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Module 4: Financing Alternatives
Topics
The Firm's Cost of Capital
Financial and Operating Leverage
Break-Even Analysis
The Firm's Cost of Capital
In this section, we examine the theory, key concepts, and calculation of the firm's weighted
average cost of capital and the advantages and disadvantages of each component of that cost to
the firm.
Definition of Cost of Capital
A firm's cost of capital is the net price it must pay for its total mix of capital financing, both debt
and equity, after considering any tax impact and the floatation costs, which constitute all the
expenses directly related to arranging the financing. This price paid is the cost of capital to the
firm, and is governed, or constrained, primarily by the rate of return required by investors who
are willing to purchase the firm's securities with the perceived risk associated with them.
The firm's cost of capital is also the firm's minimum required rate of return (or hurdle rate) on
any new capital investments. To accept any capital projects with a lower rate of return than the
cost of capital would result in a reduction of shareholder wealth because it would obviously cost
more to finance the capital investment than the return yielded. For most financial decision
making, the relevant cost of capital rate is the "marginal" weighted average cost of capital. This
cost represents the next best available, or marginal, increment of capital that the firm can raise
for future capital expenditures.
Calculating the Cost of Capital
A firm has access to three primary sources of long-term capital, some of which have variations.
These sources are:
1. debt financing market
2. preferred stock financing market
3. common stock financing market
The cost of capital of a firm equals the after-tax and after-flotation weighted average cost of the
individual components of its capital structure, with each component multiplied times its weight
in percent:
Types of Financing Marginal Costs Weight %
1 Debt financing kd wd
2 Preferred stock kps wps
3 Equity financing
3a —Retained earnings kcs wcs
3b —New common stock Kncs wncs
where:
kd = marginal cost of debt financing after tax and flotation costs
kps = marginal cost of preferred stock financing after tax and flotation costs
kcs = marginal cost of retained earnings financing after tax and flotation
costs
kncs = marginal cost of new common stock financing after tax and flotation
costs
and
wd = portion of debt financing to total capital financing in dollars
wps = portion of preferred stock financing to total capital financing in
dollars
wcs = portion of retained earnings financing to total capital financing in
dollars
wncs = portion of new common stock financing to total capital financing in
dollars
Note that in the above table we have broken the cost of capital for equity, ke, into two
subcomponents to account for the different cost structures. Retained earnings, kcs, accounts for
the current market value of previously issued common stock, and represents the charge assigned
to any use of retained earnings cash reserves. New issues of common stock that will incur
flotation costs are represented by Kncs.
As an example of computing component weights, the weight of the debt-financing component is
calculated as follows:
wd = $ debt/($ debt + $ preferred stock + $ retained earnings + $ new common stock)
The weight for the remaining components are calculated in a similar fashion. Using the above-
defined terms, the general formula for the weighted marginal cost of capital is:
kwacc = (wd)(kd) + (wps)(kps) + (wcs)(kcs) + (wncs)(kncs)
Or, to cover the fact that debt capital financing, alone of all the capital components, has a tax
shield impact (1 – Tc), we can expand the formula as shown below to incorporate this
consideration:
kwacc = (wd)(1 – Tc)(kd) + (wps)(kps)+ (wcs)(kcs) + (wncs)(kncs)
In summary, the above formula represents algebraically the summation of each component's
dollar proportion of the total capital dollars times the cost of capital rate in percent for that
component.
Some Important Considerations Regarding the Cost of Capital
1. Debt financing gets special tax treatment. It alone of the three financing methods is tax
deductible. By tax deductible, we mean that the interest payments on the debt can be
deducted in computing taxes, thereby reducing significantly the cost of debt financing to
the firm (35 percent typically).
2. The equity-financing component consists of two types of equity:
a. internal equity, or retained earnings
b. external equity, or new common stock issues
3. The resale of the firm's common stock on the secondary stock market raises no additional
capital financing for the firm. All of the firm's equity proceeds are received from the
initial stock offering.
4. The flotation costs must be deducted from any gross proceeds received from financial
fund-raising. These funds are normally deducted from the proceeds of the financing and
therefore reduce the net amount of proceeds the firm actually receives.
