asset v discounted c flow - coursewebs

Author: Chris Demaline |

MICROSOFT ASSET VALUATION USING DISCOUNTED CASH

FLOW

Asset Valuation Using Discounted Cash Flows

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Course Description

The purpose of this course is to provide an overview of the Discounted Cash-Flow

(DCF) Method of valuation. The DCF method requires that an estimated cash-flow and

a risk-adjusted discount rate be determined. This course summarizes commonly-used

cash-flow proxies and discount rate estimation tools.

COURSE LEARNING OBJECTIVES

1. Define assets and equity

2. Compare cash-flow to U.S. GAAP-based net income

3. Compare commonly-used discount rate models

4. Recognize the relationship between risk and reward

5. Recognize commonly-used discount rate models

6. Compare commonly-used discount rate models

7. Understand how assets are valued using a discounted cash flow model

Level of Difficulty: Basic

Prerequisite: None

Field of Study: Accounting


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Contents

Introduction .................................................................................................................................................. 5

Review Questions...................................................................................................................................... 6

Chapter 1. Valuation – Background ............................................................................................................. 7

Review Questions.................................................................................................................................... 14

Chapter 2. Future cash flows ..................................................................................................................... 15

Cash Flow vs. U.S. GAAP-based Net Income ........................................................................................... 15

Cash Flow Estimation Models ................................................................................................................. 17

Cash Flow Model – EBITDA ................................................................................................................. 17

Cash Flow Model – Income from Continuing Operations ................................................................... 24

Cash Flow Model – S&P Core Earnings ............................................................................................... 27

Summary – Cash Flow Estimation ........................................................................................................... 30


Chapter 3. Discount rate. ........................................................................................................................... 32

Risk – Reward Relationship ..................................................................................................................... 32

Estimating the Discount Rate .................................................................................................................. 38

Capital Asset Pricing Model (CAPM) ................................................................................................... 38

Arbitrage Pricing Model (APM) ........................................................................................................... 46

Comparison of APT and CAPM ............................................................................................................ 50

Summary – Discount Rate ....................................................................................................................... 52


Chapter 4. The complete model - Value equals estimated cash-flow divided by the discount rate ......... 56


Conclusion ................................................................................................................................................... 60

Glossary ....................................................................................................................................................... 63

Index............................................................................................................................................................ 64

Review Question Answer Feedback ............................................................................................................ 65


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Introduction

By the end of this unit, learners should be able to -

Recognize commonly-used discount rate models

According to the Financial Accounting Standard Board’s Statement of Financial

Accounting Concepts number 6,

Assets are probable future economic benefits obtained or controlled by a

particular entity as a result of past transactions or events.

Assets can also be defined algebraically as -

Assets = Liabilities + Shareholders’ Equity (i.e. Net Assets).

Shareholders’ equity is often referred to as net assets since assets minus liabilities

equals shareholders’ equity (shareholders’ equity = assets – liabilities). With this in

mind, one can also state that, for a firm with no liabilities, total assets equals total net

assets (assets = 0 + net Assets).

For simplicity and consistency in this course, liabilities will be assumed to be zero and

firms’ equity structures will be assumed to include only common stock. No preferred

stock or hybrid securities will be considered in this course. So, the terms assets, net

assets and shareholders’ equity will be used interchangeably. Also, common stock

shareholders will be assumed to hold 100% of the value of the firm’s assets and 100%

of the firm’s net assets.

Across the globe, assets are bought and sold millions of times each day. These

transactions may involve the exchange of assets ranging from -

a single share of common stock (equity) representing ownership in a large

publicly-traded entity to

a 100% sale of a small privately-held company.


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Regardless of the size of the transaction or the nature of the asset(s) involved, one

important piece of information must be determined before any of these transactions can

take place. This vital statistic is the price or value of the asset(s) in question.

Review Questions

Review Questions are required by NASBA and are designed to enhance the learning process. They are

NOT graded. Answers can be found at the end of the EBook.

1. Assets can be defined as

liabilities + shareholders’ equity. liabilities less equity. probable future economic sacrifices. benefits resulting from future transactions or events.

2. Assets can equal shareholders’ equity if

A. no liabilities are present. B. shareholder equity is less than total liabilities C. liabilities are positive and equal to shareholders’ equity. D. only current assets are owned by the company.


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Chapter 1. Valuation – Background

By the end of this chapter, learners should be able to -


Asset valuation methods have long been the focus of research and debate. Valuations

are necessary for a number of reasons. A few of the more common situations that call

for asset valuation techniques to be used involve -

Business Sales

Entire business

Partial interest

Common stock sales – primary and secondary

Estate Planning – Taxation

Real property

Collectibles

Family business

Litigation

Patent infringement

Breach of contract

Divorce

Many valuation methods are used. The choice often depends on the specific scenario

and the individual valuation analyst performing the service. Following is a review of

three commonly-used valuation methods.

Fair Market Value.

Market Comparison Method.

Earnings Method.


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Fair Market Value

Fair Market Value refers to an amount mutually and voluntarily agreed upon by both

buyer and seller. The Internal Revenue Service succinctly defines fair market value as,

“…the price that property would sell for on the open market. It is the price that would be

agreed on between a willing buyer and a willing seller, with both being required to act,

and both having reasonable knowledge of the relevant facts.” For instance, publicly-

held businesses may use the stock market to determine its fair market value. If a stock

is heavily traded and it is assumed that the market is efficient, then it can be assumed

that the total shares outstanding multiplied by the stock price per share would provide

one reasonable estimate of firm value. As of February 2012, General Mills, Inc. (GIS)

had nearly 650,000,000 shares of common stock outstanding. GIS closing price on

February 27, 2012 was $38.04 per share. Hence, the company’s market value – also

known as market capitalization - would be nearly $25 Billion.

[650,000,000 x $38.04]

Market Comparison Method

Valuation of privately-held firms may involve derivative methods. Using the market

comparison method, a private firm would be compared to a similar publicly-traded firm.

The value of the private firm would be based on the value of the public firm – adjusted

for the privately-held firm’s unique characteristics. For example, a privately-held

hardware store’s value could be derived by first calculating the value of Home Depot.

So, if Home Depot’s fair market value (market capitalization) is calculated at $72 billion,

then this figure could be compared to Home Depot’s revenue, net income, assets and

other key figures to determine a set of ratios. These ratios would then be used as a

basis to begin valuing the privately-held entity. Consider the following example which

compares Home Depot’s financial information with Handy-Helper Hardware -- a

fictional, privately-held retail hardware company.

Fair Annual Total Annual

Market Value Sales Assets Net Income


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Home

Depot:

$72,000,000,00

0

$70,000,000,00

0

$39,000,000,00

0

$3,500,000,00

0

Handy-

Helper

Hardware:

$???

$80,000,000

$28,000,000

$5,000,000

Ratio: 0.1143% 0.0718% 0.1429%

After gathering the necessary data and calculating ratios, the subjective part of the

process begins. Generally, each component ratio is given a relative weight. The final

weighted average ratio is used to determine Handy-Helper Hardware’s market value.

To find an estimated market value for Handy-Helper, assume these weights and ratios –

Annual Total Annual

Sales Assets Net Income

Ratio: 0.1143% 0.0718% 0.1429%

Weight 25% 20% 55%

The weighted average comparable ratio is then calculated as follows.

Comparable Ratio = (Annual Sales * Relative Weight) + (Total Assets * Relative

Weight) + (Annual Net Income * Weight)

Comparable Ratio = (.001143*.25) + (.000718*.20) + (.001429*.55)

Comparable Ratio = .1215%


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To solve for Handy-Helper’s market value, multiply Home Depot’s market value by the

Handy-Helper’s comparable ratio.

Handy-Helper Hardware Value = Home Depot Value * Comparable Ratio

Handy-Helper Hardware Value = $72,000,000,000 * .1215%

Handy-Helper Hardware Value = $87,480,000

This method has value but much subjectivity is involved. Mainly, the key components

(e.g., Revenue, Net Income) and the relative weights chosen can significantly affect the

calculated market value.

Earnings Method

The earnings method values assets, from individual shares of stock to entire business

enterprises, by discounting the expected future cash flows (i.e. economic earnings)

generated by the asset, then discounting those future cash flows by a risk-adjusted rate-

of-return.

Most economic earnings valuation models employ a similar formula. These methods all

use some form of discount rate and a future cash flow projection. The goal of these

models is to discount all future cash flows to present value. Consistent with the

parameters set forth in the course introduction, equity valuation models refer specifically

to the value retained by the stockholder after debt obligations has been considered. A

generic discounted cash flow (DCF) equity valuation model follows:

n

tt

t

rExpected

CFExpectedP

1

01

][


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A simplified presentation of the model components –

Where -

0P = Price (Value) of the equity per share

1CF = net cash-flow in future period (1, 2, 3...) per share

r = discount rate (i.e., required rate-of-return)

This means that the current value of an asset (e.g., share of common stock) is directly

related to the future cash flows received by the shareholder and inversely related to the

uncertainty of receiving those future cash flows.

