Home BUS 650 WEEK 4 Discussion 1 & 2

BUS 650 WEEK 4 Discussion 1 & 2

Graduate Writing level each discussion should be 250- 300 words each and need by tomorrow evening. NO PLAGIARISM I DO CHECK FOR MYSELF.

Required Resources

Text

Byrd, J., Hickman, K., & McPherson, M. (2013).

Managerial finance

[Electronic version]. Retrieved from https://content.ashford.edu/

· Chapter 7: Required Returns

· Chapter 8: Cost of Capital

Multimedia

BusinessQldGov. (2014, April 10).

Identifying business risk – Risk management series (Links to an external site.)

[Video file]. Retrieved from https://www.youtube.com/watch?v=cZwyIPGhF_U

Accessibility Statement (Links to an external site.)

Recommended Resources

Article

Fama & French (1992). The Cross Section of Expected Stock Returns. Journal of Finance (47), 427 – 46. Retrieved from ProQuest Database.

Website

Moneychimp (Links to an external site.)

. (http://www.moneychimp.com/articles/financials/fundamentals.htm)

DISCUSSION 1

Applying the Capital Asset Pricing Model (CAPM)

Analyze the Capital Asset Pricing Model (CAPM). Using the course text and an article from ProQuest as references, address the following:

· Explain how the CAPM assists in measuring both risk and return.

· Explain how the CAPM assists in calculating the weighted average costs of capital (WACC) and its components.

· Illustrate why some managers have difficulty applying the Capital Asset Pricing Model (CAPM) in financial decision making.

· Identify the benefits and drawbacks of using the CAPM.

Develop a 200 – 300 word answer supporting your position.

DISCUSSION 2

Risk Identification and Mitigation

Using the annual report from the company that you have selected for your Final Project, discuss the risks the company faces and the actions they take to mitigate those risks. Refer to the Management Discussion and Analysis section of the annual report for this information.

As part of your response consider whether you think the risk mitigation techniques are reasonable. Discuss what others concerns or advice you would offer if you had the opportunity.

Include in your post a calculation for the probability of one of the risks identified by your company. This information may not be available in the annual report, therefore you will likely need to conduct research and critical thinking to complete this calculation.

Tip: For help with reading an annual report access this handy guide from

Money Chimp (Links to an external site.)

(http://www.moneychimp.com/articles/financials/fundamentals.htm) .

Develop a 200 – 300 word explanation supporting your position.

Chapter 8

Cost of Capital

Associated Press

Learning Objectives

A�er studying this chapter, you should be able to:

Show how the discount rate is calculated and used.
Explain how the weighted average cost of capital is calculated, and outline the significance of its components.
Describe how to es�mate the discount rate for individual projects and how risk factors into the process.

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Ch. 8 Introduction

Chapter 6 described the various capital budge�ng techniques employed by corporate managers. Among the techniques, net present value (NPV) emerges as the best measure
of a project’s contribu�on to shareholder wealth. In NPV analysis, the present value of a project’s expected future cash flows is compared to the ini�al investment, and the
project is accepted if the present value exceeds the ini�al investment. Calcula�on of NPV requires the analyst to es�mate cash flows and an appropriate discount rate.
Techniques for es�ma�ng cash flows were covered in Chapter 6. In this chapter, you will learn how to es�mate the discount rate. The same es�mates of cash flows and
discount rate are also used in internal rate of return analysis. Used in IRR, the discount rate becomes a hurdle rate against which to compare the project’s IRR.

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Financing mix and cash flows for the Pogo harness project.

8.1 Estimating the Discount Rate

To illustrate the calcula�on and use of the discount rate, we elaborate on the Chapter 6 example of Pacific Offshore Ltd. (POL). Recall the NPV of POL’s Pogo harness project
is $9,110, which was found by discoun�ng the project’s net cash flows by 12.5% (the required rate of return). The project’s internal rate of return of 17.2% is greater than
the 12.5% required rate of return on the harness project; therefore, whether we use NPV or IRR, the harness project appears to be acceptable because it meets the
respec�ve decision criteria. Had the required return been 20%, for example, the project would have been rejected using either criterion. Table 8.1 reviews the details of
POL’s Pogo harness project from Chapter 6.

Table 8.1: Review of POL’s Pogo harness project details

Data Category Value

Project cost $64,384

Required rate of return 12.5%

Internal rate of return 17.2%

Net present value $9,110

We have referred to the 12.5% as the harness project’s required rate of return. To be more specific, 12.5% is the weighted average return demanded by the company’s
investors. The weigh�ngs reflect the propor�onal values of their investments. From Chapter 6, the cost of the harness project is $64,384, meaning that Paula Bauer must
raise that amount from her investors to fund tools, equipment, and working capital and to pay the cost of reconfiguring the plant. Paula has decided to fund future projects
using the firm’s current propor�onal mix of debt and preferred and common stock. POL’s current capital mix is 28% debt, 7.8% preferred stock, and 64.2% common stock.
POL, therefore, will raise about $18,000 in debt and about $5,000 in preferred stock. The balance of the funding will come from residual cash flows that belong to the firm’s
shareholders. Table 8.2 shows how POL’s capital mix will fund the Pogo harness project. Later, in Sec�on 8.2, we will show you how Paula came up with these numbers.

Table 8.2: POL’s capital mix

Capital component Propor�on Cash Value

Debt 28% $18,028

Preferred stock 7.8% $5,022

Common stock 64.2% $41,334

Cash from the harness project will flow to these investors in order of the priority of their claims: first to bondholders, then to preferred stockholders, and finally to common
stockholders. Figure 8.1 illustrates the flow of capital and cash flows, assuming that the harness project produces its expected cash flows.

Figure 8.1: Pogo harness project

POL raises capital by selling these securi�es to investors, who expect to receive a return on their investment. Any investor purchasing POL’s securi�es must expect that the
returns will be at least equal to, and preferably greater than, the required return on an investment having the same risk as the harness project. If expected returns were
lower than required, investors would look elsewhere, or they may be persuaded to buy POL’s securi�es at a discount, which would increase their expected returns. Thus,
Paula must be confident that the discount rate she uses to value the project will provide the required return to each class of POL’s investors. This discount rate is known as
the cost of capital for the project because the returns investors require are the cost, like rent, that is paid for the use of the capital.

Industrial Policy
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Dr. Bruce Sco� argues that the U.S. has a higher cost of capital than any
other country, which influences our economic system. Many companies are
harves�ng their businesses, allowing their market share to decline. Do you
agree with Dr. Sco�? If so, how would this impact your decision-making as a
financial manager?

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Cost of capital includes the rent a company pays in order to use its
capital. What other expenses could be included in cost of capital?

Associated Press

8.2 The Weighted Average Cost of Capital

The cost of capital is a weighted average of the required returns for each capital source. In this sec�on, we will
show you how to calculate the weighted average cost of capital and its components.

Calculating the Weighted Average Cost of Capital

For the Pogo harness project, the weighted average cost of capital (WACC) is the a�er-tax required returns
(interest on bonds or other types of debt is tax deduc�ble; thus, it lowers the effec�ve cost of debt to the
firm) on POL’s bonds, preferred stock, and common equity, weighted by their propor�onal contribu�on to the
project. As you can see in Table 8.3, of the $64,384 being raised, the bondholders contribute $18,028 (28%),
the preferred stockholders contribute $5,022 (7.8%), and the common stockholders contribute the remaining
$41,334 (64.2%) in residual cash flows.

Later we will explain how Paula es�mated the costs of debt, preferred stock, and common equity. First, though,
we present her worksheet for compu�ng POL’s cost of capital. Table 8.3 shows that she mul�plied the
propor�on of each capital source by its a�er-tax required return. She then summed these results to arrive at
the 12.5% cost of capital (or the project’s required rate of return).

Table 8.3: Worksheet for compu�ng POL’s cost of capital

Capital component A
Targeted propor�on
or weight

B
Project cost

A × B
Dollars raised

D
A�er-tax
required returns

A × D
Weighted Average

Debt (bonds) 28% $64,384 $18,028 6.93% 1.94%

Preferred stock 7.8% $64,384 $5,032 11.96% 0.93%

Common equity 64.2% $64,384 $41,334 15% 9.63%

Total 100% $64,384 12.5%

Paula’s worksheet may be summarized by a formula for the weighted average cost of capital.

(8.1) WACC = (Wd)(a�er-tax cost of debt) + (Wpfd)(cost of preferred stock) + (We)(cost of common equity)

where

Wd = the desired propor�on of financing provided by debt

Wpfd = the desired propor�on of financing provided by preferred stock

We = the desired propor�on of financing provided by common equity

This formula is adaptable to any combina�on of financing sources. For example, if preferred stock were not used, then Wpfd = 0, and preferred stock would drop out of the

formula. Some companies borrow from many sources, and they may have several bond issues and perhaps long-term loans from banks or insurance companies. The only
source of capital that is common to all companies is common equity. The WACC formula for a company with no preferred stock, but with two types of debt, might look like
this:

(8.2) WACC = (WB)(a�er-tax cost of bonds) + (WL)(a�er-tax cost of loan) + (We)(cost of
equity)

No ma�er how many sources of capital there are, the weights always sum to 1 (WB + WL + We = 1). This ensures that all capital sources have been included in the

calcula�on of WACC.

Discoun�ng expected cash flows by the weighted average cost of capital gives Paula the informa�on she needs to make her investment decision on the Pogo harness project.
If the NPV = 0, then the project should provide all investors with their required returns but with nothing more. This is the minimally acceptable outcome. The harness project
is expected to do be�er than that, meaning that it should add value because its NPV is $9,110.

To summarize, discoun�ng project cash flows at the WACC ensures that the minimal needs of each class of investor are met. The WACC is the appropriate discount rate f

the harness project if its risk is similar to that of the en�re company, and it is being financed with a mix of debt and equity similar to that of the company’s financing.

We may rewrite the NPV and IRR equa�ons from Chapter 6 to include WACC.

Recall Equa�on (6.1), the NPV equa�on, from Chapter 6:

where
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II = ini�al investment

OCFt = opera�ng cash flows in year t

TCF = terminal cash flows

t = year

n = life span of the project (in years)

r = required rate of return

Rewri�en to include WACC, the NPV equa�on becomes

where

CFt = total net cash flow for period t

The company should accept projects with NPV > 0.

Rewri�en to accommodate WACC, the IRR equa�on becomes

The company should accept projects with IRR > WACC because such projects have expected returns (IRRs) greater than the investor’s required return (WACC).

Next, we explain how Paula es�mated the cost of each capital component.

The Cost of Debt

The cost of debt, or Kd, is the current yield to maturity on the company’s bonds or other long-term debt securi�es.

Cost of debt = Yield to maturity

Kd = YTM

YTM reflects current credit market condi�ons and investors’ expecta�ons, and therefore it is the best indicator of returns investors require on the sale of new bonds. Recall
from Chapter 4 that YTM is the discount rate applied to the expected cash flows from a bond. This discount rate is the cost of debt for the project.

