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Theses
1-1-1973
A Cost of Capital and Capital Budgeting Decision Model Related A Cost of Capital and Capital Budgeting Decision Model Related
to New, Small, High Technology Corporations to New, Small, High Technology Corporations
Bruce R. Robinson
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A COST OF CAPITAL AMD CAPITJ^L BUDGETING
DECISION MODEL RELATED TO NEW,
SMALL, HIGH TECHNOLOGY
CORPORATIONS
A Research Paper
Presented To
the Faculty of the Graduate School of Business
Rochester Institute of Technology
In Partial Fulfillment
of the Requirements for the Degree
Master of Business Administration
by
Bruce R. Robinson
January 1973
TABLE OF CONTENTS
CHAPTKR PAGE
I. THE PROBLEM AND DEFINITION OF A NF^f SMALL FIR14 1
The Problem 1
Organization of Paper 2
A Definition of the New Small Firm 2
II. COST OF CAPITAL AND THE NEW PRODUCT INVESTMENT
DECISION WITH RISK 4
The New Product Investment and Risk Analysis
Technique 4
A Comparison to Similar Techniques 11
III. CAPITAL STRUCTURE THEORY 12
Proposed Modified Theory 13
Cost of Debt Theory 22
Cost of Retained Earnings Theory 24
Cost of Equity Theory 2?
IV. COST OF CAPITAL FOR LOCAL SMALL BUSINESSES 31
Description of Research and Analysis '}!
Cost of Eqioity and Retained Earnings for the
Surveyed Firms . 34
Cost of Debt for the Surveyed Firms 44
The Composite Fiiro and a Sample Investment
Opportunity 45
A Sample Investment Opportunity 49
CHAPTER PAGE
V. COMPUTER PROGRAM TO GENERATE IRR VERSUS RISK CURVE .... 51
VI. SUl-MARY OF RESULTS AND CONCLUSIONS 54
Summary of Results 54
Conclusions and Recommendations for Further Study . .58
BIBLIOGRAPHY 59
APPENDIX
A. THE RESEARCH LETTER OF ENQUIRY 61
B. A DESCRIPTION OF RESEARCHED FIRl'iS 63
C. STOCK PRICE CURVES 89
D. COMPUTER PR0GRA14 AND LISTED RESULTS 115
E. CAPITAL PECULIARITIES OF THE NEW SMALL FIRtI 122
CHAPTER I
THE PROBLEM AND DEFINITION
OF A NEW SMALL FIRM
Much has been written relative to capital budgeting techniques
and the cost of capital as separate decisions. In a new small firm
these two decisions become inextricably related.
I. THE PROBLEM
The recent cutback in U.S. Military Defense spending has
freed many engineers and scientist to form their own small businesses
to perpetuate their technological employment. In reviewing their
plight I have foiind these new ventures have developed, or are in
the process of developing, new highly technical products and services
such as data recorders, communications receivers, integrated circuitry,
etc. Many of these products or services are reported to have significant
technical advantages over those currently available. In a few cases the
proposed products are novel enough to be considered capable of filling
entirely new market needs. Also typical of these operations is their
attempt to provide small contract design development services to large
industry and government agencies to provide the capital necessary to
remain in business and support development of the aforementioned
commercial products. The initial capital for these firms consists
primarily of equity contributions of the entrepreneurs, close friends,
family and occasionally SBA backed loans. Many of these firms in the
Rochester metropolitan area are about to survive their first several
years of operation, have completed their new commercial product develop
ment and now must raise capital to introduce these products and initiate
manufacturing. The problem is to raise this capital in a way that will
optimize the firm's capital structure in light of the new product
risks and the component cost of capital.
II. ORGANIZATION OF PAPER
In this paper I have described a simple effective technique for
determining the risk characteristics of the expected return on a
new capital expenditure. I have defined the component costs of capital
and demonstrated how the new venture capital structure can be arranged
to satisfy the risk utility function of the owner entrepreneurs in
light of the expected returns. I have presented preliminary research
which was performed to establish initial estimates of the costs of the
various components of the capital structure. This research was performed
in up-state New York at the time of this study and is applicable to
firms conforming to the definition in Section III of Chapter I. These
estimates were then used in a hypothetical case to demonstrate the
applicability of the study and theory.
III. A DEFINITION OF THE NEW SMALL FIRM
For the purpose of this paper I will limit my definition of a
new small firm to one having the following characteristics :
l) Annual sales of less than $10 million/year
2) Employing less than 250 people
3) Based on new technological product developments or services
4) Incorporated and operating for less than five years
Though somewhat restricted, this definition is applicable to many
new ventures entered into by engineers and scientists and conforms to
the SBA definition of a small business.
CHAPTER II
COST OF CAPITAL AND THE NEW PRODUCT
INVESTMENT DECISION WITH RISK
1
The cost of capital to the firm is the effective rate the firm
must pay to acquire funds for growth and development. It will be
considered as that discount rate with the property that an investment
made above this rate will raise the value of the firm in the eyes of
the owners. Its major application is in deciding whether a proposed
new venture will be profitable. Even though there is considerable
discussion about the means of arriving at this cost of capital and its
component characteristics there is little doubt that such a rate does
exist and coxild be used to evaluate investment alternatives.
I. THE NEW PRODUCT INVESTMENT AND
RISK ANALYSIS TECHNIQUE
The new technologically based firm must convince supporters and
investors that its new ventures would produce returns on their invest
ment and woiJ-d adequately compensate for the investment risk. This
can also be stated as: the firm must assure the investors that the
capital expenditures to be undertaken by the firm woiild have an
expected rate of return at least as high as the cost of capital to the
business. In this sense, the cost of capital would include compensation
M. J. Gordon, The Investment. Financing and Valuation of the
Corporation, p. 218.
Roland I. Robinson, Financing the Dynamic Small Firm. , p. 56.
c
to the investor for risk associated with the new venture. This generally
accepted requirement of the firm may be stated mathematically as:
T^^
C
where: R is the expected value of the rate of
return on the investment considered
R^ is the cost of capital
This rate of return R is generally accepted to be that discount rate
that will permit equating future (after tax) income with present cash
outlays required for the new venture. The component variables
associated with calculating a given rate of return on the new venture
are usually assigned one value and therefore yield one calculated
return. To more thoroughly evaluate a proposed venture a minimum,
average, or maximum value for each component variable can be estimated
and each value assigned likelihood of occurrence. This variable
permits calculating a probability distribution of possible returns on
an investment. To calculate this probability distribution of R for
3the proposed new ventiore one must first estimate the following factors:
David B. Hertz, Risk Analysis in Capital Investment.
Archer and D'Ambrosio, Theory of Business Finance,
p. 400.
Minimum
Qty Likelihood
Average
Qty Likelihood
Maximxmi
Qty Likelihood
Annual Sales
less Variable
Costs and
Estimated taxes
^1 \ ^2 \ *3 "3
Fixed Annual
Operating Costs^1 \ \ \ ''3 "3
Residual Value
of Investment^1 h ^2 \ S h
Useful Life of
Investment\ \ ^2 \ "3 h
Initial Investment \ h \ \ S b
Where: 1) The annual sales less variable costs and estimated taxes (A)
would typically be given by:
ciales revenue -
manufacturing
costs
(labor & materials)
variable
selling
expense
- variable
overhead costs
- variable
facilities
costs
- estimated taxes
2) Fixed Ajmual Operating Costs (B) include the costs for
non-variable items related to plant, personnel and
eqvdpment reqviired to sustain activity on the new venture.
3) Residual Value of Investment (C) is the estimated market
value of all materials acquired for the project with the
initial investment capital. This should include
estimates for depreciation and capital gains tax.
^) Useful Life of Investment (D) is that time period prior
to technical obsolescence of the product or in some
cases market saturation.
5) Initial Investment (E) is that totality of funds required
to initiate and sustain the new venture at its inception.
6) V, W, X, Y, and Z are the related probabilities of
occurrence of each variable A, B, C, D, and E respectively.
To calculate the internal rate of return one equates cost of investment
outlay E vdth the present value of expected future receipts as given
^irA^I-B^*
Cby: E ;
= 5- ^^ ^
j = 1, 2, or 3 minimum, average, or maximum vslue
subscripts
Vi/here: R = Internal rate of returnr
Ej = The cost of investment outlay
A .- B .
= The annual receipts expected from the venture
D .= Useful life of the investment, usually in years
*J
C. = Residual value of investment
This calculation would require selection of one condition (minimum,
average, and maximum) for each of five variables out of three which
would combine to give ,C_ . ,C . -.C . ,C_ .
-,C^= 3 =
243 combinations. Therefore . 243 independent calculations would be
required to obtain the distribution curve of expected returns. I
have concluded this would require the use of a computer to arrive
at the desired distribution in a reasonable amount of time. For each
one of these 243 outcomes I assign the probability (n. = V. . W. . X.
Y. . Z.) associated with each outcome.
3 J
NOTE: It is obvious that the product will go through a product life
cycle as VTith all high technology products. It could be argued that
assiHiiing some constant estimate of each financial variable renders
the analysis less useful. This approach was considered and discarded
because it is somewhat compensated for in the variability attached
to each piece of data and further the shape of the product life cycle
is all but impossible to predict except in the general case.
Each calculated internal rate of return R will then have an
r
associated probability of occurring n. . If one classifies the
internal rates of return into equal return classes and totals the
n. probabilities associated with each return in each class it is
possible to plot a histogram probability distribution or probability
function f(R ) as shown below.*
r
f(Rr)
"lJ
1.^.
Figure #1 Return Probability Function
Summing this distribution from 0 to cjcj one can derive the
distribution function or cr^ulative distribution F(R ) of the discrete
random yariable R^as given by:
FCR,) - ^ f (Rr) fo* 0 -& X & o
?The equal return classes shovild be selected to provide the desired
distribution resolution.
10
This internal rate of return cumulative distribution can be plotted
as a discontinuous function (step function) as shown below.
VCRvlY/' !
PCRy^Rv)
Figure #2 Return Cumulative Probability Function
This ctirve indicates the probability that the actual retiu'n R
on the investment opportunity will be less than any rate of return
chosen on the abscissa (R ). It should be noted that at all pointsr
of discontinunity on this curve the greater of the two probability
values should be used.
11
The new venture can be analyzed in light of the above probability
distributions. The managers could adjust their financial structure
in light of these curves to satisfy the firm's risk utility function,
as ijill be described later.
II. A COMPARISON TO SIMILAR TECHNIQUES
It is worthwhile to note that some scholars in the field of
finance have recommended the decision rule; accept only those invest-
4ments which have a rate of return greater than the cost of capital.
