Posted: February 26th, 2023

FINC 331-WEEK 6: Capital Budgeting

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· Cost of Capital, The Cost of Retained Earnings and The Weighted Average Cost of Capital

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Discussion 1 –  Capital Budgeting

Capital budgeting is a complicated process that is essential to good investment decisions by a company. Please give an example of a capital budgeting decision a company might need to make.

Are there examples in using the cost of capital in personal life? When or how have you compared the cost of getting money to the potential benefit of that money?

Once a business computes its cost of capital, discuss how a manager might decide whether to take on a project or not.  How are capital project investments prioritized?

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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

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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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Introduction to the

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The Basics of the Cost of Capital

Valuing Different Costs

Approaches to Calculating the Cost of Capital

The WACC

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•

Defining the Cost of Capital

•

Differences Between Required Return and the Cost of Capital

• Relationship Between Financial Policy and the Cost of Capital

The Basics of the Cost of Capital

Introduction to the Cost of Capital

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• If a project is of similar risk to a company’s average business activities, it is

reasonable to use the company’s average cost of capital as a basis for project

evaluation.

• A company’s securities typically include both debt and equity; therefore, one must

calculate both the cost of debt and the cost of equity to determine a company’s

cost of capital.

• Weighted average cost of capital takes into account the amount of financing that

comes through the use of debt and the use of equity.

• IRR is the rate of return that makes the net present value of all cash flows from an

investment equal

zero.

Defining the Cost of Capital

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• Cost of capital refers to the expected returns on all of the various securities issued

by a company, often expressed as a weighted average.

• Required refers to the rate of return necessary to achieve in order to compensate

investors for taking on the risk of the individual investment.

• The risk premium can be established by understanding business risk and financial

risk.

Differences Between Required Return and the Cost of Capital

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• As opposed to strictly using cost of capital, decisions must be made using

opportunity cost of capital.

• Opportunity cost of capital is the amount of money foregone by investing in one

asset compared to another.

• Facets of financial policy include valuation, portfolio theory, hedging, and capital

structure.

Relationship Between Financial Policy and the Cost of Capital

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•

The Cost of Debt

•

The

Cost of Preferred Stock

• The Cost of Common Equity

• The Cost of Retained Earnings

• The Cost of New Common Stock

Valuing Different Costs

Introduction to the Cost of Capital > Valuing Different Costs

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• Cost of debt equals the interest rate of the debt (composed of the risk-free rate

and a credit risk premium) times one minus the corporate tax rate.

• Cost of debt is also equal to the annual interest payment of the debt divided by its

market value.

• The yield to maturity can be used in determining the cost of debt. It is is the

discount rate at which the sum of all future cash flows from the bond are equal to

the price of the bond.

The Cost of Debt

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• Preferred stock is an equity security with properties of both an equity and a debt

instrument.

• Because preferred stock carries a differing amount of risk than other types of

securities, we must calculate its asset specific cost of capital to work into our

overall weighted average cost of capital.

• The dividend is usually specified as a percentage of the par value or as a fixed

amount.

The Cost of Preferred Stock

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• A company’s current cost of equity can be difficult to determine because it is

unobservable and must be estimated.

• The cost of equity can be estimated by comparing the investment to other

investments with similar risk profiles.

• Other methods of estimating cost of equity include the capital asset pricing model,

the dividend growth model, and the bond plus model.

The Cost of Common Equity

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CAPM Method

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• Retained earnings refers to the portion of net income (or loss) that is retained by a

company rather than distributed to its owners as

dividends.

• We can think of the cost of retained earnings in relation to the opportunity cost of

how we can use these funds elsewhere.

• When deciding how to finance a new project, companies have a tendency to

follow the pecking order of finance, preferring internal sources of capital to

external sources of capital.

The Cost of Retained Earnings

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Retention Rate

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• If a mixture of internal and external sources of financing are used, a company

must determine the proportion of external financing to be used, and thus the

marginal cost of capital.

• Flotation costs include all costs of issuing the securities, such as banker’s fees,

legal fees, underwriting fees, filing costs, etc.

• Cost of new common stock is calculated using the dividend growth model, by

devaluing the current stock price by the amount of flotation cost.

The Cost of New Common Stock

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•

The Capital Asset Pricing Model

•

The SML Approach

• Discounted Cash Flow Approach

• The “Bond Yield Plus Risk Premium” Approach

Approaches to Calculating the Cost of Capital

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• CAPM determines the expected rate of return of an asset.

• The model takes into account the asset’s sensitivity to systematic risk (beta), the

expected return of the market, and the expected return of a risk-free asset.

• CAPM states that investors are only rewarded for bearing systematic risk.

• CAPM states that if the expected return is not greater than or equal to our

required return the investment should not be made.

The Capital Asset Pricing Model

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• The SML graphs the relationship between risk β (beta) and

expected return.

• All correctly priced assets lie on the SML.

• If a security is priced above the SML, it is undervalued. If it is priced below the

SML, it is overvalued.

The SML Approach

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• In the DCF approach, all future expected cash flows associated with the asset are

discounted in order to find their present values.

• To determine the value of the asset, the present values of all expected cash flows

are summed.

• When future cash flows are infinite or extend past a certain period, a terminal

value can be found and discounted back

to the present.

• Comparing a value found using the DCF approach with the actual price of an

asset determines if an asset is undervalued, overvalued, or correctly priced.

Discounted Cash Flow Approach

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Present Value Equation

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• The BYPRP approach applies to a company’s publicly traded equity.

• The yield to maturity is the discount rate at which the sum of all future cash flows

from a bond are equal to its price.

• The equity risk premium is the return that stocks are expected to receive in

excess of the risk-free interest rate.

• The BYPRP approach does not produce as accurate an estimate as the capital

asset pricing model or discounted cash flow analysis.

The “Bond Yield Plus Risk Premium” Approach

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Bond Yield Plus Risk Premium Equation

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•

Weighted Average Cost of Capital

•

The Weightings

• Factors Controlled by the Firm

• Factors External to the Firm

• Making Risk Adjustments

• Problems with WACC

The WACC

Introduction to the Cost of Capital > The WACC

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• The WACC is the minimum rate of return a company must earn on a new venture

in order to make the investment worthwhile.

• The various securities that companies use as sources of finance are expected to

generate different returns.

• To calculate WACC, multiply the cost of debt by the ratio of debt to total market

value of the company. Then add this to the cost of equity multiplied by the ratio of

equity to total market value.

Weighted Average Cost of Capital

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• The WACC must take into account the weight of each component of a company’s

capital structure.

• The calculation of the WACC usually uses the market values of the various

components rather than their book values.

• Market value is the price at which an asset would trade in a competitive auction

setting.

• Book value refers to the value of an asset according to the account balance

present on the balance sheet of a company.

• If the value of a company’s debt exceeds the value of its equity, the cost of its

debt will have more “weight” in calculating its total cost of capital than the cost of

equity. If the value of the company’s equity exceeds its debt, the cost of its equity

will have more weight.

The Weightings

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Domestic Balance Sheet

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• Capital structure refers to the way a company finances its assets through some

combination of equity, debt, or hybrid securities.

• When a higher proportion of debt is chosen, the cost of debt must factor in credit

risk.

• Changes in a company’s dividend policy provide information to investors, who

should react accordingly to either increase or decrease the value of an asset.

Factors Controlled by the Firm

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Expected Investor Return

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• Since debt expense is tax-deductible, the cost of debt is computed as an after tax

cost to make it comparable with the cost of equity.

• The Federal Reserve moderates long-term interest rates, which causes

fluctuations in the risk-free rate that affect the cost of capital.

• Economic conditions refer to the demand and supply of capital in the marketplace

that can impact how capital is raised, and therefore what the cost of capital will

be.

• Market conditions refer to the demand for higher rates of return by investors,

which will increase the cost of capital.

Factors External to the Firm

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U.S. Corporate Taxes

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• It is possible to adjust risk by figuring the differing risk into the company’s beta.

• The beta coefficient is the risk of a new project in relation to the risk of the market

as a whole.

• Therefore, if a new project of differing risk is undertaken, the beta for that project

will be weighted into the company’s overall cost of capital.

Making Risk Adjustments

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Beta Equation

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• While the relative debt and equity values can be easily determined, calculating the

costs of debt and equity can be problematic.

• The problem inherent in different methods used to calculate cost of equity is that

at least one component is an estimate.

• The terms of risk-free bonds used in determining cost of debt may not always

adequately match the terms of the company’s debt.

Problems with WACC

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U.S. Treasuries Yield

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Appendix

Key terms

• benchmark A standard by which something is evaluated or measured.

• beta Average sensitivity of a security’s price to overall securities market prices.

• beta Average sensitivity of a security’s price to overall securities market prices.

• business risk The risk associated with the operational and administrative procedures of the particular industry or company.

• capital Money and wealth; the means to acquire goods and services, especially in a non-barter system.

• capital Money and wealth; the means to acquire goods and services, especially in a non-barter system.

• capital intensity ratio the amount of fixed or real capital present in relation to other factors of production, especially labor

• coupon payment A periodic interest payment that the bondholder receives during the time between when the bond is issued

and when it matures.