Let’s assume the current market price of POL’s bonds is $1,003. The bonds mature in 6 years, bear a 9.5% coupon rate, make coupon payments semiannually, and their par
value is $1,000. Given this informa�on, Kd is found by solving for YTM in the following equa�on, which sets the price of the bonds equal to the present value of future cash

flows. We may think of the YTM as the internal rate of return of a bond.

Note that each coupon payment, $47.50, equals one-half of the coupon rate (9.5%) �mes par value ($1,000) because the bond pays coupons semiannually [(0.095)($1,000)/2
= $47.50]. There are 12 payments because the bonds mature in 6 years and pay interest twice per year (semiannually). Similar to IRR, a financial calculator or computer will
be needed to solve for YTM, but we will save you the work on this equa�on: The YTM on these bonds equals 4.72% semiannually, or 9.44% on an annual basis.

Because interest on debt is tax deduc�ble, the YTM must be adjusted for the tax effect. The tax deduc�on lowers the effec�ve cost of debt to the company. We adjust YTM
for taxes by mul�plying YTM by (1 – t), where t is the firm’s marginal tax rate. Subs�tu�ng Kd for YTM gives us Equa�on (8.6):

The Cost of Preferred Stock

As you recall from Chapter 4, preferred stock combines features of debt and equity. Preferred dividends are fixed, like bond interest, but also have an infinite life, like
common stock dividends. We recognize this as a perpetuity (a perpetual annuity), which greatly simplifies the calcula�on. The cost of preferred stock, or Kpfd, equals its

required rate of return, which is its annual dividend divided by its current market price.

Cost of preferred stock = Required rate of return = Annual dividend /Current market price

Again, let’s assume the dividend on POL’s preferred stock is $2.50 and its current market price is $21.50 per share. As Equa�on (8.7) shows, the required return on the stock
is 11.63%.

No tax adjustment is necessary for preferred stock because dividends are paid with a�er-tax cash flows.

The Cost of Common Equity, Ke

The cost of common equity, or Ke, is the most difficult of the component costs to es�mate. Chapter 7 presented the capital asset pricing model (CAPM) as one means of

es�ma�ng investors’ required return for risky assets. Although this risk-return model is the most frequently used method for es�ma�ng returns to common stock, other
models may also be used, most notably the discounted cash flow model introduced in Chapter 4. As a general rule, the analyst should approach the problem of es�ma�ngProcessing math: 0%

Websites like Yahoo! are useful for obtaining beta informa�on.
What benefit is there to obtaining the informa�on this way versus
calcula�ng it yourself?

Associated Press

common stock returns from several direc�ons and hope to generate a consensus es�mate from these varying approaches. Here, we will cover three approaches: CAPM, the
discounted cash flow model, and the equity-debt risk premium.

The CAPM Approach to Ke

Chapter 7 built on por�olio theory to show the rela�onship between required returns on investments and their market risk. The CAPM states that the required return on a
risky investment equals the risk-free rate plus the product of the asset’s beta and the market risk premium.

Required return on risky investment = Risk-free rate + Asset’s beta
(Market risk premium)

Represented as an equa�on, the CAPM is

where

R(r)i = required return for asset i

Rf = risk-free rate of return

βi = beta of asset i

Now, let’s look at the individual components of the equa�on to find the informa�on needed to solve the
CAPM.

First, we examine the risk-free return. Although no asset is totally free of risk, U.S. government T-bonds are
considered nearly riskless. Thus, T-bonds are a widely used proxy for the true risk-free rate. T-bond returns are
widely available in print and on the Web.

Next, we need an es�mate of the equity beta. Brokerage and other investment service firms es�mate betas for
many publicly traded stocks. Betas may be obtained on the Web and in print from Value Line, Standard &
Poor’s, Yahoo!, and Bloomberg. As we saw in Chapter 7, we may also es�mate beta ourselves using data on
past returns.

In place of market risk premium, we use the historical market risk premium. This is found by calcula�ng the
average amount by which the market return has exceeded T-bond returns. For example, the difference between
the S&P 500 return and the T-bond return for years 1931 through 2011 could be averaged and used as the
historical market risk premium. In that 80-year period, the market risk premium has averaged about 7.6% per
year (Damodaran, 2011). There are many other es�mates of the markets risk premium (or equity risk
premium). For more informa�on, please see the Web Resources sec�on at the end of the chapter.

For POL, Paula gathered es�mates for the risk-free return, POL’s beta, and the market risk premium. These can be found in Table 8.4.

Table 8.4: POL’s cost of equity es�mates using the CAPM

CAPM component Value

Risk-free return (T-bonds) rf = 5%

BetaPOL (from POL’s investment banker) βPOL = 1.2

Market risk premium (historical equity market risk premium) 7.6%

If we plug these numbers into Equa�on (8.8), Paula’s CAPM es�mate is

R(r)POL = rf + βPOL[market risk premium]

= 5% + 1.2(7.6%)

= 14.12%

The CAPM approach is the most popular among companies for determining their cost of equity.

The Discounted Cash Flow Approach to Ke

In Chapter 4, the constant dividend growth model for valuing common stock was introduced. To find the cost of equity, we use a form of that constant growth formula.

where

P0 = today’s price of the stock

Ke = the required return on equity, also known as the cost of equityProcessing math: 0%

gn = the normal, constant growth rate of dividends

D1 = the next dividend that the firm is expected to pay

The current price equals next year’s dividend divided by the difference between equity’s required return and the long-run dividend growth rate.

This equa�on may also be adapted to allow us to solve for Ke:

The dividend growth model for es�ma�ng the required return on common stock reflects the discounted cash flow approach to valua�on, as do the YTM for debt and the
preferred stock perpetuity model.

This approach requires a current market price, an es�mate of next year’s dividend per share, and an es�mate of the long-run dividend growth rate. Prices for traded firms’
stock are easily obtained. Value Line and many brokerage firms forecast dividends and dividend growth rates for large and ac�vely traded companies. For smaller companies,
such as POL, published forecasts are generally not available, so we must rely on our own resources. Forecasts should begin by looking at a company’s dividend history. If we
have enough data, we can calculate historical growth rates. The historical growth rate is the compound rate that equates a dividend paid several years ago with a recent
dividend payment. This process is nothing more than an applica�on of the future value of a single cash flow formula, as given in Chapter 3.

FVn = PV0 (1 + r)
n

where

FVn = the future value at the end of n �me periods

PV0 = the present value of the cash flow

r = the periodic interest rate

The difference is that rather than looking forward, we are looking back. To use the model, we must change the defini�on of its components. FVn becomes the most recent

dividend, D0. PV0 becomes the beginning historical dividend, D–n (“–n” refers to n periods in the past). Finally, the rate of return, r, becomes the compound growth rate, gn.

Equa�on (8.11) shows us what the new formula looks like:

where

D0 = the most recent dividend

D–n = the beginning historical dividend

gn = the compound growth rate

Fortunately, POL has paid a dividend for five years, so we are able to calculate a growth rate. The dividend five years ago (D–5,) was $0.60 and the most recent dividend (D0)

was $0.84. Now, let’s solve for gn.

Now that we have solved for the compound growth rate, we can plug it into the constant growth formula. The current market price of POL’s common stock is $11.25. Next
year’s dividend, D1, should equal D0 (1 + gn). D1 = $0.84(1.07) = $0.90. Now, we may solve for Ke.

Having es�mated Ke using the constant growth formula, we must remember that this formula assumes a constant growth rate into perpetuity. Therefore, this method may

not be appropriate for firms whose growth is unstable or unsustainable. Cyclical firms, such as lumber companies, o�en have earnings that fluctuate drama�cally with the
business cycle. Excep�onally high ini�al growth rates of start-up companies will eventually fall to more sustainable levels as the industry matures. For these types of firms,
the constant growth assump�on is quite difficult to apply. In prac�ce, companies appear to favor the CAPM approach to the discounted cash flow approach for determining
their cost of equity.

The Equity-Debt Risk Premium Approach to Ke

The final method for es�ma�ng the cost of equity is to add a risk premium to the cost of debt. Because equity is a residual claim with a lower priority than debt, equity is
riskier than debt; therefore, investors require that Ke exceed Kd. The difference between Ke and Kd is the equity-debt risk premium.

The risk premium, RP, is generally in the range of 3% to 6%. The method is ad hoc but works fairly well as a benchmark because the necessary data are easily obtained.
Es�mates of Ke, using CAPM and discounted cash flow models, that fall outside the range [Kd + (3% to 6%)] should prompt the analyst to revisit her es�mates. For POL, the

equity-debt risk premium approach yields the following range for Ke.

(Kd + 3%) < Ke < (Kd + 6%)

(9.4% + 3%) < Ke < (9.4% + 6%)

12.4% < Ke < 15.4%Processing math: 0%

Facebook is one of many promising companies that venture capital
firms invested in. Do you think venture capital is a beneficial way
for small companies to obtain the capital they need?

Associated Press

Recall that Paula’s es�mates of Ke using the CAPM were 14.12%, and her discounted cash flow method produced a 15% cost of equity. Those es�mates are within the range

prescribed by the equity-debt risk premium, which more or less confirms Paula’s es�mates. Weighing the results of the three approaches to es�ma�ng Ke, Paula elected 15%

as POL’s cost of equity. As with preferred stock, no tax adjustment is necessary because dividends are not a tax-deductable expense.

The Cost of Selling Securities

The cost of capital reflects returns required by investors who are supplying capital to the firm. These returns reflect the amount the investors paid for their respec�ve
securi�es. However, when a company raises funds by selling securi�es, it usually employs a company to assist it in marke�ng its securi�es. Companies that specialize in
selling new securi�es issues, called investment banks, take a cut for marke�ng and underwri�ng the issue. A securi�es issue is underwri�en when the investment bank buys
securi�es from the company and resells them to investors for a higher price. The difference between the price paid to the company and the sale price is called the
underwri�ng spread. Of course, the sale price must approximate the security’s market value. For example, let’s assume that POL is selling bonds to pay for the harness
project. Investors will buy the bonds for their current market price, $1,003. However, the underwri�ng spread reduces POL’s proceeds from the bond sale and raises POL’s
effec�ve cost of debt above the 9.44% YTM.

Costs associated with selling securi�es are called flota�on costs. Aside from the underwri�ng spread, flota�on
costs include fees paid to the investment banker for consulta�on, document prepara�on, and so on. They also
include costs of filing with regulators such as the Securi�es and Exchange Commission, as well as legal and
accoun�ng fees. Here is a list of common features of flota�on costs:

They make up a greater percentage of the value of the securi�es issues for equity than those for debt,
reflec�ng the increased risk of underwri�ng stocks.
They are propor�onally greater for issues of small dollar value.
There are significant scale economies to securi�es issues.
Some fees and other costs are rela�vely fixed.