I feel this rule is negligent. It essentially ignores the risk
associated with each projected retiirn. They go on to note that
sometimes the firm should accept investments returning less than
the overall cost of capital if the investment reduces the overall
risk of the firm. This introduces an intuitive risk correction to
the data after many too risky ventures may have been undertaken. The
technique I propose to use mil arrive at the return on investment which
meets with the utility function of the corporation owners. Thus, risk
factors are automatically taken into account in the analysis of each
investment.
Harold J. Bierman, Jr. ,Financial Policy Decisions. p. 81.
^Ibid, p. 81.
12
CHAPTER III
CAPITAL STRUCTURE THEORY
There have been many attempts to establish a theory that can
be used to predict the optimum capital structure. The most revolutionary
approach to the theory of capital structure was set forth by Modigliani
and Miller where they concluded that the cost of capital was a constant,
regardless of the firm's debt-equity structure. Their theory made the
assumption that the stockholder could compensate for corporate debt
risks through modifying his personal portfolio (arbitrage). This
assumption fails since personal leverage is not a perfect substitute
for corporate leverage. Also, they assumed the firm could be classified
in some well defined risk class and neglected taxes. Even after they
corrected for tax effects, their theory maintained that beyond a certain
debt level the required stockholder return would decrease. This runs
contrary to our notion that more risk should entail more return. They
also assvmie that the P/E ratio of stock is unaffected up to some conven-
7taional debt limit which was conveniently left undefined.
The more traditional economic approach to the cost of capital
asstmies that the firm should push its investments to the point where
J. Fred Weston, "A Test of Cost of Capital Propositions",reprinted in Archer and D'Ambrosio, The Theory of Business Finance.
p. 205.
''ibid, p. 204.
13
the marginal return is equal to the marginal cost of capital. The
originators of this concept consider maximizing the return to the
stockholder and maximizing the value of the firm (discounted earnings)
as criterion for establishing the optimal capital structure. Under
conditions of certainty this approach is able to define an optimal
cost of capital and capital structure. However, it proves inadequate
when vmcertainty of cash flow is considered. The proponents of this
technique add risk premiums, super premiums, risk discounts, and more
to their equations to adjust for risk but leave the level of these
adjustments somewhat nebulous.
I. PROPOSED MODIFIED THEORY
For the proposed new small firro capital structure theory, I will
make several assumptions:
1. There is no single long range optimal structure due to the rapidly
changing characteristics of the firm's earnings. Each invest
ment must be considered in light of the current cost of capital.
2. The firm is controlled by one or several individuals who can alter
the capital structure to compensate for changing risk and the
owners'risk utility function.
3. The outside equity capital investor in the small firm is
primarily concerned with growth opportunities as evidenced by
increased value of the firm.
Franco Modigliani and Merton H. Miller, "The Cost of Capital,
Corporation Finance, and the Theory of Investment", Reprinted in:
Archer, and D'Ambrosio, The Theory of Business Finance. p. 126.
14
4. At worse, the small firm can obtain debt financing from SBA backed
sources for one to ten year terms up to l/2 the total capital in the
firm.
5. No debt will be held by equity holders in the firm.
6. Debt limits of the firm's capital structure will be established by
the money market not the capital market.
The proposed modified theory is based on building a capital structure
and selecting investments which yield a return greater than the associated
cost of capital and commensurate with the owners'
risk utility function.
This is accomplished by developing a probability distribution of the rate
of return expected on a new venture and comparing this c\u:"ve with the
various component costs of capital. If the comparison indicates that the
return on an investment is greater than the cost of capital with a likelihood
of loss compatible with theowners'
risk utility function the investment should
be made.
As shown in Figure #3. the owner could theoretically generate a
continuous probability distribution f (R ) of the expected rates of return
on a new venture. The probability that any rate of returnR'
on the new
venture will be less than a selected abscissa value R is given by:
-^r
p(r; < R^) =
( fCR^)(
15
If one substitutes the cost of capital (R ) for the selected abscissa
value, the probability that the new venture will return less than the
cost of capital is similarly given by:
R
P(R; ^ R^) = C"^
f(R^)
I
Since this is equivalent to the probability that the firm will decrease
in value we can state:
Rc
P(decrease in value of firm) = ( f (R )/
It is this probability of a decrease in the value of the firm which must
be less than that which is defined by the owners'risk utility function.
16
Figure #3
H^^)
Probability
Rate of
Return will
be achieved on
Investments
P(R'-<. R ) = P (decrease in value of firm)
R c
Vilhere: Decrease in value of firm is defined as any return
on investments that is less than the controlling
investors expect.
17
gLooking at the weighted average cost of capital as given by:
^c=
\^L^
^dS^Vp
^
^rS.^
^eS
Where: R =weighted average cost of capital
Cy cost of trade credit
C_ =cost of debt capital
Cp= cost of preferred stock
C^= cost of retained earnings
C = cost of external equity
W = ^ of each type of capital in the capital structure
My research indicates retained earnings, equity and debt are the prime
sour<:es of capital. I will consider the characteristics of these costs
individually at a later point in the paper. The cost of capital of the
small firm is now given by:
\=
^dS^Vr^Ve
If we assume that C_ -i C^ < C. The minimum cost of capital is that cost
that first maximizes the use of debt capital (Cj^) consistent with the owners'
desire for safety from defaulting on his debt, then maximizes retained
earnings (Cp) consistent with his growth expectations for the firm. Finally,
equity capital should be used to satisfy the firm's remaining capital needs.
With reference to Figure #4, the owners of the firm would consider using
the expected return on investment curve to determine the risk associated with
s.nY given amount of debt. This amount of debt can be plotted at some value
Wj^C on the abscissa of the expected return curve.
Q
^Eugene F. Brigham, and Keith V. Smith, Cost of Capital
to the Small Firm, p. 175.
Figure #4
^CR,)
18
Probability
Rate of
Return will
be achieved on
Investment
R,r=WoCe Ry - Re
p(r; < w^c^) =
P(default) = Risk =
r^dS
f(R )r
19
The probabilities of potential default on this amount of debt is then given
by the area under the probability c\irve from 0 to W_^C_ or:
Vd
P(default) =
P(R^ < Wj^Cj^) = ( f(R)
This can be explained by analyzing the capital structure again. The first
investors not to be satisfied are the equity investors if we assume solvency
is of prime importance. Since the cost of retained earnings and eqtiity capital
are directly determined by their level of satisfaction in the case where R
goes below R the return to investors through growth or dividends goes to
zero atR' = W_C_ and all earnings go to service debt. The probability
that the debt charges will be covered is not really affected by the amount
of retained earnings or equity investment in the new firm, it is now reduced
to:
P(debt coverage) = 1 - P (R^ ^ W^^Cj^)
This assumed the situation where retained earnings or equity funds are used
to cover debt charges is totally unacceptable.
The amount of debt used is then the maximiam amount consistent with the
ownermanagers'
risk utility function associated with defaulting on loans
or covering loans from other sources. The amount of risk for each level of
debt in the capital structure is then established by the expected rate of
return curve as previously demonstrated.
20
As noted earlier, retained earnings should be used in amoxints consistent
10with the growth objectives of the firm. According to Brigham and Smith
the percentage of equity that must be obtained through external sources
, 11xs given by:
W
\^\
-
G.
G > R
where: W = percent of commonstockholders'
eqiiity in the capital structure
"Wn =percent of retained earnings in the capital structure
G = desired asset growth rate
R - the after tax return projected on existing equity
If R > G the firm is able to generate sufficient funds internally. If
R <. G it becomes more difficult to raise new equity capital. If we assume
that the firm is in its first year of operation, W > 0. Furthermore, to
be consistent with our original assumptions about growth it should be evident
that all retained earnings should be reinvested in the new venture during its
first few years of operation.
To stmimarize, the firm should acquire as much low cost debt as possible
consistent ijith the owners managers'risk utility function as determined
by projected earnings for the following year. All retained earnings should
Brigham and Smith, Og- Git. , p. I87.
-'--'ibid, p. 187,
21
be made available for reinvestment, if growth is the assumed prime objective
of the new venture and additional equity acquired only as necessary to meet
additional investment needs. This iterative approach to optimizing the
capital structure of the new firm should initially yield close to the
minimum practical cost of capital consistent with its growth and risk'
objectives. Ftirthermore,this approach will readily point out which invest
ment alternatives are not consistent with the firm's growth and risk objectives
even at the optimum cost of capital.
22
II ,
COST'
OF DEBT THEORY
If we adhere to the Modigliani and Mller propositions previously
12discarded, we would arrive at a cost of debt given by:
S=
'^t ^^-^c)
where: ^.=
after tax discount rate- applied by the investingpublic to the stock of an unlevered firm in the
same risk class
t = corporate tax rate
C_ =effective cost of debt to the firm
However, there are numerous assumptions associated with this estimate of
the cost of debt that must be noted to vigorously accept and apply this
to our decision model. These assumptions are:
1. The effective cost of debt is that return it must earn in order not
to alter shareholder welfare as indicated by stock price,
2. Some means of measuring the after tax discount rate applied by
investors to the stock of unlevered firms in the same risk class
exists.
3. There is a market for the stock which sets a price toearnings'
ratio and itsinvestors'
exercise arbitrage fully to compensate
for varying corporate debt ratios.
'^'ilbur G. Lewellen, Cost of Capital, p. 44.
23
For new ventures, the stockprice'
is often a highly volatile level deterr.ined
by a rather small market (if a market exists) sample based on the initial
prospectus of the firm or recent earnings'information. There is no well
defined risk class associated with the new firm and therefore there is
little chance of measviring the after tax discount rate applied by investors
to the stock. Therefore it is evident that an application of this cost
technique to the cost of debt is not appropriate for our model.
The more conventional approach to the cost of debt capital is the
after tax, after floatation cost, effective rate the firm must pay for
debt. It is defined explicitly as:
"The rate of return that must be earned on debt-financed
investments in order to keep unchanged the earnings
13available to common
stockholders."
This turns out to be the after tax effective yield on the debt. If we
letD' be the rate of interest on the debt adjusted for acquisition premiums
or discounts and t to equal to the corporate tax rate we have
S= ^' (^ - ^c^
It is this cost of debt, which is compensated for the tax deductability of
interest payments, that will be used as the true cost of debt in the model for
the new venture. This makes no assiomptions pertaining to the effect of debt
on the stockholders or thestockholders'
valuation of the firm's capital.
These factors are considered in the overall model and would be double counted
if considered here also.
13J. Fred Weston, Managerial Finance, p. 341.
24
III. COST OF RETAINED EARNINGS THEORY
Again starting with the Modigliani and Miller approach to the cost of
capital they conclude that the cost of retained earnings is:
"Simply that profit rate which will raise the price of the firm's
stock by enough that after capital gains taxes are deducted, its share
holders are as well off as if they had received a dividend payment instead
14and paid the associated income tax.
