of $8.70 and the net proceeds, Np, of $82 into Equation 9.3 gives the cost of preferred stock, 10.6% ($8.70 ÷ $82).

The cost of Duchess’s preferred stock (10.6%) is much greater than the cost of its long-term debt (5.67%). This difference exists both because the cost of long-term debt (the interest) is tax deductible and because preferred stock is riskier than long-term debt.

How would you calculate the cost of preferred stock?

LG 5

The cost of common stock is the return required on the stock by investors in the marketplace. There are two forms of common stock financing: (1) retained earnings and (2) new issues of common stock. As a first step in finding each of these costs, we must estimate the cost of common stock equity.

The cost of common stock equity, rs, is the rate at which investors discount the expected common stock dividends of the firm to determine its share value. Two techniques are used to measure the cost of common stock equity. One relies on the constant-growth valuation model, the other on the capital asset pricing model (CAPM).

cost of common stock equity, rs

The rate at which investors discount the expected dividends of the firm to determine its share value.

In Chapter 7, we found the value of a share of stock to be equal to the present value of all future dividends, which in one model are assumed to grow at a constant annual rate over an infinite time horizon. This model, the constant-growth valuation model, is also known as the Gordon growth model. The key expression derived for this model, first presented as Equation 7.4, is

constant-growth valuation (Gordon growth) model

Assumes that the value of a share of stock equals the present value of all future dividends (assumed to grow at a constant rate) that it is expected to provide over an infinite time horizon.

(9.4)

where

Solving Equation 9.4 for rs results in the following expression for the cost of common stock equity:

(9.5)

Equation 9.5 indicates that the cost of common stock equity can be found by dividing the dividend expected at the end of year 1 by the current market price of the stock (the “dividend yield”) and adding the expected growth rate (the “capital gains yield”).

Duchess Corporation wishes to determine its cost of common stock equity, rs. The market price, P0, of its common stock is $50 per share. The firm expects to pay a dividend, D1, of $4 at the end of the coming year, 2016. The dividends paid on the outstanding stock over the past 6 years (2010 through 2015) were as follows:

Year

Dividend

2015

$3.80 

2014

 3.62

2013

 3.47

2012

 3.33

2011

 3.12

2010

 2.97

Using a financial calculator or electronic spreadsheet, in conjunction with the technique described for finding growth rates in Chapter 5, we can calculate the annual rate at which dividends have grown, g, from 2010 to 2015. It turns out to be approximately 5% (more precisely, it is 5.05%). Substituting D1 = $4, P0 = $50, and g = 5% into Equation 9.5 yields the cost of common stock equity:

The 13.0% cost of common stock equity represents the return required by existing shareholders on their investment. If the actual return is less than that, shareholders are likely to begin selling their stock.

Recall from Chapter 8 that the capital asset pricing model (CAPM) describes the relationship between the required return, rs, and the nondiversifiable risk of the firm as measured by the beta coefficient, β. The basic CAPM is

capital asset pricing model (CAPM)

Describes the relationship between the required return, rs, and the nondiversifiable risk of the firm as measured by the beta coefficient, β.

rs = RF + [β × (rm − RF)]

(9.6)

where

Using the CAPM indicates that the cost of common stock equity is the return required by investors as compensation for the firm’s nondiversifiable risk, measured by beta.

Duchess Corporation now wishes to calculate its cost of common stock equity, rs, by using the CAPM. The firm’s investment advisors and its own analysts indicate that the risk-free rate, RF, equals 7%; the firm’s beta, β, equals 1.5; and the market return, rm, equals 11%. Substituting these values into Equation 9.6, the company estimates the cost of common stock equity, rs, to be

rs = 7.0% + [1.5 × (11.0% − 7.0%)] = 7.0% + 6.0% = 13.0%

The 13.0% cost of common stock equity represents the required return of investors in Duchess Corporation common stock. It is the same as that found by using the constant-growth valuation model.

The CAPM technique differs from the constant-growth valuation model in that it directly considers the firm’s risk, as reflected by beta, in determining the required return or cost of common stock equity. The constant-growth model does not look at risk; it uses the market price, P0, as a reflection of the expected risk–return preference of investors in the marketplace. The constant-growth valuation and CAPM techniques for finding rs are theoretically equivalent, although in practice estimates from the two methods do not always agree. The two methods can produce different estimates because they require (as inputs) estimates of other quantities, such as the expected dividend growth rate or the firm’s beta.