Financial Management of the Cost of Capital
The primary objective in managing the firm's weighted average cost of capital is to minimize the
firm's overall cost of capital financing, which will then allow the firm to:
• increase the shareholders' return through undertaking either more or higher-return
projects as allowed by the lower cost of money
• raise future funds at a lower cost
Secondary objectives in managing the firm's weighted average cost of capital are (1) to avoid
increasing debt levels to the extent that they risk illiquidity, and (2) to avoid diluting
shareholders' ownership. Also, under some unusual circumstances, there can be a downside to a
low cost of capital. For example, if this cost is so low as to allow the company to invest in lower-
return capital projects, the investors may decide they can receive a higher return at the same risk
with another firm.
The Components of Cost of Capital
The following are important factors to evaluate in establishing the optimum components in a
firm's target cost of capital.
• Each of the basic components of cost of capital has a perceived risk-return tradeoff.
• Taxes affect the cost of capital structure via debt financing.
• The incremental costs of raising capital vary by type.
• Issuing new common stock can dilute the existing shareholders' equity.
• Debt covenants and preferred stock rights can constrain future operations.
• In general, the cost of raising funds increases with each new increment.
Cost of Capital—Debt Financing
Sources of Long-Term Debt Financing
The following are sources of long-term debt financing:
• commercial loans from banks
• loans from large financial institutions (insurance companies, mutual funds)
• loans from specialist financing companies (equipment, accounts receivable, inventory,
and so on)
• loans from private investors
• issuing company bonds (limited to larger, financially sound companies)
Below, we show the costs typically associated with long-term debt financing.
Debt Financing Costs
Types of Financing
Costs
Descriptions of Financing Costs
Interest payments Interest rate (prime + risk factor) times outstanding balance
(paid over life of debt)
Broker's fee Finder's and facilitator's fees (paid up front)
Underwriting fees Assumption of issue risk by underwriter investment bank
(paid up front)
Closing costs Miscellaneous package of expenses related to closing the
deal (paid up front)
Professional fees Legal, tax, and accounting consulting fees (paid up front)
Miscellaneous expenses Costs of printing, recording, meetings, and so on (paid up
front)
Below are the advantages and disadvantages of debt financing to the firm.
Advantages Disadvantages
1. The interest on loans is tax
deductible.
1. The obligation to repay the loan increases the
risk of bankruptcy.
2. Interest rates are normally lower
than for equity financing.
2. The firm incurs restrictive covenants and
obligations.
3. The terms for principal repayment
are often negotiable.
3. The firm must maintain the collateral
requirements of secured loans.
4. Debt financing gives shareholders
financial leverage.
4. Debt financing gives shareholders financial
risk.
5. Shareholders' equity is not diluted. 5. The firm incurs issuance costs.
Calculating the Debt Component of Cost of Capital
The firm's cost of debt capital (before-tax and flotation cost) is set by the minimum rate of return
required by the creditors who are willing to purchase the firm's debt instruments.
Mathematically, this cost equals the present value of all interest payments plus the principal
repayment and is essentially the bond formula. This formula works the same way for straight
debt and for the issuance of bonds assuming, for simplicity, that the principal repayment is at the
last period.
To properly compute the firm's cost of debt capital, we must adjust the previously developed
bond formula for two factors – tax deductibility and flotation costs. First, because interest
payments are tax deductible by the firm, the after-tax cost of debt (ki) must be computed as
follows:
ki = kd (1 – Tc)
where:
kd = coupon or stated interest rate
Tc = marginal corporate tax rate
Next, remembering that the net proceeds the firm actually receives (NPd) for either a bond or
note must be reduced by any issuance costs (flotation costs):
NPd = (net proceeds – flotation costs)
Substituting these new terms into the bond formula yields:
(math formula)
or
(financial table formula)
Sample Computation of the Debt Component of Cost of Capital (ki)
Alpha sells $100 million worth of 20-year 7.8% coupon bonds. The net proceeds (proceeds after
flotation costs) are $980 for each $1,000 bond. Alpha's marginal tax rate is 40%. What is the cost
of capital for this debt financing?
NPd = $980 (The implied flotation cost is $20 per bond.)
coupon (interest) rate = 7.8%
$I = $78 [(.078)($1,000)]
$M = $1000
n = 20 years
T = 40%
First solve for kd
Then solve for ki or kd (after tax).
kd = 8.0038
ki (after tax) = kd(1 – Tc ) = (8.0038)(1 – .40) = 4.8%
Cost of Capital—Preferred Stock Financing
The sources of preferred stock financing are:
• large financial institutions
• preferred equity market
• private investors
Below are the major costs associated with issuing preferred stock.