• covariance A measure of how much two random variables change together.

• default To fail to meet an obligation.

• discount rate The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to

decrease the amounts of future cash flow to yield their present value.

• dividend payout ratio The fraction of net income a firm pays to its stockholders in dividends.

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• dividend yield A company’s total annual dividend payment per share, divided by its price per share.

• financial risk An umbrella term for multiple types of risk associated with financing, including financial transactions that include

company loans in risk of default.

• hybrid instrument A broad group of securities that pay a predictable (fixed or floating) rate of return or dividend until a certain

date, at which point the holder has a number of options including converting the securities into the underlying share.

• inflation An increase in the general level of prices or in the cost of living.

• internal rate of return IRR. The rate of return on an investment which causes the net present value of all future cash flows to be

zero.

• leverage The use of borrowed funds with a contractually determined return to increase the ability of a business to invest and

earn an expected higher return (usually at high risk).

• lobbying The act of attempting to influence decisions made by officials in the government, most often legislators or members of

regulatory agencies.

• Marginal Cost of Capital The cost of the marginal dollar of capital that a firm could raise externally.

• maturity Date when payment is due.

• Opportunity cost The cost of an opportunity forgone (and the loss of the benefits that could be received from that opportunity);

the most valuable forgone alternative.

• principal payment The payment made upon maturity of a bond

• projection period The time duration for estimating the future cash flows of a proposed investment.

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• proxy A measurement of one physical quantity that is used as an indicator of the value of another.

• proxy fight a conflict where two powers use third parties as a supplement to, or a substitute for fighting each other directly

• required return the minimum gain expected by investors

• retained earnings The portion of net income that is retained by the corporation rather than distributed to its owners as

dividends.

• risk The potential (conventionally negative) impact of an event, determined by combining the likelihood of the event occurring

with the impact, should it occur.

• slope The ratio of the vertical and horizontal distances between two points on a line; zero if the line is horizontal, undefined if it

is vertical.

• Synergy Benefits resulting from combining two different groups, people, objects, or processes.

• systematic risk The risk associated with an asset that is correlated with the risk of asset markets generally, often measured as

its beta.

• time value of money The value of money, figuring in a given amount of interest, earned over a given amount of time.

• Unsystematic risk Risk peculiar to an asset, which can be eliminated through diversification.

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Introduction to the Cost of Capital

Bond Yield Plus Risk Premium Equation

States that the required return on an equity equals the yield of the company’s long-term debt plus the equity’s risk premium.

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Yield To Maturity Graph

A hypothetical graph showing yield to maturities (or internal rates of return) for corresponding present values.

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Domestic Balance Sheet

If the person analyzing a company chooses or if the market value of a company’s debt and equity is not available, the book value can be used. The book

value of debt and equity can be found on the company’s balance sheet.

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Cost of Preferred Stock

The cost of preferred stock is equal to the preferred dividend divided by the preferred stock price, plus the growth rate.

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Systematic vs. Unsystematic Risk

As the number of stocks in a portfolio increase, the amount of unsystematic risk approaches zero. However, it is impossible to remove systematic risk,

as it concerns the economy in general.

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Present Value of the Terminal Value

Use this equation to find the present value of a future terminal value. Where TV = terminal value, k = discount rate, and n = the number of periods back

to the present.

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Example Equation

$10 divided by $100, plus 3%.

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Net Present Value Equation

Equation used to determine net present value, and therefore internal rate of return. DPV = discounted net present value, N = total number of periods in

which a cash flow occurs, t = the specific period of the cash flow, FV = the value of the future cash flow, and i = internal rate of return.

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SML Equation

The SML is the graphical representation of CAPM, and thus is found using the same equation.

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Terminal Value Equation

FCFN+1 = future cash flow one year after the projection period. k = discount rate. g = assumed constant growth rate.

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Cost of Debt Equation

Cost of debt is equal to the annual interest payment of the debt divided by its market value.

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Example Equation

Required return = 6% + 4%

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CAPM Equation

The expected rate of return = the rate of return for a risk-free asset + beta* (the rate of return of the market – the risk-free rate). The return of the market

minus the risk-free rate is also known as the risk premium.

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Equation For Cost of Debt

Cost of debt equals the interest rate of the debt (composed of the risk-free rate and a credit risk premium) times one, minus the corporate tax rate.

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WACC Equation

In this formula, V is equal to the value of the firm, or Debt (D) plus Equity (E). r(D) is the company’s rate on debt, r(E) the rate on equity. T is the

company’s marginal tax rate.

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Expected Investor Return

To calculate expected investor return, divide the dividend payment per share by the market price of the asset and add the expected growth rate.

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Oil Prices

Companies often use hedging techniques to offset price fluctuations for commodities. The fluctuation of oil prices can be seen in the above graph.

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CAPM-SML

The Security Market Line for the Dow Jones Industrial Average over a 3 year period, with the x-axis representing beta and the y-axis representing

expected return.

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Cost of New Equity

Cost of new equity equals dividends payed in year one divided by the current stock price, devalued by the amount of flotation cost, plus the growth rate.

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Obtaining Required Return

The capital asset pricing model is a good representation of how to obtain required return. It adds the risk-free rate to the risk premium of the market

adjusted to an investment’s beta.

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U.S. Corporate Taxes

Effective U.S. corporate tax rates from 1947-2011.

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Union Camp Corporation Bond Certificate

$25,000 Corporation Sinking Fund Bond Certificate.

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Present Value Equation

To find the discounted present value of an asset, it is necessary to sum the discounted present value of each future cash flow (FV) at any time period (t)

in years from the present time, using the appropriate interest rate (i).

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Example Equation

$10 in dividends. Current price of $100. Flotation cost of 3%. Growth rate of 5%.

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U.S. Treasuries Yield

Yields on 1-mont, 10-year, and 30-year U.S. government debt.

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IRR Investment Comparison

A graph showing the decision between two exclusive investments based on IRR.

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Retention Rate

The retention rate equals retained earnings divided by net income.

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Beta Equation

The beta of an investment is equal to the covariance between the rate of return of the investment, r(a), and that of the portfolio, r(p).

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CAPM Method

Expected return for a security equals the risk-free return for the market plus the beta for the security times its risk premium.

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Introduction to the Cost of Capital

The average cost of capital is:

A) a benchmark for accepting or rejecting projects.

B) fixed through time

C) the same for all companies

D) all of these

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Introduction to the Cost of Capital

The average cost of capital is:

A) a benchmark for accepting or rejecting projects.

B) fixed through time

C) the same for all companies

D) all of these

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Introduction to the Cost of Capital

Which of the following explains the differences between a

company’s required return and its cost of capital?

A) Required return measures business risk; cost of capital measures

financial risk.

B) Required return measures financial risk; cost of capital measures

business risk.

C) Required return is from the company’s perspective; cost of capital

from the investor’s.

D) Required return is from the investor’s perspective; cost of capital from

the company’s.

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Introduction to the Cost of Capital

Which of the following explains the differences between a

company’s required return and its cost of capital?

A) Required return measures business risk; cost of capital measures

financial risk.

B) Required return measures financial risk; cost of capital measures

business risk.

C) Required return is from the company’s perspective; cost of capital

from the investor’s.

D) Required return is from the investor’s perspective; cost of capital from

the company’s.

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Introduction to the Cost of Capital

A company’s cost of capital is used as a tool in relation to which

aspect of financial policy?

A) Diversifying a company’s porfolio

B) Valuing projects by discounting cash flows, and then selecting projects

with the highest return.

C) Hedging a company’s investments.

D) Evaluating a company’s capital structure.

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Introduction to the Cost of Capital

A company’s cost of capital is used as a tool in relation to which

aspect of financial policy?

A) Diversifying a company’s porfolio

B) Valuing projects by discounting cash flows, and then selecting projects

with the highest return.

C) Hedging a company’s investments.

D) Evaluating a company’s capital structure.

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Introduction to the Cost of Capital

A company has a risk free rate of 3% and a risk premium of 6%.

Its tax rate is 35%. What is the company’s cost of debt?

A) 5.85%

B) 3.15%

C) 3.9%

D) 2.1%

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Introduction to the Cost of Capital

A company has a risk free rate of 3% and a risk premium of 6%.

Its tax rate is 35%. What is the company’s cost of debt?

A) 5.85%

B) 3.15%

C) 3.9%

D) 2.1%

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Introduction to the Cost of Capital

A company has issued preferred stock that are valued at $75 a

share. The preferred dividend is $5. The company’s growth rate is

5%. What is the cost of the company’s preferred stock?

A) 11.67%

B) 6.67%

C) 1.67%

D) 5%

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Introduction to the Cost of Capital

A company has issued preferred stock that are valued at $75 a

share. The preferred dividend is $5. The company’s growth rate is

5%. What is the cost of the company’s preferred stock?

A) 11.67%

B) 6.67%

C) 1.67%

D) 5%

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Introduction to the Cost of Capital

A company issues common equity and has a beta of 1.5. The risk

free return is 3% and the market return is 7%. What is the

company’s cost of common equity?

