MBA 819: FINANCE PART CLEMSON UNIVERSITY

VALUATION

Overview

At this point we want to draw together the various discussions that we have had up to this

point in the semester. No doubt, much of the discussion seems disjoint, even inscrutable.

However, after we draw it together in the context of valuation, the pieces, while still obscure in

certain ways, should be more meaningful.

Project valuation is one of the most practical tools of the financial analyst. It is virtually a

trade, like real estate appraisal. Project valuation typically involves estimating what the stock

price of a business venture would be if it were priced by the market. Sometimes this is important

as a way of determining managerial compensation; sometimes it is important in assessing the

IPO price of a spill off; sometimes it is important in deciding whether to undertake a new

venture; and sometimes it is important in adjudicating a tort claim. It is the last that we will use

as an example.

The case we will explore involved the bust-up of the Singer Company. Singer started as a

sewing machine company. However, over the years it became a highly diversified manufacturing

firm. The company made rifles during WWII, it had numerous small machine plants here in SC

that made drills and vacuum cleaners. And, of course, it continued to make sewing machines.

In 1988, Singer was taken over by a corporate raider, Paul Bilzerian. 1 Bilzerian sold the

Singer name to James Ting, a Hong Kong businessman. Ting sold Singer Furniture Company

back to Bilzerian. A dispute arose over payments that Bilzerian was supposed to make to Ting.

Ting sued to regain control of the company. A question arose as to its value.

The Risk and Cash Flow

What we have discovered over that last month and a half is that the stock price of a

company is based on the Discounted Cash Flow that the firm is expected to enjoy over the

foreseeable future. The familiar formula is:

∞

CashFlowt

P = ∑ t

( 1+

r)

t=

0

There are two elements of the DCF equation. One, the cash flows must be forecast. Call

these ɵ C t . Two, the appropriate discount rate must be chosen. Call this ɵr .

Market participants are constantly working to evaluate the price of each stock to

determine whether it correctly reflects its fundamental DCF value. Insiders and information

gatherers acquire knowledge about the cash flows that a company can anticipate. These people

study markets and products, managerial decisions, and corporate policies. From this study, they

make informed opinions about the future cash flows of a company.

Uninformed investors are investors with no special knowledge about the future cash

flows of a company. They know what is publicly available and do not spend resources to

discover new information. They are risk averse. They form portfolios of assets in order to

achieve the highest possible utility by trading off return for lower risk. Portfolio diversification

1 Bilzerian gained notariety by going to jail for illegal stock trading. The SEC tried to pry the gains he made in the

Singer deal and others away from him. He declared bankruptcy in Florida and kept his multimillion dollar home. It

is claimed that he stashed a good bit out of the country.

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 1

MBA 819: FINANCE PART CLEMSON UNIVERSITY

has the effect of lowering risk holding return constant. In the process of choosing among assets

to hold in their portfolios, uninformed investors minimize variance by holding many, many

different assets. In the limit, they hold all assets. The amount of each asset that they hold is based

on the correlation of the return of that asset to all other assets. In choosing among assets,

investors force the returns of each asset to obey the Capital Asset Pricing Model. That is, the

CAPM identifies the expected return to each asset:

[ E( r ) − r ] = β ⋅[ E( r ) − r ]

i f i m f

This expected return is the rate of return at which the firm's cash flows are discounted.

The expected market return minus the risk free is called the Equity Risk Premium (ERP) of

which we spoke in an earlier lecture. Thus, we can write the formula that identifies the discount

formula as:

E( r ) = rɵ = r + β ⋅ ERP

i f i

This gives us three variables that we must assign values to in order to determine the

proper discount rate. They are: the risk free return, the equity risk premium, and the beta for the

project that we are evaluating.

CAPM and Valuation

A careful student might ask at this point, "Is the price of an asset fully identified in terms

of its expected future cash flows discounted at the appropriate risk adjusted rate?" The CAPM

says, "Yes!"

The Capital Asset Pricing Model says that stocks are priced according to their expected

cash flows and the covariance of these cash flows with the expected cash flows of other assets.

Hence there are only two pieces of the puzzle as shown in (1)⎯Cash Flows and r. The

appropriate r comes from (2) based on the estimation of β given in (3). No doubt, the CAPM is

imperfect empirically. However, it is complete and logically consistent.

Stock prices change everyday. The stock market moves almost everyday. The stock

market is the aggregation of all of the securities that are traded. We sometimes think of the stock

market at the Dow Jones Industrial Index, which just 30 large stocks. The market is often

identified as all NYSE stocks. At the end of 1996, there were 2777 stocks traded on the NYSE.

Sometimes well reference the market by the S&P 500, which is an index of the 500 largest

stocks, mostly NYSE. There were 8763 stocks reported by CRSP trading on the NYSE, AMEX,

and NASDAQ at the end of 1996.

The stock market is an index of all of these securities. Movement in the market is the

aggregated change in the price of each of these securities. Each security changes because of

revisions in the expectation concerning its cash flows and/or the correlation of its cash flows

with the cash flows of all other securities. In a simple characterization of the market, there are

informed traders who buy and sell assets based on new information about expected cash flows.

On the other hand, there are uninformed traders who buy and sell to rebalance their portfolios. If

all investors held all assets in a value-weighted portfolio, there would be no need to rebalance.

However, investors hold imperfectly diversified portfolios that are comprised of only a subset of

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 2

MBA 819: FINANCE PART CLEMSON UNIVERSITY

securities. As a consequence when new information about cash flows changes the value and the

variance of the assets in a suboptimal portfolio, investors must rebalance. 2

The Efficient Market Hypothesis says that the instant that information is known, it is

impounded in the price of securities. It is the case that stock prices vary more than the underlying

cash flows, when we observe them in hindsight. This is sometimes referred to as "excess

volatility." The cause of this will become the focus of future inquiry.

The Risk Free and Risk Premium

We talked at some length about two of three ingredients in the formula for the discount

rate, the risk free return and the ERP. However, it is useful to renew this discussion in particular

reference to valuation.

Cash flows come over time, and therefore they must be adjusted to reflect their current or

present value. The crucial issue is that the discount rate should match the riskiness of the cash

flows expected to accrue to the project. If the future cash flows were known with certainty, the

proper discount rate for a firm with a long life would be the U.S. Treasury long bond rate (that is,

an almost risk free investment). Since the nominal cash flows resulting from purchasing a U.S.