"
This compares reasonably well with the conventional argument that:
"The cost of retained earnings, or the return that might be earned
on investments financed by retained earnings is equal to the rate of return
15that investors expect to receive on the
stock."
However, Lewellen, in his expansion of the Modigliani and Miller approach
arrives at the following cost of retained earnings :
R-
(i-y
where: o< +- same as in prior debt formula
**<t
t = personal tax rate of investor
t = capital gains tax of investor
14 /
Lewellen, Cost of Capital, p. 65.
-'j. Fred Weston, Managerial Finance . p. 345.
25
The o<j terra still requires the definition cf a public discount rate
applied to the common stock in an unlevered firm of the same risk class.
Again this is difficult if not impossible to obtain for the new small firm.
(1 - t )However, the ratio ^^^^i"^ ^^^ opportunity ratio of tax
advantages to the investor which is different than more conventional
expressions for retained earnings. Assuming that funds are available
for dividends, if the stockholder takes the dividend he must pay
personal taxes on that dividend at a rate t . If the investor leavesP
funds in the firm in the form of retained earnings he must pay taxes
ultimately on these retained earnings in the form of capital gains on his
sales of stock in the firm. The opportunity cost associated with retained
earnings to the firm would therefore decrease as personal taxes increase
and increase as a function of capital gains tax. This ratio therefore
more accurately describes the opportunity cost associated with retained
earnings than the suggested (1 - t ) factor of Brigham and Smith in the
Cost of Capital for the Small Firm. The Brigham and Smith factor indicates
that as the capital gains tax were increased the cost of capital to the firm
decreases. However this does not logically follow. As the capital gains
tax increased the investor might logically want the firm to give him more
dividends and put a higher premium on having the firm retained earnings.
However, as his personal taxes increase he might put less premium on
receivingdividends and more premium on receiving capital gains as described
by Lewellen 's ratio.
"'Brigham and Smith, Op. Cit. , p. 188.
26
A combined expression for the cost of retained earnings can be
formulated as :
1 - tJ
S=
4 <rr^'
If t > t C^ <C'
p'^
g R^
E
t < t C >C'
p^
g R E
Where :
C' = cost of common equity less flotation cost factors
t = investor tax rate on dividendsP
t = investor capital gains tax
As with the more conventional approach, this cost is defined in terms of
the expected return on common stock and is defined in the next section as
the cost of common stock prior to flotation costs.
27
IV. COST OF EQUITY THEORY
Lewellen interprets the Modigliani and Miller approach to cost of
equity capital as :
^ tC =
E 1 - b
where: C = the cost of equity capital
o< .
= the after tax discount rate applied by the
investing public to the stock of an unlevered
firm in the same risk class
b = discount factor applied due to flotation costs, etc.
Again, as stated previously, o< . is difficult if not impossible to obtain
and carries with it several assimptions not applicable to the new small
firm, as noted previously.
However, some estimate of the rate of return investors expect on
their equity is required. Gordon has most closely approximated this as:
_,dividend
, . , ^u -
^j.
C_, =: + expected growth
-
"5 + gE price
X-
oP
'.iJhere: Cp= the rate of return investors expect on their capital
D = annual dividend payment
P = current price (some say it should be average)
g= expected growth
Lewellen, Op. Cit., p. 72.
^^J. Fred Weston, Op. Cit., p. 40?-
28
Several areas of controversy exist over the use of Gordon's model. First,
he capitalizes an infinite stream of dividends to arrive at this expression.
This assvimes some priori knowledge of the future dividend payments. This
is seldom available. The model also assumes all financing is done with
retained earnings. However, in a new venture dividends are very unlikely
to occur or be expected by the investors for the first few years. This
reduces Gordon's model to:
^E=
^
It therefore remains to be determined what the investors'after tax
expected return through growth will be vxith the new venture and the
cost of eqiiity capital can be written as:
C^ =
E 1 - b
for the new firm. Where 1 - b accounts for flotation costs.
Eqiiity capital in the new firm is acqiiired from both"inside"
investors
and outside investors and each type of capital has its own peculiar cost
characteristics. The inside investor is interested in control of the firm
to assure himself of control over his investment. Another way of looking
at the associated cost of capital is by relating the percent control to the
expected earnings. The cost of such capital may be written as:
C' =
(Projected Earnings^ ^ ownership
E^Insiders' Contribution
^ ^
19Roland Robinson, Financing the Dynamic Small Firm, p. 51 '
29
At first, this may seem to be a myopic view of the insideinvestors'
intentions. However, it can be reduced to our previous cost of equity
expression where we understand that the change in projected earnings based
on the insiders'investment is essentially oxtr definition of growth and the
percent ownership is his share of that growth. In this case, the 1-b
term goes to 1 as b goes to zero since there should be negligible costs
associated with inside investment of funds.
The inside investor can dilute the value of the commonstockholders'
equity in a firm. The initial sale of large portions of the common stock
to inside investors may make future public offerings less attractive.
For example, if the owners of the firm decide to hold 51^ of the firm's
stock for a contribution of ifo of the total equity of the firm the cost of
the capital from this source will be calculated as: For a given return on
total capital these individuals will in essence take l/2 the earnings due
other investors if there were equal distribution of stock per invested
dollar. This is often explained by making inside investors essential
to the success of the new firm and their payment is for this contribution.
This brings out the point that for every growth by a factor of 2 expected
by the outside investor the inside investor may expect a multiple of this
number. Therefore growth in earnings (g) as it is defined in the cost of
equity equation can vary considerably depending on the sophistication of the
investor.
In this sense the growth in earnings required by the inside investor
to realize his desired growth in investment is multiplied by the discount
30
factor by which his stock price was reduced and the commonstockholders'
investment is directly related to the firm's growth in earnings. This is
considered more rigorously in the Appendix E.
In summary we will use the following definitions of the costs of the
various components of capital in the newventures'
capital structure:
Cj= D'(l - t^)
C^ =
'E . 1-b
and the total cost of capital will then be given as:
^C=
^^DD'(l- t^) +
W^ g(-1
t^)+ Wgg
R(. =
Wj^D'(l - t^) + g ( ^R ^rrh
^''e )
Based on this model attempts will be made to calculate typical costs
of capital for the specified type of new small firm.
31
CHAPTER IV
COST OF CAPITAL FOR LOCAL
SMAiL BUSINESSES
The objective of this research is to obtain accurate information on the
cost of capital for new, small, high technology firms. Such information can
then be used to describe a composite firm representative of the firm in this
risk class. This composite firms capital structure can then be used in
conjection with the internal rate of retiirn versus risk computer program to
evaluate the feasibility of new ventures.
I. DESCRIPTION OF RESEARCH AND ANALYSIS
The firms studied were limited to upstate New York to permit close
contact with financial information. This was accomplished by selecting all
local firms from the over-the-counter weekly listing in the Upstate Business
Journal. After initial selection, further research was performed to
insure that the selected firms fit ray previously defined criteria for a
new, small, high technology business. This was accomplished through reviewing
the local business papers from January 1, 1972. Where this information was
not available by such means, calls or visits where made to the firm in
question. In this manner, I foiind 25 out of a possible 73 firms that met
the requirements of this study.
32
Letters were written to the financial officer of each of the 25 firms
requesting their most recent prospectus and latest financial summary. A
sample of this letter is shown in Appendix A. Thirteen positive responses
and one negative response were received in response to the letter. This
was followed by a telephone call or -visit where necessary to clarify the
financial data. These results permitted approximating the cost of capital
and capital structiire for the responding firms.
Realizing that many of the firms to be studied were financed by venture
capital businesses, reviews were made of ciirrent business literature to
locate estimates of the expectations of venture capital firms. The 1971
publication of the Boston College School of Management entitled "Venture
Capital, a Guidebook for New Enterprises"was consulted. It presented ventiire
capital information on 99 venture capital firms. It was written for the New
England Regional Commission yet included venture capital corporations
throughout the North Eastern United States. This source provided quantitative
information on the expectations of 17 venture capital firms. Quantitative
information on RAND Capital Corporation of Buffalo was also located from
local news publications.
Finally, the Upstate Business Joiirnal over-the-counter biweekly listings
were used to plot the stock performance of the 25 firms selected. These
plots were made over a nine month period from January 1972 to October 1972
and used to interpretinvestors'
expectations based on market performance of
stocks in the appropriate risk class. The nine month period was a subjective
limitation imposed by the initial publication of the Upstate Business Journal.
33
The sample mean and standard deviation on all data was calculated
20using:
Sample Mean = X =
^= I
Standard Deviation = S = / a"= I
Where: N = Number of samples
The accuracy of this estimate of the assumed normally distributed
population mean was tested using the"students"
t distribution since
the sample sizes were less than thirty. The confidence limits for the
21population mean are given by:
X + tc (^0
where: t = critical values or confidence coefficients
c
The results for each area of research are presented in the following text
and reduced with analysis oh a functional basis.
20
Murray R. Spiegel, Statistics, p. 70.
^Spiegel. 0. Cit., p. 189.
34
II. COST OF EQUITY AND RETAINED EARNINGS FOR THE SURVEYED FIRMS
As noted in the preceding discussions on the cost ofstockholders'
equity (C^), this cost is directly proportional tostockholders'
expectations.
For the purpose of this study, thesestockholders'
expectations have been
divided into two classifications. The first is the inside venture capital
investor expectations and the second is the over-the-counter secxirities and
new issue investors'expectations.
The venture capital investor usually invests"inside"
money at either
the start of a new venture or at a point when the new firm's products are
developed and ready to manufacture and sell. As noted previously, their
expected return is often higher than"outside"
investors and is reflected in
the total cost of equity by some factor K due to the higher risk factor.
This factor may be arrived at through sale of inside stock at some discount
over the stock publicly offered as shown in Appendix E. However, this
discount decreases the return to"outside"
investors which is eq\iivalent
to increasing"inside" investors'
return. Therefore, the venttire capital
investors'expectations are taken directly at face value as well as the
"outside" investors' expectations based on stock performance. The average
K factor will be based on the average data.
As shown on the following page, information on eighteen venture capital
firms has been acquired. Their exjsected return on invested capital ranges
from 12^ per year to over 100^ peryear. The average of all expectations
is 42^ per year return on invested capital. This result appears to be
representative of the industry based on the small varibility in the data
obtained. However, it is further recognized that this sample size is
indeterminately small compared to the size of the total population.
35
VENTURE CAPITAL FIRMS
SoTirce
1. Albert J. Kelley, Frank B. Campanella,John McKiernan, Vent e Capital
Authors Estimate p.