A) 6%

B) 7%

C) 9%

D) 13.5%

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Introduction to the Cost of Capital

A company issues common equity and has a beta of 1.5. The risk

free return is 3% and the market return is 7%. What is the

company’s cost of common equity?

A) 6%

B) 7%

C) 9%

D) 13.5%

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Introduction to the Cost of Capital

A company has retained earnings of $1.5 million and net income

of $8 million. What is the retention rate?

A) 0.1875

B) .08125

C) 0.8125.

D) .01875.

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Introduction to the Cost of Capital

A company has retained earnings of $1.5 million and net income

of $8 million. What is the retention rate?

A) 0.1875

B) .08125

C) 0.8125.

D) .01875.

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Introduction to the Cost of Capital

A company is thinking of issuing more common stock. Its stock’s

current market price is $50 a share with a dividend of $3 a share.

The company has a 5% growth rate and a flotation cost of 10%.

What is the company cost of new common stock?

A) 6.67%

B) 65%

C) 16.3%

D) 11.67%

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Introduction to the Cost of Capital

A company is thinking of issuing more common stock. Its stock’s

current market price is $50 a share with a dividend of $3 a share.

The company has a 5% growth rate and a flotation cost of 10%.

What is the company cost of new common stock?

A) 6.67%

B) 65%

C) 16.3%

D) 11.67%

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Introduction to the Cost of Capital

A company has a risk free rate of 3%. The market rate of return is

8% and the company has a beta of 2. What is the company’s

expected rate of return?

A) 8%

B) 19%

C) 13%

D) 10%

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Introduction to the Cost of Capital

A company has a risk free rate of 3%. The market rate of return is

8% and the company has a beta of 2. What is the company’s

expected rate of return?

A) 8%

B) 19%

C) 13%

D) 10%

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Introduction to the Cost of Capital

In the capital asset pricing model (CAPM), you derive a stock’s:

A) Beta

B) Expected return (or cost of capital)

C) Equity Premium

D) Beta, expected return (or cost of capital), and equity premium

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Introduction to the Cost of Capital

In the capital asset pricing model (CAPM), you derive a stock’s:

A) Beta

B) Expected return (or cost of capital)

C) Equity Premium

D) Beta, expected return (or cost of capital), and equity premium

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Introduction to the Cost of Capital

In order to compute the statistical values in the capital asset

pricing model (CAPM), you need information over time about:

A) The rate of return of a risk-free asset, the overall stock market return,

and a company’s rate of return.

B) a rate of return from a risk-free asset (like the 90-day U.S. Treasury bill

rate).

C) an overall stock market rate of return.

D) a company’s rate of return.

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Introduction to the Cost of Capital

In order to compute the statistical values in the capital asset

pricing model (CAPM), you need information over time about:

A) The rate of return of a risk-free asset, the overall stock market return,

and a company’s rate of return.

B) a rate of return from a risk-free asset (like the 90-day U.S. Treasury bill

rate).

C) an overall stock market rate of return.

D) a company’s rate of return.

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Introduction to the Cost of Capital

Which of the following interpretations of data related to a Security

Market Line (SML) is correct?

A) If an asset is priced at a point above the SML it is overvalued.

B) If an asset is priced at a point below the SML, it is undervalued.

C) All of these answers.

D) If an asset’s value lies on the SML, it is correctly priced.

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Introduction to the Cost of Capital

Which of the following interpretations of data related to a Security

Market Line (SML) is correct?

A) If an asset is priced at a point above the SML it is overvalued.

B) If an asset is priced at a point below the SML, it is undervalued.

C) All of these answers.

D) If an asset’s value lies on the SML, it is correctly priced.

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Introduction to the Cost of Capital

A company makes an initial $10,000 investment in a project. This

project is projected to earn $8000 in year one, $10,000 in year 2,

$12,000 in year 3, and $20,000 in year 4. If the interest rate is 5%,

what is the project’s present value?

A) $33,509

B) $43,509

C) $40,000

D) $37,619

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Introduction to the Cost of Capital

A company makes an initial $10,000 investment in a project. This

project is projected to earn $8000 in year one, $10,000 in year 2,

$12,000 in year 3, and $20,000 in year 4. If the interest rate is 5%,

what is the project’s present value?

A) $33,509

B) $43,509

C) $40,000

D) $37,619

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Introduction to the Cost of Capital

Which of the following is NOT an element in the bond yield plus

risk premium approach?

A) The company’s CAPM.

B) The future cash flows from the benchmark bond.

C) The current yield of a 10-year U.S. Treasury Bond.

D) The benchmark bond’s internal rate of return.

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Introduction to the Cost of Capital

Which of the following is NOT an element in the bond yield plus

risk premium approach?

A) The company’s CAPM.

B) The future cash flows from the benchmark bond.

C) The current yield of a 10-year U.S. Treasury Bond.

D) The benchmark bond’s internal rate of return.

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Introduction to the Cost of Capital

Which of the following is NOT a way weighted average cost of

capital (WACC) is used to analyze a company’s financial

activities?

A) WACC is the rate a company is expected to pay, on average, to its

security holders.

B) WACC influences how a company’s capital structure is balanced.

C) WACC is the minimum rate of return a company must earn on a new

venture.

D) All of these answers.

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Introduction to the Cost of Capital

Which of the following is NOT a way weighted average cost of

capital (WACC) is used to analyze a company’s financial

activities?

A) WACC is the rate a company is expected to pay, on average, to its

security holders.

B) WACC influences how a company’s capital structure is balanced.

C) WACC is the minimum rate of return a company must earn on a new

venture.

D) All of these answers.

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Introduction to the Cost of Capital

Suppose that a company has total financing where 10% comes

from bonds, 10% from a loan, and 80% from shareholders’ equity.

The bonds pay on average a 10% interest rate, the loan has a

10% interest rate, and shareholders require a 10% return. The

interest payment on the loan is tax deductible and the tax rate is

20%. What is the simple average cost of capital equal to?

A) 0.0933

B) 0.0333

C) 0.0733

D) 0.1

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Introduction to the Cost of Capital

Suppose that a company has total financing where 10% comes

from bonds, 10% from a loan, and 80% from shareholders’ equity.

The bonds pay on average a 10% interest rate, the loan has a

10% interest rate, and shareholders require a 10% return. The

interest payment on the loan is tax deductible and the tax rate is

20%. What is the simple average cost of capital equal to?

A) 0.0933

B) 0.0333

C) 0.0733

D) 0.1

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Introduction to the Cost of Capital

Suppose that a company has total financing where 10% comes

from bonds, 10% from a loan, and 80% from shareholders’ equity.

The bonds pay on average a 10% interest rate, the loan has a

10% interest rate, and shareholders require a 10% return. What is

the weighted average cost of capital (WACC) equal to?

A) 0.0333

B) 0.3

C) 0.1

D) 0.3333

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Introduction to the Cost of Capital

Suppose that a company has total financing where 10% comes

from bonds, 10% from a loan, and 80% from shareholders’ equity.

The bonds pay on average a 10% interest rate, the loan has a

10% interest rate, and shareholders require a 10% return. What is

the weighted average cost of capital (WACC) equal to?

A) 0.0333

B) 0.3

C) 0.1

D) 0.3333

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Introduction to the Cost of Capital

The weighted average cost of capital “weighting” is based on

_____.

A) the market value of the company’s debt and equity.

B) the book value of the company’s debt and equity.

C) the company’s tax rate.

D) the company’s returns on equity and debt.

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Introduction to the Cost of Capital

The weighted average cost of capital “weighting” is based on

_____.

A) the market value of the company’s debt and equity.

B) the book value of the company’s debt and equity.

C) the company’s tax rate.

D) the company’s returns on equity and debt.

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Introduction to the Cost of Capital

Which of the following correctly explains how a specific factor can

influence a company’s

weighted average cost of capital?

A) Increasing the amount of debt generally improves performance and

increases return on equity.

B) If a company increases it dividends, it leads to an increase in its

WACC.

C) Increased fixed costs will decrease a company’s WACC.

D) All of these answers.

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Introduction to the Cost of Capital

Which of the following correctly explains how a specific factor can

influence a company’s weighted average cost of capital?

A) Increasing the amount of debt generally improves performance and

increases return on equity.

B) If a company increases it dividends, it leads to an increase in its

WACC.

C) Increased fixed costs will decrease a company’s WACC.

D) All of these answers.

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Introduction to the Cost of Capital

Which of the following are factors that influence the weighted

average cost of capital (WACC) calculation and is external to the

firm?

A) The corporate tax rate.

B) Changes in interest rates.

C) The conditions in the stock market.

D) All of these answers.

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Introduction to the Cost of Capital

Which of the following are factors that influence the weighted

average cost of capital (WACC) calculation and is external to the

firm?

A) The corporate tax rate.

B) Changes in interest rates.

C) The conditions in the stock market.

D) All of these answers.

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Introduction to the Cost of Capital

A company is considering investing in a project that requires the

company to take on risks outside of the company’s current scope.

As a result, which of the following things will happen?

A) The company does not have to recalculate its WACC to evaluate the

project.