With the high cost of issuing securi�es for smaller companies, it would seem that small firms might have a
tough �me raising outside capital. Historically, this has been the case with small firms having to rely largely on
private sources of capital. However, the rapid development and dissemina�on of technology, and the
deregula�on of financial services, of transporta�on, and of telecommunica�ons have bolstered entrepreneurial
ac�vity in the United States, crea�ng new investment opportuni�es. As evidence, venture capital firms have
sprung up by the hundreds to supply early financing to promising companies. One such company was
Facebook, which went public in May of 2012. Unfortunately, the IPO was something of a flop for investors,
though the investment bankers reportedly made over $170 million of fees plus possibly another $100 million trading the shares the first weeks a�er the IPO
(venturebeat.com, 2012)!

Flota�on costs siphon money from the securi�es issue, raising the effec�ve cost of capital. Therefore, the cost to the company is greater than the return to the investor. This
means that the cost of each component must be adjusted to reflect flota�on costs. Net proceeds to the company equal the sale price to the investors minus flota�on costs.

Net proceeds to company = Sale price – Flota�on costs

Virtually all financing with bonds and preferred stock represents new issues and therefore includes flota�on costs. Common equity financing may be done through stock
sales, but more o�en it comes from retained earnings, which carry no flota�on costs. In the case of POL, the company is selling bonds and preferred stock to finance the
harness project. Common equity financing comes from retained earnings. POL’s investment banker es�mates that flota�on costs will be $20 for every bond sold and $0.60 for
each share of preferred stock. Paula adjusts the cost of debt and preferred stock to reflect these flota�on costs. Let’s look at each of these in turn.

Adjus�ng cost of POL’s debt (bonds) to reflect flota�on costs:

Based on the Pnet of $983, we recalculate YTM:

Now we have calculated four numbers masquerading as the cost of debt for POL. Table 8.5 shows costs before and a�er the tax adjustment, and with and without flota�on
costs.

Table 8.5: POL’s cost of debt es�mates before and a�er flota�on costs

Floata�on costs Before tax A�er tax

Excluded 9.44% 6.61%

Included 9.88% 6.93%

As Table 8.5 shows, the actual YTM of the bonds is 9.44%, but a�er adjus�ng for taxes and flota�on, the cost of debt to POL is 6.93%. The tax savings reduces the cost of
debt, but flota�on costs take back some of that savings. Now, let’s look at preferred stock.

Adjus�ng cost of POL’s preferred stock to reflect flota�on costs:

Because there are no flota�on costs associated with retained earnings, POL’s cost of common equity remains at 15%.
Processing math: 0%

Kre tearn = 15%

For the record, the following equa�on shows how flota�on costs would affect the cost of a new stock issue. The effect of flota�on cost is most easily illustrated with the
constant dividend growth model. As with the preferred stock adjustment, we reduce the stock price by the amount of the flota�on costs, which raises the cost of equity to
the company.

where

Pnet = P – (flota�on costs)

Note that POL’s a�er-tax cost of debt (6.93%), the cost of preferred (11.96%), and the cost of equity (15%) are the component costs that Paula used in her WACC worksheet,
Table 8.3. Using Equa�on (8.1), she mul�plied these component costs by their desired propor�ons to derive the WACC. Next, we describe how Paula selected the mix
outlined in Table 8.2 of common equity, preferred stock, and bonds to finance the harness project.

The Financing Mix and Weights in the WACC

The financing mix is called capital structure. Capital refers to long-term financing, such as that used to fund POL’s Pogo harness project. Determining the best capital
structure for a company raises some rather complicated issues, which we leave for Chapter 9.

The weights in the WACC formula could reflect any target or desired financing mix. Paula has chosen to finance the harness project using POL’s current mix of capital: 28%
debt, 7.8% preferred stock, and 64.2% common stock. Generally, firms that are sa�sfied with their current capital mix will a�empt to maintain those propor�ons.

The exis�ng mix of capital can be determined by examining the right-hand side of the financial balance sheet. Recall that the financial balance sheet reflects market values,
unlike the accoun�ng balance sheet’s book values. Current market values are certainly closer to actual values than are historical accoun�ng values. A company’s common
stock with a book value of $5 may have a current market value of $100. If it decides to sell stock to finance an investment, it will surely not sell new shares for $5.

Paula determined the current financing mix by es�ma�ng the market values for each of POL’s capital sources. First, she obtained the current prices for the company’s bonds,
preferred stock, and common stock. Next, she mul�plied these prices by the number of bonds or shares of stock outstanding to compute the market value of each
component. Summing these market values gave her the total market value of POL’s capital. These calcula�ons are shown in Table 8.6.

Table 8.6: Calcula�ng market weigh�ngs of each capital source

Capital component Price/unit Number outstanding Total market value of
component

Propor�on

Debt (bonds) $1,003.00 1,537 $1,541,611 28%

Preferred stock $21.50 20,068 $431,462 7.8%

Equity (retained cash) $11.25 313,867 $3,531,004 64.2%

Total $5,504,077 100%

Paula calculated the propor�on for each component by dividing its market value by the total market value of capital, $5,504,077.

Paula intends to finance the harness project using capital from these three sources in these propor�ons. As we saw in Table 8.3, the WACC for the harness project is 12.5%.
We may confirm this with the WACC formula:

Glancing at Equa�on (8.16), you may wonder why Paula doesn’t finance the en�re project with debt and discount it at the a�er tax cost of debt. The a�er-tax cost of debt is
only (9.9%) (1 – 0.30) = 6.93%. Discoun�ng at 6.93% rather than 12.5% would certainly raise the harness project’s NPV. The problem with this scheme is that POL must
maintain some balance between debt and equity. If debt were used this year, equity may have to be used next year to achieve the desired balance. If POL financed next
year’s project with equity, then to be consistent, it would discount that project at the 15% cost of equity. In this case, projects considered in years when debt financing is
used have a great advantage over those being evaluated in years when equity financing is used. More projects would be rejected, for example, in equity-financed years even
though they may actually be superior projects if all projects were consistently evaluated. This illustrates why it is important to discount all projects at the cost of capital and
not at the cost of debt one �me and the cost of equity the next �me, regardless of how a par�cular project is financed. We separate the investment decision from the
financing decision; that is, we evaluate investment decisions like the Pogo harness project using the long-term mix of debt and equity that we expect over the project’s life,
not the specific type of securi�es (debt, preferred stock, or common stock) that were most recently issued.

WACC reflects the firm’s long-term capital mix. A firm that finances a project with either debt or equity will temporarily unbalance its capital structure and, we can assume,
will a�empt to rebalance it the next �me around. Firms o�en unbalance their capital structure temporarily to take advantage of scale economies of large securi�es issues. In
reality, POL would never fund such a small project by selling both preferred stock and bonds because flota�on costs would be prohibi�ve. This project would probably be
funded en�rely from retained earnings, meaning that POL would temporarily unbalance its capital structure.

Field Trip: Cost of Capital Data

Ibbotson provides financial data for commercial and academic use.

Visit the Ibbotson Cost of Capital Resources Center:
h�p://corporate.morningstar.com/ib/asp/subject.aspx?xmlfile=5532.xml (h�p://corporate.morningstar.com/ib/asp/subject.aspx?xmlfile=5532.xml)Processing math: 0%

http://corporate.morningstar.com/ib/asp/subject.aspx?xmlfile=5532.xml

and the Ibbotson Cost of Capital Yearbook:
h�p://corporate.morningstar.com/ib/asp/subject.aspx?xmlfile=1420.xml (h�p://corporate.morningstar.com/ib/asp/subject.aspx?xmlfile=1420.xml)

Reflec�on Ques�ons

1. Why do you think clients would be willing to pay for this informa�on? What might they use it for?
2. Look at the module overviews on the Cost of Capital Resources Center. Is there more focus on cost of debt or cost of equity? Why do you think this is?

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http://corporate.morningstar.com/ib/asp/subject.aspx?xmlfile=1420.xml

Project and company risk can differ significantly. Do you think a
Campbell’s Soup cafe would be a successful venture for the
company?

Associated Press

8.3 Estimating the Discount Rate for Individual Projects

For many projects, the appropriate discount rate to use in the NPV calcula�on is the firm’s WACC, as outlined in the previous sec�on. However, there are circumstances in
which WACC is not the appropriate discount rate. Every company is risky, and this risk is reflected in its WACC. Investors in a par�cularly risky company demand higher
returns on their securi�es, which increases the company’s WACC. In project analysis, we are actually interested in the risk of the par�cular project rather than the company
as a whole, and we would like the discount rate to reflect the risk of the project. When we discount a project by the company’s WACC, we implicitly assume that project risk
and company risk are iden�cal. If they are not, then we should adjust the project discount rate up or down accordingly. For example, if a company increases its risk by
inves�ng in high-risk projects, investors expect a higher return; therefore, these risky projects should carry a higher discount rate.

In POL’s case, Paula believes that the Pogo harness project has the same risk as the company’s exis�ng business. Paula reasons that the harness is simply another product to
add to POL’s exis�ng line of hardware and sailing gear. Therefore, the business risk of the Pogo harness project is essen�ally iden�cal to that of the company’s exis�ng
products. Of course, she understands that there are uncertain�es in producing a new product, but no more than in the normal course of extending and upgrading an exis�ng
line of products. Paula also realizes that the relevant risk for es�ma�ng required returns is the market-wide or nondiversifiable risks of the business (as discussed in Chapter
7). The new harness is probably about as sensi�ve to market-wide forces as are POL’s current products. All are sensi�ve to economic recession (in which case sales of
discre�onary products will decline), changing tastes, changes in tax codes, and so on.

Why a Project’s Risk May Differ From the Company’s Overall Risk

While the harness fits neatly into POL’s exis�ng product line, there are many occasions when this is not the
case. In such instances, we must es�mate a discount rate that reflects the project’s risk. Here, we explain why
differences in risk might arise and how discount rates for individual projects might be es�mated. Consider
Campbell Soup. The company has a dominant posi�on in its industry and produces a product for which there is
fairly constant demand. Thus, we would expect that Campbell Soup has average or slightly below-average risk.
Now suppose that Campbell’s managers propose two hypothe�cal projects. The first is a tomato soup with a
spicy Mexican taste. The second proposal is to start a chain of small soup cafes—tenta�vely called “17 Flavors
Soup Cafes.” The cafes would feature 17 flavors (hence the name) of Campbell’s soups ready for immediate
serving.

Do these two proposals have the same risk? Let’s consider them both individually. The spicy Mexican soup is a
standard Campbell’s product. Campbell Soup has enormous experience evalua�ng, producing, marke�ng, and
distribu�ng such products. By contrast, a chain of fast-food restaurants differs markedly from any of Campbell’s
other businesses. The fast-food industry is very compe��ve, with several dominant chains vying for market
share. Campbell’s managers have li�le experience in this industry. Also, the two projects will probably respond
differently to economy-wide risk factors. For example, in a recession individuals tend to eat out less but may
consume more canned soup at home.

Campbell’s managers may reasonably conclude that the new soup flavor project should be discounted at the company’s WACC. The new soup is analogous to POL’s Pogo
harness project. On the other hand, Campbell’s managers would judge that the soup cafes add risk to company, and therefore should take a higher discount rate.