Preferred Stock Financing Costs
Types of Financing
Costs Descriptions of Financing Costs
Dividend payments Set payment amount—indefinitely
Broker's fee Finder's and facilitator's fees (paid up front)
Underwriting fees Assumption of issue risk by underwriter (investment bank)
(paid up front)
Closing costs Miscellaneous package of expenses related to closing the
deal (paid up front)
Professional fees Legal, tax, and accounting consulting fees (paid up front)
Miscellaneous expenses Costs of printing, recording, meetings, and so on (paid up
front)
Below are the advantages and disadvantages of preferred stock financing to the firm.
Advantages Disadvantages
1. Normally lower rate than common equity
financing
1. Dividend payment obligation in
perpetuity
2. No dilution of shareholders' equity 2. Dividend payments not tax deductible
3. Missed dividends cannot trigger
bankruptcy
3. Incur protective constraints and
restrictions
4. Can have a call provision for company
buy back
4. Incur issuance (flotation) costs
Calculating Preferred Stock Cost of Capital
The cost of capital of preferred stock to the firm is the rate of return required by the investors on
preferred stock, after consideration of tax and flotation costs. Remember the following points.
• Most preferred stocks are perpetuities.
• Because the firm cannot deduct dividend payments from its taxes, the after-tax cost of
preferred stock (kps) is equal to the pretax cost of preferred stock.
• The issuance (flotation) cost must be deducted from the preferred stock proceeds to arrive
at the new capital raised.
Formulas:
Again, this is the previously developed preferred stock formula, rearranged algebraically for the
cost of capital:
P = D/k Rearranged, kps = Dps/NPps
where:
NPps = preferred stock net proceeds after-issuance costs (issue price – flotation costs)
kps = preferred stock after-tax cost of capital (not tax deductible)
Dps = preferred stock dividend
Below is a sample preferred stock cost of capital calculation.
Bravo has issued three million shares of preferred stock, which pay an annual dividend of $4.05.
The issue was sold to the public at $52.00/share with an issuance cost of $2.00/share. What is the
preferred stock cost of capital?
Number of shares = 3,000,000
Dps = $4.05
Flotation cost = $2.00
NPps = $50.00 = $52.00 – $2.00
Find kps
kps = Dps/NPps
kps = 4.05/(52.00 – 2.00) = .081 =8.1%
Note: By convention all calculations are based on a per-share basis.
Cost of Capital—Equity Financing
There are two basic sources of equity financing available to the firm. The first source is called
internal equity, and it relates to the use of the cash balance retained from prior operations or the
cash portion of retained earnings. The second source is called external equity, in which new
capital funds are secured through the issuance of new common stock.
Internal Equity—The Use of the Firm's Retained Earnings
Sources of Internal-Equity Financing
There is only one source of internal-equity financing, and that is the firm's cash-available portion
of retained earnings. Remember that cash retained in the company differs from book-retained
earnings because of the accrual accounting system. To use the retained earnings as a source of
financing, you must have the cash in hand.
Below are the costs typically associated with internal-equity financing.
Internal-Equity Financing
Types of Financing Costs Descriptions of Financing Costs
Imputed required return Equal to or greater than the firm's cost of capital
Interest/dividend payments None
Broker's fee None
Underwriting fees None
Closing costs None
Professional fees None
Below are the advantages and disadvantages of internal-equity financing to the firm.
Advantages Disadvantages
1. Immediately available funds 1. Higher imputed cost than debt
2. No interest or dividends 2. Reduces firm's liquidity
3. No covenants, restrictions, or issuance
costs
3. Reduces pool for stockholder dividends
4. No dilution of shareholder equity
Calculating the Internal-Equity Cost of Capital
The cost of internal-equity capital to the firm is imputed to be the rate of return required by the
investors to purchase the firm's stock. The imputed internal equity cost of capital can be
calculated in many ways, all of which have limitations in application. Two of the more common
methods, which we have discussed before, are
1. dividend growth model
2. capital asset pricing model
Dividend growth model—In theory, the internal-equity common stock's value could be
calculated by discounting from now to infinity the stream of dividends at the investors' required
rate of return. In practice, dividends cannot be estimated with confidence, therefore a simple
approach is to assume a constant dividend growth rate (g).