B) The project would decrease the company’s cost of equity.

C) All of these things.

D) The company’s stock value would drop unless the project increase the

company’s expected returns.

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Introduction to the Cost of Capital

A company is considering investing in a project that requires the

company to take on risks outside of the company’s current scope.

As a result, which of the following things will happen?

A) The company does not have to recalculate its WACC to evaluate the

project.

B) The project would decrease the company’s cost of equity.

C) All of these things.

D) The company’s stock value would drop unless the project increase the

company’s expected returns.

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Introduction to the Cost of Capital

Which of the following is a problem associated with using the

weighted average cost of capital?

A) All of these answers.

B) The calculation is not exact as at least one component is an estimate.

C) WACC will vary for the same business based on which method you

use.

D) It may be difficult to find a risk-free rate that corresponds to the

investment being analyzed.

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Introduction to the Cost of Capital

Which of the following is a problem associated with using the

weighted average cost of capital?

A) All of these answers.

B) The calculation is not exact as at least one component is an estimate.

C) WACC will vary for the same business based on which method you

use.

D) It may be difficult to find a risk-free rate that corresponds to the

investment being analyzed.

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Capital Budgeting
Introduction to Capital Budgeting

The Payback Method

Internal Rate of Return

Net Present Value

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Cash Flow Analysis and Other Factors

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• Defining Capital Budgeting

• The Goals of Capital Budgeting

• Accounting Flows and Cash Flows

• Ranking Investment Proposals

• Reinvestment Assumptions

• Long-Term vs. Short-Term Financing

Introduction to Capital Budgeting

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• Capital budgeting, which is also called investment appraisal, is the planning

process used to determine whether an organization’s long term investments,

major capital, or expenditures are worth pursuing.

• Major methods for capital budgeting include Net present value, Internal rate of

return, Payback period, Profitability index, Equivalent annuity and Real options

analysis.

• The IRR method will result in the same decision as the NPV method for non-

mutually exclusive projects in an unconstrained environment; Nevertheless, for

mutually exclusive projects, the decision rule of taking the project with the highest

IRR may select a project with a lower NPV.

Defining Capital Budgeting

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• Basically, the purpose of budgeting is to provide a forecast of revenues and

expenditures and construct a model of how business might perform financially.

• Capital Budgeting is most involved in ranking projects and raising funds when

long-term investment is taken into account.

• Capital budgeting is an important task as large sums of money are involved and a

long-term investment, once made, can not be reversed without significant loss of

invested capital.

The Goals of Capital Budgeting

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• Accounting flows involve Journal entries, Ledger accounts and Balancing to

present a business’s financial position in an Income statement, a Balance sheet

and a Cash flow statement.

• Cash flow is the movement of money into or out of a business, project or financial

product.

• Statement of cash flows includes three parts: Operational cash flows, Investment

cash flows and Financing cash flows.

Accounting Flows and Cash Flows

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Accounting cycle

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• The higher the NPV, the more attractive the investment proposal.

• The higher a project’s IRR, the more desirable it is to undertake the project.

• As the value of the profitability index increases, so does the financial

attractiveness of the proposed project.

• Shorter payback periods are preferable to longer payback periods.

• The higher the ARR, the more attractive the investment.

Ranking Investment Proposals

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• If trying to decide between alternative investments in order to maximize the value

of the firm, the reinvestment rate would be a better choice.

• NPV and PI assume reinvestment at the discount rate.

• IRR assumes reinvestment at the internal rate of return.

Reinvestment Assumptions

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• Management must match long-term financing or short-term financing mix to the

assets being financed in terms of both timing and cash flow.

• Long-term financing includes equity issued, Corporate bond, Capital notes and so

on.

• Short-term financing includes Commercial papers, Promissory notes, Asset-based

loans, Repurchase agreements, letters of credit and so on.

Long-Term vs. Short-Term Financing

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• Defining the Payback Method

• Calculating the Payback Period

• Discounted Payback

• Advantages of the Payback Method

• Disadvantages of the Payback Method

The Payback Method

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• The payback period is the number of months or years it takes to return the initial

investment.

• To calculate a more exact payback period: payback period = amount to be

invested / estimated annual net cash flow.

• The payback method also ignores the cash flows beyond the payback period;

thus, it ignores the long-term profitability of a project.

Defining the Payback Method

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• Payback period is usually expressed in years. Start by calculating Net Cash Flow

for each year, then accumulate by year until Cumulative Cash Flow is a positive

number: that year is the payback year.

• Some businesses modified this method by adding the time value of money to get

the discounted payback period. They discount the cash inflows of the project by

the cost of capital, and then follow usual steps of calculating the payback period.

• Additional complexity arises when the cash flow changes sign several times (i.e.,

it contains outflows in the midst or at the end of the project lifetime). The modified

payback period algorithm may be applied.

Calculating the Payback Period

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• The payback period is considered a method of analysis with serious limitations

and qualifications for its use, because it does not account for the time value of

money.

• The discounted payback period takes the time value of money into consideration.

• Whilst the time value of money can be rectified by applying a weighted average

cost of capital discount, it is generally agreed that this tool for investment

decisions should not be used in isolation.

Discounted Payback

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• Payback period, as a tool of analysis, is often used because it is easy to apply

and easy to understand for most individuals, regardless of academic training or

field of endeavor.

• The payback period is an effective measure of investment risk. It is widely used

when liquidity is an important criteria to choose a project.

• Payback period method is suitable for projects of small investments. It not worth

spending much time and effort in sophisticated economic analysis in such

projects.

Advantages of the Payback Method

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• Payback ignores the time value of money.

• Payback ignores cash flows beyond the payback period, thereby ignoring the

“profitability” of a project.

• To calculate a more exact payback period: Payback Period = Amount to be

Invested/Estimated Annual Net Cash Flow.

Disadvantages of the Payback Method

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• Defining the IRR

• Calculating the IRR

• Advantages of the IRR Method

• Disadvantages of the IRR Method

• Multiple IRRs

• Modified IRR

Internal Rate of Return

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• The IRR of an investment is the discount rate at which the net present value of

costs (negative cash flows) of the investment equals the net present value of the

benefits (positive cash flows) of the investment.

• The higher a project’s IRR, the more desirable it is to undertake the project.

• A firm (or individual) should, in theory, undertake all projects or investments

available with IRRs that exceed the cost of capital. Investment may be limited by

availability of funds to the firm and/or by the firm’s capacity or ability to manage

numerous projects.

Defining the IRR

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IRR

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• Given the (period, cash flow) pairs (n, Cn) where n is a positive integer, the total

number of periods N, and the net present value NPV, the internal rate of return is

given by the function in which NPV = 0.

• Any fixed time can be used in place of the present (e.g., the end of one interval of

an annuity); the value obtained is zero if and only if the NPV is zero.

• If the IRR is greater than the cost of capital, accept the project. If the IRR is less

than the cost of capital, reject the project.

Calculating the IRR

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• The IRR method is very clear and easy to understand. An investment is

considered acceptable if its internal rate of return is greater than an established

minimum acceptable rate of return or cost of capital.

• The IRR method also uses cash flows and recognizes the time value of money.

• The internal rate of return is a rate quantity, an indicator of the efficiency, quality,

or yield of an investment.

Advantages of the IRR Method

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Internal rate of return

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• The first disadvantage of IRR method is that IRR, as an investment decision tool,

should not be used to rate mutually exclusive projects, but only to decide whether

a single project is worth investing in.

• IRR overstates the annual equivalent rate of return for a project whose interim

cash flows are reinvested at a rate lower than the calculated IRR.

• IRR does not consider cost of capital; it should not be used to compare projects of

different duration.

• In the case of positive cash flows followed by negative ones and then by positive

ones, the IRR may have multiple values.

Disadvantages of the IRR Method

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Disadvantage of IRR

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• In the case of positive cash flows followed by negative ones and then by positive

ones, the IRR may have multiple values.

• It has been shown that with multiple internal rates of return, the IRR approach can

still be interpreted in a way that is consistent with the present value approach

provided that the underlying investment stream is correctly identified as net

investment or net borrowing.

• NPV remains the “more accurate” reflection of value to the business. IRR, as a

measure of investment efficiency may give better insights in capital constrained

situations. However, when comparing mutually exclusive projects, NPV is the

appropriate measure.

Multiple IRRs

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Multiple internal rates of return

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• MIRR is a modification of the internal rate of return (IRR) and as such aims to

resolve some problems with the IRR.

• More than one IRR can be found for projects with alternating positive and

negative cash flows, which leads to confusion and ambiguity. MIRR finds only one

value.

• MIRR = {[FV(positive cash flows, reinvestment rate)/-PV(negative cash flows,

finance rate)]^(1/n)}-1.

Modified IRR

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MIRR

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• Defining NPV

• Calculating the NPV

• Interpreting the NPV

• Advantages of the NPV method

• Disadvantages of the NPV method

• NPV Profiles

Net Present Value

Capital Budgeting > Net Present Value

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• Because of the time value of money, cash inflows and outflows only can be

compared at the same point in time.

• NPV discounts each inflow and outflow to the present, and then sums them to see

how the value of the inflows compares to the other.