Note: This model assumes that the asset will be held indefinitely, so there is no

additional cash-flow component which represents the present value of the future

asset sale.

For example – to determine the value of one share of XYZ Co. common stock

Find -

The future periodic net cash flow

and an appropriate risk-adjusted discount rate.


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Assume that XYZ’s future periodic cash flow (1CF ) is $1.50/share. Next, assume that

12% is an appropriate discount rate. Based on these assumed variables, the generic

DCF equity valuation model calculates XYZ’s common stock value per share to be -

$12.50 [1.50/12%]

In theory, this value per share can be extended to encompass the value of the entire

business by multiplying the value per share times the total shares outstanding.

The generic DCF formula seems simple at first glance. After all, the equation only

contains a few basic parameters. However, accurately estimating each variable is

enormously complex.

Over the past several decades, many great financial minds have generated seminal

works related to equity valuation models.

A few notable authors are –

Eugene Fama – Significantly contributed to APT-related research

Fischer Black – One of two researchers – the other being Nobel Prize laureate,

Myron Scholes - credited with developing the Black/Sholes options pricing model.

Kenneth French - Significantly contributed to APT-related research

Stephen A. Ross – Credited with the development of the Arbitrage Pricing Theory

(APT).

Richard Roll – In accordance with fellow researcher, Stephen A. Ross, performed

research and published significant APT-related findings

William Sharpe – Credited with the initial development of the capital asset pricing

model (CAPM).

Jack Treynor – Significant CAPM follow-up research and consulting. President –

Treynor Capital Management.

Sample journal articles written by these researchers include:


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Black, F., 1986, Noise, Journal of Finance 41(3), pp. 529-543

Black, Fischer and M. Scholes, 1972, The valuation of option contracts and a test of

market efficiency. Journal of Finance, 27(2), pp.399-418.

Roll, R. and S. Ross (1980) An empirical investigation of the arbitrage pricing theory,

Journal of Finance 35(5), pp. 1073-1103.

Ross, S. (1976) The arbitrage theory of capital asset pricing. Journal of Economic

Theory, 13(3), pp341—360.

Sharpe, William (1964) Capital asset prices: A theory of market equilibrium under

conditions of risk, Journal of Finance,19 (3), pp. 425-442.

Summers, L., 1986, Does the stock market rationally reflect fundamental values?

Journal of Finance 41(3), pp. 591-601.

These researchers and other notable financial scientists continue to develop theoretical

valuation concepts. Yet, no one valuation concept has received full acceptance from the

academic and professional community.

A few of the more popular valuation theories and models incorporate one or more of the

following:

Black-Scholes Model – options valuation pricing model

Dividend Discount Model (DDM) – considers dividend payments and growth

rates to calculate equity valuation. This model considers common stock

dividends to be a reasonable proxy of cash flow available to common

stockholders.

Multi-stage Growth Model – similar to the DDM, this model considers changing

growth rates over time.

These and other valuation models and theorems are elaborate. This course will avoid

the more technical areas of this subject. Instead, this material will concentrate on the

major components shared by all discounted cash-flow models. The material will be

presented in three sections:

Future cash flows


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Discount rate

The complete model

Review Questions



1. Valuation methods are commonly used for all of the following except

A. estate planning. B. divorce litigation. C. patent litigation. D. compliance auditing.

2. Notable financial models used in asset valuation include all of the following

except the

A. CAPM. B. Dividend Discount Model. C. Arbitrage Pricing Model. D. Demaline Discount Model.


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Chapter 2. Future cash flows

By the end of this chapter, learners should be able to –

Compare cash-flow to U.S. GAAP-based net income

Compare commonly-used discount rate models

Cash Flow vs. U.S. GAAP-based Net Income

It is logical to conclude that one must first determine actual cash flow before estimating

future cash flow. Hence, determining actual periodic sustainable cash flows will be

the specific focus of this section.

The Financial Accounting Standards Board (FASB) and the International Accounting

Standards Board (IASB) have been working on a convergence project for several years.

One of their first completed projects was the release of the joint Conceptual Framework

for Financial Accounting (Phase A). FASB released this initial work on the framework

as Statement of Financial Accounting Concepts (SFAC) number 8.

SFAC 8 Conceptual Framework for Financial Reporting -

Chapter 1, The Objective of General Purpose Financial Reporting, and

Chapter 3, Qualitative Characteristics of Useful Financial Information

SFAC 8, suggests that financial information should be useful in predicting future cash-

flows. Under a subjection entitled, Financial Performance Reflected by Accrual

Accounting, SFAC 8 (OB.18) states,

Information about a reporting entity’s financial performance during a

period, reflected by changes in its economic resources and claims other

than by obtaining additional resources directly from investors and creditors

(see paragraph OB21), is useful in assessing the entity’s past and future

ability to generate net cash inflows…


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According to SFAC 5, paragraph 141, accrual accounting attempts to recognize

revenues when earned and expenses when incurred. Accrual accounting methods also

attempt to match expenses with the revenue that they help to produce.

Periodic accruals are a key part of providing timely financial information. However,

these accruals are subject to a significant amount of personal and professional

judgment. This often motivates company management to make accruals, not based on

their best estimate of economic reality, but based on what would provide the highest

compensation for management. Researchers in this field have coined the terms,

“discretionary accruals” and “earnings management” in reference to this opportunistic

behavior.

SFAC 8 suggests that one purpose of financial information is to provide an indication of

future cash-flows. However, there are several reasons that GAAP net income rarely

corresponds to actual cash-flows. Many of these differences result from accrual-based

adjustments as well as varying interpretation of GAAP from company-to-company.

Weaknesses

Manipulation is inherent in accrual-based financial information. In addition, many

components of GAAP-based earnings are the result of subjective, temporary and

volatile changes in asset and liability amounts. For example -

Depreciation and amortization

Estimation of warranty expenses

Estimation of bad debt allowance

Fair value adjustments

These are examples of items recognized in the financial statements. This type of

recognition is contingent upon the corporate accountant’s judgment and the

“independent” auditor’s approval, both of which could be skewed by the desires of

corporate management. This subjectivity often results in inaccurate balance sheet

reporting and related inaccuracies on the income statement.

Other changes in balance sheet account valuations may not be recognized in the

financial statements. For example,

An increase in land value does not appear on the balance sheet or as a

corresponding gain in net income.


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Only certain pension –related liabilities are recognized on the balance sheet.

Certain intangible assets, such as human capital (employee value), are not

directly reported on the balance sheet.

In response to confusion regarding U.S. GAAP-based valuation, FASB has changed

their focus in recent years. They have issued significant fair value guidance (see:

Accounting Standards Codification Topic 820). These changes offer guidance –

particularly as it relates to terminology and footnote disclosure.

While, theoretically, fair value accounting should result in a balance sheet with fair

market values for all assets, liabilities and equity items, in practice this is far from the

truth. The complexity of fair value calculations, along with the subjectivity, ulterior

motives and varied methods of calculations, often lead to balance sheets that are less

useful than the “historical cost” alternative. Some researchers have even suggested that

fair value accounting methods misled investor and contributed to the recent financial

crisis.

In addition, current fair value guidance does not adequately address many of the

specific areas that cause GAAP-based earnings to diverge from economic earnings.

Cash Flow Estimation Models

These limitations inherent in GAAP-based net earnings have created a need for

alternative earnings calculations. A discussion of a few common methods used to

convert GAAP-based income into a more useful cash-flow (economic earnings) figure

follow.

Cash Flow Model – EBITDA

Earnings Before Interest, Taxes, Depreciation and Amortization (EBITDA) has been

used as a cash-flow proxy for many years. EBITDA has become an increasingly

popular financial measure in recent years. It attempts to convert net income to a better

approximation of operating cash flow. EBITDA begins with the GAAP-based earnings

amount then adds back - interest, taxes, depreciation and amortization.


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Example:

Consider the following hypothetical income statement information.

Jones Sporting Goods Inc

Income Statement (Condensed)

For the Year ending December 31, 20XX

Net Sales $2,850,000

Cost of Goods Sold $1,400,000

Gross Margin $1,450,000

Sales, General & Administrative Expenses

Advertising $128,000

Depreciation and Amortization $210,000

Office Expense $85,000

Other… $300,000

Total Sales, General & Administrative Expenses $723,000

Income before Interest & Taxes $727,000

Interest

Expense $25,000

Income Taxes $230,000

Net Income $472,000


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Jones Sporting Goods EBITDA would be calculated by adding total depreciation and

amortization expenses to income before interest and taxes.