The basic formula used to represent a constant dividend stream to infinity is:
Pcs = D1/(kcs – g)
where D1, the next dividend, is related to D, the last dividend, by the following formula:
D1 = D(1 + g)
Rearranged algebraically to solve for kcs:
kcs = (D1/ NPcs) + g
or
kcs = [(D (1 + g))/ NPcs] + g
where:
Pcs = the imputed common stock price
kcs = the common stock after-tax cost of capital (not tax deductible)
D = the last common stock dividend
D1 = the next common stock dividend
g = the steady-state growth rate for dividends
Example
Echo Corporation common stock is currently selling for $22.00/share. Its present dividend is
$0.96/share, and its expected long-term dividend growth rate is 8.5%. What is Echo's cost of
internal equity (kcs)?
Organize the data:
D1 = D(1 + g)
D1 = .96(1 + .085) = 1.0416
NPcs = $22.00
Formula:
kcs = (D1/NPcs) + g
Calculation:
kcs = (1.0416/22.00) + .085 = .1323
kcs = 13.23%
Capital asset pricing model—The second model for calculating internal common stock equity
is the capital asset pricing model (CAPM). It addresses the valuation of equity cost of capital
from the standpoint of the return required by stockholders for a given level of risk.
The return required for internal common stock equity is equal to risk-free return + a risk
premium that varies from stock to stock:
kcs = rrf + Bj(rm – rrf)
where:
Bj = beta and is normally estimated by historical values between a security's return and
the market return
rrf = the risk-free rate and is usually estimated at the U.S. Treasury bill rate
rm = market risk
Example
Echo's current beta value is 0.75. Treasury bills are currently yielding 5.5%, and the market
return is 14.3%. What is Echo's internal cost of equity capital? Market return is 14.3%.
Organize the data:
rrf = –5.5%
Bj = .75
Formula:
kcs = rrf + Bj (rm – rrf) )
Calculation:
kcs = 5.5 + .75(14.3 – 5.5)
kcs = 12.1%
External Equity—The Issue of New Common Stock
The sources of external equity financing are:
• public-offering investors
• large financial institutions
• private investors
• negotiated stock purchase
Below are the costs associated with issuing new common stock financing.
New Issue Common Stock Costs
Types of Financing Costs Descriptions of Financing Costs
Broker's fee Finder's and facilitator's fees
Underwriting fees Assumption of issuance risk by the underwriter
(investment bank)
Closing costs Miscellaneous package of expenses related to closing
the deal
Professional fees Legal, tax, and accounting consulting fees
Miscellaneous expenses Costs of printing, recording, meetings, and so on
Below are the advantages and disadvantages of common stock financing to the firm.
Advantages Disadvantages
1. No interest or required dividends 1. Highest cost of capital
2. No covenants, restrictions, or preferences 2. Dilution of shareholders' equity
position
3. Improved liquidity position 3. Highest issuance (flotation) cost
4. Market uncertainty at time of issue
Calculating New-Issue Equity Cost of Capital
The cost (kncs) to raise new common stock equity is calculated in the same way as the constant
growth model discussed for internal-equity financing but modified with a provision for issuance
costs:
kncs.= (D1/NPncs) + g
where:
NPncs = proceeds from the issue of new common stock minus issuance flotation
costs
kncs = new common stock after-tax cost of capital (not tax deductible)
D = last common stock dividend
D1 = next common stock dividend
g = steady-state growth rate for dividends
Close the Cycle—Back to the Weighted Average Cost of Capital
We have now determined one or more methods to compute the cost of capital for each of the
financing components of the firm's weighted average cost of capital. The final step is to pull it all
together and calculate the firm's weighted average cost of capital:
kwacc = wd(kd)(1 – Tc) + wps(kps) + wcs(kcs) + wncs(kncs)
where:
The debt component, kd =
The preferred stock component = kps = Dps/NPps
The internal common equity
component =
kcs = (D1/ NPcs) + g or
kcs = rrf + Bj(rm – rrf)
The external common equity
component =
kncs = (D1/ NPncs) + g
Break-Even Analysis
The material covered in this topic focuses on a specific management technique that is used
widely in business to determine the expected profitability at various sales levels. This technique
is called break-even analysis and is widely accepted for two pragmatic reasons: its
straightforward assumptions and the usefulness of the information provided. The bottom line is
that in many cases this approach works.
The Objective and Uses of Break-Even Analysis
The objective of break-even analysis is to determine the break-even quantity of output (the
quantity point at which the total revenues received just equal the total expenses incurred) by
studying the relationships among the firm's cost structure, volume of output, and operating profit.