• A positive NPV means the investment is worthwhile, an NPV of 0 means the

inflows equal the outflows, and a negative NPV means the investment is not good

for the investor.

Defining NPV

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Airplane

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• Cash inflows have a positive sign, while cash outflows are negative.

• To find the NPV accurately, the investor must know the exact size and time of

occurrence of each cash flow. This is easy to find for some investments (like

bonds), but more difficult for others (like industrial machinery).

• Investors use different rates for their discount rate such as using the weighted

average cost of capital, variable rates, and reinvestment rate.

Calculating the NPV

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Net Present Value (NPV) Formula

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• When inflows exceed outflows and they are discounted to the present, the NPV is

positive. The investment adds value for the investor. The opposite is true when

NPV is negative.

• A NPV of 0 means there is no change in value from the investment.

• In theory, investors should invest when the NPV is positive and it has the highest

NPV of all available investment options.

• In practice, determining NPV depends on being able to accurately determine the

inputs, which is difficult.

Interpreting the NPV

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• When NPV is positive, it adds value to the firm. When it is negative, it subtracts

value. An investor should never undertake a negative NPV project.

• As long as all options are discounted to the same point in time, NPV allows for

easy comparison between investment options. The investor should undertake the

investment with the highest NPV, provided it is possible.

• An advantage of NPV is that the discount rate can be customized to reflect a

number of factors, such as risk in the market.

Advantages of the NPV method

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NPV Decision Table

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• NPV is based on future cash flows and the discount rate, both of which are hard

to estimate with 100% accuracy.

• There is an opportunity cost to making an investment which is not built into the

NPV calculation.

• Other metrics, such as internal rate of return, are needed to fully determine the

gain or loss of an investment.

Disadvantages of the NPV method

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Medicine

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• The NPV Profile is a graph with the discount rate on the x-axis and the NPV of the

investment on the y-axis.

• Higher discount rates mean cash flows that occur sooner are more influential to

NPV. Since the earlier payments tend to be the outflows, the NPV profile

generally shows an inverse relationship between the discount rate and NPV.

• The discount rate at which the NPV equals 0 is called the internal rate of return

(IRR).

NPV Profiles

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NPV Profile

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• Cash Flow Factors

• Replacement Projects

• Sunk Costs

• Opportunity Costs

• Externalities

• Tax Rate

• Depreciation

• Elective Expensing

Cash Flow Analysis and Other Factors

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• Cash flow factors can be used to calculate parameters to measure organizational

performance.

• Operational cash flows are those originating from the organization’s internal

business.

• Financing cash flows are those originating from the issuance of debt or equity.

• Investment cash flows are those originating from assets and capital expenditures.

Cash Flow Factors

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• The cash flow analysis must take all cash flow components into account, such as

opportunity costs and depreciation and maintenance expense.

• The replacement project’s cash flows are the additional inflows and outflows to be

provided by the prospective replacement project.

• The comparison between the replacement and the current project informs the

decision whether to undertake the replacement and, if applicable, at what point

replacement should occur.

Replacement Projects

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Replacing a window sill vs. keeping the old one

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• Only prospective costs should impact an investment decision. Therefore, sunk

costs are not to be considered when deciding whether to undertake a project.

• A sunk cost is distinct from an economic loss. A loss may be caused by a sunk

cost, however.

• Sunk costs are irrecoverable.

Sunk Costs

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• Opportunity cost can be seen as the second-best choice available to an economic

actor.

• Opportunity cost can be measured monetarily, or more subjectively in terms of

pleasure or utility.

• Opportunity cost shows not only that resources are scarce, but also that

economic choices are limited.

Opportunity Costs

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Alternative choices

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• An externality that is a cost is a negative externality, while one that is a benefit is

a positive externality.

• Prices do not reflect externalities because they affect people outside the

economic transaction.

• Negative externalities can lead to over-production, while positive externalities can

lead to under-production. The former case occurs because the producer does not

pay the external cost, while the latter occurs because the benefit is generated

without profit.

Externalities

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Pollution

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• The methods used to present a tax rate include: statutory, average, marginal, and

effective rates.

• Statutory tax rates are those imposed by law.

• Average tax rate is the total tax liability divided by taxable income.

• Marginal tax rate is the rate at a specific level of spending or income. It is also

known as tax “on the last dollar,” earned or spent.

• Effective tax rate describes when varying measures of tax are divided by varying

measures of the tax base. It is inconsistently defined in practice.

Tax Rate

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Tax Rate

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• Fair value depreciation is an estimate of the market value of an asset.

• The cost of an asset that is to be allocated by depreciation is the amount paid for

it minus any salvage value it will have at the end of its useful life.

• Methods used for apportioning the cost over a period of time include fixed

percentage, straight-line, and declining balance.

Depreciation

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Depreciated value

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• Usually this provision applies to small businesses because there are limitations on

what and how much property can be expensed.

• Though buildings were not originally eligible, a 2010 law included them.

• The total deduction for a year cannot exceed the person’s income for that year.

Elective Expensing

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Appendix

Key terms

• accounts receivable Accounts receivable also known as Debtors, is money owed to a business by its clients (customers) and

shown on its balance sheet as an asset.

• allocate To distribute according to a plan.

• APT In finance, arbitrage pricing theory (APT) is a general theory of asset pricing that holds, which holds that the expected

return of a financial asset can be modeled as a linear function of various macro-economic factors or theoretical market indices,

where sensitivity to changes in each factor is represented by a factor-specific beta coefficient.

• benefit An advantage, help, or aid from something.

• Call option A call option, often simply labeled a “call”, is a financial contract between two parties, the buyer and the seller of this

type of option. [1] The buyer of the call option has the right, but not the obligation to buy an agreed quantity of a particular

commodity or financial instrument (the underlying) from the seller of the option at a certain time (the expiration date) for a

certain price (the strike price)

• capital budgeting The budgeting process in which a company plans its capital expenditure (the spending on assets of long-term

value).

• capital budgeting The budgeting process in which a company plans its capital expenditure (the spending on assets of long-term

value).

• cash flow The sum of cash revenues and expenditures over a period of time.

• cash flow The sum of cash revenues and expenditures over a period of time.

• cash inflow Cash that is received by the investor. For example, dividends paid on a stock owned by the investor is a cash

inflow.

• cash outflow Any cash that is spent or invested by the investor.

• Common stock Common stock is a form of corporate equity ownership, a type of security.

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Capital Budgeting

• cost of capital the rate of return that capital could be expected to earn in an alternative investment of equivalent risk

• cost of capital the rate of return that capital could be expected to earn in an alternative investment of equivalent risk

• cost of capital the rate of return that capital could be expected to earn in an alternative investment of equivalent risk

• cost of capital the rate of return that capital could be expected to earn in an alternative investment of equivalent risk

• cost of capital the rate of return that capital could be expected to earn in an alternative investment of equivalent risk

• cost of capital the rate of return that capital could be expected to earn in an alternative investment of equivalent risk

• cumulative having priority rights to receive a dividend that accrue until paid

• deduction A sum that can be removed from tax calculations; something that is written off.

• Default risk Default risk, also known as credit risk, refers to the risk that a borrower will default on any type of debt by failing to

make the obligatory payments.

• discount rate The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to

decrease the amounts of future cash flow to yield their present value.

• discount rate The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to

decrease the amounts of future cash flow to yield their present value.

• discounted cash flow In finance, discounted cash flow (DCF) analysis is a method of valuing a project, company, or asset using

the concepts of the time value of money.

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Capital Budgeting

• discounted payback period The discounted payback period is the amount of time that it takes to cover the cost of a project, by

adding positive discounted cash flow coming from the profits of the project.

• duration A measure of the sensitivity of the price of a financial asset to changes in interest rates, computed for a simple bond

as a weighted average of the maturities of the interest and principal payments associated with it

• effective interest rate The effective interest rate, effective annual interest rate, annual equivalent rate (AER), or simply effective

rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual

compound interest payable in arrears.

• explicit costs a direct payment made to others in the course of running a business, such as wage, rent and materials

• gain (or loss) If an investment earns more value than it costs, the difference is the gain. If it costs more than it earns, the

difference is a loss.

• implicit costs The opportunity cost equal to what a firm must give up in order to use factors which it neither purchases nor hires.

• internal rate of return IRR. The rate of return on an investment which causes the net present value of all future cash flows to be

zero.

• liquidity Availability of cash over short term: ability to service short-term debt.

• margin Collateral that the holder of a financial instrument has to deposit to cover some or all of the credit risk of their

counterparty.

• Modified Internal Rate of Return The modified internal rate of return (MIRR) is a financial measure of an investment’s

attractiveness. It is used in capital budgeting to rank alternative investments of equal size. As the name implies, MIRR is a

modification of the internal rate of return (IRR) and, as such, aims to resolve some problems with the IRR.

• Modified Internal Rate of Return The modified internal rate of return (MIRR) is a financial measure of an investment’s

attractiveness. It is used in capital budgeting to rank alternative investments of equal size. As the name implies, MIRR is a

modification of the internal rate of return (IRR) and, as such, aims to resolve some problems with the IRR.