Another difference is that when the constant-growth valuation model is used to find the cost of common stock equity, it can easily be adjusted for flotation costs to find the cost of new common stock; the CAPM does not provide a simple adjustment mechanism. The difficulty in adjusting the cost of common stock equity calculated by using the CAPM occurs because in its common form the model does not include the market price, P0, a variable needed to make such an adjustment. Although the CAPM has a stronger theoretical foundation, the computational appeal of the traditional constant-growth valuation model justifies its use throughout this text to measure financing costs of common stock. As a practical matter, analysts might want to estimate the cost of equity using both approaches and then take an average of the results to arrive at a final estimate of the cost of equity.

As you know, dividends are paid out of a firm’s earnings. Their payment, made in cash to common stockholders, reduces the firm’s retained earnings. Suppose that a firm needs common stock equity financing of a certain amount. It has two choices relative to retained earnings: It can issue additional common stock in that amount and still pay dividends to stockholders out of retained earnings, or it can increase common stock equity by retaining the earnings (not paying the cash dividends) in the needed amount. In a strict accounting sense, the retention of earnings increases common stock equity in the same way that the sale of additional shares of common stock does. Thus, the cost of retained earnings, rr, to the firm is the same as the cost of an equivalent fully subscribed issue of additional common stock. Stockholders find the firm’s retention of earnings acceptable only if they expect that it will earn at least their required return on the reinvested funds.

cost of retained earnings, rr

The same as the cost of an equivalent fully subscribed issue of additional common stock, which is equal to the cost of common stock equity, rs.

Viewing retained earnings as a fully subscribed issue of additional common stock, we can set the firm’s cost of retained earnings, rr, equal to the cost of common stock equity as given by Equations 9.5 and 9.6.

rr = rs

(9.7)

Thus, it is not necessary to adjust the cost of retained earnings for flotation costs because by retaining earnings the firm “raises” equity capital without incurring these costs.

The cost of retained earnings for Duchess Corporation was actually calculated in the preceding examples: It is equal to the cost of common stock equity. Thus, rr equals 13.0%. As we will show in the next section, the cost of retained earnings is always lower than the cost of a new issue of common stock because it entails no flotation costs.

Retained Earnings, the Preferred Source of Financing

In the United States and most other countries, firms rely more heavily on retained earnings than any other financing source. For example, a 2013 survey of Chinese firms found that 64% of the companies surveyed listed retained earnings as one of their primary sources of funds. Bank loans were a distant second choice, mentioned as a primary source of funds by just 44% of the companies.1

Our purpose in finding the firm’s overall cost of capital is to determine the after-tax cost of new funds required for financing projects. The cost of a new issue of common stock, rn, is determined by calculating the cost of common stock, net of underpricing and associated flotation costs. Normally, when new shares are issued, they are underpriced, meaning that they are sold at a discount relative to the current market price, P0. Underpricing is the difference between the market price and the issue price, which is the price paid by the primary markt investors discussed in Chapter 2.

cost of a new issue of common stock, rn

The cost of common stock, net of underpricing and associated flotation costs.

underpriced

Stock sold at a price below its current market price, P0.

1. Business in China Survey 2013, China Europe International Business School.

We can use the constant-growth valuation model expression for the cost of existing common stock, rs, as a starting point. If we let Nn represent the net proceeds from the sale of new common stock after subtracting underpricing and flotation costs, the cost of the new issue, rn, can be expressed as2

(9.8)

The net proceeds from sale of new common stock, Nn, will be less than the current market price, P0. Therefore, the cost of new issues, rn, will always be greater than the cost of existing issues, rs, which is equal to the cost of retained earnings, rr. The cost of new common stock is normally greater than any other long-term financing cost.

In the constant-growth valuation example, we found Duchess Corporation’s cost of common stock equity, rs, to be 13%, using the following values: an expected dividend, D1, of $4; a current market price, P0, of $50; and an expected growth rate of dividends, g, of 5%.

To determine its cost of new common stock, rn, Duchess Corporation has estimated that on average, new shares can be sold for $47. The $3-per-share underpricing is due to the competitive nature of the market. A second cost associated with a new issue is flotation costs of $2.50 per share that would be paid to issue and sell the new shares. The total underpricing and flotation costs per share are therefore $5.50.

