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Chapter 13 – Risk, Cost of Capital, and Valuation

Chapter 13

RISK, COST OF CAPITAL, AND VALUATION

SLIDES

CHAPTER WEB SITES

Section Web Address

13.10 finance.yahoo.com

www.reuters.com

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13.1 Key Concepts and Skills

13.2 Chapter Outline

13.3 Where Do We Stand?

13.4 The Cost of Equity Capital

13.5 The Cost of Equity Capital

13.6 Example

13.7 Example

13.8 Using the SML

13.9 The Risk-Free Rate

13.10 Market Risk Premium

13.11 Estimation of Beta

13.12 Estimation of Beta

13.13 Stability of Beta

13.14 Using an Industry Beta

13.15 Determinants of Beta

13.16 Cyclicality of Revenues

13.17 Operating Leverage

13.18 Operating Leverage

13.19 Financial Leverage and Beta

13.20 Example

13.21 Dividend Discount Model

13.22 Capital Budgeting & Project Risk

13.23 Capital Budgeting & Project Risk

13.24 Capital Budgeting & Project Risk

13.25 Cost of Debt

13.26 Cost of Preferred Stock

13.27 The Weighted Average Cost of Capital

13.28 Firm Valuation

13.29 Example: International Paper

13.30 Example: International Paper

13.31 Example: International Paper

13.32 Flotation Costs

13.33 Quick Quiz

Chapter 13 – Risk, Cost of Capital, and Valuation

finra-markets.morningstar.com/BondCenter

CHAPTER ORGANIZATION

13.1 The Cost of Capital

13.2 Estimating the Cost of Equity Capital with the CAPM

The Risk-Free Rate

Market Risk Premium

13.3 Estimation of Beta

Real-World Betas

Stability of Beta

Using an Industry Beta

13.4 Determinants of Beta

Cyclicality of Revenues

Operating Leverage

Financial Leverage and Beta

13.5 The Dividend Discount Model Approach

Comparison of DDM and CAPM

13.6 Cost of Capital for Divisions and Projects

13.7 Cost of Fixed Income Securities

Cost of Debt

Cost of Preferred Stock

13.8 The Weighted Average Cost of Capital

13.9 Valuation with RWACC

Project Evaluation and the RWACC

Firm Valuation with the RWACC

13.10 Estimating Eastman Chemical’s Cost of Capital

13.11 Flotation Costs and the Weighted Average Cost of Capital

The Basic Approach

Flotation Costs and NPV

Internal Equity and Flotation Costs

ANNOTATED CHAPTER OUTLINE

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Chapter 13 – Risk, Cost of Capital, and Valuation

Slide 13.0 Chapter 13 Title Slide

Slide 13.1 Key Concepts and Skills

Slide 13.2 Chapter Outline

13.1. The Cost of Capital

Creating shareholder wealth depends on the magnitude, timing,

and risk of cash flows. Prior chapters have dealt with magnitude

and timing. In this chapter, we concentrate on the risk of the cash

flows.

Slide 13.3 Where Do We Stand?

Lecture Tip: Students often find it easier to grasp the intricacies of cost of

capital estimation when they understand why it is important. A

good estimate is required for:

1. Good capital budgeting decisions – neither the NPV rule nor

the IRR rule can be implemented without knowledge of the

appropriate discount rate

2. Financing decisions – the optimal/target capital structure minimizes the

cost of capital

3. Operating decisions – cost of capital is used by regulatory agencies in

order to determine the “fair” return in some regulated

industries (e.g. utilities)

Cost of capital, required return, and discount (hurdle) rate are different phrases

that all refer to the opportunity cost of using capital in one way as

opposed to alternative financial market investments of the same

systematic risk.

-required return is from an investor’s point of view

-cost of capital is the same return from the firm’s point of view

-discount rate is the same as used in a PV calculation

13.2. Estimating the Cost of Equity Capital with the CAPM

Slide 13.4 –

Slide 13.5 The Cost of Equity Capital

CAPM, RS = RF +  (RM – RF)

Implementing the Approach

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Chapter 13 – Risk, Cost of Capital, and Valuation

Betas are widely available, and T–bill rates or the rate on long-term

Treasury securities are often used for RF. The expected market

risk premium is the more difficult number to come up with –

make sure that the market risk premium used is consistent with

the risk-free rate chosen.

