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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.

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.

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

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.

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.

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

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). 