Subtracting the $5.50-per-share underpricing and flotation cost from the current $50 share price results in expected net proceeds of $44.50 per share ($50.00 minus $5.50). Substituting D1 = $4, Nn = $44.50, and g = 5% into Equation 9.8 results in a cost of new common stock, rn:

Duchess Corporation’s cost of new common stock is therefore 14.0%. That is the value to be used in subsequent calculations of the firm’s overall cost of capital.

What premise about share value underlies the constant-growth valuation (Gordon growth) model that is used to measure the cost of common stock equity, rs?

How do the constant-growth valuation model and capital asset pricing model methods for finding the cost of common stock differ?

Why is the cost of financing a project with retained earnings less than the cost of financing it with a new issue of common stock?

2. An alternative, but computationally less straightforward, form of this equation is

(9.8a)

where f represents the percentage reduction in current market price expected as a result of underpricing and flotation costs. Simply stated, Nn in Equation 9.8 is equivalent to p0 × (1 − f) in Equation 9.8a. For convenience, Equation 9.8 is used to define the cost of a new issue of common stock, rn.

LG 6

As noted earlier, the weighted average cost of capital (WACC), ra, reflects the expected average future cost of capital over the long run. It is found by weighting the cost of each specific type of capital by its proportion in the firm’s capital structure.

weighted average cost of capital (WACC), ra

Reflects the expected average future cost of capital over the long run; found by weighting the cost of each specific type of capital by its proportion in the firm’s capital structure.

Calculating the weighted average cost of capital (WACC) is straightforward: Multiply the individual cost of each form of financing by its proportion in the firm’s capital structure and sum the weighted values. As an equation, the weighted average cost of capital, ra, can be specified as

ra = (wi × ri) + (wp × rp) + (ws × rr or n)

(9.9)

where

Three important points should be noted in Equation 9.9:

• 1. For computational convenience, it is best to convert the weights into decimal form and leave the individual costs in percentage terms.
• 2. The weights must be nonnegative and sum to 1.0. Simply stated, WACC must account for all financing costs within the firm’s capital structure.
• 3. The firm’s common stock equity weight, ws, is multiplied by either the cost of retained earnings, rr, or the cost of new common stock, rn. Which cost is used depends on whether the firm’s common stock equity will be financed using retained earnings, rr, or new common stock, rn.

In earlier examples, we found the costs of the various types of capital for Duchess Corporation to be as follows:

The company uses the following weights in calculating its weighted average cost of capital:

Source of capital

Weight

Long-term debt

 40%

Preferred stock

 10 

Common stock equity

 50 

   Total

100% 

Source of capital

Weight (1)

Cost (2)

Weighted cost [(1) × (2)] (3)

Long-term debt

0.40

 5.6%

2.2%      

Preferred stock

0.10

10.6 

1.1      

Common stock equity

0.50

13.0 

6.5      

  Totals

1.00

WACC = 9.8%     

Because the firm expects to have a sizable amount of retained earnings available ($300,000), it plans to use its cost of retained earnings, rr, as the cost of common stock equity. Duchess Corporation’s weighted average cost of capital is calculated in Table 9.1. The resulting weighted average cost of capital for Duchess is 9.8%. Assuming an unchanged risk level, the firm should accept all projects that will earn a return greater than 9.8%.

As U.S. financial markets experienced and recovered from the 2008 financial crisis and 2009 “great recession,” firms struggled to keep track of their weighted average cost of capital. The individual component costs were moving rapidly in response to the financial market turmoil. Volatile financial markets can make otherwise manageable cost-of-capital calculations exceedingly complex and inherently error prone, possibly wreaking havoc with investment decisions. If a firm underestimates its cost of capital, it risks making investments that are not economically justified, and if a firm overestimates its financing costs, it risks foregoing value-maximizing investments.

Although the WACC computation does not change when markets become unstable, the uncertainty surrounding the components that comprise the WACC increases dramatically. The financial crisis pushed credit costs to a point where long-term debt was largely inaccessible, and the great recession saw Treasury bond yields fall to historic lows, making cost of equity projections appear unreasonably low. With these key components in flux, it is exceedingly difficult, if not impossible, for firms to get a handle on a cost of long-term capital.