Treasury bond are expected to occur with a probability close to 1, this rate measures the risk free

portion of the discount rate. This is the time value of money component of the overall discount

rate. Furthermore, we can take inflation out the calculation by using the TIPS yield. Thus, we

have an almost perfect representation of a truly riskless investment. This would be correct rate to

use if the cash flows from the venture under consideration were to accrue with certainty.

However, for firms, cash flows are not expected to occur with absolute certainty.

Consequently, a risk premium must be added to the risk free rate in order to account for the

imbedded uncertainty. This risk premium will vary from firm to firm and across industries.

Computer software companies have high discount rates whereas public utilities (traditionally)

have low rates. Variation across firms reflect variation in risk.

The overall level of risk is measured by the amount that more risky securities outperform

less risky ones. The most extreme dichotomy that draw is between all risky securities and U.S.

Treasury bonds. While U.S. bonds have not been a perfect measure of the riskless asset, they

come the closest. This difference, then, is our best measure of the ERP.

As we discussed earlier, there is some reasonable question about what the true level of

the ERP is. The historical difference between the market return and government bond return is

around 8 percent. This is arguably too high for several reasons. If we take the historical return on

risky securities and subtract the TIPS yield, which would account for full protection against both

default and inflation, then we get an ERP of around 6 percent. However, to fully rationalize the

current level of the market, an ERP of 3 is required. While we can't be absolutely sure about the

correct ERP, the range seems reasonably set at 3 to 6 percent.

The Estimation of Beta

The theory says that stocks are priced linearly on the basis of the beta applicable to each

security. Beta is a linear multiplier. Beta comes from the CAPM market model

r = α + β r + ε

it i i mt it

2 Of course, if new information alters the correlation of assets with the market, rebalancing is also required.

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 3

MBA 819: FINANCE PART CLEMSON UNIVERSITY

In the market model, the parameters α and β are the discount rate component of the stock

price and ε is the information component. If the company has good management or a unique

computer system or a crook for a bookkeeper, all this goes in epsilon. For instance, at the instant

that the market recognizes that a firm's management is better than it was heretofore supposed, the

stock price jumps and for that instant, ε is positive. To the extent that the company is in textiles

which vary with auto sales, this affects the rate at which the firm's cash flows should be

discounted and this is captured in β.

The theory says is that high betas have greater risk than low betas. In this context, one

would expect computer software firms to have higher betas than utilities. This is true and is an

explanation of why investors demand higher returns for holding computer software stocks than

utilities. To provide a brief example, consider AMR, the parent of American Airlines. AMR has

a beta of about 1.3. This beta is based on the historical relation between movements in AMR

stock and movements in the overall market. Since the beta exceeds one, it suggests that holding

AMR stock is riskier than holding a portfolio of stocks that resemble the S&P 500. The

interpretation of beta is that when the market increases 10 percent, AMR stock is expected to

increase on the order of 13 percent. However, when the market declines by 10 percent, the price

of AMR is expected to fall by 13 percent.

When we forecast the expected return for a particular stock like AMR that is publicly

traded we can use the information contained in the trades to asset beta. We estimate the market

model as in (2) to give us beta. Publicly traded firms are being evaluated all the time in terms of

their price relative to the two components of the DCF formula. The current price of an asset can

be wrong because its expected cash flows are in error or because the discount rate at which these

cash flows are weighted is in error.

The market model is directly estimated using Ordinary Least Squares linear regression. 3

That is, OLS estimators from

r = αɵ + β ɵ ⋅ r

i i i m

give us beta. All we need are data for returns on the i th asset and returns on the market. We run

the regression and get beta. This estimate of beta is historical. Hence, it is an estimate of the true

beta that theory says is used to set the price of common stock for the i th firm. When estimating

beta, we need to be cognizant of this. We should use as much data as is available subject to the

rule that as the business interest of the firm changes, its beta will change.

The proper market index to use in estimating beta is open to question. The true market

portfolio is unavailable. The theory says that investors hold a portfolio of all risky assets.

Because this is too costly, inefficient subsets are created. (This was the content of the discussion

of lecture 6.) For practical purposes, there are three main candidates for rm: the CRSP market

index of all securities covered by CRSP (NYSE, Amex, Nasdaq); the S&P 500; or the Dow

Jones Industrials. The DJ is the worst. It is only 30 stocks. S&P 500 is ok. It is the 500 major

stocks in the economy value weighted. The CRSP index comes both equally and value weighted.

Theory speaks to the value weighted. However, in practice, it is most common to see the equally

weighted index used. I suspect this has to do with the problem of inefficient portfolios. It would

be interesting to see if a composite index could be created from mutual funds that cover risky

ventures outside of those measured by U.S. traded common stocks.

3 There is no theoretical concern about autocorrelation because efficient markets says that autocorrelation wold

imply a trading rule that would be arbitraged away.

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 4

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Comparable Firms

When we are valuing assets that are not publicly traded, we must use other means to

estimate the value of beta that will be used in the CAPM formula to determine the proper

discount rate. The best way to do this is to identify a set of comparable firms. This is true

because the stock market has already assigned an unbiased value to the future cash flows

expected to accrue to these firms. In its pricing of these assets, the market has embodied its

evaluation of the riskiness of the cash flows in these types of enterprises.

The selection of the comparable or “twin” firms is based on the asset, firm or project

under consideration. For example, assuming that Time Inc. applied valuation models in its 1989

acquisition of Warner Communications, the comparable firms would be entertainment firms

similar to Warner rather than publishing entities similar to Time Inc.

For our case study, we must come up with comparable firms for Singer Furniture

Company (SFC). The appropriate approach in identifying comparable firms to SFC is to use a

portfolio of publicly-traded firms that focus primarily on manufacturing furniture. These

comparable firms could be considered twins of Singer Furniture Company. Value Line classifies

firms by industry so the firms that it identifies are publicly traded furniture manufacturing

enterprises that satisfy this criterion.

Value Line Investment Surveys tracks widely-followed firms that are listed on the major

stock exchanges. In all, Value Line covers around 1,700 firms in nearly 100 Value Line

designated industries. Value Line's furniture/home furnishings industry contains 9 firms which

engage in various types of furniture manufacturing during the period 1991 and 1992. The list of

the 9 firms in this Value Line industry category are shown at the end of this document with

details their business activities.

To estimate the discount rate for Singer Furniture Company, the betas from the nine

comparable firms are used. A simple calculation of the beta for a furniture company is to average

the returns of these 9 firms over some period, say, 5 years and regress this equally weighted

portfolio return on the market return. The comparable firms are discussed below:

COMPARABLE FIRMS

IN THE VALUATION OF SINGER FURNITURE CO.