Income Before Interest & Taxes $ 727,000

Add: Depreciation & Amortization $ 210,000

$ 937,000

GAAP-Based Net Income $ 472,000

Difference Between Net Income & EBITDA $ 465,000

Note the significant difference between GAAP-based Net income and EBITDA.

Benefits.

EB I TDA

Interest

Interest is removed from the calculation for comparability purposes. When interest

expense is removed, one can compare firms with different leverage. Removing interest


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also allows analysts to review potential future cash flows on the assets if the debt were

paid in full (e.g., asset acquisition/takeover).

EBI T DA

Taxes

The reason for removing taxes is that it is an uncontrollable expense. In theory,

management decisions will not affect tax rates. Hence, the tax expense should be

removed from all net income calculations to create comparable operating figures.

Removing taxes also permits acquiring firms to review potential future cash flows based

on their own tax rates.

EBIT D A

Depreciation

Depreciation and Amortization are “non-cash” expenses. Adding those expenses back

to net income provides a better proxy for cash flow in the current period. In fact, this is

why the same reconciliation is made when preparing the Statement of Cash Flows

(Indirect Method).

According to SFAC 5, depreciation is a systematic and rational allocation of a long-lived

asset over more that one accounting period. Depreciation is a system of allocation not

valuation. Since depreciation is arbitrary it is not considered in the cash flow

calculation using EBITDA.


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Depreciation Example – Differing GAAP methods result in differing amounts of periodic

depreciation.

Capital Asset: Delivery Truck

Cost: $45,000

Estimated useful life: 5 years or 25,000 miles

Salvage Value: $5000

Annual Mileage: 1: 22,000 2: 28,000 3: 26,000 4: 27,000 5: 21,000

Comparison of three acceptable GAAP depreciation methods:

1 2 3 4 5

straight line $ 8,000 $ 8,000 $ 8,000

$

8,000 $ 8,000

double-declining

balance $ 18,000 $ 10,800 $ 6,480

$

3,888 $ 832

units of production

($.32/mi ) $ 7,040 $ 8,960 $ 8,320

$

8,640 $ 7,040


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As depicted in the table and graph, differing GAAP-approved methods result in differing

amounts of periodic depreciation. This arbitrary allocation of capital asset costs results

in a net income figure that is not consistent with economic earnings.

EBITD A

Amortization

As technology continues to play a more prominent role in the economy, amortization

and the accounting methods used to recognize amortization are beginning to have a

material effect on overall GAAP-based earnings.

Accounting for intangibles and amortization is covered in FASB ASC topic 350.

For instance, FASB ASC 350-20-25-3, Intangibles – Goodwill and Other – Goodwill –

Recognition requires that costs associated with developing intangible assets that are

not specifically identifiable, have indeterminate lives, or are inherent in continuing

operations be expensed. This treatment results in skewed financial reports that show a

lower net income in the current period and a lower asset valuation going forward. It also

suggests that periodic amortization may be lower than economic reality, since many

intangible assets were immediately expensed.

Depreciation Comparison

$-

$5,000

$10,000

$15,000

$20,000

1 2 3 4 5

Year

$

straight line

double-declining

balance

units of production ($.32/mile )


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Due to the difficulty in accurately presenting intangible asset information, FASB and the

IASB regularly consider adjustments to intangible asset guidance. However, the

inherent complexity in the calculations and relatively high cost associated with

performing these appraisals makes the issue of intangible asset valuation an ongoing

challenge.

For the reasons presented, the EBITDA method of cash flow estimation eliminates

some of the subjectivity present in GAAP-based net earnings.

Limitations.

EB I TDA

Interest

The amount of interest expense is dependent upon the firm’s capital structure. This

structure is likely a significant and ongoing characteristic of the company. So, removing

the interest expense from the calculation is not logical for most investors. However, if a

firm is a takeover target, the potential buyer may remove the interest cost, and then

replace it with the finance costs of the acquiring firm. So, interest expense is not being

removed but recalculated based on assumed changes in the company’s controlling

shareholders.

EBI T DA

Taxes

Even though – for the most part – income tax expense is not influenced by management

behavior, it is still (assuming a firm will earn future net income) an ongoing cash

expense. Much as with interest, a potential investor would only remove taxes from the

calculation if they were planning on acquiring the entire firm. Thus, the projected tax

expense would replace the reported tax expense.

EBIT D A


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Depreciation

While it is accurate to say that depreciation and amortization are non-cash expenses.

They both are still expenses. Depreciation systematically expenses a capital asset over

the course of multiple years. At some point these assets need to be retired and

replaced. Financial analysts often account for this by considering capital expenditures

(CAPEX) as part of their cash flow model. In other words, EBITDA removes the firm’s

depreciation estimate and financial analysts replace that expense figure (depreciation)

with their own estimate (CAPEX). Finally, EBITDA does not account for some of the

same limitation associated with the operating income method. For instance, EBITDA

does not consider certain components of GAAP-based earnings resulting from

temporary, subjective and volatile changes in asset and liability amounts.

EBITD A

Amortization

ASC Topic 350, Intangibles - Goodwill and Other is not a cure-all for the inherent

problems associated with accounting for intangibles. However, it is a marked

improvement over previous GAAP. According to Topic 350, amortization is no longer

considered a completely arbitrary expense. Firms no longer regularly amortize the cost

of intangibles that have indefinite life. Instead, firms are now required to regularly

evaluate their reported intangible assets (e.g., goodwill) to determine if the reported

amount is accurate. Thus, if a company has recognized amortization expense, financial

statement users can reasonably infer that the firm’s intangible assets have lost real

value. It can then be assumed that future cash flows associated with those intangible

have also been hampered.

Cash Flow Model – Income from Continuing Operations

GAAP-based income statements contain intermediate measures of income. Income

from continuing operations is separately presented from net income if the two figures

differ. The two figures may differ when an entity experiences one or more economic


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events that are not related to the firm’s going concern. Examples include extraordinary

items and discontinued operations. Before May 2005, cumulative effect of accounting

changes would have also been included in this section. However, pre-codification

Statement of Financial Accounting Standard (SFAS) 154 virtually eliminated this income

statement category, instead requiring retrospective treatment of voluntary accounting

changes. The purpose of this division between income from continuing operations and

net income is to provide a net income figure that better characterizes the firm’s future

cash-flow potential.

Hence, a straightforward way to adjust net income to net cash-flow is to use the income

from continuing operations figure provided on the income statement. The following

scenario exemplifies this technique.

Jordon & Nile Company

Income Statement (condensed)

For the Year Ended December 31, 20XX

($000)

Net Sales Revenues: 15,000

Cost of goods sold: 6,200

Gross profit on sales 8,800

Operating expenses: 3,500

Income from continuing operations before income tax 5,300

Income tax expense 1,800

Income from continuing operations 3,500

Discontinued operations (net of tax): (820)


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Extraordinary items: 255

Net income 2,935

Jordon & Nile’s income from continuing operations is already calculated on the income

statement.

Income from continuing operations 3,500,000

Net income 2,935,000

Difference Between Net Income & Income from operations 565,000

This, rather simplistic adjustment, suggests that actual cash flows are nearly 20%

higher than GAAP-based net income. More importantly, the income from operations

figure should not fluctuate due to the firm’s peripheral economic activity.


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Benefits

The primary benefit of the income from continuing operations method is its ease of

calculation. Actually, since a firm’s income from continuing operations is already

presented on their GAAP-based income statement, the figure is readily available without

any calculation being necessary.

Income from continuing operations – as its name suggests – also eliminates many of

the effects of discontinued or otherwise nonrecurring activities. This adjustment leaves a

consistent basis from which to estimate future economic earnings

Limitations

While the phrase, “income from continuing operations” may lead one to believe that this

figure should closely mirror continuing net cash flows, there are a few things that may

cause net cash flows and income from continuing operations to diverge. First, income

from continuing operations is a GAAP-based accrual figure. It does not make

adjustments for non-cash allocations such as depreciation and amortization. Second,

not all unusual or infrequent economic activity is excluded from the continuing

operations figure. Per ASC 225-20, Income Statement – Extraordinary and Unusual

Items, an item must be both unusual and infrequent to be excluded from continuing

operations figures. Accordingly, certain peripheral non-systematic revenue and

expenses may be encompassed in the continuing operations figure.

Cash Flow Model – S&P Core Earnings

In November 2001, Standard and Poor’s released a white paper delineating their new

profit measure – core earnings. Similar to the Income from operations measure

presented previously, the core earnings measure starts with GAAP-based net income

adjusted for three items -

extraordinary items,

cumulative effect of accounting changes, and

discontinued operations


28 | P a g e

This figure, called “as reported earnings”, is then adjusted to eliminate the effects of

other peripheral economic items. The desired result is a periodic profit figure that will

more accurately reflect current economic profit.

The adjustments to GAAP-based earnings are summarized below.