According to CFO Magazine, at least one firm resorted to a two-pronged approach for determining its cost of capital during the uncertain times. Ron Domanico is the chief financial officer (CFO) at Caraustar Industries, Inc., and he reported that his company dealt with the cost-of-capital uncertainty by abandoning the conventional one-size-fits-all approach. “In the past, we had one cost of capital that we applied to all our investment decisions … today that’s not the case. We have a short-term cost of capital we apply to short-term opportunities, and a longer-term cost of capital we apply to longer-term opportunities … and the reality is that the longer-term cost is so high that it has forced us to focus only on those projects that have immediate returns,” Mr. Domanico is quoted saying.a

Part of Caraustar’s motivation for implementing this two-pronged approach was to account for the excessively large spread between short- and long-term debt rates that emerged during the financial market crisis. Mr. Domanico reported that during the crisis Caraustar could borrow short-term funds at the lower of Prime plus 4 percent or LIBOR plus 5 percent, where either rate was reasonable for making short-term investment decisions. Alternatively, long-term investment decisions were being required to clear Caraustar’s long-term cost-of-capital calculation accounting for borrowing rates in excess of 12 percent.

Why don’t firms generally use both short- and long-run weighted average costs of capital?

aRandy Myers, “A Losing Formula” (May 2009), www.cfo.com/article.cfm/13522582/c_13526469.

Firms can calculate weights on the basis of either book value or market value using either historical or target proportions.

Book value weights use accounting values to measure the proportion of each type of capital in the firm’s financial structure. Market value weights measure the proportion of each type of capital at its market value. Market value weights are appealing because the market values of securities closely approximate the actual dollars to be received from their sale. Moreover, because firms calculate the costs of the various types of capital by using prevailing market prices, it seems reasonable to use market value weights. In addition, the long-term investment cash flows to which the cost of capital is applied are estimated in terms of current as well as future market values. Market value weights are clearly preferred over book value weights.

book value weights

Weights that use accounting values to measure the proportion of each type of capital in the firm’s financial structure.

market value weights

Weights that use market values to measure the proportion of each type of capital in the firm’s financial structure.

Historical weights can be either book or market value weights based on actual capital structure proportions. For example, past or current book value proportions would constitute a form of historical weighting, as would past or current market value proportions. Such a weighting scheme would therefore be based on real—rather than desired—proportions.

historical weights

Either book or market value weights based on actual capital structure proportions.

Target weights, which can also be based on either book or market values, reflect the firm’s desired capital structure proportions. Firms using target weights establish such proportions on the basis of the “optimal” capital structure they wish to achieve. (The development of these proportions and the optimal structure are discussed in detail in Chapter 13.)

target weights

Either book or market value weights based on desired capital structure proportions.

When one considers the somewhat approximate nature of the calculation of weighted average cost of capital, the choice of weights may not be critical. However, from a strictly theoretical point of view, the preferred weighting scheme is target market value proportions, and we assume this scheme throughout this chapter.

Chuck Solis currently has three loans outstanding, all of which mature in exactly 6 years and can be repaid without penalty any time prior to maturity. The outstanding balances and annual interest rates on these loans are as follows:

Loan

Outstanding balance

Annual interest rate

1

$26,000  

  9.6%

2

9,000

10.6

3

45,000 

7.4

After a thorough search, Chuck found a lender who would loan him $80,000 for 6 years at an annual interest rate of 9.2% on the condition that the loan proceeds be used to fully repay the three outstanding loans, which combined have an outstanding balance of $80,000 ($26,000 + $9,000 + $45,000).

Chuck wishes to choose the least costly alternative: (1) to do nothing or (2) to borrow the $80,000 and pay off all three loans. He calculates the weighted average cost of his current debt by weighting each debt’s annual interest cost by the proportion of the $80,000 total it represents and then summing the three weighted values as follows:

Given that the weighted average cost of the $80,000 of current debt of 8.5% is below the 9.2% cost of the new $80,000 loan, Chuck should do nothing and just continue to pay off the three loans as originally scheduled.

What is the weighted average cost of capital (WACC), and how is it calculated?

What is the relationship between the firm’s target capital structure and the weighted average cost of capital (WACC)?

Describe the logic underlying the use of target weights to calculate the WACC, and compare and contrast this approach with the use of historical weights. What is the preferred weighting scheme?