BASSETT FURNITURE INDUSTRIES, INC. manufactures a wide range of bedroom, dining room, and living

room furniture. Also makes various lines of occasional chairs, tables, wall units, upholstered furniture, mattresses

and box springs. Plants are located primarily in Virginia, North Carolina, and Florida. Products are sold to dealers

through commissioned sales representatives. Sales to J. C. Penney accounted for 13% of total 1992 sales. 1992

depreciation rate: 4.3%. Estimated plant age: 17 years. Has about 8,100 employees; 2,400 shareholders. Insiders

own 2% of common.

FLEXSTEEL INDUSTRIES, INC. manufactures chairs, sofas, loveseats, sofa-sleepers, and recliners for home

markets (64% of 1992 sales). Distribution through approximately 3,000 furniture retailers and department stores

plus several national chains. Also makes seating products for the recreational vehicle field (28%), where it is a

leading supplier to the van conversion business. Commercial seating division (8%) established in 1986. Operates 8

plants in 8 states. 1992 depreciation rate: 6.45%. Estimated plant age: 10 years. Average number of 1992 employees:

2,040; 1,600 shareholders. Insiders own 24% of the stock.

HON INDUSTRIES INC. is one of the largest manufacturers of metal and wood office furniture in the United

States. Sells a complete product line, including file cabinets, desks, chairs, wall systems and credenzas. Major

emphasis is on the mid-priced range. Also sells computer-related products and manufactures factory-built fireplaces

for homes. Sold Prime-Mover, 12/88. Bought Gunlocke, 10/89. 1991 deprecation rate: 6.4%. Has about 5,600

employees, 4,466 shareholders.

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 5

MBA 819: FINANCE PART CLEMSON UNIVERSITY

KIMBALL INTERNATIONAL, INC. manufactures and markets office furniture and seating under the Kimball,

National, and Harpers brands; office furniture systems (Cetra); hospitality, healthcare and reproduction furniture

(Kimball); and pianos (Bosendorfer and Kimball). Kimball also manufactures for other end-users electronic

assemblies, TV and audio cabinets, home furniture, molded plastics carbide, cutting tools and metal stampings. 1992

depreciation rate: 8.0%. Estimated plant age: 6.9 years. Has about 7,600 employees; 635 Class A shareholders,

2,525 Class B shareholders. Insiders own about 32% of Class A, 21% of Class B.

LADD FURNITURE INC. is a leading manufacturer of wood, metal, and upholstered furniture for bedrooms, dining

rooms, living rooms, and kitchens, mainly in the low-medium to high-medium price range. Also makes plywood

furniture components and runs a trucking fleet. Acquired American Furniture 10/86; Pennsylvania House and Jordan

Brown 7/89. Has 22 manufacturing plants and 4 warehouse facilities is seven states and Mexico. 1991 depreciation

rate: 10.9%. Has about 6, 340 employees, 970 share holders. Insiders own 38% of common; Brinson Partners, Inc.

5.1%

LA-Z-BOY CHAIR CO. is the largest manufacturer of reclining chairs in the United States. Other residential

products include occasional tables, wall units, dining room and bedroom furniture. Also sells furniture to offices and

healthcare businesses. Acquired La-Z-Boy Canada Ltd., in '79; Burris Industries, '85; RoseJohnson, '85; Hammary,

'86; Kincaid, '87. 1991 depreciation rate: 8.0%. Estimated plant age: 6 years. Has about 8,150 employees; 8,080

shareholders. Directors and officers own 13% of stock; Monroe Bank & Trust (as trustee of a number of revocable

and irrevocable trusts), 24%.

LEGGETT & PLATT, INC. manufactures spring assemblies for mattresses, boxsprings, and upholstered furniture;

mechanical assemblies for action chairs and convertible sofas; polyurethane foam; bases for furniture; and

diversified specialty products. The company also makes and sells sleep-related finished furniture and carpet

cushioning materials. 1991 sales breakdown; bedding components: 31% of total, furniture components: 24%,

finished products: 22%. Has about 10,400 employees; 5,540 shareholders of record. 1991 depreciation rate: 8.7%.

Estimated plant age: 5 years.

HERMAN MILLER, INC. is a leading producer of "open space" free-standing modular office partitions and

furniture for offices, institutions, health care facilities, and laboratories. Has 14 plants in the United States, 2 in

United Kingdom. Also licenses manufacturing rights in Japan. About 90% of sales are through independent dealers.

Foreign sales: 17% of total. R&D: 2.5%. 1992 depreciation rate: 7.4%. Estimated plant age: 6 years. Has about

5,490 employees, 13,000 shareholders. Officers and directors own 3.6% of stock; Ariel Capital Management, 7.8%;

Trimark Investment, 9.8%; Reich & Tang, 7.3%.

SHELBY WILLIAMS INDUSTRIES, INC. designs, manufactures, and distributes furniture, primarily to the hotel

and food service industries. Also designs and manufactures furniture for health care, university, and office facilities;

and produces wall coverings and distributes textiles for furniture. Acquired preview Furniture Corp. 5/85; Sellers &

Josephson, Inc. 6/86; chair operations of Thonet 2/87; Pacific Home furnishings 8/88. 1991 depreciation: 6.1%

Estimated plant age: 6 years. Has about 1,602 employees, 3,200 shareholders.

The Effect of Capital Structure on Beta

Our inquiry thusfar has led us to the conclusion that the expected return to an asset is

equal to the risk free return plus beta times the risk premium, where the risk premium is the

expected return to the market minus the risk free return. This is the simple CAPM analysis, and

while there is some empirical slippage, these, like black-holes in space, do not greatly affect our

everyday lives. By this I mean that CAPM is still a very useful tool in understanding the way

financial markets work and in practicing financial economics. In the practice of financial

economics, there is one detail that we have yet to fully explore. That is the relationship between

beta and capital structure.

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 6

MBA 819: FINANCE PART CLEMSON UNIVERSITY

The typical U.S. corporation has debt in addition to equity. While shareholders are the

residual claimants and thus own the equity, they cannot claim all the value of the corporation as

debt holders have a fixed claim. The total value of the firm is

V = D + E,

where V is total firm value, D is debt, and E is equity. As we learned in the last lecture, the debt

to equity ratio across all corporations is somewhere around .5, but it has a lot of variation.