Included in Core Earnings –

Employee stock option grant expense

Restructuring charges from ongoing operations

Write-downs of depreciable or amortizable operating assets

Pension costs

Purchased research & development expenses

Excluded from Core Earnings –

Goodwill impairment charges

Gains/losses from asset sales

Pension gains

Unrealized gains/losses from hedging

Merger/acquisition related expenses

Litigation or insurance settlements and

Items included in core earnings are those items which are put into the calculation of

core earnings if they were not already included in the firm’s as reported figure. Items

excluded from core earnings are removed from the as reported earnings figure

calculation.

Generally core earnings are less than GAAP-based earnings. Consider the comparison

for General Mills from fiscal 2007 – fiscal 2011.

Per Share Data ($)

2011 2010 2009 2008 2007

GAAP Earnings: 2.70 2.24 1.90 1.85 1.59

S&P Core Earnings: 2.62 2.09 1.44 1.65 1.52


29 | P a g e

S&P Core Earnings are lower each year. In 2009, core earnings were nearly 25% lower

than GAAP earnings.

Benefits

Proponents of core earnings figures suggest that the core figure provides a more

accurate measure of continuing earnings potential. One could infer from the Standard &

Poor’s core earnings white paper that the core earnings calculation is more reliable and

more useful than as stated earnings. By removing the item not central to operations, the

core earnings figure provides a better starting point for which to estimate future

economic earnings.

Limitations

Compared to the other profit measures presented thus far, the core earnings calculation

is the measure that best mirrors actual cash flow. However, to a lesser degree it shares

limiting characteristics with the income from continuing operations figure.

First, core earnings do not make adjustments for non-cash allocations such as

depreciation. Second, much but not all unusual or infrequent economic activity is

excluded from the continuing operations figure.


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Summary – Cash Flow Estimation

The discounted-cash flow method (DCF) is one common equity/business valuation

approach. This course summarizes a few of the more popular cash-flow proxy models

used to complete that portion of the DCF.

EBITDA

Income from Continuing Operations

Standard & Poor’s Core Earnings

Each model presented has its own set of benefits and limitations. Most importantly, no

one method is perfect. Accordingly, any discounted-cash flow valuation model that

implements one of these cash-flow proxies is subject to some level of error. Finally,

note that these cash-flow proxies are only the starting point for developing cash-flow

forecasts to use in a DCF valuation model. Once a single-period cash-flow proxy is

determined, that cash-flow estimate must then be combined with other information (e.g.

a series of historical periodic cash-flow estimates and forecasted economic changes) to

better forecast future cash-flows. It is that estimate of future cash-flows which must be

discounted by an appropriate risk-adjusted rate, to determine an asset’s value. A

discussion of these calculations is the topic of section two.

Review Questions



1. Fair value accounting is directly addressed in

A. ASC Topic 450. B. ASC Topic 220. C. ASC Topic 820. D. ASC Topic 330.


31 | P a g e

2. Examples of GAAP-based expenses that are commonly subject to estimation

include

A. cash. B. warranty expense. C. gain on publicly-traded securities available for sale. D. cash dividends payable.

3. Income from continuing operations

E. excludes amortization expense. F. is not included on GAAP-based income statements. G. can be used as a proxy for economic earnings (cash-flow). H. excludes all adjustments for voluntary accounting method changes.

4. Before calculating an asset value using the DCF method, the single period cash-

flow estimate must be

A. multiplied by two. B. combined with other data to determine future cash-flows adjusted for probable

economic changes. C. multiplied by the risk-adjusted discount rate-of-return. D. adjusted for the tax benefit associated with future depreciation charges.


32 | P a g e

Chapter 3. Discount rate.


Recognize the relationship between risk and reward


Compare commonly-used discount rate models

Risk – Reward Relationship

Previously, the reader was introduced to a simple generic discounted cash-flow (DCF)

equity valuation model:

Where:



r = required rate-of-return (i.e. risk-adjusted discount rate)

Two methods are commonly used to determine the discount rate (the denominator)

used in the discounted cash-flow equation.

Capital Asset Pricing Model (CAPM) – [a risk calculation model which calculates

equity risk by adjusting market-level risk by individual company risk as measured

by the individual equity’s relative volatility (beta).] and


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Arbitrage Pricing Theory (APT) – [Like CAPM, APT is a risk calculation model.

However, individual equity risk is calculated by combining multiple risk factors as

opposed to simply considering the equity’s beta.]

These risk estimation methods are rather complex. This section will focus on the

specifics that comprise the two theories and summarize their

components,

benefits and

limitations

in a straightforward, comprehendible manner.

Before addressing the specifics of CAPM and APT, the general risk-reward

relationship will be explored.


34 | P a g e

Note: In financial terms, “risk” is the interplay linking peril and progress.

When referring to the DCF model, risk entails the uncertainty related to the amount and

timing of projected cash-flows used in the numerator of the discounted cash-flow

projection. The goals of CAPM and APT are to accurately reflect equity risk so that the

required rate-of-return (discount rate) can be determined. Note that as the cash-flows

become more uncertain, the perceived risk increases.

By decomposing these concepts, one arrives at the following:

Risk increases as uncertainty increases. Conversely, as uncertainty decreases, risk

decreases. Required rate-of-return increases as risk increases. So, assuming cash-

flow projections are held constant, one can surmise that the value of an asset

decreases as the level of projected cash-flow become more uncertain.

This relationship is graphically illustrated by the Security Market Line (SML). The SML

displays the relationship between the relative sensitivity of a particular equity’s return

compared to market returns (beta) and that equity’s expected return. As the stock’s beta

increases the expected (required) rate-of-return also increases.


35 | P a g e

Security Market Line – Graphic Representation

Where:

E(rtn) – Expected return (i.e., required rate-of-return)

MRP – Market Risk Premium

Rf – Risk-free rate

Beta ( ) – Sensitivity to Market returns

These terms will be further discussed in subsequent sections of this course.


36 | P a g e

Uncertainty.

Merriam-Webster (www.m-w.com), suggests that the term “uncertain” is synonymous

with the term, “doubtful”. For use in valuation analysis, “uncertainty” refers to the

likelihood of receiving future cash-inflows from an investment of current cash out-flows.

One of Ben Franklin’s famous quotes, “Nothing in life is certain except death and taxes”,

could be slightly amended. Most modern American financial researchers agree that

repayment of United States treasury debt is also certain – or at least – close enough.

The interest rate on United States Treasury debt is commonly considered to be a “risk-

free” rate of return. Some disagreement lies in the term that should be used. Many

researchers use the 3-month U.S. T-bill as a risk-free (certain) benchmark. Still others

use the 10-year T-bond, 30-year T-bond or some other U.S. treasury debt instrument.

Whichever rate is chosen to represent the benchmark of “certainty”, this rate is then

theoretically considered to be the least amount that an investor will accept in exchange

for the use of their funds. An investor will expect to receive a premium over and above

the “risk-free” rate for investing in any project that is less than guaranteed to return a

certain, specific future cash flow.

Integrating this information into the DCF model, one can see that the purchase price of

U.S. treasury debt will be relatively high, resulting in a relatively low return (i.e., yield or

interest rate).

Where -

billtP = Amount paid for treasury debt instrument


37 | P a g e

Now consider a similar debt security investment with the same anticipated cash flows –

interest plus return of face value – and timeline. However, this 3-month security, known

affectionately as the, “Z-bill”, is issued by the mythical national government of Zualau –

a nearly bankrupt small island country located 200 miles southwest of Nowhere. The

following DCF valuation model displays the “Z-bill’s” higher expected risk and its related

lower valuation.

Where:

billzP = Amount paid for “risky” debt instrument

Based on the information provided thus far, one could infer that,

billzbillt PP [All else remaining the same]

In an efficient (or even semi-efficient) financial market, it can be presumed that

individuals will expect to be compensated commensurate with the risk that they are

willing to bear.


38 | P a g e

Once an effectively risk-free security is determined, then its total return can be used as

a risk-free rate-of-return proxy. The total return to be used is another area of

controversy. One must decide to use either the current yield, a historic average yield, a

moving average yield or some other return calculation. For simplicity, this course will

assume that the 3-month U.S. T-bill is an acceptable proxy for risk-free rate. The 3-

month U.S. Treasury bill has had an approximately 3.5% average yield over the past 50

years. So, this 3.5% figure will be assumed to be a reasonable estimate of the risk-free

rate for any calculations performed henceforth.

Estimating the Discount Rate

Capital Asset Pricing Model (CAPM)

Background

The CAPM method was originally developed by renowned financial researcher, William

F. Sharpe. Sharpe’s theory was initially published in the mid 1960’s; it has received

great notoriety ever since.

Sharpe postulated that an asset’s risk of future cash-flows can be calculated by

comparing the historic variability of its price to a benchmark.