The cost of capital is an extremely important rate of return, particularly in capital budgeting decisions. It is the expected average future cost to the firm of funds over the long run. Because the cost of capital is the pivotal rate of return used in the investment decision process, its accuracy can significantly affect the quality of these decisions.

Underestimation of the cost of capital can make poor projects look attractive; overestimation can make good projects look unattractive. By applying the techniques presented in this chapter to estimate the firm’s cost of capital, the financial manager will improve the likelihood that the firm’s long-term decisions will be consistent with the firm’s overall goal of maximizing stock price (owner wealth).

LG 1 Understand the basic concept and sources of capital associated with the cost of capital. The cost of capital is the minimum rate of return that a firm must earn on its investments to grow firm value. A weighted average cost of capital should be used to find the expected average future cost of funds over the long run. The individual costs of the basic sources of capital (long-term debt, preferred stock, retained earnings, and common stock) can be calculated separately.

LG 2 Explain what is meant by the marginal cost of capital. The relevant cost of capital for a firm is the marginal cost of capital necessary to raise the next marginal dollar of financing to fund the firm’s future investment opportunities. A firm’s future investment opportunities in expectation will be required to exceed the firm’s cost of capital.

LG 3 Determine the cost of long-term debt, and explain why the after-tax cost of debt is the relevant cost of debt. The before-tax cost of long-term debt can be found by using cost quotations, calculations (either by calculator or spreadsheet), or an approximation. The after-tax cost of debt is calculated by multiplying the before-tax cost of debt by 1 minus the tax rate. The after-tax cost of debt is the relevant cost of debt because it is the lowest possible cost of debt for the firm due to the deductibility of interest expenses.

LG 4 Determine the cost of preferred stock. The cost of preferred stck is the ratio of the preferred stock dividend to the firm’s net proceeds from the sale of preferred stock.

LG 5 Calculate the cost of common stock equity, and convert it into the cost of retained earnings and the cost of new issues of common stock. The cost of common stock equity can be calculated by using the constant-growth valuation (Gordon growth) model or the CAPM. The cost of retained earnings is equal to the cost of common stock equity. An adjustment in the cost of common stock equity to reflect underpricing and flotation costs is necessary to find the cost of new issues of common stock.

LG 6 Calculate the weighted average cost of capital (WACC), and discuss alternative weighting schemes. The firm’s WACC reflects the expected average future cost of funds over the long run. It combines the costs of specific types of capital after weighting each of them by its proportion. The theoretically preferred approach uses target weights based on market values.

In the chapter opener you learned that Alcoa’s weighted average cost of capital was around 12 percent, but its investments were earning returns closer to 5 percent. From 2010 to 2012, Alcoa invested roughly $1 billion in capital expenditures. Suppose Alcoa spends $1 billion expanding its manufacturing facilities today, and that investment produces a net cash flow of $50 million (5 percent of $1 billion) every year in perpetuity. Calculate the NPV of that investment using a 12 percent discount rate. How much value does the $1 billion investment create or destroy? Does it seem that Alcoa should be pursuing growth in this market?

(Solutions in Appendix)

LG 3

LG 4

LG 5

LG 6

Individual costs and WACC Humble Manufacturing is interested in measuring its overall cost of capital. The firm is in the 40% tax bracket. Current investigation has gathered the following data:

• Debt The firm can raise debt by selling $1,000-par-value, 10% coupon interest rate, 10-year bonds on which annual interest payments will be made. To sell the issue, an average discount of $30 per bond must be given. The firm must also pay flotation costs of $20 per bond.
• Preferred stock The firm can sell 11% (annual dividend) preferred stock at its $100-per-share par value. The cost of issuing and selling the preferred stock is expected to be $4 per share.
• Common stock The firm’s common stock is currently selling for $80 per share. The firm expects to pay cash dividends of $6 per share next year. The firm’s dividends have been growing at an annual rate of 6%, and this rate is expected to continue in the future. The stock will have to be underpriced by $4 per share, and flotation costs are expected to amount to $4 per share.
• Retained earnings The firm expects to have $225,000 of retained earnings available in the coming year. Once these retained earnings are exhausted, the firm will use new common stock as the form of common stock equity financing.

• a. Calculate the individual cost of each source of financing. (Round to the nearest 0.1%.)
• b. Calculate the firm’s weighted average cost of capital using the weights shown in the following table, which are based on the firm’s target capital structure proportions. (Round to the nearest 0.1%.)