The discount rate for a firm depends on the business risk of the firm's overall cash flows. The

risk of common stock (as proxied by the estimated value of beta) reflects the business risk of the

future cash flows and the assets held by the firm. In addition, to the extent that the firm issues

debt to finance its investment opportunities, shareholders bear financial risk as well. The more

that a firm relies on debt financing, the riskier its common stock. That is, borrowing creates

financial leverage, and hence risk. In CAPM jargon, as a firm increases its debt/equity ratio, its

beta goes up correspondingly.

The beta for the business risk inherent in a venture, company, corporation, etc., can be

called the "asset" beta. The beta for the equity portion of a common stock corporation is simply

the equity beta. The relationship between the asset beta and the equity beta is:

E

β = β + β

D + E

a e d

D

D + E

It is common though not entirely accurate to assume that the debt beta is zero. In this simplifying

case, the equity beta is equal to the asset beta times one plus the debt-equity ratio.

L

NM

D

βe = βa

+ 1

E

The implication is that for a group of firms, for instance, firms whose business is almost

entirely in electric utility service, the equity betas should vary based on the debt-equity ratio.

That is, the higher the debt-equity ratio, the higher the observed equity beta. Similarly, we can

calculate the underlying asset beta by weighting the observed equity and debt betas by their

respective capital structure proportions.

Calculation of the Asset Beta

To estimate the discount rate for Singer Furniture Company, the betas from the nine

comparable firms were used. Two methods were used to obtain equity betas for the nine

comparable firms. First, Value Line Investment Surveys reports betas for these companies.

Second, betas for these nine stocks were calculated using monthly stock returns over the 1987-91

period. The Value Line betas come from the December 31, 1991 issue and are shown in the first

column below. They range from .65 to 1.1. The calculated betas are displayed in the second

column. They are quite similar to the Value Line betas with few exceptions. The two different

estimates are averaged in the third column.

Table 1

Betas in the Furniture Industry

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 7

O

QP

MBA 819: FINANCE PART CLEMSON UNIVERSITY

Beta Reported

in Value Line

Beta Estimated

From Monthly

Stock Returns

BASSETT FURNITURE INDUSTRIES, INC. 0.80 0.72 0.76

FLEXSTEEL INDUSTRIES, INC. 0.65 0.88 0.77

HERMAN MILLER, INC 0.85 1.33 1.09

HON INDUSTRIES INC. 0.75 0.73 0.74

KIMBALL INTERNATIONAL, INC. 0.95 0.83 0.89

LADD FURNITURE INC. 1.10 1.30 1.20

LA-Z-BOY CHAIR CO. 0.80 0.95 0.88

LEGGETT & PLATT, INC. 0.85 1.10 0.98

SHELBY WILLIAMS INDUSTRIES, INC. 1.00 0.93 0.97

INDUSTRY AVERAGE 0.92

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 8

Data

Average of the

Betas

Notes:

Betas estimated from monthly returns including dividends over the period December 31, 1986 through

December 31, 1991 and using the S&P 500 return for the market return.

Value Line Betas taken from Value Line Investment Survey of the Furniture/Home Furnishings Industry,

dated January 24, 1992.

The next table shows the calculation of the unlevered betas based on the equity betas and

the capital structure of the comparable firms.

Table 2

Asset Betas and Capital Structure in the Furniture Industry

Average

Beta

Equity Value

(millions)

Value of

Debt

(millions)

Ratio of Equity

Value to Total

Value

Unlevered

Beta

BASSETT FURNITURE INDUSTRIES, INC. 0.76 $274.752 $0.000 1.00 0.76

FLEXSTEEL INDUSTRIES, INC. 0.77 $73.216 $0.700 0.99 0.76

HERMAN MILLER, INC. 1.09 $478.688 $54.700 0.90 0.98

HON INDUSTRIES INC. 0.74 $544.349 $33.600 0.94 0.70

KIMBALL INTERNATIONAL, INC. 0.89 $431.460 $4.400 0.99 0.88

LADD FURNITURE INC. 1.20 $176.514 $125.300 0.58 0.70

LA-Z-BOY CHAIR CO. 0.88 $364.614 $55.900 0.87 0.76

LEGGETT & PLATT, INC. 0.98 $566.565 $179.400 0.76 0.74

SHELBY WILLIAMS INDUSTRIES, INC. 0.97 $66.959 $11.000 0.86 0.83

Notes:

INDUSTRY AVERAGE 0.79

Debt and equity data are taken from Value Line Investment Survey of the Furniture/Home Furnishings Industry, dated January

22, 1993.

MBA 819: FINANCE PART CLEMSON UNIVERSITY

Other Applications of Asset Betas

Electric Utility Betas

There are at least two other research topics where the notion of asset betas as opposed to

equity betas have been analyzed. Both involve the electric utility industry.

Years ago, Sam Peltzman extended Geo. Stigler's theory of government regulation. The

Peltzman model predicted that economic regulation was a way in which the government allowed

for controlled monopolization in which firms extract some but not all of the monopoly rents

available from their markets. He argued that the regulatory process was like a buffer between

firms and consumers.

On the basis of this buffer theory, Peltzman predicted that regulated monopolies would

have lower systematic risk, i.e., lower betas, because when times were good, they would be

restrained by government, but when times were bad, government would let them gouge the

consumers a little more to make up for the bad times.

One of Peltzman's students, Seth Norton, pointed out (JLE 10/85) that the Peltzman effect

was a prediction about unlevered betas. Peltzman had tested his hypothesis using levered betas

and found only weak results. When Norton went back and unlevered electric utility betas, the

Peltzman effect showed up quite strongly. Norton was insightful in seeing the obvious. Everyone

knows that utilities typically have more debt, 4 and that their debt, at least until the nuclear crisis,

was always higher grade than average. This extra levering is a straightforward market response

to the fact that the asset betas are lower, thus making the bankruptcy cost of debt lower.

Electric Utility Unbundling

As competition is unfolding in the electric industry, the process is causing betas to

increase. This is an interesting result to students of financial economics. Obviously, what is

going on is the evaporation of the Peltzman effect. As companies face competition, the buffer

that they used to enjoy is going away.

Note that it is not fair to claim that competition is making beta go up because it is

increasing the risk that one company will beat out another in the industry scramble. Such risk is

idiosyncratic and can be diversified away by holding a portfolio of all the firms in the electric

utility industry.

The process of allowing competition in the electric industry has been labeled unbundling.

Electric utilities are being forced to allow competitor to access the customers that are connected

to their lines. This is the same thing that happens in telecommunication where multiple

companies vie to supply long distance service to the same household by offering that household

service over the lines of the local distribution company. In electricity, there will be multiple

competitors offering electric generation over the lines of the local utility.