One of the problems is that we really do need an expectation, but we only

have past information, and market risk premiums do vary

through time. Early in 2000, Federal Reserve Chairman Alan

Greenspan indicated that part of his concern with the state of

the U.S. stock markets at that time was the reduction in the

market risk premium. He felt that investors were either

becoming less risk averse, or they did not truly understand the

risk they were taking by investing in stock.

Nonetheless, the historical average is often used as an estimate of the

market risk premium.

Advantages and Disadvantages of the Approach

-This approach explicitly adjusts for risk in a fashion that is consistent

with capital market history.

-It is applicable to virtually all publicly traded stocks.

-The main disadvantage is that the past is not a perfect predictor of the

future, and both beta and the market risk premium vary through

time.

A recent study finds that almost ¾ of U.S. companies use the

CAPM in capital budgeting, indicating that industry has largely

approved this approach for estimating the cost of equity.

Slide 13.6 –

Slide 13.7 Example

Slide 13.8 Using the SML

Lecture Tip: Some students may question how you value the stock

for a firm that does not pay dividends. In the case of growth-

oriented, non-dividend-paying firms, analysts often look at the

trend in earnings or use similar firms to project the future date of

the first expected dividend and its future growth rate. However,

such processes are subject to greater estimation error, and when

companies fail to meet (or even exceed) estimates, the stock price

can experience a high degree of variability. It should also be

pointed out that no firm pays zero dividends forever – at some

point, every going concern will pay dividends. Microsoft is a good

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Chapter 13 – Risk, Cost of Capital, and Valuation

example. Many people believed that Microsoft would never pay

dividends, but even it ran out of investments for all of the cash that

it generated and began paying dividends in 2003, with an even

larger one-time dividend being paid in late 2004.Even Apple, with

its massive cash pile, began paying dividends in 2012.

.A The Risk-Free Rate

Slide 13.9 The Risk-Free Rate

No bond is completely risk free; however, Treasury securities

come as close as possible to this description. Nonetheless, even

these still have interest rate risk, so the question of maturity is a

relevant one.

Since the CAPM is a period model, most agree that a short-term

(such as T-bill) rate should be chosen. However, since projects are

generally long-lived, we need to use an average anticipated one-

year rate, which can be estimated using implied forward rates built

into the yield curve.

Historically, longer-term (20-year) government bonds have had a

term premium of approximately 1-2% over T–bills. So, if, at the

time of the project, 20-year notes are yielding 4.5% and the term

premium is 2%, then the implied risk-free rate for the average one-

year rate is 2.5% = 4.5% – 2.0%.

Another approach is to select a Treasury security whose maturity

matches the project under consideration.

.B Market Risk Premium

Slide 13.10 Market Risk Premium

The MRP can be estimated using two methods.

Method 1: We could use historical data. In chapter 10, we

estimated that 7% might be a good approximation.

Method 2: We could use the dividend discount model (DDM).

Rearranging the DDM provides the following:

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s 1

Whereas we previously applied this to an individual stock,

we could also relate this to the market as a whole. The

dividend yield on the S&P500 is readily available, and

analysts’ forecasted dividend growth (say, over the next

five years) can be used as an estimate for g.

13.3. Estimation of Beta

Measuring Company Betas: Prior chapters define beta as a

measure of systematic risk, i.e., how an asset moves relative to an

index. Although in theory we would like an index that measures all

assets, practically we use a broad stock market index such as the

S&P500.

Slide 13.11 Estimation of Beta

Beta is defined in the prior chapter as: S = i,M / M2;

Financial publications, such as ValueLine, provide beta estimates.

Slide 13.12 Estimation of Beta

In practice, there are some problems in estimating beta:

1. Betas may vary over time.

2. The sample size may be inadequate.

3. Changing financial leverage and business risk influences

betas.

Solutions

1. Problems 1 and 2 (above) can be moderated by more

sophisticated statistical techniques.

Problems 1 and 2 relate to the selection of the measurement period.

Beta is conventionally measured with either (a) 60 monthly

observations over a five-year period or (b) weekly observations

over two to five-year periods. For example, ValueLine uses five

years of weekly observations.

Daily returns often have too much measurement error, especially in

thinly traded stocks. The choice of the measurement interval is a

trade-off between statistical accuracy and timeliness. A long

measurement period provides more observations and gives a higher

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Chapter 13 – Risk, Cost of Capital, and Valuation

statistical confidence in the beta estimate. On the other hand, a

long measurement period may include outdated information, and

the beta estimate will be incorrect. Most of the statistical

techniques mentioned in solution 1 are beyond the scope of most

financial management courses. One example, that could be used is

the adjustment for regression towards the mean (beta of an average

stock = 1) by Value Line.