2. First Connecticut SBIC - p.4l+
3. Bxirgess & Leith - p.66*
4. Creative Resources, Inc. p.68*
5. Explorer Fund, Inc. p.70*
6. Federal Street Capital Corp. p.71*
7. Financial Investors of Boston, Inc. p. 72*
8. Gardner & Preston Moss, Inc. p.76*
9. Kidder, Peabody & Co., Inc. p.81*
10. Koch Venture Capital, Inc. p.82*
11. Paine Venture Fund, p.87*
12. Resoiirces Technology Management Co. p.88*
13. Technology Search Associates, p.89*
14. Baker Technology Associates p.96*
15. Carr Management Company p.100*
16. Diebold Venture Capital p. 108*
17. Neuwirth Financial p.121*
18. Rand Capital Corp. **
Buffalo, New York
Expected Return
25 - 405g/year
12%Iyear
5 times in 5 years
(38^/year)
10 times in inv. period
5-10 times in 5 years
(38^/year)
35 - 50^/year
2 times in 2 years
40 - 50^/year
20 - 30^/year
10 times in 3 - 5 years
(75^/year)
10 times in 5 years
(75^/year)
5 times in 5 years
(38^/year)
40^/year
40^/year
10 times in inv. . period
10 times in 7 years
(405g/year)
5-8 times in 3-5 years
(60^/year)
30^/year
5 times in 5 years
(38^/year)
* From Albert J. Kelley, Frank B. Campanella, John McKiernan,
Venture Capital.
** From Upstate Business Journal. , May 2, 1972, p. 10.
36
Since the sample size for the venture capital data is less than 30, and
if we assume the population very large and normally distributed, the
accuracy of the estimated mean will be evaluated based on the "students"
t distribution with X = 42 and s = 16.27.
Within specified limits of confidence the population mean can be estimated
>,22
by:
42 - y^ I
"^conf. limit '^ 16.27 \/ 15 < ^conf. limit
or z/ lies in the interval:
42 - tconf . limit
At the 55^ confidence level the population mean was calculated as:
41.5^ < yi/ <- k2.5%
At the 95^ confidence level the population mean was calculated to be:
36.4^ < /^ <: 47.6^
This indicates that there is a better than 5^/5^ chance that the mean of the
total population of venture capital firms'annual expected returns on
investments is 42^ + 0.5^. Further, this calculation indicates there is
a 95^ chance that the entire venture capital population expects from
36.4/S to 47.6^ annual return on its investments if the preceding assumptions
hold true.
22
Murray R. Spiegel, Statistics, p. I89.
37
The second stockholder classification for which attempts have been
made to estimate expected gains through stock appreciation are piirchasers
of over-the-counter stocks and new issue investors. In estimating this
factor the following assumptions were made:
1. The growth expectations of this type investor can be reflected in the
current market in which he invests.
2. The local OTC stocks and NASDC listed upstate stocks with a high
technology basis are representative of the stock market for new
high technology ventures. They are in the appropriate risk class.
As evidenced by the research on each of the 25 firms of local interest
all but two were found acceptable for this study. Gould Pumps was found
to have sales well beyond the previously defined limit and Megadyne closed
its doors during the coiirse of the study.
For the 25 firms studied the bid and asked price fluctuations were
plotted over a nine month period from January 1, 1972 as shown in Appendix C.
As noted earlier, my basic premise is that theinvestors'
stock appreciation
expectations on new high technology issues are directly reflected by the
recent performance of stocks in similar risk class. If we assume an
23investor will use only one of three basic strategies:
1. Invest to maximize his maximum gain.
2. Invest to maximize his minimum gain.
3. Invest to minimize his maximim loss.
The later two strategies would tend to force an investor toward the large
exchange stocks which are much less volatile. The first strategy is felt to
be most appropriate for investors in new small high technology firms.
~Z3Kyohei Sasaki, Statistics for Modern Business Decision
Making, p. 213.
38
In general, it is assumed that this type of investor concentrates on
the largest potential gains possible in the appropriate risk class
investment. I have also neglected the trading cost and bid/ask
differentials for this analysis taking the most optimistic view of the
market in line with perceived investor attitudes. A summary of the
stock price fluctuations is shown in the chart on the next page.
39
SUMMARY OF STOCK PRICE CHANGES FROM DECEMBER 31, I97I TO OCTOBER 31, 1972
Average Maximum Maximxm
Change Increase Decrease
AD DATA 0% +2005^ -200^
AQUASONICS-700% +3005^ -13005^
COMPUTER CONSOLES - 18^ + 51^ - 67%
DETECTION SYSTEMS, INC. - 26^ + 20^ - 50%
FERRONICS, INC. - 10^ +1005^ .150^
GOULD PUMPS**0% + 35^ - 31^
GRAHM MANUFACTURING - 30^ + 38^ - 43^
GRAPHIC SCIENCES - 33^ + 35^ - 36^
HAMILTON DIGITAL - 34^ + 50^ - 45^
INFODATA SYSTEMS - 55% + 20^ - 615^
KAYEX - 665^ +160^ - 77^
LASEP. ENERGY 0% +100^ - 50^
MARINE RESOURCES - 66^ + 87^ - 83?^
MEGADYNE* +600^ + 600^ - k6%
MESON + 40^ + 90^ - 47^
METRIX - 78^ +350^ - 90^
PHOTOMETRICS + 485^ +100^ - 40^
R. D. PRODUCTS - 80^ + 16% - 80^
ROCHESTER INSTRUMENT SYSTE14S + 41^ +1005^ - 44^
SCIENTIFIC RADIO, INC. + 25^ + 39^ - 13^
SYKES DATATRONICS + 46^ +133^ - 50^
TAPECON, INC. + 50^ +120^ - 55%
TEL PAGE +100^ +100^ - 50%
TRANSMATION- 505^ + 25^ - 55%
YONDATA- 50^ + 16^ - 50%
** Data not used since firm was found too large for this study.
* Data not used for analysis since firm was out of business by November 1972
41
As noted in the theory, the cost of equity is defined as :
Since many firms floated their own new issue and those that paid
commissions and had noticable flotation costs showed b < 10^, it
will be neglected in light of the large value of g(lOl^). If one
considers the insideinvestors'
expectations of 41^ it is unreasonable
to assume K <! 1. Therefore, at best the results indicate that mean
investors'expectations lie between 41^ (most conservative ) and 101^^
(most optimistic). Both extreme values will be used sequentially in the
composite capital structure.
That is:
C = 41^^1 -
C^= 101^
As noted in the theory, the cost of retained earnings will be defined as;
C
which for this study can be reduced to:
1 - t
Cr=
Cg (Y
^)
V/here: t =investors' tax rate on dividends
P
t = investors'capital gains tax
g
42
With long term capital gains tax, 1/2 that of ordinary income we can
write:
1 - t 1 - t
)
1 - t 1 - t(tr^ ) = (. ^
1 - tg
'1 -
-5t
When this factor is plotted for practical investor tax rates as shown
below it is evident that it is not extremely sensitive to tax rates.
J \
0.-4 -
X
A-
o 80
yvp
43
The average value of the factor is 0.75. Therefore one can reasonably
assume C = 0.75 C in the average case. However, the research indicatesH ill
that few firms had sufficient retained earnings to consider in their
capital structure i.e., W "7^ 0. ^^^ ^rH?~ ^*
44
III. COST OF DEBT FOR THE SURVEYED FIRMS
As noted in the theory on the cost of debt capital, this cost should
be defined as :
V;here:D'
is the rate of interest adjusted for acquisition costs
t is the corporate tax rate.
Of the 25 firms surveyed, sufficient information for calculating the
average interest rate on debt capital was available on 9 firms.
The weighted average value of the interest rate information collected
was found to be 8^ with a standard deviation of 0.88^. Since the sample
size was small (9) the"student"
t distribution was again used to relate
the results to the assumed normal total population. At the 55% confidence
level the actual population mean interest rate could lie between 8.2 and
8.3 percent. At the 95^ confidence level the actual population mean interest
rate could lie between 7-67^ and 8.87^.
This small variation in interest rates is a result of several factors.
First, it was likely that most firms delt with the same banking community
in upstate New York. Second, it was found that many loans were SBA backed
and therefore had a maximum interest rate fixed by the federal government.
Most of the firms had minimal earnings due to heavy investments into
the research and development of new products. Therefore, the minimum tax
rate of 22^ will be used as it is applicable to annual net earnings under
$20,000. The combination of &i% interest rate and 22/S tax rate produces an
average cost of debt capital given by:
45
Cjj= 8i (1 - 0.22) = (,.h%
This cost will be used in the estimate for the cost of debt of the
composite firm.
IV. THE COMPOSITE FIRJ'I AND A SAMPLE INVESTMENT OPPORTUNITY
The cost of capital has been defined as:
S=
Vl-^
Ve^Vr
-^
^D^D
Where: W is the relative weight of each component in the capital structure.
C is the effective cost of that component.
The research surveyed 25 firms to determine the effective cost of the
various components of this capital structure. In summary, this led to
the following estimates :
C^ = hl% to 101^E
\= 0.75 Cg
%= 6.4^
The relative weight of each of these components was also sampled and
is summarized on the following page. The accounts payable portion of
the capital structure was found to average 11^ of the firms total capital.
This, however, was in line with an. average payment period of thirty days to
take full discounts in all but one case. Since this cost of debt is
effectively 0 when the discount is taken, it follows that the (WC) product
for this portion of the capital structure is also zero. The "student" t
distribution was again used to relate these findings to an assumed normal
SUIMARY OF CAPITAL STRUCTURES
46
Accounts Payable Debt Stockholders ' Equity
Firm #1 335^ 20^ 43^
Firm #2 155^ Z5% k9%
Firm #3 M 60%
Firm #4 10^ ZG% 55$
Firm #5 9^ 0 86%
Firm #6 \(>% 58^ 23%
Firm #7 6% 37^ 5k%
Firm #8 5% 28^ 6k%
Firm #9 Q% 0 92%
Firm #10 \Qf% 62% 21^
Firm #11 5% ke% 40^
Firm #12 11^ 57% 26^
Firm #13 4^ 0 72%
Sample Meian 11^ 30^ (40^) 53%
Sample Std. Dev. 7.5i 23^ (14.5^) 225^
55 Conf. Lim.* + 0.3 + 0.8 (+ 0.6) + 0.8
95 Conf. Lim.* + 4.2^ +11,8 (+ 8.8) +11.3^
Number of Firms
in Statistic 12 13 (10) 13
?"Students" t distribution estimate
It should be obvious from the above summary that not all components of the
capital structure are included. The s\m of the three components will
therefore be less than 100^.