Unbundling in telecomm was achieved by making AT&T divest its local telephone

service subsidiaries. Unbundling in electricity has not yet gone so far. However, the local electric

utilities (where there is competition, which is regrettably not here in SC) are mandated to

functionally separate their operations into generation, transmission, and distribution. T&D will

remain regulated while generation is competition. The local utility is supposed to charge rates for

its T&D that recover only the costs of providing those services. The price that is charged for

generation is then competitively determined.

Of course, it is a very difficult task to split this baby. The utilities have a strong interest

some political clout in setting T&D charges at levels that continue to return the same monopoly

4 D/E is around .8 compared to .5 for other industrial companies.

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 9

MBA 819: FINANCE PART CLEMSON UNIVERSITY

rents that they have always enjoyed. The practical way that they attempt to do this is by loading

their own generation costs into the T&D charges that they are allowed to charge competiting

suppliers. One very subtle but nontrivial way that they do this is by petitioning the regulatory

commission to allow them to continue to use the allowed rate of return that was formerly

approved for GT&D for T&D only. In other words, the utility asks (and so far has been allowed)

to receive a return on its investments in transmission and distribution based on the riskiness of

generation, transmission, and distribution.

In a paper we published in the Public Utilities Fortnightly, we pointed out the fallacy of

this approach using the basic CAPM analysis. 5 The business risk of electricity is a linear

combination of the business risk of GT&D. If G is unbundled from T&D, the risk of only T&D

should be used to calculate the allowed rate of return. We argue that G is more risky than T&D.

Consequently, if the charges for T&D are based on a more risky return calculated by including

G, the charges are too high. Utilities are being allowed a monopoly reward (no big surprise).

Competition is not bring the full measure of savings and benefits to consumers.

This paper was followed by a letter to editor in which the writer made the classic

sophomore mistake of arguing that risk goes down when the utility functions are integrated in

one company, and therefore risk in T&D will go up when the functions are unbundled. As you

can imagine, my letter in reply was sharply worded.

5 “The Wires Charge: Risk and Rates for the Regulated Distributor,” with Robert E. McCormick and Cleve B. Tyler,

Public Utilities Fortnightly, September 1, 1997, 26-33.

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 10

MBA 819: FINANCE PART CLEMSON UNIVERSITY

VALUATION⎯II

Review

We are exploring the case of the valuation of the Singer Furniture Company. This case

developed out of the bust-up of the Singer Company. As you recall, Singer started as a sewing

machine company. However, over the years it became a highly diversified manufacturing firm.

The company made rifles during WWII, it had numerous small machine plants here in SC that

made drills and vacuum cleaners. And, of course, it continued to make sewing machines.

In 1988, Singer was taken over by a corporate raider, Paul Bilzerian. 6 Bilzerian sold the

Singer Sewing Machine name and operations to James Ting, a Hong Kong businessman. Ting

sold Singer Furniture Company back to SFAC, Inc., a holding company controlled by Bilzerian.

A dispute arose over payments that Bilzerian was supposed to make to Ting. Ting sued to regain

control of the company. A question arose as to its value. What we tried to do was construct an

estimate the value of SFC that would have been reasonable if the firm had been appraised in

1992.

We left off with the calculation of the asset beta for SFC. It was .79. We will use this

shortly in the valuation of SFC.

Discount Cash Flow Formula Revisited

The DCF valuation method assesses the value of the company based on the earnings

flowing from the productive assets and on-going operation of the enterprise. The purpose of the

technique is to determine the present value equivalent to the stream of future earnings that makes

the owner, current or prospective, indifferent between the cash equivalent and the rights to the

earnings flows.

The DCF formula commonly used to value businesses is:

5

CashFlowt

CF5 / ( r − g)

P = ∑ + t

5

( 1+ r)

( 1+

r)

t = 1

where P is the present value of the business, Cash Flow is the estimated net cash flow the

enterprise is generating, g is the real growth rate in these cash flows in the long term, r is the

discount rate. This formula assumes that the business will grow for a period of 5 years at a rate

higher than the real growth rate. The cash flows forecast for these first 5 years will reflect this.

Their mature value at the end of 5 years is then used in the constant growth formula and this, too,

is discounted back from 5 years out. One way of thinking about this is to assume that the

business is managed to maturity and then sold. The constant growth formula tells us what the

sale price would be.

In the case of SFC, it was assumed that the business was mature and that the last year for

which financials were available represented the cash flows that could be expected into the future.

Based on this assumption, the constant growth formula is appropriate:

6 Bilzerian gained notariety by going to jail for illegal stock trading. The SEC tried to pry the gains he made in the

Singer deal and others away from him. He declared bankruptcy in Florida and kept his multimillion dollar home. It

is claimed that he stashed a good bit out of the country.

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 11

MBA 819: FINANCE PART CLEMSON UNIVERSITY

P

CF

=

r − g

The Components of Cash Flow

The actual computation of cash flows to be used in the DCF method begins with earnings

before interest expenses but after taxes. Several adjustments are made to these earnings after

taxes in order to derive an estimate of expected future cash flow. These adjustments include the

add-back of depreciation, and the deduction of capital expenditures and increases in working

capital. These points are discussed below.

Add-back of depreciation

Consider the following example:

Sales 80,000

Cost of Goods Sold -20,000

Depreciation (deducted) -40,000

Earnings before Taxes 20,000

Taxes (35%) -7,200

Earnings after Taxes 12,800

Depreciation (added back) +40,000

Cash Flow (before cap. exp.) 52,800

As shown here, the cash flow exceeds earnings after taxes by $40,000 due to the

add-back of depreciation. This point is very important for valuation. The value of a firm depends

on the accrual of cash flows, not just profits. As depreciation is not an actual cash expense, it

should be added back to profits after taxes in order to derive cash flows. Thus, not adding back

depreciation to after-tax profits would underestimate the value of the firm. Depreciation is an

expenses that the IRS allows to be deducted from current earnings when computing current tax

liabilities. However, even though depreciation is a current tax shield, it is not a current expense.

It represents the current recovery of cash that was used to purchase productive assets in the past.

In that sense, it represents the cash flow associated with the value of the assets in place in the

business. Hence, it is crucial to include this value in the cash flow of the company used to assess

the value of the company.

Subtraction of capital expenditures

Capital expenditures are cash outflows. Capital expenditures are investments in the

business that are expected to produce future cash flows. Capital expenditures are not

automatically deducted from earnings in the income accounting statement because IRS rules do

not allow the immediate expensing of capital expenditures. The add-back of depreciation and

subtraction of capital expenditures translates the accounting picture of the firm, which is formed

by guidelines based on the rules of taxation by government, into the financial picture of the cashflow

value of the enterprise.