2. Problem 3 can be lessened by adjusting for changes in

business and financial risk.

3. Look at average beta estimates of several comparable firms

in the industry. (see below)

.A Real-World Betas

.B Stability of Beta

Although a firm’s beta is relatively stable over time, it will be

impacted by changes in product line, technology, regulations, and

leverage, among other things.

Slide 13.13 Stability of Beta

.C Using an Industry Beta

Industry versus Company Beta:

An industry is a portfolio of individual companies. Therefore, the

beta estimate for an industry is more accurate than the beta

estimate for a single company. However, using an industry beta in

place of the company beta will be incorrect if:

1. the company has a significant amount of business in more

than one industry

2. the financial leverage of the company is very different

from the industry average.

The second problem of using industry beta can be solved by

adjusting the industry beta for the company’s financial leverage,

which we discuss below.

Slide 13.14 Using an Industry Beta

13.4. Determinants of Beta

Slide 13.15 Determinants of Beta

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.A Cyclicality of Revenues

Highly cyclical firms generally have higher betas. However, this is

not the same as revenue variability.

Slide 13.16 Cyclicality of Revenues

.B Operating Leverage

There is almost always some flexibility in production to decide

between fixed and variable costs. Fixed costs generally magnify

forecasting errors, as well as reduce the firm’s flexibility in the

production process.

The Basic Idea: Operating leverage is the degree to which a project

or firm uses fixed costs in production. Plant and equipment and

non-cancelable rentals are typical fixed cost items.

Implications of Operating Leverage: Since fixed costs do not

change with sales, they make good situations better and bad

situations worse, i.e., they “lever” results.

Measuring Operating Leverage: Degree of Operating Leverage

(DOL) is the percentage change in EBIT relative to a percentage

change in sales.

Operating leverage magnifies the effect of cyclicality on beta.

Slide 13.17 –

Slide 13.18 Operating Leverage

.C Financial Leverage and Beta

Financial leverage is determined by the extent of fixed financing

costs, which is determined by the level of debt in a firm’s capital

structure.

Portfolio betas are weighted averages of the betas of the underlying

securities. Since a firm is essentially a portfolio, its asset beta, in a

similar fashion, is a weighted average of debt and equity betas.

Debt does not vary, at least dramatically, with changes in market

indexes. So, debt betas are typically assumed to be 0. In addition,

the separation theorem suggests asset betas do not change with

financing decisions. Thus, there is a strict relation between

leverage and equity beta.

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Chapter 13 – Risk, Cost of Capital, and Valuation

ASSET = EQUITY × S/(S+B) + DEBT × B/(S+B)

where S is Equity and B is Debt.

If debt beta = 0, then:

ASSET = EQUITY × S/(S+B)

EQUITY = ASSET × (1 +

)

Lecture Tip: Adjusting for taxes would provide:

EQUITY = ASSET × (1 + (1-

)

Slide 13.19 Financial Leverage and Beta

Slide 13.20 Example

13.5. The Dividend Discount Model Approach

Slide 13.21 Dividend Discount Model

The Dividend Growth Model is an alternative for estimating the

cost of equity capital. According to the dividend growth model,

P0 = D1 / (Rs – g)

Rearranging and solving for the cost of equity gives:

Rs = (D1 / P0) + g

which is equal to the dividend yield plus the growth rate (capital gains yield).

Implementing the Approach

Price and latest dividend are observed; g must be estimated.

Estimating g – typically use historical growth rates or analysts’

forecasts.

Advantages and Disadvantages of the Approach

-Approach only works for dividend paying firms

-Rs is very sensitive to the estimate of g

-Historical growth rates may not reliably predict future growth

-Risk is only indirectly accounted for by the use of the price

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Chapter 13 – Risk, Cost of Capital, and Valuation

Lecture Tip: Ask the class to consider a situation in which a company

maintains a large portfolio of marketable securities. Now ask them

to consider the impact this large security balance would have on a

company’s current and quick ratios and how this might impact the

company’s ability to meet short-term obligations. The students

should easily remember that a larger liquidity ratio

implies less risk (and less potential profit). Although the revenue realized from

the marketable securities would be less than the interest expense

on the company’s comparable debt issues, these holdings would

result in lowering the firm’s beta and WACC. This example allows

students to recognize that the expected return and beta of an

investment in marketable securities would be below the company’s

WACC, and justification for such investments must be considered

relative to a benchmark other than the company’s overall WACC.