47
population. At the 55% confidence level, the population mean would lie at
11^ + 0.3^ and at the 35% confidence level 11^ + 1^.2%. This variation is
still within practical limits for assuming that most firms sampled are
taking full discounts on their accounts payable.
Debt was found to average thirty percent of the capital structure in
the firms analyzed. It was found to average forty percent in those firms
having debt in their capital structure, as shown in parenthesis. The lack
of significant amounts of debt in the capital structure is not too unusual
when one considers that several of the firms analyzed are new and have little
or no revenue on sales. The worse case analysis I will use for the composite
corporation consists of a minimum amount of debt since its effective cost is
much less than the cost ofstockholders'
equity. Further, it is realistically
in line with the high risk firms analyzed to have a minimiam amount of debt.
The variability in the estimate of the population mean was found to be
+0,8^ and +11.8^ for the 55% and 95^ confidence levels respectively. This
wide variability in this estimate is mainly a result of the lack of debt in
23% of the samples. Furthermore, two firms leased their products and there
fore were heavily debt financed. The percentage of debt in the capital
structure will be taken at Wj. = 30^ for the composite firm in light of
the above analysis.
The percentage ofstockholders'
eq\iity in the capital structure of
the firms analyzed was found to be 53'^ with a standard deviation of + 22^.
This large variability in the data is directly a result of the lack of
debt in several finns with excessive debt in others as noted above. Using
48
the "students" t distribution, the uncertainty in estimating the population
mean was determined. At the 551 confidence level the population mean
(assumed normal distribution) could be said to lie between 52.2% and 53.3^
and at the 95^ confidence level between 41.7^ and 64.3^. This estimate is
considered representative of the population in the appropriate risk class
and therefore 53^ is used as the percent equity in the composite firm
(W^= 53^).
In summary, the composite firm could be described as:
Cost of Equity
Percent of Eq\iity
Cost of Retained Earnings
Percent of Retained Earnings
Cost of Debt
Percent of Debt
Cost of Accounts Payable
Percent of Accounts Payable
When applied to our original equationthis yields:
Ct=
w^Cj^-^
WgCg+
W^C^+
Wj^C^
= (0)(11) + (.53)(41 to 101) + (0)(0) + (.30)(6.4)
C^= (21 to 53.5) + 1.9
C^ 55: 23 to 56^
For the composite firm I will use W^^C^= 1.9^ and W^C^
= 21 to 53.5^
s 41% to
^E= 53^^
^R= 0.75 C
\0
% 6.4^
%3056
^L= 0
\ 11^
49
V. A SAMPLE INVESTI4ENT OPPORTUNITY
I have assimilated a sample investment opportunity from my personal
experience to assist in illustrating how the cost of capital and capital
budgeting model may be used. This sample is svimmarized on the next page
in the format outlined in Chapter II. Each variable is based on marketing
product information obtained from a small firm appropriate for the study.
The probability of occurrence of each event was subjectively assigned based
on the experience of several marketing and engineering personnel. There are
many techniques which may be used to develop subjective estimates of the
type used in the sample. It is not the purpose of this paper to limit
the models applicability by limiting it to one technique for assigning
subjective probabilities to the input variables. The technique used may
be suboptimal and its optimization should be the subject of another study.
50
SAMPLE INVESTMENT OPPORTUNITY
Minimum Average Maximum
Qty Likelihood Qty Like! i hood Qty Likelihood
Annual Sales
Less Variable
Costs Plus
Estimated Taxes 25K 0.1 lOOK 0.7 350K 0.2
Fixed Annual
Operating Costs
Residual Value
of Investment
Useful Life of
Investment
Initial Investment
2OK
40K
0.2
0.3
0.1
0.2
50K
lOK
0.6 lOOK 0.2
0.4
0.8
20K 0.3
10 0.1
lOOK 0,75 15OK 0.05
NOTE: K = 1000 multiplier
51
CHAPTER V
COMPUTER PROGRAM TO GENERATE
IRR VERSUS RISK CURVE
The computer program outlined in the flow chart on the following
page, (Figure #5) takes data related to the proposed new venture and
provides data to plot a histogram of the probability of occurrence of
various internal rates of return on a new ventxire.
The program starts by reading the following variables:
A(J) = Annual sales less variable costs and estimated taxes
B(J) = Fixed annual operating costs
C(J) = Residual value of investment
D(J) = Useful life of investment
E(J) = Cost of initial investment
V(J) = Probability of A(j) occurring
W(J) = Probability of B(j) occurring
X(J) = Probability of C(j) occurring
Y(J) = Probability of D(j) occurring
Z(J) = Probability of E(J) occurring
'flhere J = 1, 2, 3 minimum, average, maximum value of each variable
52
Through DO Loops nested five deep all possible combinations of the five
variables are selected along with their associated probabilities of
occurrence. The value of S is set equal to 1 initially and incremented by
1 with each calculation to keep track of the 243 results. The rate of return
RR is initially set to zero and subsequently incremented in steps of 1/2%,
The value of LD is incremented from 1 to the useful life of investment (BD)
and through the associated DO loops, the present value of each year's
revenue is calculated. The residual value of the investment is then brought
forward to its present value and added to the present value of each year's
revenue. This process is repeated in l/2^ increments until the calculated
present value of revenue is greater than or equal to the cost of the
initial investment. The rate of return at this point is stored as RRF(l).
The probability of FFR(l) occurring is then calculated and stored as
P(l). All variables selected for the Ith iteration are then printed out
along with P(l) and RRF(l), I is incremented by one and a new set of
variables are selected. After all 243 possible values of RRF(l) are
calculated with their associated P(l) the program could group the data
into appropriate ranges, I then could total the probability of an occiu-rence
as PX(PRR) whose abscissa ranges are less than each PRR to arrive at data
for plotting the cumulative probability distribution of returns.
s>rART
REAP kc:y)^c::,
,'^.:-:
YCo)-,^CT)
r ^ x+ 1
DO i O 5
BA=A.-.,Tj ,
'r-'{-
/-<-
DO 0:i
JA = 1. 2
EB = Ba A ) EW =W CTA)
-X
^C^ -Xi76y/
D.
j-cM-
/
\
\
'D).:^
N - O
\06
JL"X
t4= 100 7
RR=^R.R-f 0.5
LD = &D
\
DO \03
ELA -EA -h (SA.-SB)/ Cl
&.B=E.A-f CBC/(\+RR)B
PCX) = &V BW 'd-< Bv
H-H4-i
Ev^-
^ rrfcx) ^p:i)
53
I. =X-t-r
X
Do \2.4
VI RR ^\jSO
\
DO 'il-}-
XF
^^i -^ \-
\ IN-
,
y
\ f
PXCMRK;-r-.~} \- r'V V-
1-
^122
1! 12-4J-
DO 127
\kIRR=^U50
.PC
'
''- ;. r-^ I]
127 I
'P< (fN^K ^\)
\ --,
C u Kv'
, \z-^n -JZ
54
CHAPTER VI
SUMMARY OF RESULTS AND CONCLUSIONS
The aforementioned computer program was used with the sample
investment opportunity to define its risk and return characteristics.
These results were then compared to the cost of capital components.
I. SUMMARY OF RESULTS
The computer program internal rate of return and risk data was plotted
as a probability distribution histogram in Figure #6 on the next page.
This curve indicates that there is a 25.5% chance that the internal rate
of retxirn will be less than 0.5^, a 29.5^ chance it will be between 40
and 6Qf% and a 31^ chance it will be greater than 100^^. The data was
grouped in 20% internal rate of return ranges due to the wide range of
possible returns obtained. This wider range of grouping the data also
reduces the likelihood of assuming excessive precision in the estimating
process.
The cumulative probability distribution of returns is shown in Figure
#7- The curve shows the probability that the abscissa value of return
will not be achieved. It also permits easy analysis of the sensitivity
of the venture to varying amounts of the component costs of capital. The
weighted cost of debt and total weighted average cost of capital data
derived from the research are plotted as straight lines from their abscissa
values.
55
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m"--W--
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-^:-!T
m
-H-;- xtht_ "-JTJ
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^fl3-;t=
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32
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44
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1
:- -
i \ :-.t
!
4h
WAX
m -I ; I
-Sf
4f+
--rr-
1-4-1
-
\Z\'l
PT
i:t;
+4;
4:4
4r
ti:ti
hKh
TV-'s::.
"T"
1
II .
-h-r
-i-
^^:
HI20 40 fco ao oo
57
The utility of this approach to optimizing capital structure can now
be readily demonstrated. The weighted cost of debt whose typical value
for the new small firm was found to be 1.9^ is shown graphically as the
vertical line nearest the origin of Figure #6. In line with this proposed
approach, if one decreased the amount of debt financing used for this
venture to near zero, the likelihood of defaulting on payment would be
25.5%. For the typical small firm in this risk class, the likelihood of
defaulting on its debt would be 27.2^. However, of more significance is
the apparent result that an increase in the amount of debt by a factor of
two to 60% of the total capital would produce an insignificant increase
in the likelihood of default. It would also significantly reduce C_, and
therefore significantly reduce the likelihood of stockholder dissatisfaction.
The two plotted total cost of capital lines reflect the variability in
expected equity costs obtained from the research. If one chooses the minimum
return to investors C_ as appropriate, the probability of the firm's
min
success in the eyes of the investors is 70^. If one chooses the maximum
return to investors C_ the probability of the firm's success in the eyes
max
of the investors is reduced to 41.5^. However, the insensitivity of the
returns to varying amounts of debt showed that a factor of two increase
in debt should not increase significantly the risk of default on debt.
Furthermore, this increase in debt would permit reductions in the higher
costing equitycomponents of capital and reduce the overall costs of
capital. For example, theincrease in debt proposed earlier would increase
the probability of the firm's success in the eyes of the stockholders to
70^ from h\.5%. This is because C would be reduced to 28% due to a
max
57^i change in the weight of equity.
58
The above example demonstrates the utility of this approach. However,
it is recognized that any application of this technique must also take into
consideration the attitude of the debt sources and the difficulty associated
with reducing equity holdings in a successful firm of this type.
II. CONCLUSIONS AND RECOMJffiNDATIONS FOR FURTHER STUDY
I have concluded that the proposed technique for evaluating capital
investment alternatives and optimally adjusting the capital structure of
new small firms has demonstrable utility. It permits effective visual
correlation of a proposed new ventxires risk with the way it is financed.
This correlation permits variations in the new firms capital structure to
achieve minimum risk and cost of capital.