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 12

MBA 819: FINANCE PART CLEMSON UNIVERSITY

Accounting for changes in net working capital

When a firm grows, there is a corresponding increase in working capital. The three

primary components are accounts receivable, inventory, and accounts payable. From a valuation

perspective, changes in working capital are not immediately reflected in the income statement.

The income statement appears to show an increase in cash flow when the firm grows, but not all

of the apparent increase in cash is available to the owners of the enterprise because some of it is

taken up in the expansion of working capital. For example, an increase in accounts receivable

from one year to the next implies that the cash inflow from sales is actually less than the sales

level reported on the income statement. Consider the following example.

Sales 8,000,000

Accounts Receivable at

beginning of Year

1,000,000

Accounts Receivable at end of

Year

1,500,000

Net Change in Working Capital 500,000

Cash Inflow 7,500,000

Thus, cash inflow is $500,000 less than sales due to the resulting increase in receivables.

With respect to the other two primary components of working capital, increases in inventory

have the same effect as increases in receivables, whereas increases in payables have the opposite

effect. The basic calculation is to subtract increases in net working capital from earnings after

taxes in the same fashion that depreciation is added back to those earnings.

Changes in working capital must be accounted for in the construction of cash flows using

the DCF method of valuation. Because working capital often grows as earnings grow, a

conservative approach is to assume that they grow at the same rate.

Construction of Cash Flows for Singer Furniture Company

To value a firm using the DCF model, historical financial figures are important only to

the extent that they can be used to forecast future estimates of cash flows. The value of the firm

depends on the expected future cash flows rather than the prior actual cash flows.

The Singer Furniture Company was taken over in 1989 by SFAC. We used the financials

in 1991 as the forecast of the cash flows that could be expected from then on. The financial

performance in the first two years were not as good, but arguably reflected the change in

ownership and management. By the end of 1991, the business operation should have begun

adjustment to this restructuring and the financial reports of that year present a reasonable picture

of the cash flows that the business should have been expected to achieve into the future. We

assumed, conservatively, that the business would not grow any larger in real terms. However, we

did assume that growth would occur due to inflation. A benchmark growth rate of 3.92 percent

based on the average annual compound inflation rate from 1982 through 1991 was used. 7

TABLE 1 shows the cash flows for Singer Furniture Company. The values for earnings

before interest and taxes, depreciation, capital expenditures, and working capital are based on the

audited financial statements as of the end of 1991. Taxes are assumed to be 35 percent.

The value for Increases in Working Capital in 1991 is based on the assumption that the

value of Working Capital in 1991 was the optimal value. If working capital in 1991 was optimal

7 This value is computed from Ibbotson, 1995.

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 13

MBA 819: FINANCE PART CLEMSON UNIVERSITY

then it is predicted to grow over time based on the growth rate assumed for cash flows. Hence,

this value is deducted from the Cash Flows Net of Taxes to arrive at the value of Net Cash

Flows. This Net Cash Flow estimate is predicted to be the base level of real cash flows into the

future. The formula for Increases in Working Capital in the year 1991 is (g/(1+g)) times Working

Capital in 1991, where g is the growth rate (assumed in benchmark case to be driven only by

inflation).

For the benchmark estimate of the value of SFC, it is assumed that the life of the firm is

indefinite. In association with the values shown in TABLE 1, this implies that the capital

expenditures deducted from the after-tax earnings of SFC in 1991 are expected to recur annually

in order to replenish the capital stock of the company so that the stock of physical capital in place

in 1991 can be maintained indefinitely.

Tax Shields

One final consideration in the valuation process is the treatment of debt. The DCF

formula as it has been discussed thus far gives an estimate of the value of an unlevered company.

Because of the way federal income taxes law treat interest payments, it is generally beneficial for

firms to employ debt in their capital structure. Interest payments to bondholders are a tax

deduction from earnings, but similar dividend payments to shareholders are not. In the process of

valuation, the approach is straightforward. First the value of the all equity firm is computed

based on the preceding components. Then the value of the tax shields created by shifting capital

structure from all equity to part debt and part equity are computed. The overall value of the firm

is the sum of the component parts.1

The value of tax shields provided by debt are calculated as follows. The interest expense

from the income statement, which is the interest rate times the level of debt, is multiplied times

the corporate tax rate that was used to devalue the taxable earnings as shown in TABLE 1.

Interest Expense = Borrowing Rate • Level of Debt

Annual Tax Shields = Interest Expense • Tax Rate

In other words, since corporate taxes are avoided on the interest expenses, the money that would

have been paid to the government goes instead in the pocket of the stock holders. This number is

the annual flow resulting from the tax savings. If debt is assumed to be a permanent part of the

capital structure, the value of the firm is increased by the discounted present value of these tax

shields. To compute the value of the firm associated with tax shields the annual flow is

discounted to the present using a formula similar to the one used to discount the cash flows from

earnings.

Two factors must be considered. A discount rate must be chosen, and an assumption

about the long-run capital structure of the firm must be made. Two assumptions that are

parsimonious in this regard are: First, the discount rate used to value the tax shields is the same

as the interest rate that generates the interest expense, and second, the level of debt in the firm,

rather than the debt to equity ratio, is expected to be a constant. Using these assumptions gives:

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 14

MBA 819: FINANCE PART CLEMSON UNIVERSITY

(a) Discounted Value of Tax Shields = Annual Tax Shields / Discount Rate

(b) = [ Tax Rate • Debt • Interest Rate ] / Interest Rate

(c) = Tax Rate • Debt

The divisor in line (a) includes the discount rate, r, but not the growth rate, g, from the constant

growth formula because of the assumption that the debt level will remain constant. Next, the

interest rate is substituted for the discount rate so that in line (b), the interest rate can be canceled

out leaving line (c). Line (c) says that the capitalized value of the tax shields is simply the level

of debt times the corporate tax rate. Note that if the debt to equity ratio is assumed to remain

constant through time, the level of debt would grow and the capitalized value of the tax shields

would be larger.

In the case of SFC, the long-term debt level is around $25 million and is assumed to be a

permanent part of the capital structure of the business.