Estimating a Risk-Adjusted Discount Rate for NPV Analysis

Chapter 7 introduced the capital asset pricing model and the idea that the capital markets price only market risk. This follows from the no�on that unique risk is generally
absent from well-diversified por�olios. Projects also contain mostly market risk; therefore, we may use the CAPM to determine a project’s discount rate.

(8.17) Required return on a project = Risk-free rate + Project beta (Market risk premium)

The project beta, commonly called an asset beta, is not the same as the common stock beta. As introduced in Chapter 7, asset beta measures the project’s market risk. Next,
we discuss how to es�mate a beta that is appropriate for evalua�ng the Campbell Soup “17 Flavors Soup Cafes” ini�a�ve.

Estimating a Project’s Beta

Recall from Chapter 7 that beta is a measure of the extent to which the returns on a stock move with changes in the returns of a market por�olio, such as the S&P 500. One
widely used technique for es�ma�ng a project’s cost of capital is the pure-play method. A pure-play is a publicly traded firm that engages primarily in the same line of
business as the project being considered. If the pure-play firm has close to the same financing mix as the project, then the beta of this pure-play’s assets may then be found
and used as a proxy for the project’s beta. The pure-play’s beta can be used as the beta in the CAPM to es�mate the appropriate risk-adjusted discount rate (RADR) for the
project.

Iden�fying a publicly traded pure-play firm is seldom easy. For the soup cafes, Campbell’s managers may begin with small chains of specialized fast-food restaurants. Another
chain of soup cafes would be ideal, but what if none exist? We would then look to other small chain restaurants that fit the profile. Wendy’s would likely be a be�er proxy
than McDonald’s because of size. Perhaps Baskin-Robbins would be be�er yet: Baskin-Robbins is not too large, and has a specialized menu, and ice cream is somewhat
seasonal, as is soup. Ideally, several publicly traded pure-play firms would be iden�fied.

Aside from iden�fying appropriate business lines for the pure-play firms, Campbell’s managers must also consider their capital mix. We said that to use the pure-play
company’s beta directly, the pure-play’s risk and financing must be close to that of the project. Financing is an issue because the equity betas of companies with the same
business risk (same asset beta) will differ according to how much debt each company has. The more debt a company has, the higher the equity beta will be. The intui�on
behind this result (more debt, higher beta, all else being equal) is that the risk of the assets is fixed, so as low-risk debt replaces equity in a company’s financing mix that

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asset risk has to go somewhere. If the debt is safe because of priority payments and contractual obliga�ons, then the equity absorbs more and more of the risk producing a
higher beta.

To avoid the effect of leverage on beta, the best choice for a pure-play comparison firm is an all equity-financed firm. The beta of an all equity-financed firm is iden�cal to its
asset beta. If a pure-play can be found with no debt, the project’s required return may be es�mated directly using the CAPM. The project’s required return could then be
used as the discount rate for NPV or as the hurdle rate for IRR. Suppose, for example, there exists a chain of soup cafes that is all equity financed, and the beta for this
company is 1.3. This beta may then be transferred to Campbell’s cafe project, and a RADR could then be es�mated.

We will assume rf = 4% and the market risk premium is 9%

If the capital structure of the pure-play firm includes debt, we may es�mate the asset beta using the Hamada (1972) equa�on:

where

βequity = beta of the pure-play’s common stock

t = the pure-play’s tax rate

D/E = ra�o of the firm’s debt to equity, both at market value

If we find a pure-play with debt of $1 million and equity worth $2 million, a tax rate of 30%, and βequity equal to 1.5, we can es�mate its asset beta as follows:

This beta could then be plugged into Equa�on (8.18) and used to es�mate the project’s appropriate discount rate.

RADR = 4% + 1.11(9%) = 13.99% or 14%

Of course, for many projects a pure-play cannot be found. The methods for es�ma�ng the RADR under such circumstances range from ad hoc techniques (like adding or
subtrac�ng a few percentage points to the firm’s exis�ng WACC) to developing betas based on accoun�ng informa�on. Ad hoc es�mates require careful judgment on the part
of the analyst. Should Campbell Soup, for example, add 2% to its current WACC to reflect the added risk of the cafes, or should it add 5%? Other new projects may be
perceived as being less risky than exis�ng lines of business, so a few percentage points would be subtracted from the current WACC. The difficul�es encountered using this
method are obvious, but at �mes there is no choice. Accoun�ng betas are found by measuring the co-movement of an accoun�ng-based standard of performance for a pure-
play firm with a benchmark performance standard from a broad sample of other firms. This technique is beyond the scope of this text but is useful when a pure-play firm
does not have publicly traded stock.

Ideally, each project will have its own discount rate reflec�ng its risk. In prac�ce, large companies use divisional hurdle rates, so that, for example, projects in a home
appliances division carry a different RADR than do projects in broadcas�ng division.

Use and Misuse of Risk-Adjusted Discount Rates

The risk-adjusted discount rate calcula�on depends on iden�fying pure-play companies. Because such companies are illusory, the calcula�on is subject to second-guessing
and cri�cism, especially by those units in the company that are assigned a high RADR. Unit managers may cry foul and claim that the calcula�on is unreliable and
discriminatory. The only defense against such charges is to make explicit the assump�ons and calcula�ons used to generate the RADR. Although the process is inevitably
flawed, it must be shown to be as free of bias as possible. Top managers may also use arbitrary RADRs as a pretext for altering the alloca�on of resources within the
company. In this case, the distrust of the technique by unit managers is fully jus�fied.

Cri�cal Thinking Ques�ons

1. Why do you think managers con�nue to use RADR, despite its flaws?
2. What kind of informa�on would you include in your defense of a high RADR?

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Ch. 8 Conclusion

Choosing the correct rate at which to discount project cash flows is crucial to valuing a capital project. The discount rate is the weighted average of the required return for
each class of investor. The principal investor classes are the bondholders, preferred stockholders, and common stockholders. Each of these investor classes contributes capital
to the firm as a whole, rather than to individual projects, and each is compensated for the risk that it incurs by inves�ng in the firm. The discount rate that provides each
investor class with its required rate of return is the weighted average cost of capital (WACC).

The WACC is the appropriate discount rate for a project whose risk is equal to that of the firm as a whole. However, the cash flows of projects that increase firm risk—and,
therefore, the risk of its investors—should be discounted at a rate greater than the WACC. In the same way, cash flows of projects that reduce firm risk should be discounted
at a rate less than the WACC. The rate that reflects project-specific risk is the risk-adjusted discount rate (RADR).

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Ch. 8 Learning Resources

Key Ideas

The required return on an investment is the weighted average of the returns demanded by the company’s investors.
The basic discount rate for capital investments is the company’s cost of capital.
The weighted average cost of capital (WACC) is the weighted average of the required returns for each capital source. Weigh�ngs are the propor�onal contribu�ons from
each capital source.
Discoun�ng project cash flows by the WACC means that projects will be accepted only if they are expected to provide at least the required returns to all investors.
The cost of debt is the yield to maturity (YTM) on the company’s bonds or other long-term debt securi�es.
The cost of preferred stock is its annual dividend divided by its current market price.
The cost of common equity may be es�mated using the CAPM, a discounted cash flow (dividend growth) model, or an equity-debt risk premium.
The difference between returns to equity and returns to debt is the equity-debt risk premium.
Investment banks assist companies in marke�ng new securi�es offerings. When an investment bank buys securi�es from the issuing company and resells them to investors,
it is underwri�ng the securi�es offering. The difference between the price paid to the company and sale price to investors is the underwri�ng spread.
Venture capital firms supply high-risk capital to small firms prior to an ini�al public offering of stock.
Capital structure is the mix of debt, preferred equity, and common equity. Short-term financing is excluded. When possible, the propor�ons of each component in the
capital structure should be calculated using market rather than book weights.
A project should be discounted at the WACC, rather than at the costs of individual capital components, regardless of how the project is financed. WACC is the appropriate
discount rate for projects whose risk is about equal to the risk of the company as a whole.
A pure-play is a publicly traded firm that engages primarily in the same line of business as the project being considered. The Hamada equa�on may be used to convert the
equity beta of a pure-play firm into an asset beta.
The risk-adjusted discount rate (RADR) applies to projects whose risk is substan�ally different from company risk.

Key Equa�ons

Cri�cal Thinking Ques�ons

1. A fellow student comments that if a project has an NPV equal to zero, then the project will generate no cash flows for the common stockholders. You argue that it will
produce such cash flows. What is your argument? (By the way, you are correct. It will produce cash for the common stockholders.)

2. Accoun�ng balance sheets reflect the book values of claims, based on the historical contribu�ons of capital suppliers. Suppose a firm raised its ini�al capital 10 years ago, and
its accoun�ng statements currently reflect a capital mix of half debt and half equity. No more debt has been issued since the original bonds were sold. Interest rates have not
changed, but the firm has been excep�onally successful.

a. Do you think common stockholders would be willing to sell their stock today for its book value?
b. Interest rates have not changed, but the firm’s bonds are selling at a premium, above their book values. Why?
c. If the firm has been wildly successful, and given your answers to parts (a) and (b), what do you think has happened to the total market value of the firm? Is it above or

below its total book value?
d. How do you think the firm’s capital mix, based on market values, compares to the 50–50 mix reflected on the accoun�ng balance sheet?

3. Explain why (1 – t) does not appear in the cost of preferred and the cost of common equity formulas.
4. Suppose a firm uses all equity financing, but half that financing is internal equity and half is external equity.

a. Name the capital components for the firm.
b. What will be the weights for each component?
c. Write the firm’s WACC formula.

5. A project with an NPV = 0 provides all corporate investors with their required return; therefore all investors are sa�sfied. Do you agree or disagree with this statement?
Explain.

6. There are three methods of es�ma�ng the cost of corporate equity. Name or briefly describe these methods.

Key Terms

Click on each key term to see the defini�on.

SLIDE 1 OF 13

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asset beta
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

Refers to the systema�c or market risk of an investment asset.

capital structure
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The mix of debt and preferred equity in a company’s por�olio.

cost of capital
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The rate of return that must be earned in order to sa�sfy investors.

cost of common equity
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The investors’ required return on common equity.

cost of debt
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The required return of investors in the company’s bonds. Usually, the cost of debt is measured by finding the yield to maturity of outstanding bonds.

cost of preferred stock
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The investors’ required return on preferred stock.

equity-debt risk premium
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

A representa�on of the difference between returns to equity and returns to debt.

flota�on costs
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The transac�on costs incurred when raising capital externally, for example, when selling newly issued stock or bonds.

investment bank
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

A financial services company that specializes in selling new securi�es issues for client firms.

pure-play
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

An ac�vely traded firm whose sole product is similar to an investment project being analyzed. By finding the required return for the pure-play, the appropriate return
requirement for the investment project can be es�mated.

risk-adjusted discount rate (RADR)
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

A rate of return that has been adjusted to reflect the risk in a new investment project vis-à-vis the risk of the firm’s exis�ng projects.

underwri�ng
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

A method of selling securi�es in which the investment bank buys the securi�es from the client firm and resells them to investors.

underwri�ng spread
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The price at which the investment bank sells securi�es to the public minus the price paid to the client firm.

venture capital firms
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

Businesses and individuals that finance high-risk start-up ventures, usually before an ini�al public offering of stock.

weighted average cost of capital (WACC)
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The discount rate that may be found by incorpora�ng the required returns (costs) for each capital source used to finance the firm.