Further research should be performed to accurately describe an effective
technique to subjectively assign probabilities to the component characteristics
of a proposed new venture. F\irthermore,correlation coefficients could be
developed for each component of the new venture decision matrix which would
permit a more accurate estimate of the total new venture probability
characteristics. It is also felt that techniques for rapidly modifying
the capital structvire could be developed within obvious practical limitations.
Recognizing that this additional work is essential does not negate the
utility of the proposed analytical tool. This is more evident when one
compares it to the oversimplified techniques now currently employed to
analyze new ventures. This technique should immediately provide a useful
adjunct to the current analytical techniques and provide a more sensitive
financial gioide to new venture investors and entrepreneurs.
59
BIBLIOGRAPHY
Bierman, Harold J. Financial Policy Decisions, London:
The Macmillan Company, 1970.
Brigham, Eugene F. and Smith, Keith V., "Cost of Capital to
the Small Firm", Engineering Economist. Vol 13, #1
Fall 1067, p. 1-26.
Gordon, M. J., The Investment, Financing, and Valuation of
the Corporation. Homewood 111.: R. D. Irwin, 1962.
Hertz, David B. , "Risk Analysis in Capital Investment",The Theory of Business Finance . ed. Stephen H. Archer
and Charles A. D'Ambrosio. New York: The Macmillan
Company, 1971.
Kelley, Albert J. , Campanella, Frank B. , and McKiernan, John,Venture Capital A Guidebook for New Enterprises
.
Chestnut Hill, Mass: Boston College, 1971.
Lewellen, Wilbur G. , The Cost of Capital. Belmont California:
Wadsworth Pub. Co., I969.
Lockwood, Leonard (ed. ) Upstate Business Journal. Volume 2.,
Rochester, New York, 1972.
Loehwing, David A., "Loosening the Purse Strings", New York:
Barron's, April 24, 1972, p. 3.
Modigliani, Franco, and Miller, Merton H. , "The Cost of Capital,
Corporate Finance,and The Theory of
Investment"
,The
Theory of Business Finance, ed. Stephen H. Archer and
Charles A. D'Ambrosio, New York: The Macmillan Company, 1971.
Robinson, Roland I., Financing The D.ynamic Small Firm, Belmont,
California: Wadsworth Publishing Company, I968.
Sasaki, Kyohei, Statistics for Modern Business Decision Making.
Belmont, California: Wadsworth Publishing Company, I968.
Small Business Administration, The Small Manufacture and His
Specialized Staff. Washinton, D.C.: U. S. Government
Printing Office, I967.
Small Business Administration, Publication OPI-I6. Washington, D.C.:
U. S. Government Printing Office, February 1970.
60
Speigel, Murray R. , Statistics, New York: McGraw-Hill Book Co., I96I.
Weston, J. Fred and Brigham, Eugene F. , Managerial Finance, 3r'd ed.
New York: Holt, Rinehart, and V/inston, I969.
Weston, J. Fred, "A Test of Cost of Capital Propositions", The
Theory of Business Finance, ed. Stephen H. Archer and
Charles A. D'Ambrosio. New York: The Macmillan Co., 1971.
Zwick, Jack, A Handbook of Small Business Finance, Washington, D.C:
U. S. Government Printing Office, I965.
61
APPENDIX A
A SAMPLE OF THE LETTER WHICH WAS SENT TO THE RESEARCHED FIRI-IS
4l Penn Lane
Rochester, New York 14625October 18, 1972
Financial Officer
TEL-PAGE CORPORATION
401 Sherman Street
Rochester, New York
Dear Sir:
I am reviewing the characteristics of Rochester
area small businesses as part of my graduate studies
at RIT. I have selected your firm for analysis in
this thesis. I would appreciate a copy of your most
recent prospectus and your latest financial siimmary
to aid in this study.
Yours truly,
B. R. Robinson
63
APPENDIX B
A DESCRIPTION OF RESEARCHED FIRl^S
64
AD DATA SYSTEMS
830 Linden Avenue
Rochester, New York
AD DATA SYSTMS is a nine year old electronics firm specializing
in conversion of information into a form readable by computers. It
employes 125 people with net 1971 sales of $861,133, earnings of
($129,208) on assets totaling $1,230,310. Its performance in sales
and earnings over the last five years has been cyclic with a generally
upward trend.
August 27, 1971 CAPITAL STRUCTURE:
Effective
% of Total Capital Cost/year
Accounts Payable 6% 36% (assumed)
Debt 37% 8,01^
Stockholders'Equity 5k%
Of the 54^ capital representing shareholders'
equity it was found that
the totalstockholders' investment in the firm has been diluted through
losses by 36^. Forty-eight percent of thestockholders'
equity was
obtained in the public offering of I968 and represents only 7.4^ of the
outstanding shares of stock.
Sources of Information:
1. AD DATA SYSTEMS, INC., Prospectus dated May 10, I968.
2. AD DATA SYSTEMS, INC., 1971 Annual Report
65
AQUASONICS, INC.
Aquasonics was started in Rochester and was reported on January 18 -
20, 1972 to be in production of an all-terrain vehicle. It was reported
the firm raised an urgently needed l/2 million and that it was originally
formed to make a jet propelled boat. It had difficulties trying to make
bus shelters and the stock was trading in the l/4 to 3/4 range. No
further information was made available.
Source of Information:
Upstate Business Journal, January 18-20, 1972, p. 1.
66
COMPUTER CONSOLES, INC.
1257 University Avenue
Rochester, New York
Computer Consoles is a four year old firm which sells DATA
MANAGEMENT SYSTEMS. It had 1971 sales of $1,578,683, a net loss
of $879,249 and has assets totaling $2,635,332. Its sales have
increased steadily over the last four years; however, losses have
been sustained consistently.
December 3I, I97I CAPITAL STRUCTURE:
Effective
% of Total Capital Cost/year
Accounts Payable 15.4^
Debt 25.4^ 9^
Stockholders'
Equity 49^
The 49^stockholders'
eqxiity represents only 30^ of the total invest
ment by stockholders. Fvirthermore, 53^ of the total investment by
stockholders was in the form of 8% cumulative preferred stock.
Sources of Information:
1. Computer Consoles, Inc., 1971 Annual Report
2. Computer Consoles, Inc., Applications Reports, 2O5O, 2O5I, and 2052.
3. Computer Consoles, Inc., Interim Reports, June 30, 1972, and
April 1, 1972.
67
DETECTION SYSTEf'iS, INC.
400 Mason Road
Fairport, New York 14450
DETECTION SYSTEMS is a four year old firm engaged in the design,
manufacture and installation of electronic instrusion alarm systems.
It has 1972 total revenue of $818,091 with a net loss of $260,490 based
on the 1972 annual report. However, the July 31, 1972 quarterly report
indicates earnings of $3,990 on sales of $293,125. The firm's total
assets as of March 31, 1972 were $424,020.
March 31, 1972 CAPITAL STRUCTURE:
Effective
% of Total Capital Cost /year
Accounts Payable 33.7$
Debt 20^ 3^
Stockholders'
Equity ^2.7%
The h2.7%stockholders'
equity represents only '^3.5% of the total
investment by stockholders. A public offering with 7.7% potential
discount resulted in an equity contribution of 60^ of total stock
holder investment with only 21.3^ control.
Sources of Information:
1. DETECTION SYSTEMS, INC. 1972 Annual Report.
2. Three Month Report, June 30, 1972, of DETECTION SYSTEMS, INC.
3. DETECTION SYSTEMS, INC., May I5, I969 Prospectus.
68
FERRONICS, INC.
66 North Main Street
Fairport, New York 14450
Ferronics was incorporated in I968 to engage in mamofacturing and
marketing ceramic magnetic materials used primarily in the electronics
and the computer industry. Its current annual rate of sales is $640,000
with a net quarterly income $1,511 for the July - September 1972 quarter.
Total assets as of September 30, I972 were $666,920.
September 30, 1972 CAPITAL STRUCTURE:
Effective
% of Total Capital Cost/year
Accounts Payable 5.25^
Debt 27.8^ 7.2hr%
Stockholders'
Equity 63.8^
The 63.8^stockholders'
equity represents 51^ of the total investment by
stockholders. A July 10, I97O offering of 7.45^ of the outstanding stock
(12.6^ underwriting discount) produced 65^ of the total stockholders'
investment.
Sources of Information:
1. FERRONICS, INC. consolidated Balance Sheet and Income Statement
September 30, 1972.
2. FERRONICS, INC., July 10, 1970 Prospectus.
3. FERRONICS, INC., 1970, 1971 Annual Reports .
69
GOULD PUMPS
Seneca Falls, New York
Gould Pumps are designed and manufactured for use by household
consumers, marine equipment, anti-polluation equipment, and nuclear
power plants. It had 1971 (end of third quarter) earnings of $2,492,925
on sales of $39,292,680. Based on my previous criteria for a small
business, this firm will not be considered further in this analysis
and will be used for background only.
Sources of Information:
Upstate Business Journal, February 1-3, 1972, p. 1.
70
GRAHM MANUFACTURING COMPAIviY, INC.
Batavia, New York 14020
"Grahm man\ifacturers heat exchanges, condensers, steam jet ejectors,
fume scrubbers, relief valves, and related equipment for the petroleum,
petro-chemical, chemical and other processindustries." (From first
source of information below). It had I97I net income of $524,000 on sales
of $11,224,000. It has shown growth in earnings of 42% in the last two
years. The firm has assets as of December 31, 1971 of $7,815,000.
CAPITAL STRUCTURE:
Debt 38%
Stockholders'
Equity 60%
Source of Information:
1. Upstate Business Journal, July 11, I968, p. 18.
71
GRAPHIC SCIENCES
Danbury, Connecticut
Graphic Sciences originated in Rochester, New York to make telephone
transceivers in competition with Xerox. It had 1972 earnings of $658,659
on revenues of 9.8 million. It manufactures devices for transmitting
copies by telephone. No detailed financial information was obtainable.
Sources of Information:
1. Upstate Business Journal: September 5, 1972, p. 1.
July 27, 1972, p. 4.
February 8, 1972, p. 6.
72
HAMILTON DIGITAL CONTROLS, INC.
Utica, New York
Hamilton Digital Controls was a pioneer in high performance shieldless
magnetic recording heads and now sells a shieldless head for cassette
recorders and a low wear version of the same item. It has recently
introduced a vocal recorder which translates computer output into words.
As of August 8, 1972 it had latest fiscal year income of $217,800 on sales
of $1,082,000. It had a current sales backlog of 1 million and will be
expanded into a facility twice as large as it occupied as of August 8, 1972.
No further financial details were available.
Source of Information:
Upstate Business Journal, August 8, 1972, p. 8.
73
INFODATA SYSTEMS, INC.