Components

Specifically, Sharpe developed the CAPM to determine the risk associated with an

individual equity by comparing its price variability with the variability of the stock market

as a whole. This relative sensitivity to market returns is referred to as stock market-

related beta coefficient, stock beta or simply, beta.

Beta ( )

Beta is a measure of relative systematic risk. It is commonly used to compare the

volatility of an individual common stock’s price to the volatility of the stock market as a

whole. Normally, a widely-known stock index is used as a stock market proxy, Example

indexes include:

Dow Jones - Wilshire 5000 Total Stock Market Index


39 | P a g e

o billed as the most comprehensive United States stock market

measurement index - represents the performance of all U.S. equity

securities with readily available price data

The New York Stock Exchange Composite

o represents about 80% of the total market capitalization of all U.S publicly-

traded companies

Value Line Index

o stock market index containing 1,700 companies representing various U.S.

stock exchanges

Standard and Poor’s 500 Index – most widely-used by finance researchers

o Consists of 500 of the largest U.S. companys’ stocks – chosen

considering characteristics such as: market value, liquidity and sector

group.

These indexes are frequently used as a surrogate for the equity market as a whole. An

individual stock’s beta is determined by comparing the periodic changes in the stock

index to the periodic changes in the individual stock’s price. By definition, the stock

market as a whole has a beta equal to 1. An individual stock whose periodic price

changes more than the index has a beta of greater than 1. A stock price that is less

volatile than the index has a beta of less than 1. The chart below depicts hypothetical

periodic price changes of two individual stocks and a market index. This chart

graphically displays the volatility difference between stocks with a high beta (> 1) and

stocks with a low beta (< 1).


40 | P a g e

The CAPM first suggests that common stock equities – such as those that compose the

Standard & Poor’s 500 Index – are relatively more risky than U.S. treasury securities.

Hence, a stock market risk premium (MRP) is automatically incorporated into the value

of common stocks that are traded in an efficient market. This risk premium is generally

calculated by subtracting the risk-free rate from the stock market expected (mean)

return. Certain institutions, for example, Ibbotson Associates, specialize in providing

historical data and analysis of financial information such as current and historical:

market risk premium (MRP)

Relative Stock Volatility

-40.0%

-30.0%

-20.0%

-10.0%

0.0%

10.0%

20.0%

30.0%

40.0%

1 4 7 10 13 16 19

Time

% c

han

ge

(Vo

lati

lity

)

Market Index

1.5 beta stock

.5 beta stock


41 | P a g e

T-bill yields,

T-bond yields,

dividend yields and stock market returns, including various

- Dow Jones equity averages,

- NASDAQ information, and

- Standard & Poor’s index data.

According to Ibottson’s web site (www.ibbottson.com),

…Ibottson products and personnel will supply the data, explain and

illustrate the concepts, and provide the analytical tools you need to help

you gather grow and retain assets...

Depending on which source is used to assemble the MRP, and which figures are used

to represent the risk-free rate and the stock market return, this risk premium usually

ranges from 5 – 8% per annum. For simplicity, a 7% MRP will be assumed to be

sufficiently accurate for any future calculations presented in this course.

CAPM is mathematically described by the following equation:

market stock torelativebeta

a

fafa RMRPRR

premium risk marketMRP

rate freeriskf

R

rate) (discount asset individual anofriskaR


42 | P a g e

So, the risk of a specific asset, such as a share of a firm’s common stock, can be

determined by adding the risk-free rate to an adjusted MRP based on the individual

asset’s relative price stability.

Illustration – CAPM

Consider the following hypothetical information relating to XYZ Corporation’s common

stock equity shares.

stock beta = 1.25

Now, one only needs to link this information to the Capital Asset Pricing Model. The

solution is the risk-adjusted discount rate.

This discount rate (7.875%) would then be used as a basis for the denominator in the

discounted cash-flow model.

Pxyz = CF1/Rxyz


43 | P a g e

Once the expected future cash-flow (CF1) is properly calculated the empirical value of

XYZ’s common stock (Pxyz) can be calculated.

The following graph and table compare an asset’s price based on the uncertainty of one

particular cash-flow.

Value of $1 - Expected Cash-Flow

$-

$20.00

$40.00

$60.00

$80.00

$100.00

$120.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Required Rate-of-Return (risk)

Pri

ce


44 | P a g e

The graph and table show that as the required rate-or-return (risk) increases, the price

of the related asset decreases.

Benefits

CAPM’s primary benefit is its apparent simplicity. One only needs to determine a few

simple variables. These factors include a risk-free rate and a stock beta. Both of these

figures are widely available. Many publishers provide both current and historical U.S.

Treasury security yields including Moody’s, Standard and Poor’s and Ibottson. The

official U.S. treasury website, www.treasury.gov, also provides a wide variety U.S.

treasury securities information. Stock betas are available from a variety of sources

including financial research publishers, Standard and Poor’s and Value Line.

One may assume that use of any historical financial data in an attempt to forecast future

financial information is flawed. However, empirical evidence suggests that stock betas

tend to remain relatively constant over time. In addition, even though treasury rates

vary over time, they tend to invariably revert toward their long-term mean.

Limitations

Even though empirical evidence suggests that betas tend to remain relatively constant

over time, certain events may permanently and significantly change a firm’s future stock

beta. A few examples include:

Price $ CF risk

$ 100.00 1.00 1%

$ 50.00 1.00 2%

$ 33.33 1.00 3%

$ 25.00 1.00 4%

$ 20.00 1.00 5%

$ 16.67 1.00 6%

$ 14.29 1.00 7%

$ 12.50 1.00 8%

$ 11.11 1.00 9%

$ 10.00 1.00 10%

$ 9.09 1.00 11%

$ 8.33 1.00 12%

$ 7.69 1.00 13%

$ 7.14 1.00 14%

$ 6.67 1.00 15%


45 | P a g e

Top Management change,

Financial characteristics changes (leverage adjustments)

Industry and competitive changes

New Legislation

Another significant CAPM limitation is that a stock beta cannot be determined unless a

legitimate market for the equity exists. In other words, privately-held securities or thinly-

traded securities may not have an accurately developed stock market-related beta

coefficient.

Finally, the determination of the discount rate may be overly simplistic. The CAPM

assumes that all individual, non-diversifiable components of an individual asset’s risk

are linked to the stock market. Hence, the only adjustment to the risk-free rate is an

addition of a general market risk premium manipulated by the asset’s volatility as it

relates to the volatility of a stock market index.

Summary of CAPM

Stephen Sharpe’s Capital Asset Pricing Model was a significant advancement in the

field of finance. The CAPM is a succinct mathematical model that offers a reasonable

proxy of an asset’s risk and subsequent required rate-of-return. CAPM is a useful risk

measurement model but a model that has its limitations. Many contemporary financial

researchers feel that the CAPM is too simplistic to fully reflect all of the variables that

determine an individual equity’s risk characteristics. One, potentially more useful, risk

calculation method was developed by Stephen Ross, Richard Roll and other finance

researchers. This risk evaluation method is known as the Arbitrage Pricing Theory.


46 | P a g e

Arbitrage Pricing Model (APM)

Background

The Arbitrage Pricing Theory (APT) was originally developed by finance professor,

Stephen A. Ross. Ross’ theory was initially published in the mid-1970’s, It has received

much attention and has been the topic of great debate ever since.

The Arbitrage Pricing Theory can be expressed mathematically as a multi-factor risk

model. For precision this model will be referred to as the Arbitrage Pricing Model

(APM). This course will discuss the APT and express the APM in elementary terms by

minimizing the discussion of many of its more complex components. The specifics of

the APT can become rather convoluted. However, its basic assumptions are

straightforward. APT gets its name from one of its preliminary assumptions. That

assumption is that, in an efficient equity market, arbitrage (riskless profits) will be quickly

and effectively eliminated by knowledgeable investors. In simple terms, all available

information including:

Consensus forecasts of future developments such as anticipated

changes in interest rates,

inflation and

other economic factors

are already priced into the equity market.

Components

The APM, unlike the Capital Asset Pricing Model, does not depend upon equity-relative

stock market volatility. Arbitrage Pricing Theory implies that a particular equity risk can

be determined by summing multiple sources of macroeconomic risk. The main

components of APT can be mathematically represented with the APM:

Where:


47 | P a g e

Ri = Risk of the individual equity

rf = risk-free rate

bi = risk factors

i = weight of related risk factor (factor loading)

e = random volatility = 0 --- (presupposed by experience)

APT assumes that all random variability can be removed from a stock portfolio if the

portfolio of stock consists of enough complementary stock holding. Hence, APT

assumes that the random volatility (e) can be completely removed (e=0).

Thus, an individual stock’s total risk is the risk-free rate plus the summed and properly

weighted total of each non-diversifiable risk factor. That concept is simple enough.