Web Resources
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https://content.ashford.edu/books/AUBUS650.13.1/sections/front_matter/books/AUBUS650.13.1/sections/front_matter/books/AUBUS650.13.1/sections/front_matter/books/AUBUS650.13.1/sections/front_matter/books/AUBUS650.13.1/sections/front_matter/books/AUBUS650.13.1/sections/front_matter/books/AUBUS650.13.1/sections/front_matter/books/AUBUS650.13.1/sections/front_matter/books/AUBUS650.13.1/sections/front_matter/books/AUBUS650.13.1/sections/front_matter/books/AUBUS650.13.1/sections/front_matter/books/AUBUS650.13.1/sections/front_matter/books/AUBUS650.13.1/sections/front_matter/books/AUBUS650.13.1/sections/front_matter/books/AUBUS650.13.1/sections/front_matter#

For more informa�on on other es�mates of the market’s risk premium (or equity risk premium), read Pablo Fernandez’s paper “Equity Premium: Historical, Expected,
Required and Implied.” Available at SSRN:
h�p://ssrn.com/abstract=933070 (h�p://ssrn.com/abstract=933070) .

A very simple cost-of-capital calculator is available at the following website. To test your skill, you could make up a simple set of assump�ons and see if you and the online
calculator get the same answer for the WACC.
h�p://www.wacccalculator.com/ (h�p://www.wacccalculator.com/)

Morningstar is a well-known financial informa�on provider that produces cost-of-capital es�mates that are published in an annual yearbook. These yearbooks are costly;
nevertheless, it is instruc�ve to peruse their website to see the scope of issues and informa�on that surrounds es�ma�ng the cost of capital.
h�p://corporate.morningstar.com/ib/asp/subject.aspx?xmlfile=5532.xml (h�p://corporate.morningstar.com/US/asp/home2.aspx?xmlfile=7083.xml)

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http://ssrn.com/abstract=933070

http://www.wacccalculator.com/

http://corporate.morningstar.com/US/asp/home2.aspx?xmlfile=7083.xml

Chapter 7

Finding the Required Rate of Return for an Investment

Associated Press

Learning Objectives

A�er studying this chapter, you should be able to:

Explain the significance of required return and its components.
Describe the rela�onship between risk and return and how to measure for both.
Iden�fy how to use required return to determine valua�on.

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Ch. 7 Introduction

Investors come in many forms. They may be individuals who invest in corporate stocks, re�rement accounts that invest in bonds, partnerships that invest in apartment
buildings, or corpora�ons that invest in produc�ve projects. One thing all these investors have in common is their desire to increase their wealth, which is done by iden�fying
projects whose value is expected to exceed their cost. If we invest $100 today in a project that produces cash flows worth $125 in today’s terms, then we increase our
wealth by $25. Equa�on (7.1) is the basic formula for es�ma�ng the value of an investment, which is found by discoun�ng the expected future cash flows back to today’s
equivalent value at a rate of return that is appropriate given the investment’s risk. This fundamental formula for assessing value was first introduced in Chapter 2 and further
developed in Chapters 4 and 5, while Chapter 3 explored cash flows in some detail.

One part of the formula that hasn’t been covered is how to es�mate the required return that is appropriate to use as the discount rate in the valua�on calcula�on. Finding
the required rate of return is the topic of this chapter (and is expanded upon in Chapter 8).

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Like children, who need to be bribed with the promise of a reward
for their good behavior, investors require a worthwhile incen�ve
before they will commit to an investment.

Beyond/SuperStock

7.1 The Building Blocks of the Required Return

In Chapter 2, we introduced the idea that investors are assumed to be ra�onal and risk averse. Because they
are (mostly!) ra�onal, investors will give up control of their money for a period of �me by inves�ng only if they
expect to increase their wealth. Therefore, investors have an almost ins�nctual return requirement as they
invest. For example, a ra�onal investor would always want to earn at least the risk-free rate of return when
inves�ng in some security or project. Otherwise, they would be se�ling for a return lower than what they
could be assured of by simply deposi�ng the funds in a savings account that is guaranteed by both the bank
and the government through the Federal Deposit Insurance Corpora�on (FDIC). The FDIC guarantees the first
$250,000 of funds deposited to an individual’s bank account. So we establish that the first building block for
assessing a required return is the risk-free interest rate.

For most investments, however, the risk-free rate is only the first component of the required return. Virtually
all investments have some risk associated with them, so investors also require what is known as a risk
premium to compensate them for this risk exposure. Recall that we assume that investors are risk averse,
which implies that to bear risk they require compensa�on in order to subject themselves to distasteful
uncertainty. This is a li�le like one of the authors of this text who used to pay his children five cents if they
would eat all of their broccoli because his kids were “broccoli averse.”

Now we have the two fundamental building blocks of the required return for an investment: the risk-free return and a risk premium.

R(r) = Risk-free rate of return + Risk premium

Given these intui�ve building blocks, we will now take a closer look at returns, risk, and their rela�onship to one another in order to fully develop the methods for more
precisely es�ma�ng the required rate of return for an investment.

Different Types of Returns

It’s useful to do some thinking about different kinds of returns that investors might discuss when they are considering investment performance. One type of return is the
historical return, also known as an actual or realized return. If you buy a share of stock for $20 and a year later you sell it for $22, you have earned a historical or
realized return equal to 10% per year ($2 gain on a $20 investment). The actual return you earned is 10%. This may be the same or it may be quite different than the
expected return that you were hoping for when you bought the stock. Perhaps your friend who is a stock broker told you that she had calculated a target selling price of
$30 for the stock. If you believed her forecast, then you were expec�ng a 50% return when you decided to buy the stock. Clearly, if you were expec�ng a 50% return but
the actual return was only 10%, then it’s likely that you were disappointed in result. But were you sa�sfied with the 10% that you earned? To answer that, we need to
know your required return for the stock. The es�ma�on of the required return for an investment is the subject of this chapter, but it is generally acknowledged that risk
contributes to one’s required return. So if this was a super risky stock, you may have had a required return equal to 25%. In this case, you would have been pre�y
unhappy with the result. On the other hand, if the stock was considered a low risk investment, then you might have had a return requirement of only 8%, and you were
probably very sa�sfied with the 10% actual return, given the stock’s low risk.

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Changes in interest rates and other factors can affect rates of return.
Investors must be aware of the risks they are taking and understand
probabili�es and expected rate of return in their business. At what point
would you consider a poten�al investment to be too risky? Why must
financial managers consider the risk-return tradeoff when making financial
decisions?

7.2 Risk and Return

The trade-off between risk and return is second nature to us: We understand that if we are going to invest in a bond issued by United Airlines, we would do so only if we
expected to receive a rate of return greater than we would receive if we invested in a bond issued by the U.S. Treasury. Why? United Airlines is generally considered riskier
than the US government. One of the great intellectual challenges of finance over the past fi�y years was to find a method for measuring risk, and then find a formula that
quan�fies the rela�onship between risk and return. Using our example, we need to find a method for quan�fying how much risk United Airlines has and then discover a
method for es�ma�ng the return that investors should require given that level of risk.

Risk-Return Tradeoff

Measuring Return

But before delving into how to measure risk, let’s look at how to measure returns. For simplicity’s sake, we will use stocks to illustrate returns and risk. A single period’s
historical return is given by the formula

(7.2) Return over a period = Rt = (Pricet – Pricet – 1 + Dividendt)/Pricet – 1

Example: If you buy a share of stock for $40, hold it for one year during which you collect a dividend of $2 a share, and then sell the stock for $40.50, what was your return?

The answer is ($40.50 – $40 + $2)/$40 = 2.50/40 = 0.0625 = 6.25%.

This stock formula can be generalized for any investment’s return:

(7.3) Return over a period = Rt = (Valuet – Valuet – 1 + Cash flowt)/Valuet – 1

In words, the return for the period is equal to the change in value of the asset during the period, plus any cash flows paid by the asset during the period, divided by the
value of the asset at the beginning of the period.

It would be really useful to predict returns (for one thing, you would get rich if you could consistently forecast returns!). Unfortunately, in order to predict returns, you would
like to know what price changes will be in the future so these future prices can be plugged into the return formula. But, as you learned in Chapter 2, market efficiency
implies that compe��ve market prices reflect all available informa�on. Therefore, we cannot say what future price changes will be and therefore what returns will be. This is
because price changes will only reflect new informa�on, and it’s anybody’s guess whether that informa�on will be good news or bad news for the company or for the
economy. Because it is nearly impossible to predict returns, we o�en use the historical average return as our best es�mate of the expected future return. Take cau�on with
this approach. When using an average to predict the future, one should use a rela�vely long run average since almost anything can happen in the short term. For example,
between 1950 and 2010, the average annual return for the stock market (as proxied by the S&P 500 index) has been about 11% per year. This is considered a be�er es�mate
than, say, the five-year average stock market return between 2007 and 2012, which averaged about zero!

Measuring Risk

We begin our discussion of risk by considering uncertainty. We are not certain what return we will receive in the future when we invest. With some investments, we feel a
greater level of uncertainty than we do with others. For example, if an investor chooses to buy a five-year cer�ficate of deposit at an FDIC-insured bank, most investorsProcessing math: 0%

Returns are based on returns from 3/2010 to 3/2012.

would feel there is very li�le uncertainty about how much their deposit will be worth a�er the five-year period. However, if the funds were invested in Facebook common
stock, there is a wide range of poten�al values that the stock could have five years a�er the investment is made. One might wonder, “How much riskier is Facebook stock
than a cer�ficate of deposit? Is it twice as risky? Ten �mes as risky? Twenty �mes as risky?”

In order to answer that ques�on, we need a metric for measuring risk. We begin by introducing the concept of an investment’s total risk. We will define total risk as the
variability of returns, measured by their standard devia�on. For simplicity’s sake we will be using historical returns to measure risk because, as previously discussed, future
returns are difficult to predict. Note that we are assuming in this case that past risk is a good predictor of future risk, which may be OK, but as you become a more
sophis�cated analyst, this es�mate may be adjusted up or down depending on what you know about the prospects of the firm or the investment that you’re analyzing.

(7.4) Total risk = Standard devia�on =

Standard devia�on measures the typical distance (or devia�on) of a return from the average (or expected) return. So a stock that has a standard devia�on of 15% has more
uncertainty regarding its returns than a stock with a standard devia�on of only 10%. To see this, look at Figure 7.1, which illustrates the distribu�on of returns for two stocks,
Peabody Coal and Pacific Gas and Electric (PG&E). These histograms show the frequency of weekly returns from March 2010 un�l March 2012. No�ce that PG&E’s returns
are much more �ghtly clustered, whereas Peabody’s have long tails, par�cularly a long tail to the le� of its center. Both of these distribu�ons have about the same average
return (0.00), but there is much more uncertainty about the return of Peabody because the standard devia�on of its returns is 0.068 per week while Pacific Gas and Electric’s
standard devia�on is only 0.023. Therefore, judging by this historical data, risk-averse investors would be much more concerned about owning Peabody because of the
uncertainty surrounding its returns.