• mutually exclusive Describing multiple events or states of being such that the occurrence of any one implies the non-

occurrence of all the others.

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Capital Budgeting

• mutually exclusive Describing multiple events or states of being such that the occurrence of any one implies the non-

occurrence of all the others.

• net present value profile a graph of the sum of all cash inflows and outflows adjusted for the time value of money at different

discount rates

• Opportunity cost The cost of an opportunity forgone (and the loss of the benefits that could be received from that opportunity);

the most valuable forgone alternative.

• Opportunity cost The cost of an opportunity forgone (and the loss of the benefits that could be received from that opportunity);

the most valuable forgone alternative.

• Opportunity cost The cost of an opportunity forgone (and the loss of the benefits that could be received from that opportunity);

the most valuable forgone alternative.

• Opportunity cost The cost of an opportunity forgone (and the loss of the benefits that could be received from that opportunity);

the most valuable forgone alternative.

• Opportunity cost The cost of an opportunity forgone (and the loss of the benefits that could be received from that opportunity);

the most valuable forgone alternative.

• parameter A variable kept constant during an experiment, calculation, or similar.

• payback period the amount of time required for the return on an investment to return the sum of the original investment

• Preferred Stock Preferred stock (also called preferred shares, preference shares or simply preferreds) is an equity security with

properties of both an equity and a debt instrument, and is generally considered a hybrid instrument.

• reinvestment rate The annual yield at which cash flows from an investment can be reinvested.

• retrospective Affecting or influencing past things; retroactive.

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Capital Budgeting

• return Gain or loss from an investment.

• sunk cost A cost that has already been incurred and which cannot be recovered to any significant degree.

• Swap In finance, a swap is a derivative in which counterparties exchange cash flows of one party’s financial instrument for

those of the other party’s financial instrument.

• time value of money The time value of money is the value of money, figuring in a given amount of interest earned over a given

amount of time.

• time value of money The value of money, figuring in a given amount of interest, earned over a given amount of time.

• time value of money The value of money, figuring in a given amount of interest, earned over a given amount of time.

• variable something whose value may be dictated or discovered.

• Weighted average cost of capital The weighted average cost of capital (WACC) is the rate that a company is expected to pay

on average to all its security holders to finance its assets. The WACC is the minimum return that a company must earn on an

existing asset base to satisfy its creditors, owners, and other providers of capital, or they will invest elsewhere.

• Weighted average cost of capital The weighted average cost of capital (WACC) is the rate that a company is expected to pay

on average to all its security holders to finance its assets.

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Capital Budgeting

NPV Profile

The NPV Profile graphs how NPV changes as the discount rate used changes.

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Zhuhai sea front development

Payback is the amount of time it takes to return an initial investment; however, it does not account for the time value of money, risk, financing, or other

important considerations, such as the opportunity cost.

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Calculating IRR

Cash flows and time

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Replacing a window sill vs. keeping the old one

Replacement project analysis tells a company whether the costs of a replacement project provide a suitable return on investment.

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Net Present Value (NPV) Formula

NPV is the sum of of the present values of all cash flows associated with a project. The business will receive regular payments, represented by variable

R, for a period of time. This period of time is expressed in variable t. The payments are discounted using a selected interest rate, signified by the i

variable.

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Disadvantage of IRR

NPV vs discount rate comparison for two mutually exclusive projects. Project A has a higher NPV (for certain discount rates), even though its IRR (= x-

axis intercept) is lower than for project B

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Capital Budeting

Windows of opportunity come into play when budgeting for capital because they can provide opportunities for firms to maximize returns on investment.

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Discount rates

Bundesbank discount interest rates from 1948 to 1998. The vertical scale shows the interest rate in percent and the horizontal scale shows years.

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Private Equity

Private equity firms, such as NBGI, provide funds for companies unable or uninterested in obtaining funds publicly.

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Calculating IRR

IRR is the rate at which NPV = 0.

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Reinvestment

Reinvestment to expand business

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Reinvestment Factor

Describe how the reinvestment factors related to total return.

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Financing

To manage business often requires long-term and short-term financing.

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Truck

Expensing is applied to property used in a business, such as trucks.

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Pollution

Pollution is an example of a negative externality.

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Airplane

Before purchasing a new airplane, airlines evaluate the NPV of the plan by calculating the PV of the revenue it can earn from it and the PV of its cost

(e.g., purchase cost, maintenance, fuel, etc. ).

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Internal rate of return

Internal rate of return is the rate at which the NPV of an investment equals 0.

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Capital Investment in Plant and Property

The payback method is a simple way to evaluate the number of years or months it takes to return the initial investment.

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Tax Rate

The tax rate is a percentage of the taxable base.

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Depreciated value

Depreciation measures how much of an asset is used up in a certain amount of time.

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Cash flow

The movement of money into and out of a business, project or financial product.

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Medicine

Drug developers must try to calculate the future revenues of a drug in order to find the NPV to determine if it is worth the cost of development.

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Discount rate

Discount rate set by Central Bank of Russia in 1992-2009.

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Alternative choices

Choosing one alternative means another is foregone.

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Machinery

Being able to accurately find the NPV of a piece of machinery means having a good idea when all costs are going to occur (when it will need fixing) and

when it will generate revenue (when it will be used on a job).

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Monthly liquidity of an organic vegetable business

Cash demand is high from April to August. The business is more likely to use payback period to choose a project.

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NPV formula

Each cash inflow/outflow is discounted back to its present value (PV). Then they are summed. Therefore, NPV is the sum of all terms.

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Calculation of the MIRR

MIRR is calculated as follows:

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Multiple internal rates of return

As cash flows of a project change sign more than once, there will be multiple IRRs. NPV is a preferable metric in these cases.

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IRR

Showing the position of the IRR on the graph of NPV(r) (r is labelled ‘i’ in the graph).

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Capital Investment in Plant and Property

The payback method is a simple way to evaluate the number of years or months it takes to return the initial investment.

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Goals of capital budgeting

The main goal of capital budgeting is to rank projects.

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Calculating IRR

NPV formula with r as IRR

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Investment Proposal

Choosing the best investment proposal for business

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Accounting cycle

The basic cycle from open period to close period.

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Sunk

Sunk costs are irrecoverable.

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NPV Decision Table

NPV simply and clearly shows whether a project adds value to the firm or not. It’s easy of use in decision making is one of its advantages.

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Cash

Cash flows reflect cash entering or leaving the organization.

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Capital Budgeting

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MIRR

The formula for calculating MIRR.

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Capital Budgeting

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Capital Budgeting

Which of the following is a correct definition of a capital budgeting

method?

A) Equivalent annuity method essentially value projects as if they were

risk bonds.

B) Real option analysis is the ratio of payoff to investment of a proposed

project.

C) The profitability index is the time required for an investment to “repay”

the original investment.

D) The internal rate of return is the discount rate that gives a net present

value of zero.

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Capital Budgeting

Which of the following is a correct definition of a capital budgeting

method?

A) Equivalent annuity method essentially value projects as if they were

risk bonds.

B) Real option analysis is the ratio of payoff to investment of a proposed

project.

C) The profitability index is the time required for an investment to “repay”

the original investment.

D) The internal rate of return is the discount rate that gives a net present

value of zero.

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Capital Budgeting

Which of the following is a function of corporate capital

budgeting?

A) To rank projects by profitability.

B) To evaluate the performance of managers.

C) All of these answers.

D) To encourage managers to consider problems before they arise.

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Capital Budgeting

Which of the following is a function of corporate capital

budgeting?

A) To rank projects by profitability.

B) To evaluate the performance of managers.

C) All of these answers.

D) To encourage managers to consider problems before they arise.

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Capital Budgeting

Which of the following is the correct order of steps in a basic

accounting flow?

A) Analyze the transactions, make journal entries, prepare statements,

make adjusting entries.

B) Analyze the transactions, make journal entries, make adjusting entries,

prepare statements.

C) Make journal entries, analyze the transactions, make adjusting entries,

prepare statements.

D) Make journal entries, prepare statements, analyze the transactions,

make adjusting entries.

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Capital Budgeting

Which of the following is the correct order of steps in a basic

accounting flow?

A) Analyze the transactions, make journal entries, prepare statements,

make adjusting entries.

B) Analyze the transactions, make journal entries, make adjusting entries,

prepare statements.

C) Make journal entries, analyze the transactions, make adjusting entries,

prepare statements.

D) Make journal entries, prepare statements, analyze the transactions,

make adjusting entries.

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Capital Budgeting

A company is analyzing a variety of potential investments using

different capital budgeting methods. Which of the following

represents the most profitable choice based on the information

provided?

A) The company picks a project with profitability index of 1.25 over a

project with a PI of -.25.

B) The company picks a project with an accounting rate of return 5% over

one with an ARR of 3%.

C) The company picks a project with a 5 year payback period over one

with a 3 year payback period.

D) The company picks a project with an NPV of $250,000 over one with

an NPV of $300,000.

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Capital Budgeting

A company is analyzing a variety of potential investments using

different capital budgeting methods. Which of the following

represents the most profitable choice based on the information

provided?