However, the difficulty arises when one attempts to determine what the individual risk

factors are and - subsequently - the relative weights of those risk factors. Many

research studies have been performed in an attempt to quantify these parameters and

variables.

Over the years, Richard Roll and Stephen Ross have found that a few particular

economic factors seem to correlate to general equity market risk. These factors

included shocks in:

inflation,

yield curve shifts,

aggregate net production (GNP) and

investor confidence

Other researchers have tested similar factors in different ways.

For example, another multi-factor model was discussed in the following article,

Berry, M., Edwin Burmeister and Marjorie B. McElroy (1988) Sorting out risks using

known APT factors. Financial Analysts Journal. March-April, pp 29-41.

The authors consider the validity of using unanticipated changes in certain

macroeconomic variables including:

default risk,


48 | P a g e

the term structure of interest rates,

inflation,

the long-run expected growth rate of profits and

While it is commonly assumed that the risk factors range from such things as inflation,

unemployment and credit risk to individual company financial performance volatility, no

one universal set of factors and factor loads has been developed.

So, while the multi-factor risk theory is very impressive, it is very difficult to implement in

practice. Even so, consider the following very basic hypothetical scenario.

Illustration -

ABC Company – risk analysis using the Arbitrage Pricing Model (multi-factor risk model)

as developed using APT.

Risk Factors* and

Relative weights** (factor loading)

Risk factor 1 9.5%

Risk factor 2 8%

Risk factor 3 11.5%

Relative weight of risk factor 1 0.5



Risk-free rate 3.50%


49 | P a g e

2.035.115.3.035.08.5.035.095.035. abcR

%5.9abcR

*Required additional rate- of-return due to this generic factor

**Total weight must equal 1 (100%)

Benefits – APT/APM

The Arbitrage Pricing Theory is considered by most finance researchers to be a

theoretically sound risk determination method. Some empirical evidence suggests that

Arbitrage Pricing Models provide more accurate risk information than the Capital Asset

Pricing Model. This is because APT considers a broad range of relevant factors in

determining a particular equity’s unique risk profile. This theory also makes the

standard adjustment of adding a “benchmark” or risk-free rate to the other factors in

order to determine an individual stock’s required rate-of-return.

Limitations– APT

While the Arbitrage Pricing Theory is considered by most finance researchers to be a

theoretically sound risk determination method, APT has several practical limitations.

Most notably, the particular risk factors and the relative weights of those risk factors are

difficult if not impossible to determine. Hence, APT’s practical implementation is

difficult. In “real-life” situations, CAPM offers a much more feasible risk measurement

process.

While a list of multiple risk factor proxies seems to relate to much of the equity market

risk characteristics, there is still no definite way of knowing if these are the actual risk

factors. In other words, these factors may or may not directly represent the stock market

risk.

Also, APT does not consider risk associated with one specific firm. A few examples of

firm-specific risk factors not included in APT are changes in the particular companies -

product mix,

pricing structure,


50 | P a g e

marketing strategy and

personnel

Summary of APT/APM

APM is a multi-factor mathematical model that estimates an individual asset’s particular

risk factors and subsequently provides a proxy of that asset’s risk and required rate-of-

return.

While not perfect, Multi-factor Models, as derived from Stephen Ross and Richard Roll’s

Arbitrage Pricing Theory, are considered by many to be a significant improvement over

CAPM in the asset risk measurement field.

Comparison of APT and CAPM

Multi-factor Arbitrage Pricing Models - as derived from Arbitrage Pricing Theory - are

generally considered to be a more scientific approach to risk measurement than the

single-factor Capital Asset Pricing Model

Distinguished researchers, Eugene Fama and Kenneth French co-authored the

following article -

Fama E. and K. French, (1996) Multifactor Explanations of Asset Pricing Anomalies.

Journal of Finance 51(1) pp55-84.

This article displayed results of empirical research showing that a multi-factor (3 factors)

model provided more predictive discount rate information than a single-factor model.

This, in turn resulted in a more useful discounted cash-flow valuation model than that

provided by a single-factor beta model (CAPM).

However, other researchers have offered empirical defenses of the CAPM as compared

to APT. Consider the following article authored by notable researcher and consultant,

Jack Treynor.

Treynor, Jack L. (1993). In defense of the CAPM, Financial Analysts Journal, 49 (3),

p11-14.

In this report, Treynor suggests that CAPM and APM are very similar in their specific

characteristics. Through a series of rather complex mathematical computations, he

attempts to show that both models have similar limitation. Treynor stops short of

suggesting that the CAPM is the better model, he simply suggests that both models are

equally imperfect.


51 | P a g e

It is clear that both the APT method and the CAPM suffer from certain, related practical

and theoretical limitations. Both models assume that,

An efficient stock market exists, which means that

knowledgeable investors make rational decisions that

continuously create “fair” asset prices and

the risk-return trade-off is systematic.

Regardless of finance theorists’ varying opinions, in practice, CAPM is more commonly

used than APM because –

CAPM is considered to be more straightforward model than APT/APM and

CAPM’s necessary components are more widely understood and more

commonly available.


52 | P a g e

Summary – Discount Rate

In this section, two common risk (required rate-of-return) proxy models were discussed -

1. Capital Asset Pricing Model.

Where -

Ra = risk of individual asset

Rf = risk-free rate

MRP = market risk premium

aβ = beta relative to stock market

2. Arbitrage Pricing Theory-based multi-factor model.

Where -


rf = risk-free rate

bi = risk factors


53 | P a g e

I = weight of related risk factor (factor loading)

e = random volatility = 0

The background and specific components of each supposition were described. The

background of each section was then followed by a hypothetical illustration using the

related model. Finally, the benefits and limitations of each model were described.

After careful analysis, one can see that neither the Arbitrage Pricing Theory nor the

Capital Asset Pricing Model is irreproachable. Yet, both models were originally - and

still are considered to be - significant advancements in finance and the specialized craft

of asset valuation.


54 | P a g e

Review Questions



1. When referring to the DCF model, risk refers to the uncertainty of the _____ of

projected cash-flows used in the numerator of the discounted cash-flow

projection.

A. Accuracy and Liquidity B. Amount and Solvency C. Pros and Cons D. Amount and Timing

2. In financial terms, “uncertainty” refers to the likelihood of

A. receiving future cash-inflows from an investment of current cash out-flows. B. current cash inflows being received from future cash out-flows. C. incurring risk associated with present cash in-flows. D. obtaining current cash-inflows as a result of past cash-outflows.

3. The CAPM method was originally developed by which financial researcher?

A. William Sharpe B. Myron Scholes C. Stephen Ross D. Ken Blanchard

4. The following is used as a proxy for the U.S. stock market as a whole.

A. Dow Jones Utility Index [DJUI] B. S & P 500 Index C. Value Line Investment Survey D. TOPIX

5. A significant limitation associated with CAPM is that a stock beta cannot be

determined unless

A. a legitimate and efficient market for the asset exists. B. the risk-free rate is known. C. the MRP is known.


55 | P a g e

D. future price changes are known.

6. The CAPM differs from the APM in that the CAPM includes a specific parameter

that represents

A. inflation. B. interest rates. C. stock beta. D. factor loading.


56 | P a g e

Chapter 4. The complete model - Value equals estimated cash-flow divided by the

discount rate


Understand how assets are valued using a discounted cash flow model

The relationship presented in the graphic above is, by now, quite familiar to the reader.

It is a mathematical expression that can be interpreted to mean -

An asset’s value today (P0) equals estimated cash-flows (CF1) divided by

the discount rate (r).

As was discussed earlier in the course, value can be determined once the cash flow

projection and the discount rate are determined.

Consider the following simple hypothetical information:

Alpha-Omega, Inc

Financial Information

Cash-Flow Estimates (per share):

Using EBITDA: $1.25


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Income from Continuing Operations: $1.31

Discount Rate Estimates:

CAPM: 15%

APT: 13%

Using the above information, an analyst can proceed to calculate value using the DCF

model. Several computation methods could be employed. For instance, an analyst

could choose to use -

EBITDA and CAPM figures,

EBITDA and APT figures,

income from Cont. Operations and APT figures or

many other potential combinations of factors

Oftentimes, analysts will choose to combine multiple factor calculations to form an

arithmetic mean.

To illustrate, the parameters - “CF1” and “r” - could be calculated as follows:

CF1 = [EBITDA + Income from Continuing Operations]/2

r = [CAPM + APT]/2


58 | P a g e

Substituting the values provided in the example, the stock price (value) per share would

be determined as –

Thus, the estimated stock price per share would be $9.14.

While this example is simplistic, it adequately displays how DCF can be used to

estimate asset valuation.