Figure 7.1: Historical distribu�on of returns for Peabody Coal
and PG&E

It is important to keep in mind where the uncertainty illustrated in Figure 7.1 actually comes from: Risk is measured by the variability of returns, and returns are generated
by price changes as we saw in Equa�on (7.4). Recall that price changes are caused by the arrival to the marketplace of new informa�on, which investors and analysts
anxiously await in order to adjust their view of the company’s or investment’s worth. Risk, therefore, has at its founda�on informa�on and the investment’s sensi�vity to that
informa�on. As an example, consider what might happen to a company’s stock value, and therefore its returns, if the United States announced that it will impose a
significant tax on carbon emissions. The prices of oil companies would likely fall drama�cally as one would imagine gasoline costs increasing and demand decreasing, lowering
oil company profits. However, a hydroelectric-based u�lity company might see li�le change in its value since it does not produce carbon so its cost and pricing structure
would remain unchanged—its value might actually increase as demand for clean energy would likely rise.

The risk of adverse price movements can be decreased by diversifica�on. For example, in the previous example, consider what would happen to an investor’s por�olio
(collec�on of investment assets) if the investor held both oil company stocks and hydroelectric u�lity stocks. The oil stock values would fall because of the carbon tax, but
this risk would be mi�gated by the posi�ve response to the tax by hydroelectric firms. In this case, the fall in gas stock prices is offset by the posi�ve response of the u�lity
stocks. Risk is decreased in this case because of the different reac�ons by the two industries to the same informa�on. When one has investments in a variety of companies,
there is a good chance that what affects one company nega�vely may actually have li�le impact, or perhaps a posi�ve impact, on the value of another stock in the por�olio.

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Por�olio diversifica�on refers to the reduced risk to individuals who invest
in various assets with different characteris�cs. How has financial
globaliza�on led to more opportuni�es for por�olio diversifica�on?

The Benefits of Financial Globaliza�on: Risk
Diversifica�on

Total risk can, therefore, be broken down into risk that may be diversified away (called diversifiable risk) and risk that cannot be avoided or mi�gated (called systema�c or
nondiversifiable risk). Diversifiable risk is o�en characterized as “firm-specific” risk and “industry-specific” risk. Nondiversifiable risk is o�en referred to as market risk. Just so
you know all the terms you might run into, diversifiable risk is also referred to as unsystema�c risk, whereas market risk is also called systema�c risk. Investors are primarily
concerned with nondiversifiable risk because they can eliminate a great deal of the diversifiable risk by simply holding a large number of different stocks. Table 7.1 breaks
down diversifiable and nondiversifiable risk.

(7.5) Total risk = Diversifiable risk + Nondiversifiable risk

(7.6) Diversifiable risk = Firm- and industry-specific risk = Unsystema�c risk

(7.7) Nondiversifiable risk = Market risk = Systema�c risk

Table 7.1: Classifying risk

Names for risk that can be diversified away Names for risk that cannot be diversified away

Industry- and firm-specific risk Market risk

Diversifiable risk Nondiversifiable risk

Idiosyncra�c risk Systema�c risk

Unsystema�c risk Economy-wide risk

Example: CEO quits Example: Recession

Firm-specific risk is associated with events such as a company making a poor product decision, being sued, having a CEO get indicted or die, having a big fire at a factory, or
having a compe�tor develop a new product. All of these would adversely affect the value of the company, but if an investor is well-diversified, the impact will be minimal to
the overall por�olio because such an event impacts only a single firm. Also, with enough firms in a por�olio, there is a good chance that when a firm-specific bad event
happens to company A, you may have another company that experiences firm-specific good news. For example, suppose that on the same day that Firm A losses a lawsuit,
Firm B discovers oil, so these events would tend to offset one another in your por�olio. Some�mes, a news event for one company ripples through the industry. If Apple
announces a new, more powerful but less expensive iPad, that will almost certainly affect the prospects of other companies making tablet computers. If one airline company
has several planes grounded for safety inspec�ons, other airlines might benefit as passengers switch their flight plans.

Industry-specific risks are also largely avoidable via diversifica�on because events that harm a par�cular type of industry will not necessarily have a nega�ve effect on other
stocks in a por�olio that represent firms in other industries. For example, low interest rates may hurt the profits in the banking industry, yet they actually help the housing-
building industry. Therefore, holding a por�olio of stocks (in other words, being diversified) enables the nega�ve impact of low interest rates on one industry to be offset by
the posi�ve effect these rates have on other industries within the investor’s por�olio.

Nondiversifiable risks are difficult to avoid regardless of how many stocks you own, or how diversified your investment por�olio becomes. Some events have nega�ve effects
that pervade the en�re economy. For example, unemployment hurts almost all companies as consumer demand falls lowering sales and profits, and savings fall making
capital scarce. These kinds of far-reaching events are referred to as nondiversifiable or market risks. High infla�on, war, economic recessions, and oil embargos all have a
nega�ve impact on almost all of the firms in one’s por�olio, regardless of how many stocks you own!

Because much of the risk of inves�ng may be avoided simply by diversifying one’s por�olio, it is argued that we need not concern ourselves with these diversifiable risks. It
is, for example, just as easy to buy a mutual fund that holds shares of 500 different companies as it is to load up on a single firm’s stock. Clearly, the mutual fund strategy
avoids much of the risk that the investor in a single security faces. In fact, the standard devia�on (the variability) of a diversified por�olio’s returns can easily be reduced by

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The por�olio standard devia�on of returns decreases as the number of randomly selected stocks in the
por�olio increases.

Luxury markets like Porsche dealerships are highly suscep�ble to
the rise and fall of the economy. Do you tend to feel more or less
inclined to invest in these companies?

Associated Press

about half compared to the average standard devia�on of the individual stocks in the por�olio. The diversifica�on effect of lowering risk is shown in Figure 7.2 where we can
see that increasing the number of even randomly selected stocks in a por�olio can drama�cally reduce the por�olio’s standard devia�on of returns.

Figure 7.2: The diversifica�on effect

Since investors can easily and inexpensively eliminate most diversifiable risk from their por�olios, we assume that everyone does so. Thus, the risk that is relevant to the
investor is the nondiversifiable risk of an investment. The ques�on becomes, how can we measure this risk? To measure market risk, we u�lize a metric called beta. Beta
measures a firm’s typical responsiveness to informa�on that impacts the en�re market—like informa�on about economic growth, poli�cal news, infla�onary expecta�ons, the
balance of trade, natural disasters, and so on. By defini�on, the average sensi�vity to this kind of informa�on would be measured by the responsiveness of the market
por�olio. The market por�olio theore�cally would be totally diversified and would include virtually all investment instruments including all of the stocks and bonds that are
traded. In prac�ce, there is no such thing as a true market por�olio so a proxy is used as an approxima�on. Typically, the S&P 500 Index is used as that proxy. The beta of
the market por�olio is defined as being equal to posi�ve one.

A firm may be more sensi�ve than the average to economic informa�on, in which case the firm’s beta would
be greater than one. A company that is twice as sensi�ve as the average firm to economic events will have a
beta of 2.00, whereas a firm that is less sensi�ve than average will have a beta below one. Here is an example.
Take a firm that sells luxury goods, like a Porsche automobile dealership. We might assume that when the
economy is booming, this business does really well, but when the economy is doing poorly, luxury sports car
sales suffer dras�cally. Let’s suppose that Porsche dealership’s beta is 1.70, meaning that it is 1.7 �mes as
sensi�ve as the overall market to “macroeconomic” type events. So, if the government announces that
economic growth is very strong, we might hear that the S&P 500 por�olio had a return of 5% that day in
response to this good economic news. But because a Porsche dealership is more sensi�ve than average to such
informa�on, its stock would likely return around 8.5% on the same day (found by taking the product of 1.7 ×
5% = 8.5%). If, on the other hand, the market por�olio declines by 10% one month because of bad economic
news, then the dealership’s stock would be expected to fall by around 17%.

Of course, these are the expected returns for the Porsche dealership and may not be equal to the firm’s actual
returns on those days because there are always firm-specific factors that may affect a single stock’s return. For
example, on the day that the government announces strong economic growth (good news and we expect the

8.5% return), it may be the dealership also learns that the company is being sued, so the firm’s stock could actually fall in value on the date because of this nega�ve firm-
specific announcement.

Some businesses are less sensi�ve to market-level informa�on than the average firm is. An example might be an electric u�lity company, say Pacific Gas and Electric (PG&E).
When the economy is doing well, Pacific Gas and Electric does well because there is more demand for electricity. When �mes are bad, demand for power falls, but it doesn’t
fall too far because, unlike Porsche sports cars, electricity is close to being a necessity. So with this rela�vely low sensi�vity, Pacific Gas and Electric has lower than average
market risk, and its beta is less than one. In June 2012, Yahoo! Finance reported PG&E’s beta as 0.29. If the country goes into a recession and the market as proxied by the
S&P 500 declines by 10%, PG&E, with its beta of 0.29, would see its stock price drop by only about 3% on average.

Betas are typically es�mated using historical returns and linear regression es�ma�on. Linear regression is a sta�s�cal technique for es�ma�ng a best-fit line through points
plo�ed in an x-y coordinate system like the graphs typically used in algebra. The idea is that the slope of this line will capture the average rela�onship between the x- and
the y-variables. So if the slope is 1.5 for a regression line, then for each unit increase in the x-value, the y-value will (on average) increase by one and a half units. Regression
is used to es�mate a variety of rela�onships, like the effect that the �me spent studying has on the grade point average of students. For our purposes, we use returns for the
S&P 500 as our x-values, and corresponding returns for the stock that we are interested in as our y-values. The regression’s slope, therefore, is an es�mate of the stock’s
average responsiveness to market-wide returns, or its beta.Processing math: 0%

A stock’s beta is the slope of the line-of-best fit through the sca�erplot of market returns (S&P500) and the
company’s returns.

Since betas are sta�s�cal es�mates, they can vary depending on the sample of data being used for the es�mate. Figure 7.3 es�mates the beta for PG&E by plo�ng the
corpora�on’s returns against those of the S&P 500. As you can see, the beta we es�mate (0.43) differs from the beta reported by Yahoo! in June 2012 (0.29). The difference
can be a�ributed to different data sets; Yahoo! based their report on 36 monthly returns, whereas we have based our es�mate on 24 weekly returns.

