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ACC501 Business Finance Handouts

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BUSINESS FINANCE

 

The Primary textbook for the course is

  • Essentials of Corporate Finance, by Ross, Westerfield and Jordan, fourth edition, McGraw Hill

Publishers, ISBN 0-07-121057-7

 

Reference books will be

  • Introduction to Finance by Lawrence J. Gitman and Jeff Madura, Addison-Wesley Publishers
  • Foundations of Financial Management by Stanley B. Block and Geoffrey A. Hirt, McGraw Hill

Publishers

 

Course Contents

  • An overview of Financial Environment
  • Financial Statements, Taxes and Cash Flows
  • Time Value of Money and Discounted Cash Flow Valuation
  • Valuation of Stocks and Bonds
  • Net Present Value and other Investment Criteria
  • Capital Investment Decision
  • Risk and Return
  • Cost of Capital
  • Leverage and Capital Structure
  • Raising Capital
  • Working Capital Management
  • Dividends

 

Finance: A Quick Look

  • Four Basic Areas
  • Business Finance
  • Investments
  • Financial Institutions
  • International Finance

 

Business Finance

 

Addresses the following three questions:

  • What long-term investments should the firm engage in?
  • How can the firm raise the money for the required investments?
  • How much short-term cash flow does a company need to pay its bills?

 

Investments

  • Deals with financial assets such as stocks and bonds.
  • It covers the following issues
  • Pricing Financial Assets
  • Associated Risks and Rewards
  • Determining best mixture of financial investment
  • Career opportunities in investment
  • Stock Brokerage
  • Portfolio Management
  • Security Analysis

 

Financial Institutions

  • Businesses dealing in financial matters
  • Banks and Insurance companies

 

International Finance

·           Covers international aspects of corporate finance, investment and financial institutions

WHY STUDY FINANCE?

 

 

  • Marketers have to work with budgets
  • Need to get greatest payoffs from marketing expenditures and programs
  • Cost and Benefit analysis of projects
  • So finance is vital for

 

  • Marketing research
  • Design of marketing and distributions channels
  • Product pricing

 

  • Accounting and Finance
    • Accountants are required to make financial decisions as well as understand the implications of new financial contracts
  • Financial analysts make extensive use of accounting information

 

  • Management and Finance
    • Business Strategy is always disastrous if financial planning is not adhered to .

 

What is Business Finance?

 

  • In order to start any new business, the following issues become vital
  • What long-term investment should be taken on?
    • From where to get the long-term financing to pay for investment? Bring in other owners or borrow the money?
  • How to manage everyday financial activities?

 

The Financial Manager

 

To create value, the financial manager should:

 

  • Try to make smart investment decisions.
  • Try to make smart financing decisions.

Hypothetical Organization Chart

 

 

Board of Directors

 

 

 

Chairman of the Board & Chief Executive Officer (CEO)

 

 

 

President & Chief Operating Officer (COO)

 

 

 

 

Vice President & Chief Financial Officer (CFO)

 

 

 

Treasurer                                                         Controller

 

 

 

Cash Manager


Credit Manager


Tax Manager


Cost Accounting

 

 

Capital


Financial


Financial


Data Processing

 

 

 

Business Finance and Financial Manager

  • Financial Management Decisions
  • Capital Budgeting
  • Capital Structure
  • Working Capital Management

 

Financial Management Decisions

  • Capital Budgeting
  • The process of planning and managing a firm’s long-term investments
  • Financial managers concern with how much, when  and how likely is cash expected to receive
  • Evaluating the size, timing and risk of future cash flows is the essence of capital budgeting

 

Financial Management Decisions

 

 

Total Value of Assets:


Total Firm Value to Investors:

 

 

Current Assets


Current Liabilities

 

 

 

Fixed Assets

1- Tangible

2-Intangible


Long-Term Debt

 

 

Shareholders’Equity

 

Financial Management Decisions

 

 

 

The Capital Budgeting Decision

 

 

Current Assets


Current Liabilities

 

 

 

 

Fixed Assets

1 Tangible

2 Intangible


 

What long-term investments should the firm engage in?


Long-Term Debt

 

 

Shareholders’ Equity

 

 

 

The Capital Structure Decision


Financial Management Decisions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

70% Debt


 

30%Equity

 

 

 

 

 

 

 

Current Assets


Current Liabilities

 

 

 

Fixed Assets

1 Tangible

2 Intangible


How can the firm raise the money for the required investments?