The Discount Rate

The discount rate for Singer Furniture Company was calculated based on the facts as

known in 1992. The discount formula is:

rSFC = rf + β SFCERP

The beta that we use in the formula is the asset beta for the comparable firms that we discussed

in the last lecture; its value is .79. In 1992, the 30-year U.S. Treasury Bond rate was 7.7 percent

and the ERP was 7.3 percent, which at that time was the premium of common stocks over longrun

T-bonds for the previous 70 years. (The possibility of a declining ERP or excessive growth

was not yet imagined.)

Evaluating the formula using the estimates of the various component parts gives a rate

appropriate to use in discounting the future cash flows of Singer Furniture Company of 13.47

percent.

The Implied Value Of Singer Furniture Company

Incorporating the discount rate, inflationary growth rate, and the estimated value of cash

flows given in TABLE 1, the unlevered value of Singer Furniture Company can be calculated.

TABLE 2 displays the valuation estimate. The unlevered value of SFC is shown in row (4) of

TABLE 2. Row (6) shows the value of the tax shields that are afforded by the face value of the

debt that company was carrying in 1991. The sum of the unlevered value plus the value of the

tax shields represents the full value of the enterprise as it looked in 1991.

To arrive at the net equity value of the enterprise, the face value of the debt must be

subtracted from the total value of the firm. This leaves the equity value of the firm and is shown

in row (9) of TABLE 2. The per share value is given by dividing by the number of shares

outstanding. The per share value is shown on the last row, (11), of TABLE 2. It is estimated to

be $13.38 using the benchmark assumptions.

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 15

MBA 819: FINANCE PART CLEMSON UNIVERSITY

TABLE 1

Cash Flows to Singer Furniture Company, 1991

Earnings before Interest and Taxes $3,110,465

less taxes at 35% ($1,088,663)

Cash Flow Net of Taxes $2,021,802

plus Depreciation in 1991 $3,372,857

less Capital Expenditures in 1991 ($1,431,682)

less Increases in Working Capital ($1,100,241)

Net Cash Flow $2,862,736

Notes: EBIT, depreciation, capital expenditures, and working capital taken from SFC financials. The

value for Increases in Working Capital is based on the assumption that the value of Working Capital

in 1991, $29,189,109, was the optimal value. Increases in Working Capital are the growth rate divided

by 1 plus the growth rate times Working Capital. Growth rate for cash flows shown in Table 2.

TABLE 2

Value of Singer Furniture Company

(1) Net Cash Flow $2,862,736

(2) Growth Rate of Cash Flows 3.92%

(3) Discount Rate 13.47%

(4) Value of All Equity Firm $29,966,883

(5) Annual Tax Shield (1991) $986,560

(6) Value of Tax Shields (Debt Level

$8,976,508

times Tax Rate)

(7) Value of Firm (levered) $38,943,391

(8) Face Value of Debt $25,647,166

(9) Value of Equity, Net of Debt $13,296,225

(10) Shares Outstanding 993988

(11) Price of Stock per share $13.38

Notes: The growth rate of cash flows is the annual average rate of inflation over

the period 1982 through 1991, from Ibbotson, 1995, p. 204-205.

PROJECT EVALUATION: PROBLEMS AND ISSUES

Comparing DCF to Other Valuation Methods

The discounted cash flow valuation model forecasts the future cash flows of the

corporation or assets and then discounts these cash flows back to the present to obtain the current

or present value of the enterprise. Of all the valuation methods it is the least affected by unusual

circumstances because it makes specific assumptions about the expected future cash flows of the

business being valued. It relies on the use of comparable firms only to estimate the correct rate at

which to discount the expected future cash flows. Most importantly, this approach is the

fundamentally sound and theoretically correct way to value assets and firms. It is based on the

principles of the financial and economic theory of asset pricing.

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 16

MBA 819: FINANCE PART CLEMSON UNIVERSITY

P/E Multiples

A common approach to valuing private companies and divisions of publicly-traded

corporations is to apply price/earnings multiples from comparable firms that are publicly traded.

The appeal of this approach is its simplicity. The drawback is that P/E multiples are indicators of

equity values rather than total firm values and can often be influenced by accounting techniques

as well as the fact that the market price of common stock embodies the capitalized value of the

expectation of future events. These future events may imply cash flows that are very different

from the current earnings of the enterprise.

Cash Flow Multiples

Some valuation experts use cash flow multiples to value firms. The cash flow multiple

approach is similar to the P/E multiples technique in that it uses the market value of comparable

firms. However, the cash flow multiple is preferable because the information necessary to

implement it is more relevant. Rather than using earnings which are sensitive to accounting

techniques, it uses cash flows. Even so, it still suffers from the fact that it uses the stock market

valuation of the assets generating the current cash flows. These stock market valuations may be

based on expectations of future rather than current cash flows.

Weighted Average Cost of Capital

An alternative way to measure the total value of the firm is to discount the total cash

flows to the firm using the weighted average cost of capital. The formula for the weighted

average cost of capital is given by:

D

r r

D E r

E

= D ⋅( 1− τ ) + E

+ D + E

where r is the discount rate associated with the WACC, D is the value of debt, E is the value of

equity, rD is the interest rate on debt, rE is the risk adjusted discount rate for equity, and τ is the

tax rate on equity income.

The problem with this formula is that to use it we need to know everything we are trying

to determine. Since E is the PDV of equity, we cannot implement this formula by looking at our

own enterprise. However, we can look at comparable firms.

Other Methods of Project Valuation

There are two other methods of project evaluation than DCF that are fairly standard.

They are the payback period and internal rate of return. Let’s consider DCF in contrast to these

other methods.

The payback period looks at the time necessary to recover the initial investment. Not very

sophisticated and as a consequence not always an accurate description of the project. Internal

rate of return is an analytical technique that determines the interest rate that causes the net

present value of a project to be zero. In other words, if we were to apply the DCF rule, to a

project we would get some number which is the dollar value of the project. The IRR method uses

that same calculation but searches across interest rates until the highest rate is found, which is the

one that sets the DCF to zero.

Consider the following set of projected cash flows from ventures A-D:

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 17

MBA 819: FINANCE PART CLEMSON UNIVERSITY

t A B C D

0 -1000 -1000 -1000 -1000

1 100 0 100 200

2 900 0 200 300

3 100 300 300 500

4 -100 700 400 500

5 -400 1300 1250 600

Payback 2 4 4 3

DCF -406.8 510.7 530.9 519.5

IRR n/a 20.9% 22.8% 25.4%

Notice that the payback period approach does not distinguish between projects B and C.

Moreover, it does not recognize that project A is not good (unless you are a scam artist). Internal

rate of return won’t calc for project A, which is ok because it is negative DCF, but the problem

of negative cash flows at the end messes up the IRR as well as the payback approach.