Figure 7.3: Es�ma�ng beta for PG&E

The Capital Asset Pricing Model

Now we know how to measure returns and how to measure nondiversifiable risk (by using beta). Next we need to learn how to u�lize these metrics to es�mate the required
rate of return for an investment. Recall from the beginning of the chapter that the “building blocks” of a required return include the risk-free rate and a risk premium. These
two elements are present in an equa�on called the capital asset pricing model (CAPM). We need this model to quan�fy the rela�onship between investor’s required rate of
return and the risk of an investment. Here is the CAPM as it was originally developed:

(7.8) Required return for an investment = Rf + Beta[E(Rmkt) – Rf]

where

Rf = the risk-free rate of return

E(Rmkt) = the expected return on the market por�olio

Beta = the stock’s beta

This theore�cal rela�onship between risk and return was one of the path breaking achievements in economics in the 1960s, for which several academics were awarded the
Nobel Prize. Like many theories, however, there are challenges when using the CAPM in prac�ce. For example, no one knows what the expected return on the market,
E(Rmkt), is equal to. The model also assumes there is a single, observable risk-free rate, when in reality there is no investment free of risk and there is more than one

possible rate that can be used as a close proxy for risk-free. Because of these problems, most prac��oners use a different form of the model which is given here:

(7.9) Required return for an investment = Rf + Beta(Market risk premium)

Rf can be thought of as the rate that links the CAPM to current market condi�ons. This is important because interest rates are constantly changing due to changes in
infla�on, economic ac�vity, or government policies. We use yields on outstanding debt issued by the U.S. government as a proxy for the risk-free rate, choosing the Treasury
bill or bond that best matches the life of the asset we are evalua�ng. So, for stocks that have an almost perpetual life, long-term U.S. Treasury bond yields are o�en used for
the risk-free rate. The market risk premium (MRP) is the amount of return yielded by the market por�olio over and above the treasury yield. It can be thought of as the
return required for each addi�onal unit of risk as measured by beta. O�en, the MRP is assumed to equal its historical average, which is about 5% to 7%, depending on
whose data you use.

Here is an example of using the CAPM. Let’s es�mate the required return for Nordstrom’s (Ticker: JWN) stock given that Nordstrom’s beta is 1.58, as reported on Yahoo!
Finance in June 2012 (h�p://finance.yahoo.com/q/ks?s=JWN+Key+Sta�s�cs (h�p://finance.yahoo.com/q/ks?s=JWN+Key+Sta�s�cs) ). Nordstrom’s has a fairly high beta because it is
considered a high-end or almost luxury retailer, not dealing in necessity goods. Consequently, when �mes are tough, some people may discon�nue shopping at Nordstrom’s
and may buy their shoes and clothing at a more moderately priced retailer. Let’s also assume that T-bonds are yielding 4.5% per year, and that the historical average market
risk premium (the average return of the market por�olio over and above the risk-free return) is about 6%. Using this informa�on, we may es�mate the required return for
Nordstrom’s stock using the CAPM.

RNordstroms = Rf + BNordstroms(Market risk premium) = 0.045 + 1.58(0.06) = 0.1398 = 13.98%
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http://finance.yahoo.com/q/ks?s=JWN+Key+Statistics

A second example would be required rate of return for PG&E’s stock. Using the published beta of 0.29 and the risk-free rate and market risk premium above we would
compute PG&E’s required rate of return as:

RPG&E = Rf + BPG&E(Market risk premium) = 0.045 + 0.29(0.06) = 0.0624 = 6.24%

No�ce that the much lower beta of PG&E results in a much lower required rate of return compared to Nordstrom.

Applying Finance: Finding Beta Using Excel

Finding an asset’s beta using Excel is a two-step process: first, compute returns from prices; second, use the LINEST func�on to compute the beta (slope of a regression
line).

We downloaded stock prices for Dow Chemical (Ticker: DOW) from Yahoo! Finance using its historical price feature. We then downloaded the index data for the S&P 500
(Yahoo! Ticker: ^GSPC). We use the adjusted close price to make sure dividends are included in the price. Our data are weekly and run from Friday, February 3, 2012,
through Friday, June 22, 2012. We compute returns using the formula from the text:

(Change in price)/Beginning price

Since we are using adjusted prices we don’t need to explicitly include dividends in the returns equa�on. Figure 7.4 shows the spreadsheet of prices showing the price
series, the returns formulas and the LINEST formula.

Figure 7.4: DOW Chemical spreadsheet, LINEST

Figure 7.5 shows the same spreadsheet with the numerical results shown. Using this small sample of data, Dow’s beta es�mate is 1.63.

Figure 7.5: DOW Chemical spreadsheet, numerical

Determining an Asset’s Beta
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During the discussions of the Porsche dealership, Nordstrom’s, and PG&E, we said that it is the nature of the products and services that are sold by a company that
determine the company’s risk. Luxury goods, like sports cars, tend to have more market risk than do necessi�es like electricity. Demand for durable goods, items that are
long-lived and can be repaired like cars and appliances, will fluctuate more as the economy rises and falls than demand for food or medicine. If a company has invested in
produc�ve assets to make luxury or durable goods, then it is likely to have a high beta (higher than 1 or the market average beta). Similarly, if the factories and equipment
make food or electricity or things that are necessary (or that have steady demand), the company will have a lower beta (less than one). Thus, it is the assets of a company
and the products those assets make that determine the company’s beta. Companies that produce similar goods that are sold in similar markets will have similar betas
because those companies will be impacted similarly by the kind of macroeconomic news that creates market risk. Assess your expecta�ons of beta by comple�ng the exercise
in the Field Trip: Expecta�ons of Beta feature.

Field Trip: Expecta�ons of Beta

Pick three firms that you think may have low betas and three that you think may have high betas. Visit Yahoo! Finance or Google Finance to look up their betas.

Visit Yahoo finance: h�p://finance.yahoo.com/ (h�p://finance.yahoo.com/)

Google finance: h�p://www.google.com/finance (h�p://www.google.com/finance)

Reflec�on Ques�on

Are there any surprises? Can you think of some reasons that these betas are different from what you expected?

In theory, the asset beta of a Porsche dealership should be very nearly the same as the asset beta of, say, a BMW dealership. This is because they are similar businesses
offering similar products. If both the Porsche and the BMW dealerships had no debt financing, then both of their asset betas would be iden�cal to the betas of their stock.
This is because the stock would represent the only claim against the assets, so the risk of the assets would translate directly to the risk of the stock. In this case, both
dealerships’ stock, being in the same business, would probably have almost iden�cal betas and both would also have almost iden�cal required rates of return.

However, most companies use debt financing in addi�on to equity financing. This use of debt is also known as leverage. The use of leverage increases the risk of equity
because debt, with its priority claim, forces equity holders to bear the risk that there will be lower cash flows available for them a�er debt payments are made. For this
reason, the betas of stock differ even among firms in the same industry because of the varying amount of debt that the companies borrow. Asset betas, therefore, depend
primarily on the nature of a company’s business, whereas equity betas—the betas of inves�ng in just a company’s stock—depend on both a firm’s asset beta and on its use
of leverage. A specific technique used for es�ma�ng an asset beta, called the pure-play approach, is covered in the next chapter.

Portfolio Betas

There are �mes when investors may want to es�mate the required return for a por�olio or stocks or other investment assets. For example, we may want to compare the
actual, realized return on a por�olio to the required return on that por�olio in order to assess the performance of the manager who is in charge of the por�olio’s
investments. If the realized return exceeds the required return given the por�olio’s risk, then the manager is performing at or above expecta�ons. If, on the other hand, the
realized return is below the required return for the por�olio, then the manager is performing below expecta�ons, and may find his or her posi�on in jeopardy.

Por�olio betas are found by taking the weighted average of the betas of the assets held in the por�olio, where the weights are determined by the amount invested in each
asset. For example, consider the por�olio in Table 7.2.

Table 7.2: Sample por�olio

Stock Stock’s beta Amount invested Weight

Acme, Inc. 1.20 $100,000 .10

XYZ Corp. 1.50 $150,000 .15

ABC Corp. 0.70 $500,000 .50

Delphi, Inc. 1.00 $250,000 .25

The weights represent the propor�on of total investment that is invested in each asset. For example, the total investment in this por�olio is $1,000,000, so the investment of
$150,000 in XYZ’s stock represents 15% of the total, making the weight for XYZ .15. In this case, the por�olio’s beta is the sum:

Beta por�olio = (1.20)(.10) + (1.50)(.15) + (.70)(.50) + (1.00)(.25) = .945

To illustrate the usefulness of this number, it could be used to es�mate the risk of this por�olio versus another por�olio or a mutual fund. It could also be plugged into the
CAPM to give an es�mate of the required return for this por�olio.

One warning: beta is not a good measure of risk unless the investor is what is known as “well diversified.” Usually, if you own more than 20 stocks, you are considered well-
diversified. However, if these stocks are concentrated in only a couple of industries, then you are probably not effec�vely diversified. Diversifica�on is a subjec�ve and
rela�ve term, so, as a rule, it’s be�er to be more diversified than to be less diversified. Next, we will look at why it is prudent to invest in several stocks and other assets (like
bonds and real estate) that are not concentrated in only a few industries (or geographic loca�ons).

Correlation and Diversification

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http://finance.yahoo.com/

http://www.google.com/finance

This graph shows what perfect nega�ve correla�on between two stocks (A and B) might look like.

In a more advanced mathema�cal presenta�on of diversifica�on’s effect, you would learn that diversifica�on depends on asset returns having imperfect correla�on with one
another. In other words, if all stocks in a por�olio went up and down together, then they would be perfectly correlated, and there would be no point in diversifying. For
example, if a disaster happened to one stock, it would also happen to all the other stocks because they are perfectly posi�vely correlated to one another. As a result,
because they would likely have high posi�ve correla�ons with one another, it is not a good idea to concentrate your por�olio in only one industry or even just a few
industries.

On the other hand, stocks with lower correla�ons make great choices for forming a well-diversified por�olio. In fact, the most efficient diversifica�on happens when we mix
nega�vely correlated assets in our por�olios because their risks will offset one another. To illustrate, consider this example. Suppose you owned stock A whose returns were
perfectly nega�vely correlated with another, stock B. Whenever A’s return went up, B’s went down and vice versa. Imagine that they both varied around an average return of
10%. If you were lucky enough to locate these two stocks, and you put your money in each one to form a special two-stock por�olio, your por�olio would earn exactly 10%
but you would experience zero variability. That is because every �me A had a return below 10%, B would have a return above 10% because of its perfect nega�ve
correla�on. In other words, you could have a risk-free por�olio with a 10% return. Of course, it is not easy (perhaps impossible) to find two stocks with perfect nega�ve
correla�on. Figure 7.6 shows a graphic representa�on of two stocks with perfect nega�ve correla�on.

Figure 7.6: Returns with perfect nega�ve correla�on

The good news is that you can always reduce risk by mixing assets whose returns are imperfectly correlated, and you do this without lowering their average return.
Furthermore, since almost all investment assets are imperfectly correlated, you can get the risk-reducing benefits of diversifica�on by simply mixing together even a randomly
selected bunch of stocks (as was shown in Figure 7.2). Of course, with a li�le insight, you can improve the benefits of diversifica�on by being sure to not focus on one
industry group and by mixing in, for example, a few interna�onal stocks (can you figure out why, in terms of correla�on?).

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Knowing the market price of a stock is
beneficial, but it can o�en be more
advantageous to know how to make your
own es�mate of a required return.