A) The company picks a project with profitability index of 1.25 over a

project with a PI of -.25.

B) The company picks a project with an accounting rate of return 5% over

one with an ARR of 3%.

C) The company picks a project with a 5 year payback period over one

with a 3 year payback period.

D) The company picks a project with an NPV of $250,000 over one with

an NPV of $300,000.

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Capital Budgeting

A firm is trying to choose the most profitable project to invest in.

Which of the following should be used as the company’s discount

rate?

A) The company’s profitability index.

B) The company’s reinvestment rate.

C) The company’s weighted average cost of capital.

D) The company’s internal rate of return.

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Capital Budgeting

A firm is trying to choose the most profitable project to invest in.

Which of the following should be used as the company’s discount

rate?

A) The company’s profitability index.

B) The company’s reinvestment rate.

C) The company’s weighted average cost of capital.

D) The company’s internal rate of return.

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Capital Budgeting

A company needs to obtain short-term financing due to an

unexpected event. Which of the following options should it NOT

pursue to meet its financial needs?

A) Issuing commercial paper.

B) Obtaining an asset-based loan.

C) Entering into a repurchase agreement.

D) Issuing corporate bonds.

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Capital Budgeting

A company needs to obtain short-term financing due to an

unexpected event. Which of the following options should it NOT

pursue to meet its financial needs?

A) Issuing commercial paper.

B) Obtaining an asset-based loan.

C) Entering into a repurchase agreement.

D) Issuing corporate bonds.

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Capital Budgeting

Which of the following is the best reason to use the payback

method to evaluate investments?

A) The payback method helps gauge a project’s risk.

B) If you use the payback method, you do not need to perform additional

analyses.

C) The payback method covers all cash inflows and outflows for the

duration of the investment.

D) The payback method is easy to use and understand for most people,

regardless of training.

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Capital Budgeting

Which of the following is the best reason to use the payback

method to evaluate investments?

A) The payback method helps gauge a project’s risk.

B) If you use the payback method, you do not need to perform additional

analyses.

C) The payback method covers all cash inflows and outflows for the

duration of the investment.

D) The payback method is easy to use and understand for most people,

regardless of training.

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Capital Budgeting

Calculate the detailed modified payback period for a project with

the following cash flows:Year 0: -$2000Year 1: $1000Year 2: –

$1000Year 3: $1000Year 4: $3000Year 5: $2000

A) 3 years.

B) 3.33 years.

C) 4 years.

D) 4.33 years.

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Capital Budgeting

Calculate the detailed modified payback period for a project with

the following cash flows:Year 0: -$2000Year 1: $1000Year 2: –

$1000Year 3: $1000Year 4: $3000Year 5: $2000

A) 3 years.

B) 3.33 years.

C) 4 years.

D) 4.33 years.

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Capital Budgeting

Calculate the detailed modified payback period for a project with a

discount rate of 5% the following cash flows:Year 0: -$2000Year 1:

$1000Year 2: -$1000Year 3: $1000Year 4: $3000Year 5: $2000

A) 4 years.

B) 3.44 years.

C) 4.44 years.

D) 3.56 years.

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Capital Budgeting

Calculate the detailed modified payback period for a project with a

discount rate of 5% the following cash flows:Year 0: -$2000Year 1:

$1000Year 2: -$1000Year 3: $1000Year 4: $3000Year 5: $2000

A) 4 years.

B) 3.44 years.

C) 4.44 years.

D) 3.56 years.

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Capital Budgeting

In which of the following situations would using the payback

method to evaluate an investment be a good idea?

A) To assess projects that require little investment when compared to the

size of the company.

B) To determine which project of several options is the best investment.

C) To assess the value of potential capital or technological

improvements.

D) All of these answers.

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Capital Budgeting

In which of the following situations would using the payback

method to evaluate an investment be a good idea?

A) To assess projects that require little investment when compared to the

size of the company.

B) To determine which project of several options is the best investment.

C) To assess the value of potential capital or technological

improvements.

D) All of these answers.

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Capital Budgeting

Which of the following disadvantages of the payback method can

be rectified?

A) The payback method does not account for the time value of money.

B) The payback method ignores cash flows beyond the payback period.

C) The payback method does not consider opportunity cost.

D) The payback method does not gauge the risk of an investment.

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Capital Budgeting

Which of the following disadvantages of the payback method can

be rectified?

A) The payback method does not account for the time value of money.

B) The payback method ignores cash flows beyond the payback period.

C) The payback method does not consider opportunity cost.

D) The payback method does not gauge the risk of an investment.

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Capital Budgeting

Which of the following is a way the internal rate of return (IRR) is

used in capital budgeting?

A) To determine the average annual return of an investment.

B) All of these answers.

C) As a means to compare the profitability of different investments.

D) As the effective interest rate for savings and loans.

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Capital Budgeting

Which of the following is a way the internal rate of return (IRR) is

used in capital budgeting?

A) To determine the average annual return of an investment.

B) All of these answers.

C) As a means to compare the profitability of different investments.

D) As the effective interest rate for savings and loans.

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Capital Budgeting

A project has an initial investment requirement of $100,000. In

year 1, it should earn $25,000; in year two, $30,000; and in year

3, $50,000. What is the project’s internal rate of return?

A) 5%

B) 6.5%

C) 6

D) 7.5%

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Capital Budgeting

A project has an initial investment requirement of $100,000. In

year 1, it should earn $25,000; in year two, $30,000; and in year

3, $50,000. What is the project’s internal rate of return?

A) 5%

B) 6.5%

C) 6

D) 7.5%

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Capital Budgeting

Which of the following describes an advantage the internal rate of

return has over net present value for capital budgeting purposes?

A) The IRR method is clear an easy to understand.

B) Internal rate of return is an indicator of the efficiency, quality or yield of

an investment.

C) The IRR method recognizes the time value of money.

D) All of these answers.

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Capital Budgeting

Which of the following describes an advantage the internal rate of

return has over net present value for capital budgeting purposes?

A) The IRR method is clear an easy to understand.

B) Internal rate of return is an indicator of the efficiency, quality or yield of

an investment.

C) The IRR method recognizes the time value of money.

D) All of these answers.

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Capital Budgeting

In which of the following situations would it be appropriate to use

the IRR method to make an investment decision?

A) To compare two investments that have different durations.

B) To assess a project which cash flows fluctuate between positive and

negative.

C) To compare two projects that have an equal initial investment.

D) All of these answers.

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Capital Budgeting

In which of the following situations would it be appropriate to use

the IRR method to make an investment decision?

A) To compare two investments that have different durations.

B) To assess a project which cash flows fluctuate between positive and

negative.

C) To compare two projects that have an equal initial investment.

D) All of these answers.

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Capital Budgeting

You are analyzing two different investments and will present your

findings to company executives. Both projects have cash flows

that alternate between positive and negative. Which budgeting

method should you use to evaluate the projects?

A) Modified Internal Rate of Return.

B) Internal Rate of Return.

C) Net Present Value.

D) Payback period method.

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Capital Budgeting

You are analyzing two different investments and will present your

findings to company executives. Both projects have cash flows

that alternate between positive and negative. Which budgeting

method should you use to evaluate the projects?

A) Modified Internal Rate of Return.

B) Internal Rate of Return.

C) Net Present Value.

D) Payback period method.

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Capital Budgeting

Under the internal rate of return rule in capital budgeting, which of

the following statements does not apply?

A) The cash inflows can be estimates.

B) The internal rate of return can be equal to the cost of capital.

C) The internal rate of return can vary throughout the life of a project.

D) The initial investment can cover the cost from purchasing new

equipment.

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Capital Budgeting

Under the internal rate of return rule in capital budgeting, which of

the following statements does not apply?

A) The cash inflows can be estimates.

B) The internal rate of return can be equal to the cost of capital.

C) The internal rate of return can vary throughout the life of a project.

D) The initial investment can cover the cost from purchasing new

equipment.

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Capital Budgeting

A project has a finance rate of 8% and a reinvestment rate of

10%. The project requires an initial investment of $10,000. In year

one, it will have cash flows of $12,000; year two, -$5000; year

three, $8000. What is the project’s MIRR?

A) 5.8%

B) 7.3%

C) 18.4%

D) 12.1%

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Capital Budgeting

A project has a finance rate of 8% and a reinvestment rate of

10%. The project requires an initial investment of $10,000. In year

one, it will have cash flows of $12,000; year two, -$5000; year

three, $8000. What is the project’s MIRR?

A) 5.8%

B) 7.3%

C) 18.4%

D) 12.1%

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Capital Budgeting

Which of the following is a correct definition of Net Present Value.

A) The sum of the present values of all a project’s revenues and

expenses.

B) NPV = PVinflows + PVoutflows

C) All of these answers.

D) A means of evaluating a project’s profitability.

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Capital Budgeting

Which of the following is a correct definition of Net Present Value.

A) The sum of the present values of all a project’s revenues and

expenses.

B) NPV = PVinflows + PVoutflows

C) All of these answers.

D) A means of evaluating a project’s profitability.