Long-Term Debt

 

 

Shareholders’ Equity

 

 

 

Capital Structure

 

  • The value of the firm can be thought of as a pie.
  • The goal of the manager is to increase the size of the pie.
  • The  Capital Structure decision can be viewed as how best to slice up the pie.
  • If how you slice the pie affects the size of the pie, then the capital structure decision matters.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Financial Management Decisions

 

The Net Working Capital Investment Decision

 

 

 

 

 

Current Assets


 

Net Working Capital


Current Liabilities

 

 

 

Long-Term Debt

 

 

 

 

 

 

 

Fixed Assets

1 Tangible

2 Intangible


How much short-term

cash flow does a company need to pay its bills?


Shareholders’ Equity

 

 

 

 

The Corporate Firm

  • The corporate form of business is the standard method for solving the problems encountered in raising large amounts of cash.
  • However, businesses can take other forms.

 

Forms of Business Organization

  • Three major forms
  • Sole proprietorship
  • Partnership
    • General
    • Limited
    • Corporation
      • Limited liability company

 

Sole Proprietorship

Advantages

  • Easiest to start
  • Least regulated
  • Single owner keeps all the profits
  • Taxed once as personal income

 

Disadvantages

  • Limited to life of owner
  • Equity capital limited to owner’s personal wealth
  • Unlimited liability
  • Difficult to sell ownership interest

 

 

 

 

 

 

 

Partnership

 

  • Two or more owners (partners)
    • General  partnership:  all  partners  share  in  gains  and  losses  and  all  have  unlimited  liability  for  all partnership debts
    • Limited partnership: one or more general partners will run the business and have unlimited liability but there will be one or more limited partners who do not actively participate in the business and their liability is limited to their contribution.

 

Advantages

  • Two or more owners
  • More capital available
  • Relatively easy to start
  • Income taxed once as personal income

Disadvantages

  • Unlimited liability

 

There are two types of partnership

  • General partnership
  • Limited partnership
  • Partnership dissolves when one partner dies or wishes to sell
  • Difficult to transfer ownership

THE CORPORATE FIRM

 

The  corporate  form  of  business is  the standard  method for  solving  the problems encountered  in raising large amounts of cash. However, businesses can take other forms.

 

Forms of Business Organization

 

Three major forms

  • Sole proprietorship
  • Partnership
    • General
    • Limited
  • Corporation
    • Limited liability Company

 

Sole Proprietorship

 

Advantages

  • Easiest to start
  • Least regulated
  • Single owner keeps all the profits
  • Taxed once as personal income

 

Disadvantages

  • Limited to life of owner
  • Equity capital limited to owner’s personal wealth
  • Unlimited liability
  • Difficult to sell ownership interest

 

Partnership

  • Two or more owners (partners)
    • General  partnership:  all  partners  share  in  gains  and  losses  and  all  have  unlimited  liability  for  all partnership debts
    • Limited partnership: one or more general partners will run the business and have unlimited liability but there will be one or more limited partners who do not actively participate in the business and their liability is limited to their contribution.

 

Advantages

  • Two or more owners
  • More capital available
  • Relatively easy to start
  • Income taxed once as personal income

 

Disadvantages

  • Unlimited liability
  • General partnership
  • Limited partnership
  • Partnership dissolves when one partner dies or wishes to sell
  • Difficult to transfer ownership

Corporation

A business created as a distinct legal entity owned by one or more individuals or entities.

  • Forming of corporation involves preparing
  • Charter including corporation’s name, intended life, business purpose and number of shares
  • Set of bylaws which describes the regulations for the business

 

Separation of Ownership and Control

 

 

 

 

Board of Directors

 

 

 

 

 

Management

 

 

 

 

 

Assets                                   Debt

 

Equity

 

 

 

 

 

Corporation

Advantages

  • Limited liability
  • Unlimited life
  • Separation of ownership and management
  • Transfer of ownership is easy
  • Easier to raise capital

 

Disadvantages

  • Separation of ownership and management
  • Double taxation (income taxed at the corporate rate and then dividends taxed at personal rate)

 

Goal of the Corporate Firm

  • The  traditional  answer  is  that  the  managers  of  the  corporation  are  obliged  to  make  efforts  to maximize shareholder wealth.
  • Alternatively, the goal of the financial manager is to maximize the current value per share of the existing stock

 

The Set-of-Contracts Perspective

  • The firm can be viewed as a set of contracts.
  • One of these contracts is between shareholders and managers.
  • The managers will usually act in the shareholders’ interests.
    • The shareholders can devise contracts that align the incentives of the managers with the goals of the shareholders.
    • The shareholders can monitor the managers behavior.
    • This contracting and monitoring is costly.