Based on IRR, project D is the best. Based on DCF, the nod would go to project C. Why

is the IRR rule wrong? Under what circumstances might it be right?

Projects with different lives.

Consider two projects:

t A B

0 -10 -10

1 6 4

2 6 4

3 4.75

PV .41 .500

PV(N,∞) 2.38 .202

IRR 13% 12.8%

Choice between simple one-time projects is simple. Use maximum present value rule.

However, the IRR rule picks project A and because project A returns the cash flows sooner, we

are suspicious that it has some value we are not capturing some important aspect of value in our

maximum present value rule.

That suspicion is revealed if we consider that the projects may be replicated. Assume that

the projects can be rolled over. When project A is completed after 2 years, another infusion of

$10 can again recover two year’s of $6 payouts. Similarly for project B after three years. What

we need is a formula to characterize this value.

For one-period compounding:

PV ( N, ∞ ) = PV ( N ) ⋅

N

( 1+

r)

N

( 1+ r)

−1

where PV(N) is the net present value of the project that lasts N periods, and PV(N,∞) is that

project replicated an infinite number of times.

For continuous compounding:

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 18

L

NM

O

QP

MBA 819: FINANCE PART CLEMSON UNIVERSITY

−

e

PV ( N, ∞ ) = PV ( N ) ⋅

1−

e

Duration

The analysis of projects with fixed lives raises the question of how to determine the

optimal life of a project. While these kinds of problems can be elaborate, a simple case sets the

tone. Consider growing trees. Trees are planted. As they grow, they increase in value. Call this R.

R is a function of t, R(t). The present value of the tree project is

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 19

L

NM

−rt

PV = R( t) e − c

where c is the cost of planting. The optimal life of the trees can be found by differentiating

present value with respect to t:

dPV

dt

rN

−rN

+

O

QP

1 . 8

dR( t)

−rt −rt

= e − rR( t) e = 0

dt

This simplifies to the Fisherian Rule. The trees should be cut when their growth rate in value is

equal to the interest rate:

dR / dt

R

An example serves to illustrate. Let c be $15; let the growth function be R = A( + t)

/ 1 2

1 , where A

is $10; let r be .05. The derivative of the growth function is:

Fisher’s Rule is then:

dR( t)

dt

= r

= ( + t)

− 1

10 1

2

1

2

−1/

2

dR / dt 5( 1+

t)

1

= = 1/ 2

R 10( 1+

t) 2( 1+

t)

which gives t*=9.

Naturally, we are lead to ask what would happen in this case if we allowed for replanting.

As solved above, the tree project is a one-shot deal. The more common event is that the trees are

cut and then replanted. In the case of replanting, the project can be characterized as:

= r

−rt −rt −rt −rt −r

2t

PV = [ R( t) e − c] + [ R( t) e − c] e + [ R( t) e − c] e + ...

8 If the original project is discounted using continuous compounding, its PV is .34 instead of .41.

MBA 819: FINANCE PART CLEMSON UNIVERSITY

That is, the project is undertaken once, and then again, and again. The cycle continues into the

future infinitely. This process can be recast as one economic agent starting the project and then

selling it after one cycle to another economic agent who will continue it. In this way we can

rewrite the problem as:

This formulation solves easily as:

PV = [ R( t) e − c] + PVe

PV

−rt −rt

−rt

R( t) e − c

=

−rt

1−

e

After some uninteresting algebra, the optimization rule becomes:

*

dR( t )

dt

= rR( t ) + rPV

* *

This says that at the optimal cutting time the appreciation in value of the trees is exactly equal to

the opportunity cost of the standing timber plus the opportunity cost of the land.

Returning to our example, the solution in this case is a bit more cumbersome, but it can

be shown that the optimal cutting time with replanting is slightly less than 5 years.

It is instructive to consider how the IRR treats the problem of the trees. In the single

period problem, the internal rate of return solves the optimal life of the trees at 4 years. The

algebra of this is shown below, but it is not particularly important. The main point is that the IRR

rule very closely approximates DCF with replication, though it is not exactly correct. The reason

that IRR is close in cases where replication is possible is because it implicitly assumes that the

project that maximizes the internal rate of return is best because that return can be earned again

and again. Generally, this is not so. This is why assessing projects based on their true discount

rate and then choosing projects based on maximizing DCF is the proper strategy for maximizing

wealth.

IRR in the Growth Problem

Maximize i subject to

it

R( t) e c

− = 1.

Returning to our example where R=A(1+t) 1/2 , substitute for R in (1) above and then take the log

of both sides.

This simplifies to

1

ln A + ln( 1 + t) − it = ln c

2

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 20

MBA 819: FINANCE PART CLEMSON UNIVERSITY

max

{ t} i

1

ln A + ln( 1+

t) − ln c

= 2

t

which is maximized over the choice of t. The function has a unique maximum at around 4 years.

Constrained Capital Budgeting

What if you are offered a choice between two projects. One requires and initial

investment of $100 but pays back $1000 in present value terms. The other requires an initial

investment of $50,000 but pays back $2000. Which project is better?

The size of the difference in the numbers is staggering. No doubt every one of you has

doubts that the second project is better even though it is the right choice based on the DCF rule.

But how can this be? Is the rule missing something?

Our intuition about the choice between the two projects is based on some basic sense of

risk. We see the first project as less risky and hence the better payoff. We simply cannot believe

that the second $1000 is worth the risk of the extra $49,900 investment.

The DCF rule can be made to come into line with our intuition, at least somewhat, if we

consider the problem of project evaluation from the prospective of a constrained capital budget.

Simply enough, from a constrained cap. budget perspective, project one is a throw away. Of

course we do it. Project two, however, may require tapping additional sources of finance.

This analysis can be summarized by using a DCF Index. Create an index for each project

which is the present value of the cash inflows divided by the initial cash outflow. Thus, each

positive DCF project has an DCF index that is greater than zero. Some by more, some by less.

Next, a project capital exp. index is created by taking the ratio of the initial investment of each

project and dividing by the capital budget. Projects are chosen by sorting through the alternative

investments until the overall present value index is maximized subject to the capital budget

constraint.

One last word: it is important to recognize that the DCF approach is built on the concept

that the discount rate properly embeds risk into the decision making. Recognize that part of the

intuition of balking at the proper choice between the two project alternatives listed above is that

you may not fully appreciate the treatment of risk in the context of CAPM.

**Lecture** 3.doc; Revised: March 25, 2009; M.T. Maloney 21