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Capital Budgeting

When evaluating the cash flows from a project, a financial

manager needs to analyze the:

A) The costs of the project

B) costs, benefits, and opportunity costs of the project.

C) The benefits of the project

D) The costs and benefits of the project

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Capital Budgeting

When evaluating the cash flows from a project, a financial

manager needs to analyze the:

A) The costs of the project

B) costs, benefits, and opportunity costs of the project.

C) The benefits of the project

D) The costs and benefits of the project

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Capital Budgeting

The net present value can be:

A) Positive

B) Negative

C) Positive, Zero, or Negative

D) Zero

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Capital Budgeting

The net present value can be:

A) Positive

B) Negative

C) Positive, Zero, or Negative

D) Zero

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Capital Budgeting

A company is considering a project that has a discount rate of 5%.

In the first year, it will have -$100,000 in cash flows. In year 2, it

will have cash flows of $100,000, and in year 3 the project will

generate $200,000. What is the project’s NPV?

A) $358,708

B) $168,232

C) $190,476

D) $193,204

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Capital Budgeting

A company is considering a project that has a discount rate of 5%.

In the first year, it will have -$100,000 in cash flows. In year 2, it

will have cash flows of $100,000, and in year 3 the project will

generate $200,000. What is the project’s NPV?

A) $358,708

B) $168,232

C) $190,476

D) $193,204

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Capital Budgeting

The sum of cash revenues and expenditures over a period of

time.

A) Cash

B) Assets

C) Account Receivables

D) Cash Flow

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Capital Budgeting

The sum of cash revenues and expenditures over a period of

time.

A) Cash

B) Assets

C) Account Receivables

D) Cash Flow

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Capital Budgeting

Under the present value concept, a lottery winner would rather

receive:

A) None of these, as the best answer depends on the interest rate that

the lottery winner faces.

B) $10,000 per year for the next 5 years than receive $50,000 today.

C) $10,000 per year for the next 5 years than receive $40,000 today.

D) $10,000 per year for the next 5 years than receive $30,000 today.

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Capital Budgeting

Under the present value concept, a lottery winner would rather

receive:

A) None of these, as the best answer depends on the interest rate that

the lottery winner faces.

B) $10,000 per year for the next 5 years than receive $50,000 today.

C) $10,000 per year for the next 5 years than receive $40,000 today.

D) $10,000 per year for the next 5 years than receive $30,000 today.

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Capital Budgeting

Each choice listed below represents a net present value of a

potential project. If you were a CFO of a company which project

would you choose?

A) NPV = $200,000

B) NPV = $500,000

C) NPV = $0

D) NPV = -$100,000

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Capital Budgeting

Each choice listed below represents a net present value of a

potential project. If you were a CFO of a company which project

would you choose?

A) NPV = $200,000

B) NPV = $500,000

C) NPV = $0

D) NPV = -$100,000

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Capital Budgeting

Which of the following is an advantage of using the NPV method

to evaluate different projects?

A) All of these answers.

B) It allows for easy comparisons of potential investments.

C) NPV can be customized to reflect the financial concerns and demands

of the company.

D) NPV converts future revenue to current dollars, allowing the company

to quantify a project’s value.

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Capital Budgeting

Which of the following is an advantage of using the NPV method

to evaluate different projects?

A) All of these answers.

B) It allows for easy comparisons of potential investments.

C) NPV can be customized to reflect the financial concerns and demands

of the company.

D) NPV converts future revenue to current dollars, allowing the company

to quantify a project’s value.

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Capital Budgeting

Which of the following is NOT included in calculating a project’s

NPV?

A) The project’s opportunity cost.

B) The exact discount rate.

C) The exact amounts of cash flow related to the project.

D) All of these answers.

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Capital Budgeting

Which of the following is NOT included in calculating a project’s

NPV?

A) The project’s opportunity cost.

B) The exact discount rate.

C) The exact amounts of cash flow related to the project.

D) All of these answers.

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Capital Budgeting

Which of the following reasons is a reason why a higher discount

rate generally means a lower NPV?

A) Most projects do not pay off until years later, and those cash flows are

highly discounted.

B) A higher discount rate emphasizes earlier cash flows, which is when

the expenses are incurred.

C) When the discount rate is large, there are larger differences between

PV and FV for each cash flow.

D) All of these answers.

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Capital Budgeting

Which of the following reasons is a reason why a higher discount

rate generally means a lower NPV?

A) Most projects do not pay off until years later, and those cash flows are

highly discounted.

B) A higher discount rate emphasizes earlier cash flows, which is when

the expenses are incurred.

C) When the discount rate is large, there are larger differences between

PV and FV for each cash flow.

D) All of these answers.

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Capital Budgeting

Which of the following is a way cash flow factors can be used to

improve a business?

A) It can be used to .determine a project’s rate of return or value

B) It can be used to determine problems with a business’s liquidity.

C) All of these answers.

D) It can be used to evaluate the “quality” of income generated by

accrual accounting.

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Capital Budgeting

Which of the following is a way cash flow factors can be used to

improve a business?

A) It can be used to .determine a project’s rate of return or value

B) It can be used to determine problems with a business’s liquidity.

C) All of these answers.

D) It can be used to evaluate the “quality” of income generated by

accrual accounting.

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Capital Budgeting

Which of the following criteria is NOT taken into consideration

when analyzing a possible replacement project?

A) The cashflows the current project has generated in the past.

B) The depreciation associated with the old and potential replacement

investment.

C) The discounted cash flows from the old and potential replacement

investment.

D) The sunk cost associated with the original project.

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Capital Budgeting

Which of the following criteria is NOT taken into consideration

when analyzing a possible replacement project?

A) The cashflows the current project has generated in the past.

B) The depreciation associated with the old and potential replacement

investment.

C) The discounted cash flows from the old and potential replacement

investment.

D) The sunk cost associated with the original project.

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Capital Budgeting

Which of the following could be a sunk cost?

A) The original cost of the item.

B) The expected economic loss of a transaction.

C) All of these answers.

D) Irrational decision-making that led to a transaction.

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Capital Budgeting

Which of the following could be a sunk cost?

A) The original cost of the item.

B) The expected economic loss of a transaction.

C) All of these answers.

D) Irrational decision-making that led to a transaction.

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Capital Budgeting

Which of the following is an example of an opportunity cost?

A) If you watch a game instead of going for a run, the cost is poorer

personal health.

B) If invest in one of two projects, the cost is the lost revenue from the

other project.

C) All of these answers.

D) If you buy a candy bar instead of a soda, the cost is thirst.

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Capital Budgeting

Which of the following is an example of an opportunity cost?

A) If you watch a game instead of going for a run, the cost is poorer

personal health.

B) If invest in one of two projects, the cost is the lost revenue from the

other project.

C) All of these answers.

D) If you buy a candy bar instead of a soda, the cost is thirst.

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Capital Budgeting

Which of the following describes how an externality can affect a

market?

A) A positive externality can lead to overproduction.

B) A negative externality can lead to over-production.

C) The cost of externalities can always be quantified and “internalized” by

a party to the transaction.

D) Prices in a competitive market reflect the full costs and benefits of

production.

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Capital Budgeting

Which of the following describes how an externality can affect a

market?

A) A positive externality can lead to overproduction.

B) A negative externality can lead to over-production.

C) The cost of externalities can always be quantified and “internalized” by

a party to the transaction.

D) Prices in a competitive market reflect the full costs and benefits of

production.

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Capital Budgeting

The tax rate that applies to the last dollar of the tax base and is

often applied to the change in one’s tax obligation as income rises

is called _____.

A) the statutory tax rate

B) the average tax rate

C) the effective tax rate

D) the marginal tax rate

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Capital Budgeting

The tax rate that applies to the last dollar of the tax base and is

often applied to the change in one’s tax obligation as income rises

is called _____.

A) the statutory tax rate

B) the average tax rate

C) the effective tax rate

D) the marginal tax rate

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Capital Budgeting

Which of the following is an element needed to calculate an

asset’s depreciation?

A) The cost of the asset minus the asset’s salvage value.

B) The estimated useful life of the asset.

C) A method of apportioning the cost of the asset.

D) All of these answers.

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Capital Budgeting

Which of the following is an element needed to calculate an

asset’s depreciation?

A) The cost of the asset minus the asset’s salvage value.

B) The estimated useful life of the asset.

C) A method of apportioning the cost of the asset.

D) All of these answers.

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Capital Budgeting

Which of the following is NOT a limitation of section 179?

A) The maximum deduction a taxpayer may take in a year is $25,000.

B) The deduction may not exceed the taxpayer’s aggregate income for

the year.

C) Taxpayers must make the section 179 election if it put property into

service that qualifies.

D) The deduction is decreased by the difference between the value of

new Sec.179 property and $200,000.

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Capital Budgeting

Which of the following is NOT a limitation of section 179?

A) The maximum deduction a taxpayer may take in a year is $25,000.

B) The deduction may not exceed the taxpayer’s aggregate income for

the year.

C) Taxpayers must make the section 179 election if it put property into

service that qualifies.

D) The deduction is decreased by the difference between the value of

new Sec.179 property and $200,000.

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Capital Budgeting

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