More specifically, the break-even quantity of output is the quantity of output (in units) that
results in an EBIT level equal to zero. The use of the break-even model enables the financial
officer to answer two critical questions: (1) What is the minimum quantity of output that must be
sold to cover all operating costs—that is, to break even—and (2) what will be the expected
EBIT, or operating income, at various levels of output above and below the break-even point?
Some of the major applications of break-even analysis are:
• setting product-pricing policy
• determining the effects of labor contract provisions
• evaluating competitive and comparative price-cost structures.
• making financial decisions
Essential Elements of the Break-Even Analysis
The essential elements of break-even analysis relate to the assumed behavior of certain costs
within the cost structure. To use this model, the firm must place all its costs in two categories—
variable costs and fixed costs—and also determine the range of volume that may be sold over the
period. Let's examine these components.
Variable Costs
Variable costs tend to vary as the output volume changes. Variable costs are incurred per each
unit of output. For example, direct materials are considered a variable cost because they vary
directly with the quantity of products produced. If I am producing 50 widgets and each one
requires $10.00 of material costs, then the variable cost of material is $10.00 per unit. Of course,
materials are not the only variable cost component of a product. Other common variable costs
include
• direct labor
• direct materials
• utility costs (associated with the production area)
• packaging
• freight-out (on products sold)
• freight-in (on materials)
• sales commissions
The above variable costs are additive to create a total variable cost per unit for each product
being sold. To illustrate, let's create the variable cost per unit for one widget.
Direct labor $ 5.00/unit
Direct materials $10.00/unit
Packaging $ 1.00/unit
Utility cost $ 4.00/unit
Total variable cost = $20.00/unit
The following tabular and linear graphical relationships further illustrate the concept of variable
costs.
Variable Cost Relationship
Units Sold Variable Cost/Unit Total Variable Costs
(Units x Cost/Unit) $20.00 $ 0.00
1 $20.00 $ 20.00
5 $20.00 $ 100.00
10 $20.00 $ 200.00
20 $20.00 $ 400.00
50 $20.00 $1,000.00
Fixed Costs
In addition to variable costs, there are many costs encountered in business that are constant and
do not vary in total as the sales volume or the quantity of output changes over some range of
output. For example, administrative salaries are generally considered fixed because they are
normally the same month after month and do not normally fluctuate with volume. Other typical
examples of fixed costs are:
Depreciation $20,000 annual change
Amortization $ 3,000 annual change
Insurance premiums $ 8,000 annual expense
Property taxes $ 6,000 annual expense
Computer systems $ 5,000 annual lease cost
Overhead $10,000 supervisory costs
Lease costs $ 8,000 annual office lease
Total fixed costs $60,000 Total annual fixed
Fixed costs for a period are also additive. The total fixed cost for a given period (month, quarter,
or year) is unchanged regardless of the quantity of product output or sales. Note, however, over
some longer relevant range, say a decade, these fixed costs may become variable. Theoretically,
in the really long run there are no fixed costs, because with enough time every cost becomes
variable.
Using the previously developed unit variable cost ($20.00) and annual fixed cost ($60,000) the
following tabular and linear graphical relationships further illustrate the concept of variable
costs.
Variable Cost Relationship
Units Sold Fixed Cost Total Variable Cost
(units cost/unit)
$60,000 $ 0.00
1,000 $60,000 $ 20,000
5,000 $60,000 $ 100,000
10,000 $60,000 $ 200,000
20,000 $60,000 $ 400,000
The Relevant Range of Unit Volume Sold
Break-even analysis is normally only valid over a predetermined range of output. The relevant
unit volume range usually begins with zero and goes up to some maximum production capability
for the period. Beyond this range, a new set of cost data must be constructed.
Development of the Break-Even Model(s)
To develop a break-even model for the firm, the financial manager must first identify the most
relevant output volume range. Then for this range, all product-related costs must be categorized
into variable, fixed, or semivariable cost categories. Finally, the manager must approximate the
impact of all costs in the semivariable category (those costs that are not purely fixed or variable,
such as step function cost) and judiciously allocate each of them to either the fixed or variable
cost categories for the purposes of this calculation.
To determine the total revenue for any given volume of output, multiply the unit revenue from
the sale of product (P) by the quantity of units sold (Q).
Total revenue = (P)(Q)
Two Variations of the Break-Even Model
There are two basic approaches to the break-even analysis model, depending on what level of
financial data is available: (1) the break-even units methodology and (2) the break-even dollars
methodology.