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Review Questions



1. The DCF model contains a factor represented by “r” which stands for

A. Risk-adjusted discount rate. B. Cash flow. C. Net Income. D. Current Value.

2. A financial analyst could estimate an asset’s value with a DCF model by

A. using EBITDA to calculate future cash-flow proxy and CAPM to calculate the risk-adjusted discount rate.

B. using EBITDA as a risk-adjusted discount rate proxy and APT to calculate the estimated future cash-flow.

C. using Income from Operations as a cash-flow proxy and EBITDA to calculate the risk-adjusted discount rate.

D. using APT as a cash-flow proxy and CAPM to calculate the risk-adjusted discount rate.

3. One could calculate expected future cash-flows by

A. using the CAPM. B. using a figure calculated as an average of APT and CAPM. C. observing the Security Market Line. D. using a figure calculated as an average of income from continuing operations

and EBITDA.


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Conclusion

This course presented a discussion of the art and science of asset valuation, including a

brief discussion of valuation methods applications. Next, the discounted-cash-flow

model was introduced as a common asset/equity valuation method.

Where:



r = required rate-of-return (i.e. risk-adjusted discount rate)

A few of the more popular cash-flow proxy models were used to determine the

numerator.

Income from Continuing Operations,

EBITDA and

S&P core earnings

Each model presented has its own set of benefits and restrictions. No one method is

perfect. Thus, any discounted-cash flow valuation model that implements one of these

cash-flow proxies is subject to some level of fault.

Once a single-period cash-flow proxy is determined, that cash-flow estimate must then

be combined with other information (e.g. a series of historical periodic cash-flow

estimates and forecasted economic changes) to better forecast future cash-flows. It is

that estimate of future cash-flows which is discounted by an appropriate risk-adjusted

discount rate to determine an asset’s value.


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Next, the discounted cash-flow model’s discount rate (i.e., denominator) was

considered. The discount rate was shown to be inversely related to the uncertainty of

the future estimated cash-flows. Two common risk models were discussed:

1. Capital Asset Pricing Model.

Where -

Ra = risk of individual asset

Rf = risk-free rate

MRP = market risk premium


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aβ = beta relative to stock market

2. Arbitrage Pricing Theory-based multi-factor model.

Where -


rf = risk-free rate

bi = risk factors

I = weight of related risk factor (factor loading)

e = random volatility = 0

The background and specific mechanism of each supposition was explained. The

background of each section was followed by a hypothetical illustration using the related

model. Finally, the advantages and disadvantages of each model were described.

It was determined that neither the Arbitrage Pricing Theory nor the Capital Asset Pricing

Model was perfect. However, both models are generally considered to be significant

asset valuation tools.

A presentation of the interchange between the cash-flow estimation methods and the

discount rate proxy models showed how the figures can be incorporated into the DCF

formula to determine a reasonable estimate of an asset’s value.


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Glossary

Arbitrage Pricing Theory (APT) – Risk calculation model whereby individual equity risk

is calculated by combining multiple risk factors

Beta – Relative systematic risk measure

CAPEX – Capital expenditures

Capital Asset Pricing Model (CAPM) - A risk calculation model which calculates equity

risk by adjusting market-level risk by individual company risk as measured by the

individual equity’s relative volatility

Discount rate – Rate at which future cash flows are adjusted to present value

EBITDA – Earning before interest, taxes, depreciation and amortization

Economic profit – Represent sustainable cash flows

Fair Market Value (FMV) - Amount mutually and voluntarily agreed upon by both buyer

and seller.

Market comparison method – Valuation method that compares relative firm values

Market Risk Premium (MRP) – Expected additional return from stocks that relate to the

stocks’ additional risk.

Required rate-of-return – Return necessary to compensate for the related risk.


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Index

Arbitrage Pricing Theory, 12, 33, 46, 47, 50,

51, 53, 54, 62, 64

beta, 33, 34, 35, 38, 39, 42, 45, 46, 51, 53, 62,

64

CAPEX, 24, 64

Capital Asset Pricing Model, 33, 38, 42, 46,

47, 50, 51, 53, 54, 61, 62, 64

Discount rate, 1, 10, 11, 12, 14, 32, 34, 42, 43,

46, 51, 56, 60, 61, 63, 64

EBITDA, 17, 19, 20, 23, 24, 30, 57, 58, 60, 64

Economic profit, 28, 64

Fair Market Value, 7, 8, 64

Market comparison method, 7, 8, 64

Market Risk Premium, 35, 65

Required rate-of-return, 11, 32, 34, 35, 46, 50,

51, 53, 60, 65


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Review Question Answer Feedback

Introduction

1. Answer Feedback:

A. The double entry accounting equation is defined as “Assets = Liabilities + Shareholders’ Equity.

B. A = L + SE C. This is a component of the liabilities definition. D. Assets result from PAST transactions or events. 2. Answer Feedback:

A. Assets = Liabilities + Shareholders’ Equity. Hence, “Assets = $0 (Liabilities) + Shareholders’ Equity” is equivalent to “Assets = Shareholders’ Equity”.

B. If total liabilities are greater than shareholder equity then liabilities are not equal to $0. If liabilities are not equal to $0, then assets cannot equal shareholder equity per the accounting equation: Assets = Liabilities + Shareholders’ Equity.

C. If liabilities are not equal to $0, then assets cannot equal shareholder equity per the accounting equation: Assets = Liabilities + Shareholders’ Equity. Assets = Liabilities + Shareholders’ Equity so if Liabilities = 0, the Assets = Shareholders’ Equity.

D. Assets = $0 (Liabilities) + Shareholders’ Equity” is equivalent to “Assets = Shareholders’ Equity”. The firm could own current assets and/or noncurrent assets

Chapter 1. Valuation – Background

1. Answer Feedback:

A. Valuation methods are often used for estate planning. B. Valuation methods are often used for divorce litigation. C. Valuation methods are often used for patent litigation. D. While it is conceivable that valuation methods may be used in certain types of

compliance auditing it is common for valuation methods to be used in estate planning, divorce litigation and patent litigation.

2. Answer Feedback:

A. Capital Asset Pricing Model - often used to determined discount rate B. A version of the DCF valuation model C. Arbitrage Pricing Model - often used to determined discount rate


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D. Neither I (the course author) nor anyone else with my surname has yet to invent a revolutionary valuation model.

Chapter 2. Future cash-flows

1. Answer Feedback:

A. ASC Topic 450 addresses contingencies. B. ASC Topic 220 addresses comprehensive income. C. ASC Topic 820 addresses fair value. D. ASC Topic 330 addresses inventory.

2. Answer Feedback:

A. Cash is valued at its face amount by definition. B. Expenses related to warranty offers should be recognized in the same period that

the related product or service is sold. Hence, an estimate of future warranty cost is necessary.

C. This is a gain not an expense. D. This is a liability previously determined by the board of directors – it is not subject

to estimation.

3. Answer Feedback:

A. This method includes amortization expense. B. This line item is included on GAAP-based income statements. C. Income from continuing operations can be used as a proxy for economic

earnings (cash-flow) because it excludes certain “non-continuing” items. D. Voluntary accounting method changes are accounted for retroactively.

4. Answer Feedback:

A. No specific cash-flow multiple is an assumed part of the DCF method. B. The initial cash-flow estimate may need to be adjusted for probable future

economic changes. C. Once the future cash-flows are determined then they are divided by the discount

rate. D. Tax-related cash-flow are already considered in the initial calculation of cash-

flows.

Chapter 3. Discount rate determination

1. Answer Feedback:


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A. Uncertainty and level of accuracy are synonymous – liquidity is a risk factor but it is not related to the amount and timing of future cash flows.

B. Amount is correct but solvency is a term referring to a firm’s ability to pay debt. C. Risk relates to uncertainty of the amount and timing of project cash flows not the

pros and cons. D. Risk relates to uncertainty of the amount and timing of project cash flows, not

the pros and cons.

2. Answer Feedback:

A. “Uncertainty” refers to the likelihood of receiving future cash-inflows from an investment of current cash out-flows.

B. “Uncertainty” refers to the likelihood of receiving future cash-inflows from an investment of current cash out-flows.

C. Risk is equivalent to uncertainty”. Also, “uncertainty” is related to future cash-flows, not current cash-flows.

D. “Uncertainty “related to future cash-flows not current cash-flows.

3. Answer Feedback:

A. William Sharpe is credited for developing the CAPM and publishing his findings in the mid-1960’s.

B. Myron Scholes is credited for developing the Black-Scholes options valuation model, not the CAPM.

C. Stephen Ross was not involved is developing the CAPM. D. Ken Blanchard is a notable business management theorist. He is not a finance

researcher.

4. Answer Feedback:

A. DJUI is an index of utility stocks only. It is not considered to be a proxy for the stock market as a whole.

B. S & P 500 Index is a measure including a broad range of equities. The S & P 500 Index is commonly used as a proxy for the U.S. stock market as a whole.

C. Value Line Investment Survey is an equity research publication not an index. D. TOPIX is an index of Japanese equities not U.S. equities.