.A Comparison of DDM and CAPM

The DDM and CAPM are internally consistent, but academics generally favor

the CAPM and companies seem to use the CAPM more

consistently.

The CAM has two primary advantages:

1. It explicitly adjusts for risk

2. It is applicable to companies that pay no dividends

Lecture Tip: Students are often surprised when they find that the

two approaches (DDM and CAPM) typically result in different

estimates. Suggest that it would be more surprising if the results

were identical. Why? The underlying assumptions of the two

approaches are very different. The constant growth model is a

variant of a growing perpetuity model and requires that dividends

are expected to grow at a constant rate forever and that the

discount rate is greater than the growth rate. The SML approach

requires assumptions of normality of returns and/or quadratic

utility functions. It also requires the absence of taxes, transaction

costs, and other market imperfections.

13.6. Cost of Capital for Divisions and Projects

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Chapter 13 – Risk, Cost of Capital, and Valuation

When a firm has different operating divisions with different risks,

its WACC is an average of the divisional required returns. In such

cases, the cost of capital for projects of average risk in each

division needs to be established. If you do use the firm’s WACC

across divisions, then riskier divisions will receive the bulk of the

funding, and less risky divisions will have to forgo what would be

good projects if the appropriate discount rate were used. This will

lead to an increase in risk for the overall firm.

Slide 13.22 –

Slide 13.24 Capital Budgeting & Project Risk

To estimate the cost of capital for a division, a “pure play”

approach could be used, although finding exactly similar firms

may be difficult, particularly considering underlying financial and

operational structure.

Lecture Tip: It may help students to distinguish between the average cost of

capital to the firm and the required return on a given investment if

the idea is turned around from the firm’s point of view to the

investor’s point of view. Consider an investor who is holding a

portfolio of T-bills, corporate bonds, and common stocks. Suppose

there is an equal amount invested in each. The T-bills have paid

5% on average, the corporate bonds 10%, and the common stocks

15%. Thus, the average portfolio return is 10%. Now suppose that

the investor has some additional money to invest and they can

choose between T-bills that are currently paying 7% and common

stock that is expected to pay 13%. What choice will the investor

make if he uses the 10% average portfolio return as his cut-off

rate? (Invest in common stock 13%>10%, but not in T-bills

7%<10%.) What if he uses the average return for each security as

the cut-off rate? (Invest in T-bills 7% > 5%, but not common stock

13%<15%.)

Lecture Tip: You may wish to point out here that the divisional

concept is no more than a firm-level application of the portfolio

concept introduced in the section on risk and return. And, not

surprisingly, the overall firm beta is therefore the weighted

average of the betas of the firm’s divisions.

13.7. Cost of Fixed Income Securities

.A Cost of Debt

Slide 13.25 Cost of Debt

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Chapter 13 – Risk, Cost of Capital, and Valuation

Cost of debt (RD) – the interest rate on new debt can easily be estimated using

the yield-to-maturity on outstanding debt or by knowing the bond

rating and looking up rates on new issues with the same rating.

The only adjustment is to reduce the cost to account for the tax

deductibility of the interest expense. Thus, the after–tax cost of

debt should be used:

after-tax debt cost = (1-T)*borrowing rate

Lecture Tip: It is beneficial to reemphasize the distinction between the

coupon rate, the current yield, and the yield-to-maturity. The cost

of debt is equal to the yield-to-maturity because it is the market

rate of interest that would be required on new debt issues. The

coupon rate, on the other hand, is the firm’s promised interest

payments on existing debt, and the current yield is the income

portion of total return. If you do not emphasize this point, some

students want to just use the coupon rate on current debt.

Lecture Tip: It may be helpful to mention and differentiate between the three

types of weightings in the capital structure equation: book, market,

and target. Market values should be used since these represent the

current opportunity cost of investment.

It is also helpful to mention that the total market value of equity incorporates

the market value of all three common equity accounts on the

balance sheet (common stock, additional paid-in capital and

retained earnings).

Lecture Tip: The cost of short-term debt is usually very different from that of

long-term debt. Some types of current liabilities are interest-free,

such as accruals. However, accounts payable has a cost associated

with it if the company forgoes discounts. The cost of notes payable

and other current liabilities depends on market rates of interest for

short-term loans. Since these loans are often negotiated with

banks, you can get estimates of the short-term cost of capital from

the company’s bank. The market value and book value of current

liabilities are usually very similar, so you can use the book value

as an estimate of market value.