The Break-Even in Units Methodology
The break-even model is just a simple adaptation of the firm's income statement, which
expresses net profit in the following format:
Sales – total costs = profit
or
Sales – (total variable costs + total fixed costs) = profit (or EBIT)
The two general methodologies for applying this formula are shown below.
a. The contribution-margin analysis method
This method is quite useful, but requires knowledge of unit variable and total fixed costs.
We use a two-step process of first calculating the unit contribution, and then dividing it
into the total fixed costs to yield the break-even volume.
1. Calculate the unit contribution margin, which is the difference between the unit
selling price (P) and the unit variable cost (V): unit contribution margin = (P – V).
2. Then, divide the fixed cost (F) by the calculated unit contribution margin to
determine the break-even quantity in units.
2. The algebraic analysis method
1. Define the variable terms:
• QB = the break-even level of units sold (quantity)
• P = the unit sales price
• F = the total fixed cost for the period
• V = unit variable cost
2. Then set up the algebraic equation as developed in detail in your textbook:
QB = F/(P – V)
Note that this algebraic formula uses the same theory as the contribution-margin approach logic
discussed above.
The Break-Even Point in Dollars Methodology
When the required detailed information on unit costs or prices is unavailable, or if multiple
products are involved, you can compute the break-even point in terms of sales dollars rather than
units of output. In general, an analyst can normally compute a break-even point in sales dollars
by using data typically published in the firm's annual report.
Because variable cost per unit and the selling price per unit are assumed to be constant, the ratio
of total variable costs to sales (VC/S) is a constant for any level of sales. Therefore, if the break-
even level of sales is denoted S*, the corresponding equation is:
S* = F/(1 – (VC/S))
where:
S* = break-even level of sales in dollars
F = fixed cost in dollars
VC = variable cost in dollars
S = sales in dollars
The algebraic development of this formula is detailed in your textbook.
For an illustration of how this process works, let's examine a typical break-even problem.
The projected cost structure for Nanotech Industries for upcoming fiscal year 2004 is
summarized below. During this year, Nanotech projects to sell between 40,000 and 120,000 units
of Nano Widgets, which is its only product line. The projected selling price for a Nano Widget is
$20.00/unit.
Nano Widgets Cost Structure for FY 2004
Variable-Cost Components Fixed-Cost Components
Labor $5.00/unit Depreciation $350,000
Material $3.00/unit Insurance $50,000
Utilities $1.00/unit Lease cost $100,000
Packaging $1.00/unit
1. What is Nanotech's projected break-even point for Nano Widgets in units for FY 2004?
2. What is its projected profit from Nano Widgets at 100,000 units?
1. The first step in this process is to calculate the variable cost per unit for one Nano
Widget:
Variable-Cost Components Labor $ 5.00/unit Material $ 3.00/unit Utilities $ 1.00/unit Packaging $ 1.00/unit
Variable cost $10.00/unit
2. The next step is to calculate the total fixed cost for the period, FY 2004:
Fixed-Cost Components Depreciation $350,000
Insurance $ 50,000 Lease cost $100,000
Total fixed costs $500,000
3. Now we can summarize our data as follows:
Selling price P $20.00/unit (given)
Variable cost V $10.00/unit (calculated)
Fixed cost F $500,000 (calculated)
Part 1. What is Nanotech's projected break-even point for Nano Widgets in units for FY
2004?
QB = F/(P – V)
QB = $500,000/(20.00 – 10.00)
QB = $500,000/(10.00)
QB = 50,000 units
Part 2. What is its projected profit from Nano Widgets at 100,000 units?
Now we have to supply some financial logic by remembering the formula for profit:
Total sales – total costs = profit
or:
Sales – (total variable costs + total fixed costs) = profit (or EBIT)
Total sales quantity sold times price per unit = (Q P)
Total variable cost quantity sold times variable cost per unit = (Q V)
Total fixed cost $500,000
Quantity sold 100,000 units (given)
(Q P) – [(Q V) + F)] profit
(100,000 $20.00) – [(100,000 10.00) + 500,000] = profit
$2,000,000 – $1,500,000 profit
$500,000 projected profit at sales of 100,000 units
Limitations of the Break-Even Analysis Method
Although break-even analysis is a powerful analytical tool, it must be used consistent with its
assumptions and limitations. Its theoretical limitations are listed below.
• The cost-volume-profit relationship is assumed to be linear.
• The total revenue curve is presumed to increase linearly with each incremental increase
in volume of output.
• A constant production and sales mix is assumed.
• The break-even computation is a static form of analysis (no provision for change).
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