5. Answer Feedback:

A. A legitimate/efficient market for the asset needs to exist in order to calculate the stock’s beta coefficient.

B. The risk-free rate does not determine beta. C. The MRP does not determine beta. D. Future price changes are never known – they can only be predicted or estimated.


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6. Answer Feedback:

A. The CAPM does not include a separate parameter that represents inflation. B. The CAPM does not include a separate parameter that represents interest. C. The CAPM includes a separate parameter that represents beta. The APM does

not include this parameter. D. The CAPM does not include a separate parameter that represents factor loading

since only one factor (beta) is considered.

Chapter 4. The complete model - Value equals estimated cash-flow divided by the

discount rate

1. Answer Feedback:

A. The “r” stands for risk-adjusted discount rate. B. Cash flow is represent by CF1 C. Net Income is not used in the DCF formula D. Current Value (Price) is represented by “P0” in the model

2. Answer Feedback:

A. An asset’s valuation can be calculated using EBITDA to calculate future cash-flow proxy and CAPM to calculate the risk-adjusted discount rate.

B. An asset’s valuation cannot be calculated using EBITDA as a risk-adjusted discount rate proxy and APT to calculate the estimated future cash-flow because EBITDA is a cash-flow estimate and APT is a discount rate estimate.

C. An asset’s valuation cannot be calculated using Income from Operations as a cash-flow proxy and EBITDA to calculate the risk-adjusted discount rate because EBITDA is a cash-flow estimate not a discount rate estimate

D. An asset’s valuation cannot be calculated using APT as a cash-flow proxy and CAPM to calculate the risk-adjusted discount rate because APT is used to calculate the risk-adjusted discount rate, not the cash-flow estimate.

3. Answer Feedback:

A. One could NOT calculate expected future cash-flows by Using the CAPM because the CAPM is used to calculate the discount rate not the expected cash-flow amount.

B. One could NOT calculate expected future cash-flows by sing a figure calculated using an average of APT and CAPM because the CAPM and APT are used to calculate the discount rate not the expected cash-flow amount.


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C. One could NOT calculate expected future cash-flows by observing the Security Market Line (SML) because the SML displays the relationship between risk and reward. The SML does is not used to calculate expected future cash-flows.

D. One could calculate expected future cash-flows by using a figure calculated using an average of income from continuing operations and EBITDA.


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CPE Exam

Instructions: Please select the single best answer and transfer it to the preceding

sheet.

1. Assets are best defined as

A. probable past obligations of a firm. B. probable future economic benefits C. liabilities minus equity. D. equity – expenses.

2. Fair market value can be defined as

A. an amount mutually and voluntarily agreed upon by both buyer and seller. B. sales price of thinly-traded stock. C. an amount determined by one person. D. net book value.

3. The market method of valuation is best described by which of the following?

A. Trading prices of heavily-traded stock B. Wholesale store price index C. Discounted valuation of future cash-flows based on a market-adjusted discount

rate D. Deducing the value of one firm by comparing it to a similar firm in the same

industry

4. The DCF valuation method considers ______ and their associated risks.

A. estimated future cash-flows B. historical cash-flows C. current net assets D. discontinued operations

5. The DCF valuation method considers estimated future cash-flows and the

______ associated with the related equity shares.

A. risk B. dividends C. expenses D. EBITDA


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6. Income from continuing operations

A. includes all expenses related to discontinued operations. B. does not include depreciation. C. does not include effects of extraordinary items. D. includes an adjustment for permanent working capital increases.

7. Which cash-flow proxy method adds back depreciation to GAAP-based net

income?

A. Continuing Operation B. EBITDA C. Direct Equity D. Both b and c

8. One difference between the “Income from Continuing Operations” method and

the EBITDA method is that the “Income from Continuing Operations” method

does not consider

A. depletion. B. risk-flow assumptions. C. CAPEX. D. the randomness of depreciation allocations.

9. The income from continuing operations method adjusts GAAP-based net income

for all of the following except

A. depreciation. B. discontinued operations. C. extraordinary items. D. depreciation and extraordinary items.

10. Valuation methods are often used during

A. party planning. B. compliance auditing. C. patent litigation. D. marriage counseling services.


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11. The general Discounted Cash-Flow valuation model can be expressed by which

of the following mathematical models?

A. i jrx

divdiv 12

B. r

CFP o0

C. r

CFP 1

0

D. r

divCF 1

0

12. The market comparison method of valuation is best described by which of the

following statements.

A. Trading prices of heavily-traded stock. B. Wholesale store price index compared to retails prices. C. Discounted valuation of future cash-flows based on a market-adjusted discount

rate. D. Deducing the value of one firm by comparing it to a similar firm in the same

industry.

13. When referring to the DCF model, risk refers to the level of uncertainty of _____

cash-flows used in the numerator of the discounted cash-flow projection.

A. GAAP-based B. historical C. projected future D. known

14. The discount rate [i.e., required rate-of-return] increases as

A. economic profits increase.

B. risk increases.

C. uncertainty decreases.

D. certainty of cash-flows increases.

15. The return of a short-term U.S. treasury security, such as the 3-month T-bill, is

often used as a proxy for


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A. investor confidence. B. real estate values. C. risk-free rate of return. D. market risk premium.

16. The Security Market Line employs ___as a proxy of the sensitivity of equity’s

returns compared to market returns.

A. return B. theta C. sigma D. beta

17. Which researcher is credited with developing the Arbitrage Pricing Theory?

A. William Black. B. Myron Scholes. C. Stephen Ross. D. W. F. Sharpe.

18. The ___ uses beta as a proxy for a security’s relative risk.

A. APT B. Security Market Line C. SLM D. DCF

19. The CAPM can be modeled as

A.

faifaRMRPxRR .

B. r

CFP 1

0

.

C.

fafaRMRPRR

.

D.

fafaRMRPRPRICE

.

20. The Arbitrage Pricing Model (APM) includes a parameter “Rf”. This parameter

characterizes

A. risk factors. B. the numeric value zero. C. a risk-free rate.


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D. a stock market related beta coefficient.

21. The CAPM includes a parameter “ ”. This parameters represents

A. dividend payments. B. a numeric value between zero and one. C. discounted cash-flows. D. a stock market related beta coefficient.

22. One limitation of the Arbitrage Pricing Theory is that it

A. does not use stock market-related beta. B. includes too many risk factors. C. does not include a risk-free rate component. D. does not identify particular risk factors or relative factor loads.

23. The CAPM resembles the APM in that both include

A. adjustments to account for preferred stock returns. B. an adjustment to account for a risk-free rate. C. an adjustment to account for the stock market-related beta. D. multiple risk factors.

24. In practice, CAPM is more commonly used than APT/APM because

A. CAPM’s component values are more commonly available. B. APM’s necessary components are better understood and more widely available. C. APM is less accurate risk determinant than CAPM. D. CAPM considers an individual risk characteristic and factor loadings.

25. APT proposed a ____ risk proxy model.

A. single-factor B. constant C. multi-factor D. redundant

26. The Arbitrage Pricing Model is illustrated by which of the following equations?

A. erbrbrbrbc i nfi ni nfiifiifii ...

32211 .

B. erbrbrbrbrR i nfi ni nfiifiififi ...

32211 .


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C.

fafaRMRPRR

.

D. r

CFP 1

0 .

27. The model: fafa

RMRPRR represents

A. the SML B. the CAPM C. the APT D. the Dividend Growth Model

28. Which discount rate estimation model is considered to be virtually faultless?

A. No discount rate model is without fault. B. APM/APT. C. Black-Scholes. D. Arbitrage Pricing Theory.

29. The DCF model contains a factor represented by “CF1” which stands for

A. Risk-adjusted discount rate. B. Cash flow. C. Net Income. D. Current Value.

30. One could estimate an equity price using DCF by

A. using EBITDA as a risk-adjusted discount rate proxy and APT to calculate the estimated future cash-flow.

B. using EBITDA to calculate future cash-flow proxy and CAPM to calculate the risk-adjusted discount rate.

C. using Income from Operations as a cash-flow proxy and EBITDA to calculate the risk-adjusted discount rate.

D. using APT as a cash-flow proxy and CAPM to calculate the risk-adjusted discount rate.

31. An expected risk-adjusted discount rate could be calculated by taking the _____

of the discount rate as calculated by the APT and the EBITDA.

A. average B. sum


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C. difference D. covariance

32. An expected risk-adjusted discount rate could be calculated by taking the

average of the ________ as calculated by the Arbitrage Pricing Model and the

Capital Asset Pricing Model.

A. discount rate B. inflation rate C. risk-free rate D. prime rate

33. Earnings manipulation is inherent in

A. management reports B. the CAPM C. accrual-based financial statements D. dividend payment policy

asset v discounted c flow - coursewebs

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