  Source of capital

  Weight

  Long-term debt

   40%

  Preferred stock

   15 

  Common stock equity

   45 

     Total

  100%

• c. In which, if any, of the investments shown in the following table do you recommend that the firm invest? Explain your answer. How much new financing is required?

  Investment opportunity

  Expected rate of return

  Initial investment

  A

  11.2%

  $100,000

  B

   9.7 

   500,000

  C

  12.9 

   150,000

  D

  16.5 

   200,000

  E

  11.8 

   450,000

  F

  10.1 

   600,000

  G

  10.5 

   300,000

  Warm-Up Exercises

  All problems are available in MyFinanceLab.

  LG 3

  E9–1

  A firm raises capital by selling $20,000 worth of debt with flotation costs equal to 2% of its par value. If the debt matures in 10 years and has a coupon interest rate of 8%, what is the bond’s YTM?

  LG 4

  E9–2

  Your firm, People’s Consulting Group, has been asked to consult on a potential preferred stock offering by Brave New World. This 15% preferred stock issue would be sold at its par value of $35 per share. Flotation costs would total $3 per share. Calculate the cost of this preferred stock.

  LG 5

  E9–3

  Duke Energy has been paying dividends steadily for 20 years. During that time, dividends have grown at a compound annual rate of 7%. If Duke Energy’s current stock price is $78 and the firm plans to pay a dividend of $6.50 next year, what is Duke’s cost of common stock equity?

  LG 6

  E9–4

  Weekend Warriors, Inc., has 35% debt and 65% equity in its capital structure. The firm’s estimated after-tax cost of debt is 8% and its estimated cost of equity is 13%. Determine the firm’s weighted average cost of capital (WACC).

  LG 6

  E9–5

  Oxy Corporation uses debt, preferred stock, and common stock to raise capital. The firm’s capital structure targets the following proportions: debt, 55%; preferred stock, 10%; and common stock, 35%. If the cost of debt is 6.7%, preferred stock costs 9.2%, and common stock costs 10.6%, what is Oxy’s weighted average cost of capital (WACC)?

  Problems

  All problems are available in MyFinanceLab.

  LG 1

  P9–1

  Concept of cost of capital Mace Manufacturing is in the process of analyzing its investment decision-making procedures. Two projects evaluated by the firm recently involved building new facilities in different regions, North and South. The basic variables surrounding each project analysis and the resulting decision actions are summarized in the following table.

  Basic variables

  North

  South

  Cost

  $6 million

  $5 million

  Life

  15 years

  15 years

  Expected return

  8%

  15%

  Least-cost financing

     Source

  Debt

  Equity

     Cost (after-tax)

  7%

  16%

  Decision

     Action

  Invest

  Don’t invest

     Reason

  8% > 7% cost

  15% < 16% cost

  • a. An analyst evaluting the North facility expects that the project will be financed by debt that costs the firm 7%. What recommendation do you think this analyst will make regarding the investment opportunity?
  • b. Another analyst assigned to study the South facility believes that funding for that project will come from the firm’s retained earnings at a cost of 16%. What recommendation do you expect this analyst to make regarding the investment?
  • c. Explain why the decisions in parts a and b may not be in the best interests of the firm’s investors.
  • d. If the firm maintains a capital structure containing 40% debt and 60% equity, find its weighted average cost using the data in the table.
  • e. If both analysts had used the weighted average cost calculated in part d, what recommendations would they have made regarding the North and South facilities?
  • f. Compare and contrast the analyst’s initial recommendations with your findings in part e. Which decision method seems more appropriate? Explain why.

  LG 3

  P9–2

  Cost of debt using both methods Currently, Warren Industries can sell 15-year, $1,000-par-value bonds paying annual interest at a 12% coupon rate. As a result of current interest rates, the bonds can be sold for $1,010 each; flotation costs of $30 per bond will be incurred in this process. The firm is in the 40% tax bracket.

  • a. Find the net proceeds from sale of the bond, Nd.
  • b. Show the cash flows from the firm’s point of view over the maturity of the bond.
  • c. Calculate the before-tax and after-tax costs of debt.
  • d. Use the approximation formula to estimate the before-tax and after-tax costs of debt.
  • e. Compare and contrast the costs ofdebt calculated in parts c and d. Which approach do you prefer? Why?
  Personal Finance Problem