Rochester, New York
Infodata Systems provides computer services and information
management systems to industry and government. It has received
patents on its Inquire information management system and has at least
one contract which could be worth $500,000 over a three year period.
It also sells a comprehensive time scheduling, accounting, and manage
ment reporting computer management system to radio and television
broadcasting stations. No fiirther information was available on this firm.
Sources of Information:
Upstate Business Journal: July 18, 1972, p. 1
September 5, 1972, p. 8.
74
KAYEX CORPORATION
1000 Milstead
Rochester, New York
Kayex is a local manufacture of electronic semi-conductor devices.
It also has a subsidiary which does special colar imaging and whose sales
represent about 1/4 of gross sales. Its I97I fiscal year sales were 1.1
million down 4.8% from 2.1 million the previous year. This resulted in a
net loss of $931,000 versus $216,654 a year earlier. It reported gross
sales for the first half of this year dropped to $575,845 from $642,665.
This firm openly refused to send me copies of its latest financial report
for obvious reasons.
Sources of Information:
Upstate Business Journal: August 22, 1972, p. 9.
July 30. 1972. p. 7.
April 18, 1972, p. 7.
March 21, 1972, p. 8.
75
LASER ENERGY, INC.
320 North Washington
East Rochester, New York
LASER ENERGY was incorporated January 2, I969 and was to manufacture
and market a low-priced laser and process optical thin film coatings.
It financed its initial operations with $275,000 from inside investors
(700,000 shares @ l<!!/share, 250,000 shares @ $l/share) and raised an
additional $491,574 (200,000 shares @ $3/share), through a public offering
in October I969. The firm showed a net loss of $105,526 on sales of
$154,521 in 1971 and had assets totaling $499,965 as of September 30, 1971.
September 30, I97I CAPITAL STRUCTURE:
Effective
% of Total Capital Cost /year
AccoiJints Payable 8%
Debt 0%
Stockholders'
Equity 92%
The October 28, I969 offering was underwritten at a cost of 15% with
$2.60/share proceeds to the company.
Sources of Information:
1. LASER ENERGY, INC., Prospectus, Dated October 28, I969.
2. LASER ENERGY, INC., 1971 Annual Report.
76
MARINE RESOURCES, INC.
1268 Atlantic Avenue
Rochester, New York
Marine Resources was established in I968 to develop high
technology products for underwater exploration and investigation.
According to F. Robert Hill, the firm has consolidated its local
operations with its Submersible Products Division in Florida. Accordingly,
he did not care to disclose their most recent financial data.
Sources of Information:
Letter from F. Robert Hill, President; dated April 4. 1973.
77
MEGADYNE INDUSTRIES, INC.
Rochester, New York
Megadyne Industries was a manufacturer of microelectronics started
)y two scientists from General Dynamics in I965. It sold 350,000 shares
it $2/share in the 60's and never saw a profitable year of operation.
Controlling interest was purchased in 1970 with the resignation of one
"ounding scientist with 200,000 shares piirchased for $l/share. The firm
ilosed its doors in November reportedly due to financial troubles. No
specific financial information was available.
Source of Information:
Upstate Business Journal: November 28, 1972, p. 1.
78
IffiSON ELECTRONICS COMPAlvlY, INC.
380 Cottage Street
Rochester, New York
Meson makes solid state timing devices and does a large amount of
subcontract electronics work. It had sixmonths'
sales as of December 31, 1972
of $436,828 with earnings of $24,500. This compares to a $13,275 loss a
year earlier. It introduced a new electronic ignition system on August 1, 1972
which is projected to significantly increase future sales. No further
financial information was available at this time.
Sources of Information:
Upstate Business Journal: August 11, 1972, p. 17-
March 13, 1972. p. 1.
February I5, 1972, p. 1 and 3.
79
METRIX DATA SYSTEMS, INC.
1166 Brooks Avenue
Rochester, New York
Metrix manufactures and sells badge identification systems, data
acquisition systems, and a water use recorder. The water use recorder
eliminates meter routemen and its use is now being tested by the Monroe
County Water Authority. It has deferred much of its preoperational and
promotional expenses and showed a net loss of $80,634 for the 1971 fiscal
year. It sold 75,000 shares of stock in 1971 for $6.50 per share. No
further information was available as this firm is still in a start-up
situation.
Source of Information:
Upstate Business Journal, August 18, 1972, p. 4.
80
PHOTOMETRIC DATA SYSTE1'4S CORPORATION
Holt Road
Rochester, New York
Photometric Data Systems manufactures automatic film transports, a
new type of photographic playback system, and a new ultra high speed
microdensitometer. It had 1972 net loss of $126,201 on sales of $523,752
and had assets totaling $819,006.
June 30, 1972 CAPITAL STRUCTURE:
Effective
of Total Capital Cost /year
Accounts Payable 9.6%
Debt 62% 7.7%
Stockholders'
Eqiiity 21%
Of the 21%stockholders'
equity, it represents only 40% of the total
stockholders'
investment.
Sources of Information:
1. Photometric Data Systems Corporation 1972 Annual Report.
2. Photometric Data Systems Corporation, 1972 Presidents News Report.
81
R. D. PRODUCTS, INC.
Victor, New York
R. D.Products'
principle business is the design, development and
distribution of photo-identification systems to banks, retail stores,
commercial credit card companies, schools, industry, and government
agencies. It showed a net loss of $72,290. (Prior to extraordinary
items) on sales of $372,775 for the 6 months ending January 31, 1972.
The firm had assets of $881,669 as of January 31, 1972.
January 31, 1972 CAPITAL STRUCTURE:
Effective
% of Total Capital Cost /year
Accounts Payable 5.1^
Debt 45.6% 7%
Stockholders'
Equity 40%
The 40%stockholders'
equityrepresents only 21% of the total investment
by stockholders.
Source of Information:
R. D. Products, Inc., May 25, 1972 Notice of Annual Meeting
of shareholders.
82
ROCHESTER INSTRUMENT SYSTEMS, INC.
275 North Union Street
Rochester, New York 14605
Rochester Instrument Systems manufactures and services sophisticated
electronic instruments primarily for use by the electric utility and process
control industry. It had 1971 net income of $260,341 on sales of $5,771,261.
It had assets totaling $4,580,592 as of October 1, I97I with a clear
strong record of groxvrth over the last ten years.
October 1, 1971 CAPITAL STRUCTURE:
Effective
% of Total Capital Cost /year
Accounts Payable 10.3^
Debt 25.8% 7.7%
Stockholders'Equity 55%
The 55%stockholders'
equity represents 100% of the totalstockholders'
investment. A 1971 offering (10% discount) of 192,872 shares was fully
subscribed resulting in an equity contribution of 62% of total stockholder
investment with only 27% control.
Sources of Information:
1. Rochester Instrument Systems, Inc., September 7, I97I Prospectus.
2. Rochester Instrument Systems, I97I Annual Report.
y. Rochester Instrument Systems, June 30, 1972, March 30, 1972,
Quarterly Reports.
83
SCIENTIFIC RADIO SYSTEl^IS
401 Lye11 Avenue
Rochester, New York 14606
Scientific RadioSystems'
major product line is high frequency
single sideband communications equipment used as a substitute for phone
communications in underdeveloped countries and by government agencies.
Its current annual rate of sales is $1,480,000 and has just completed its
first profitable period of operation. The firm had total assets of
$481,198 as of June 30, 1971.
June 30, 1971 CAPITAL STRUCTURE:
Effective
% of Total Capital Cost/year
Accounts Payable 9.1^ 36"^ (assumed)
Debt 0%
Stockholders'
Equity 86%
The 86%stockholders'
equity represents only 47.5% of the total
stockholders' investment. A January 27. 1970 public offering (10% discount)
of 100,000 shares at $8.50 per share resulted in an equity contribution of
80% of total stockholder investmentwith only 23% control. This offering
was self-underwrittenand quickly fully subscribed.
Sources of Information:
1. SCIENTIFIC RADIO SYSTE^iS. INC., January 27, 1972 Prospectus.
2. Long Island Investor. June 30, 1971, Volume 3 - Number 5.
3. SCIENTIFIC RADIO SYSTEl^iS, INC., June 30, 1971 Annual Report.
4. Personal interview irith David Hoffman. Vice President, Treasurer,
and Director.
84
SYKES DATATRONICS. INC.
375 Orchard Street
Rochester, New York 14606
Sykes Datatronics'product line is primarily for the minicomputer
market using cassette transport products and datacommunications'
products. Its 1972 sales were $1,636,000 with net income of $46,000.
Total assets as of February 29, 1972 were $1,856,268.
February 29, 1972 CAPITAL STRUCTURE:
Accounts Payable
Debt
Stockholders'
Equity
% of Total Capital
Effective
Cost /year
16% 36% (assimed)
58% 9.1%
23'^
Sources of Information:
1. Sykes, 1972 Annual Report
2. Sykes, August 31, 1972 Six Month Report
85
TAPECON, INC.
475 River Street
Rochester, New York
Tapecon is a specialty converter of electrical and industrial tapes
and metal foils. It has reported earnings of $29,987 for the calendar
year 1972 against losses of $12,907 for the prior year's comparable
period. The shipments during the first half year were $955,207 with a
$233,608 backlog. No further financial information was available on
Tapecon at this time.
Sources of Information:
Upstate Business Journal: August I5, 1972, p. 1.
Kay 2, 1972, p. 7.
May 9, 1972, p. 10.
86
TEL-PAGE CORPORATION
401 Sherman Street
Rochester, New York
Tel-Page is engaged in the sale and rental of mobile telephone and
radio paging services. The firm showed a net income for the year ended
December 31, 1971 of $13,712 on sales of $531,351. It had assets of
$810,366 as of December 31, 1971.
December 31, 1972 CAPITAL STRUCTURE:
Effective
% of Total Capital Cost /year
Accounts Payable 10.8%
Debt 57% 8.95^
Stockholders'
Equity 25.6%
It should be noted that 81% of debt is installment loans on equipnent with
interest rate assumed to be 10%. F\irther, it was evident that the 25.6%
stockholders'
equity represents only 58% of the totalstockholders'
investment.
Sources of Information:
1. Tel-Page Corporation 1971 Annual Report.
2. Tel-Page Corporation July 5, 1972 Proxy Statement.
87
TRANSMATION, INC.
Rochester, New York
Transmation is a local electronics firm which has also operated a
small plastics subsidiary. The Product Packaging Corporation plastics
subsidiary was reported to have orders in excess of $200,000 in February 1972
but was sold in September 1972 for $50,000. Transmation recorded a loss
on the subsidiary sale of $111,000 of which $62,000 was included in its
losses of the first fiscal quarter of 1972. No further financial information
was available on Transmation, Inc.