.B Cost of Preferred Stock

Slide 13.26 Cost of Preferred Stock

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Chapter 13 – Risk, Cost of Capital, and Valuation

Preferred stock is a perpetuity, so its price is equal to the coupon

paid divided by the current required return.

Rearranging this formula, the cost of preferred stock is:

RP = C / PV

There is no tax adjustment because dividends are not tax

deductible.

13.8. The Weighted Average Cost of Capital

Slide 13.27 The Weighted Average Cost of Capital

After-tax cash flows require an after-tax discount rate. Let TC denote the

firm’s marginal tax rate. Then, the weighted average cost of capital

is:

WACC = (S/(B+S))RS + (B/(B+S))RD(1-TC)

With preferred stock:

WACC = (S/(B+P+S))RS + (P/(B+P+S))RP + (B/(B+P+S))RD(1-TC)

WACC – overall return the firm must earn on its assets to maintain the value

of its stock. It is a market rate that is based on the market’s

perception of the risk of the firm’s assets.

13.9. Valuation with RWACC

.A Project Evaluation and the RWACC

The discussion of NPV in prior chapters relied on a discount rate to

be applied to the estimated cash flows. We now know how this

discount rate (i.e., the RWACC) is calculated.

.B Firm Valuation with the RWACC

Slide 13.28 Firm Valuation

Remember from our discussion of NPV, that a firm’s value is just

the sum of the NPV of all its projects. Thus, as with any asset, the

firm’s value is the PV of all its future cash flow.

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Chapter 13 – Risk, Cost of Capital, and Valuation

With the WACC, we can discount our estimate of future cash flow,

which should represent all cash flow (free cash flow, or

distributable cash flow). As usual, we would need to apply a

terminal valuation at some point.

Once firm value is obtained, we would subtract the market value of

the debt to find the equity value. We could then divide by the

number of shares outstanding to find a per share price.

13.10. Estimating Eastman Chemical’s Cost of Capital

Several web sites are utilized to find the information required to compute the

WACC.

1. Go to a site such as finance.yahoo.com; type in EMN and choose key

statistics. Get the market value of equity (price*shares outstanding)

and beta. This can also be found at www.reuters.com.

2. Find the yield on 20-year Treasuries and subtract the historical

yield difference. Next, decide on an estimate of the market risk

premium, such as 7%. Estimate Rs using the CAPM.

3. Go to https://finra-markets.morningstar.com/BondCenter to find

the weighted average of the yield-to-maturity for bond issues.

Book value and market value of debt is often similar, so you may

want to use the book value for simplicity.

4. Use market value weights to compute the WACC.

Slide 13.29 –

Slide 13.31 Example: International Paper

13.11. Flotation Costs and the Weighted Average Cost of Capital

Flotation costs represent the expenses incurred upon the issue, or float, of

new bonds or stocks. If a firm lacks sufficient available funds to support a

new project, it may incur incremental flotation costs

The WACC is unchanged as a result of the flotation costs, as it represents

the risk of the project, not the source of funds. The NPV, however, is

impacted (typically negatively) since the flotation costs represent a

relevant incremental cash flow.

.A The Basic Approach

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Chapter 13 – Risk, Cost of Capital, and Valuation

The net proceeds in an offering are equal to the total amount raised

less flotation costs. Thus, to finance a given amount for a project,

additional funds must be raised in the offering. The net effect is

that the total funds raised are:

Amount Raised = Necessary Proceeds / (1- % flotation cost)

The flotation cost percentage (f) is a weighted average measure

based on the average cost of issuance for each funding source and

the firm’s target capital structure.

fA = (E/V)* fE + (D/V)* fD

where E is equity; D is debt; and V is total firm value.

Slide 13.32 Flotation Costs

.A Flotation Costs and NPV

When flotation costs are positive, which is generally the case, the

NPV is lower when these costs are accounted for.

.B Internal Equity and Flotation Costs

Firms rarely issue external equity, focusing rather on generating

internal funds to cover the costs of projects. When this is the case,

the best approach is to assign a flotation cost of zero to the equity

portion of the average flotation cost.

Slide 13.33 Quick Quiz

To access Appendix 13A (Economic Value Added and the Measurement of Financial

Performance) go to www.mhhe.com/rwj.

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