Stockbyte/Ge�y Images

7.3 Required Returns and Valuation

Now that we know how to es�mate required returns, we want to consider once again the �me value of money problems and security valua�on. This is because required
returns are used as the discount rates in these valua�on formulas. To illustrate, suppose that PG&E just paid an annual dividend of $1.82 per share and that we believe
dividends will grow at a 2% annual rate in the future. In this case, we can use the constant growth stock valua�on formula to es�mate the value of PG&E’s stock (and we will
use the form of the model with D0 in the numerator because we were given the last dividend paid). Recalling that PG&E’s required return was 6.24%,

Value of PG&E stock = ($1.82)(1.02)/(0.0624 – 0.02) = $1.8564/.0424 = $43.78

Suppose we did this es�ma�on of value and looked up an actual quote for PG&E’s stock on the Internet. If the price is currently
$43.00, this would mean that the stock appears to be underpriced on the market, which would indicate that it is a bargain according
to our es�mates. However, before we run out to buy PG&E stock, which we think may be worth $1.64 more per share than its price,
we need to consider market efficiency. Remember that market efficiency says that the market price (the $43.00) is the best available
es�mate of value. Now, we must decide whose es�mate we put more faith in: our es�mate ($44.64) or the market’s ($43.00)? If we
believe in market efficiency, we would probably not make the investment.

There are �mes, however, when we need to value an asset or a closely held stock for which no market price exists. In this case, we
have li�le choice but to rely on our own es�mates. In these cases, the ability to es�mate the required return is essen�al. For
example, before Facebook went public in 2012, there was no exis�ng market price for the stock, yet the firm’s ownership had to
place an ini�al price on the shares. If the price they chose was too high, no one would buy the stock, and the offer would be
unsuccessful. If the offer price was too low, then the original owners would be selling a stake in their company for too li�le. To get
the price correct, Facebook’s management, ownership, and financial advisors had to es�mate the firm’s value, which depended on an
accurate es�mate of its risk and the required return of investors given that risk level.

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Ch. 7 Conclusion

In this chapter, the building blocks of required returns were introduced. Most of the chapter used stock to illustrate and explore the rela�onships between risk and investors’
return requirements. The calcula�on of returns, of total risk (standard devia�on of returns), and of market risk (beta) were covered. The benefit of diversifica�on by
elimina�ng certain types of risk was discussed as was the effec�veness of how diversifica�on is linked to the correla�on between investments’ returns. The capital asset
pricing model, used to es�mate the required return for an investment, was also covered and illustrated. The concept of an asset beta was also introduced. Chapter 8
extensively uses the CAPM along with the asset beta as a means to discover the overall required return for the en�re firm rather than just the return requirement for its
equity, which we focused on in this chapter. The theories and techniques explored in Chapter 7 will be vitally important for those of you who one day will enter a career in
the investments field, but the insights will also be important for everyone who becomes an investor whether they are inves�ng for re�rement or for their child’s college fund.

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Ch. 7 Learning Resources

Key Ideas

A ra�onal investor will always want to earn at least the risk-free rate of return when inves�ng in some security or project. Otherwise, they would be se�ling for a return
lower than what they could be assured of by simply deposi�ng the funds in a savings account.
Virtually all investments have some risk associated with them, so investors also require what is known as a risk premium to compensate them for this risk exposure.
The two fundamental building blocks of the required return for an investment are the risk-free return and a risk premium. The required return for an investor = (Risk-free
rate of return) + (Risk premium).
An investment’s total risk is the variability of returns and is measured by their standard devia�on. For simplicity’s sake, we will be using historical returns to measure risk
because expected returns are difficult to predict.
Returns are generated by price changes caused by the arrival to the marketplace of new informa�on, which investors and analysts anxiously await in order to adjust their
view of the company’s or investment’s worth.
Total risk can be broken down into risk that may be diversified away and risk that cannot be avoided or mi�gated.
Firm-specific risk is associated with events specific to the firm that adversely affect the value of the company, but if an investor is well-diversified, the impact will be
minimal to the overall por�olio because such an event impacts only a single firm.
Industry-specific risks are largely avoidable via diversifica�on because events that harm a par�cular type of industry will not necessarily have a nega�ve effect on other
stocks in a por�olio that represent firms in other industries.
Nondiversifiable or market risks are difficult to avoid regardless of how many stocks you own or how diversified your investment por�olio becomes. Some events have
nega�ve effects that pervade the en�re economy.
To measure market risk, we u�lize a metric called beta. Beta measures a firm’s typical responsiveness to informa�on that impacts the en�re market.
The market risk premium (MRP) is the amount of return yielded by the market por�olio over and above the Treasury yield. It can be thought of as the return required for
each addi�onal unit of risk as measured by beta.
Companies that produce similar goods, sold in similar markets, will have similar betas because those companies will be affected similarly by the kind of macroeconomic
news that creates market risk.
Por�olio betas are found by taking the weighted average of the betas of the assets held in the por�olio, where the weights are determined by the amount invested in each
asset.
Diversifica�on depends on asset returns having imperfect correla�on with one another. In other words, if all stocks in a por�olio went up and down together, then they
would be perfectly correlated, and there would be no point in diversifying.
Stocks with lower correla�ons make great choices for forming a well-diversified por�olio. In fact, the most efficient diversifica�on happens when we mix nega�vely
correlated assets in our por�olios because then their risks will offset one another.
Required returns are used as the discount rates in valua�on formulas such as �me value of money problems and security valua�on.

Key Equa�ons

Cri�cal Thinking Ques�ons

1. Total risk is measured by the standard devia�on of returns. Jot down the formula for the standard devia�on and then comment on what part of the formula has to do with
devia�ons and what part is related to calcula�ng the standard of these devia�ons. (Hint: devia�on may be thought of as departure from what is typical and standard may be
thought of as the average or what is expected).

2. The theore�cal development of the CAPM calls for use of the risk-free rate. Swiss government bonds have typically had a lower risk ra�ng than any other government bond.
Why isn’t the Swiss bond, therefore, the standard for use in the CAPM worldwide?

3. The average return on the S&P 500 has been in the neighborhood of 11%, and in 1980 U.S. Treasury bonds were yielding about 15%. Imagine you were an investor in 1980.
How do the circumstances at that �me help explain why it is be�er to use the market risk premium (of around 6%) rather than [Rmkt – Rf] when es�ma�ng the required return

with the CAPM?
4. Beta is the measure of market risk. Look at the businesses listed below and see if you can iden�fy one that could very likely have a rela�vely high total risk but a low beta.

Explain your reasoning.

a. The manufacturer of diamond-encrusted dog collars.

b. A company that specializes in finding and salvaging old shipwrecks from the Age of Discovery (the 1500s and 1600s).

SLIDE 1 OF 4

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c. A casino

5. When you es�mate betas using historical data and linear regression, you must make some of the following choices: what index to use as a proxy for the market por�olio (the
S&P 500, the Wilshire 5000, and the NYSE Composite Index are a few of the possibili�es); the length of the return period (daily returns, weekly returns, and monthly returns
are all used); the length of the historical record (two, three, or five years are candidates). Each combina�on of these choices will yield a slight (or maybe even a major)
difference in the es�mated beta. How many different betas for a single firm could you and your classmates get on the same day by making different choices among these
op�ons?

6. Security A has a standard devia�on of returns equal to 20% and a beta of 1.50. Security B has a standard devia�on of 16% and a beta of 1.80. Which security probably has the
higher required return? Explain.

Key Terms

Click on each key term to see the defini�on.

beta
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

A measure of an asset’s systema�c risk, also known as its market risk. The average stock has a beta of one, while stocks with greater than average market risk will have betas
greater than one and those with less risk will have betas less than one. Beta is used to find the required return for an asset using the CAPM.

capital asset pricing model (CAPM)
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

A formula that quan�fies the connec�on between an investment’s market risk and its required rate of return, specifically the required return on an asset equals the riskfree
rate plus a risk premium. The risk premium is the asset’s beta �mes the market risk premium. The CAPM is the equa�on of the security market line.

correla�on
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

A sta�s�cal measure of the co-movement of asset returns. Correla�on varies between the nega�ve return and the posi�ve one, while a correla�on of zero means that the
two assets are “uncorrelated” and move independently. Perfect posi�ve correla�on means that the two assets’ values move together in the same direc�on. Nega�vely
correlated assets tend to move in opposite direc�ons.

diversifiable risk
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

Risk that can be avoided through diversifica�on.

diversifica�on
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The mixing of investments in a single por�olio that can reduce risk exposure. Diversifica�on’s benefits are most drama�c when the correla�ons between assets in the
por�olio are low or even nega�ve.

diversifica�on effect
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The reduc�on in risk (standard devia�on) that occurs through the blending of stocks into a por�olio.

historical return
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The past performance of a security or index.

leverage
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

A descrip�on of the propor�on of debt used in a firm’s capital structure.

market

por�olio
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

A theore�cal bundle of investments that includes every kind of asset available in the financial market. Because a market por�olio is completely diversified, it is subject only
to systema�c risk.

market risk premium (MRP)
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The difference between the rate of return on the market (e.g., S&P 500) and the risk-free return (e.g., Treasury bonds).

A collec�on of assets or investments. Inves�ng in a por�olio can reduce risk exposure compared to inves�ng in a single asset.

por�olio betas
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/froProcessing math: 0%

The weighted average of the betas of the assets held in the por�olio, where the weights are determined by the amount invested in each asset.

required rate of return
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The minimum return investors must expect in order to be interested in inves�ng in an asset.

risk averse
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

Characteris�c in which people focus more on losses than on equivalent gains. Risk aversion implies that investors must be paid to bear risk.

risk-free rate of return
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The return an investor earns on a risk-free asset.

risk premium
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The added return necessary to compensate investors for taking added risk.

S&P 500 Index (Standard & Poor’s 500)
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

A price index of 500 stocks represen�ng a broad cross sec�on of industries o�en used to represent the en�re stock market’s ac�vity.

systema�c or nondiversifiable risk
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

Risk that cannot be avoided through diversifica�on.

total risk
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

The overall poten�al for financial loss. The variability of returns, measured by their standard devia�on.

unsystema�c risk
(h�p://content.thuzelearning.com/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/front_ma�er/books/AUBUS650.13.1/sec�ons/fro

Risk that affects primarily one company or industry. Unique risk may be mi�gated by diversifying one’s por�olio.

Web Resources

This chapter has introduced some measures of risk. Follow this link to take a quiz assessing your own risk tolerance:
h�p://njaes.rutgers.edu/money/riskquiz/ (h�p://njaes.rutgers.edu/money/riskquiz/ )

Professor Aswath Damodaran of NYU maintains a list of betas for different industries. These may be viewed and the sectors compared at the following website. It might be
interes�ng to compare the average betas in two sectors, like gambling versus natural gas u�li�es to see if the betas conform with your intui�on.
h�p://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/Betas.html (h�p://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/Betas.html)

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http://njaes.rutgers.edu/money/riskquiz/

http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/Betas.html

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