Sources of Information:
Upstate Business Journal: February 22-24, 1972, p. 9.
September 12, 1972, p. 7-
88
YONDATA CORPORATION
40 St. Paul Boulevard
Rochester, New York
Yondata is principally engaged in the design, assembly and implementation
of special purpose computer systems along with operating a time-shared computer
facility.
April 30, 1972 CAPITAL STRUCTURE:
% of Total Structure
Accounts Payable 4. 1%
Debt 0%
Stockholders'
Equity 72%
Lease agreements have been reflected in the balance sheet at 21.3^ of the
total liabilities . The 72^ stockholders'
equity represents only 5^% of the
initialstockholders'
investment. The firm publicly issued 34.4% of its
outstanding stock @ $l/share June 3, 1969. It was self londerwritten with
no commissions or discounts offered.
Sources of Information:
1. Yondata Corporation, August 22, 1972 Annual Report.
2. Yondata Corporation, June 3, I969 Prospectus.
89
APPENDIX C
STOCK PRICE CURVES
The stock price fluctuation were plotted for a nine month
period as listed in selected issues of Upstate Business Journal.
90
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APPENDIX D
COMPUTER PROGRAM AND LISTED RESULTS
The computer printout that follows is an abbreviated version of that
described in the Chapter V flow chart. It takes the matrix for estimated
product profits, costs, and life and the matrix for their respective
probabilities of occurrence and separates the data for all 243 possible
outcomes. It operates on each set of data and prints out the internal rate
of return, probability of occurrence of that rate of return and a reference
number for the data selected.
^16
TYl-29
1.000 C B. R. ROBINSON - A CAPITAL BUDGETING MODEL
2.000 DIMENSION A(3), B(3)> C(3), D(3), E(3)* V(3)* XC3)
2.500 DIMENSION W(3), Y(3)* ZC3), RRF(243)> P(243)
3.000 DIMENSION PX(IOO), CP(IOO)
4.000 11 FORMAT (F10.2)
4.500 13 FORMAT (4F10.5)
5.000 10 READ (5, 11) (A(J), B(J), CCJ)* D(J)* E(jy,
5.200 1 J 1* 3)
5.500 12 READ (5, U) (V(J)^ W(J), X(J), Y(J), Z(J),
5.700 1 J 1* 3)
5.950 I = 1
6.000 DO 105 J s 1^ 3
7.000 BA = A(J)
7.500 BV VCJ)
8.000 DO 105 JA I, 3
9.000 BB s B(JA)
9.500 BV W (JA)
10.000 DO 105 JB = 1* 3
11.000 BC C(JB)
11.500 BX X(JB)
12.000 DO 105 JC = 1* 3
13.000 BO D(JC)
13.500 BY = Y(JC)
14.000 DO 105 JD = 1* 3
15.000 BE = E(JD)
15.500 BZ Z(JD>
16.500 RR = 0
16.700 N 0
17.000 106 CONTINUE
17.200 N = N + 1
17.500 IF (N - 200) 109, 109, 107
13.000 109 RR 3 RR + .5
18.200 EA a 0
18.400 EB = 0
18.500 LD BD
19.000 DO 108 L = l> LD
20.000 EA EA + (BA - BB) / ( I + RR/100)**L
21.000 108 CONTINUE
22.000 EB EA ? (BC / Cl + RR/100)**BD)
23.000 IF ( EB .GE. BE ) GO TO 106
24.000 107 RRF(I) = RR
25.000 P(I) BV * BW * BX * BY * BZ
27.000 WRITE (3, 13) RRF(I)* P(I), I
27.500 1=1+1
28.000 105 CONTINUE
29.000 END
117
BTM SYSTEM-B IS UP
12/26/ '72 11:45
ILOGINt BAl 15348>R0BINSON
ID= U
GOOD DAY,BTM IS UP, PLEASE DELETE ALL OUTDATED FILES, TOM
!ED1T
*EDIT DA7
IN20
20.000 .2
4e
TYl-30
1.000
2.000
3.000
4.000
5.000
6.000
7.000
8.000
9.000
10.000
1 1.000
12.000
13.000
14.000
15.000
16.000
17.000
18.000
19.000
20.000
21.000
22.000
23.000
24.000
25.000
26.000
27.000
28.000
29.000
30.000
*END
25000.
20000.
1.
2.
40000.
100000.
50000.
10000.
5.
100000.
350000.
100000.
20000.
10.
150000.
.1
.2
.3
.1
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.6
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.8
.75
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,05
!EDIT
?EDIT INTERNAL
?IN17.5
17.500
? IN20
20.000
IF (N - 200) 109, 109, 107
EA = EA + (BA - BB) / (1 + RR/100)**L
liO
IFORTRAN
OPTIONS* BO
EXTENDED FIV-H VERSION DOO
*? END OF COMPILATION **
(LOAD
ELEMENT FILES:
OPTIONS:
F:5 3 DAT, IN
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121
122
APPENDIX E
CAPITAL PECULIARITIES OF THE Hm SM.ALL FIRM
The small new firm has several obvious financial peculiarities which
include inside investors, the SBA, and the SBIC. The inside investor is
usually considered part of the entrepreneural group that originates the new
venture. The SBA (Small Business Administration) is a government agency
under the department of commerce which was established explicity to aid
small business. The SBIC (Small Business Investment Companies) are
independent government backed investment companies established to provide
venture capital to small businesses. Along with these, the new small firm
starts with a serious lack of trade credit and is assumed a poor credit risk.
The initial capital for the new firm has been found to come largely from
the original owner entrepreneur. More specifically, about half the money
2used to start small businesses is supplied by the owners. The owners and
members of the original investing group are referred to as inside investors.
This group is often issued stock at a considerable discount from those shares
sold publicly to the non-controlling investors. These entrepreneiu'S expect
some larger return on their investment which can be expressed as by constant
K times the return expected by the outside investor. Also associated with
such inside investors is the lack of flotation costs. Because of these
factors the cost of capital from inside sources can be given by:
^SBA, The Small Manufacturer and His Staff, p. 2?.
^Ibid. p. 27.
123
Inside C =
KgE
If/here K -
multiple due to higher expectations of inside investors
g= growth expectations of outside investor
The overall cost of capital expression should then be written
Cg= Inside
C^+ Outside C
Cp=
Kg +
as ;
1-b
Through interviews with several small businessmen it became evident that these
insiders appear to be rather difficult to locate and prefer to remain in the
background for obvious reasons.
There are distinct advantages for wealthy individuals to invest in
small businesses that fall under the Internal Revenue Code Section 1244 rules.
This code provides an asymetrical tax advantage to the investor.
"An investor in a high income tax bracket stands to retain 75% of his
gains but lose after taxes only 35% of his gross losses if he is in the marginal
tax bracket of 65%.
Though of obvious value to the small firm raising capital, this
asymetrical relationship may perpetuate more problems than it benefits if
the investors decide to write off their losses in the first few years of the
firm's operation.
The Small Business Administration is a federal government agency
established in 1953 by congress to help small businesses grow and prosper.
Eligibility for SBA loans is specified as:
Roland I. Robinson, Financing the Dynamic Small Firm, p. 23.
^Ibid, p. 23.
^SBA Publication OPl-6, February 1970, p. 2.
124
"Most businesses that are independently owned and operated and not
dominant in their fields; that cannot obtain private financing on reasonable
terms and are not eligible for financing from other Government agencies,
and that qualify as "small"under SEA's size standards, which generally are
based on dollar volume of business or number ofemployees."
For a manufacturing firm the above book goes on to note that the firm must
have less than 250 to 1,000 employees to qualify. The SBA will back up to
90^ of a bank loan with bank interest rates limited to 8%. In some cases the
SBA will provide half the loaned capital at a maximum 5^ interest rate with
the commercial bank providing the remaining f\inds. Loans of this type are
limited to $350,000 SBA share mth a maxim-um 10 year maturity for construction
loans and 6 year maturity for working capital. Collateral for these SBA
loans may include:
"Real estate or chattel mortgage; assignment of warehouse receipts for
marketable merchandise; assignment of certain type of contracts, guarantees
or personal endorsements; in some instances assignment of current receivables
Q
and inventories stored in bonded or otherwise acceptablewarehouse."
The SBA through the above program is one of the lowest cost sources of debt
capital to the new small business. Because of the loan guarantee program
and the presumed high risk associated with the new small business it is
apparent that coiTimercial banks would prefer SBA backed loans to conventional
loans. Since their resistance to conventional loans is one criterion for SBA
SBA, "A Handbook of Small Business Finance."'p. 68.
^Ibid, p. 69.
Q
Ibid, p. 69.
125
backed loans it further seems evident that SBA backed loans may be the only
source of debt capital for the new small firm. If we consider the SBA backed
loan as the sole practical source of debt capital which is obtainable at a
maximum 8% rate we would have:*
C^= 0.08 (1 - T^)
The corporate tax (T^) rate for small business depends on their income. If
we ass\OTe that income during the first two years of operation is less than
$25,000 this tax rate would be 22^.
The corporation is taxed at a marginal rate of 48^ on each dollar earned
Q
above $25,000. However, if plowed back earnings are considered -VLtal to the
growth of the new firm and growth is the objective of the owners it seems
reasonable to assume that capital budgeting techniques could be implemented
during the first two years of operation to keep earnings less than $25,000
and the marginal tax rate at 22"^ instead of 48^. This would produce an
assumed cost of debt of:
C^= 0.08 (1 - 0.22) = 6,3^
This should be substantiated in the text of the research.
The Small Business Investment Companies are SBA backed sources of equity
capital for small businesses established by the Small Business Investment Act
of 1958-. These are privately owned and profit motivated corporations
operating under broad SBA guidelines and may invest up to 20^ of their paid-
in-capital plus surplus into any one small business. Currently there are
* Note: Some venture capital is often provided in the form of convertable bonds.
However, the owners expectations will be considered equivalent of that
of equity.
J. Fred Weston, Managerial Finance .
^RA fl Handbook of Small Business Finance, p. 7I.
126
288 SBIC's with 51 boasting equity of $1 million or more and each specializing
in some specific industrial group.
Trade credit for the new small business is often given at extremely
high rates as mentioned earlier. Robert P. H\ingate in Interbusiness Financing:
Economic Implications for Small Business has isolated the factors which determine
trade credit terms and these terms which effect strict or cash terms are:
A. Small quantity purchased
B. Industrial type buyer
C. Weak credit rating
D. Weak competition within the industry
All of these factors are likely to apply to the new, small, high technology,
manufacturing firm considered in this paper and substantiate the initial
assumptions that trade credit will not be used extensively initially.
11David A. Loehning, Barrens
.April 24, 1972, p. 3-
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