 

The Agency Problem

  • Agency relationship
  • Principal hires an agent to represent their interest
  • Stockholders (principals) hire managers (agents) to run the company
  • Agency problem
  • Conflict of interest between principal and agent
  • Management goals and agency costs

 

Managerial Goals

  • Managerial goals may be different from shareholder goals
  • Expensive perquisites
  • Survival
  • Independence
  • Increased growth and size are not necessarily the same thing as increased shareholder wealth.

 

Do Shareholders Control Managerial Behavior?

  • Shareholders vote for the board of directors, who in turn hire the management team.
  • Contracts can be carefully constructed to be incentive compatible.
  • There is a market for managerial talent—this may provide market discipline to the managers—they

can be replaced.

  • If the managers fail to maximize share price, they may be replaced in a hostile takeover.

 

Managing Managers

  • Managerial compensation
  • Incentives can be used to align management and stockholder interests
  • The incentives need to be structured carefully to make sure that they achieve their goal
  • Corporate control
  • The threat of a takeover may result in better management
  • Other stakeholders

THE FIRM AND THE FINANCIAL MARKETS

 

 

Firm issues securities (A)

 

 

 

Retained  cash flows (F)


 

 

 

Financial markets

 

Current assets Fixed


 

Cash flow from firm (C)


 

Dividends and debt payments (E)


Short-term

debt

Long-term debt

Equity shares

 

 

 

 

 

 

Ultimately, the firm must be a

cash generating activity.


 

Government


The cash flows from the firm

must exceed the cash flows from the financial markets.

 

 

 

 

Financial Markets

 

Primary Market

  • When a corporation issues securities, cash flows from investors to the firm.
  • Usually an underwriter is involved

 

Secondary Markets

  • Involve the sale of “used” securities from one investor to another.
  • Securities may be exchange traded or trade over-the-counter in a dealer market.

 

Financial Markets

 

 

 

 

 

 

 

Stocks and Bonds

 

Firms                                                                       Isnecvuersittoierss

Money


Ali


 

money


Maria

 

 

 

Primary Market

 

 

Secondary Market

Dealer Vs. Auction Markets

 

  • Auction markets are different from dealer markets in two ways:
  • Trading in a given auction exchange takes place at a single site on the floor of the exchange.
  • Transaction prices of shares are communicated almost immediately to the public. Listing

 

The Balance Sheet

 

  • An accountant’s snapshot of the firm’s accounting value as of  a particular date.
  • The Balance Sheet Identity is:

Assets ≡ Liabilities + Stockholder’s Equity

  • When  analyzing  a  balance  sheet,  the  financial  manager  should  be  aware  of  three  concerns:

accounting liquidity, debt versus equity, and value versus cost.

 

The Balance-Sheet Model of the Firm

 

 

TotalValue of Assets


TotalFirmValue to Investors

 

Current Assets


Current Liabilities

 

 

 

 

 

Fixed Assets

1. Tangible

2. Intangible


Long-Term Debt

 

 

 

Shareholders’ Equity

 

 

 

 

 

Net Working Capital

 

Net Working Capital ≡ Current Assets – Current Liabilities

 

–NWC > 0

when

Current Assets  >  Current Liabilities

–NWC < 0

when

Current Assets  <  Current Liabilities

–NWC = 0

when

Current Assets  =  Current Liabilities

•NWC usually grows with the firm for the healthy firms.

 

The Balance-Sheet Model of the Firm

 

The Net Working Capital Investment Decision

 

 

 

 

 

Current

Assets


 

Net Working Capital


Current Liabilities

 

 

 

 

 

Long-Term Debt

 

 

 

 

 

Fixed Assets

1. Tangible

2. Intangible


How much short-term

cash flow does a company need to pay its bills?


Shareholders’ Equity

 

 

 

 

 

Building the Balance Sheet

 

A firm has

  • current assets of $100,
  • Net fixed assets of $500,
  • Short term debt of $70, and
  • Long term debt of $200

 

Now…

  • Total Assets are $100 + 500 = $600
  • Total Liabilities are $70 + 200 = $270
  • Shareholders’ equity is $600 – 270 = $330

 

Building the Balance Sheet

 

Liabilities and

Assets                                                            Shareholders’ Equity

 

Current Assets

$100

Current Liabilities

$ 70

Net Fixed Assets

  500

Long Term Debt

200

Shareholders’ equity         330

Total liabilities and

Total Assets                   $600     Shareholders’ equity                    $600

 

The Balance Sheet of the XYZ Corporation

 

 

XYZ CORPORATION

Balanace Sheet

20X2 and 20X1

(in $ millions)

 

Liabilities (Debt)

Assets                                    20X2   20X1          and Stockholder'sEquity              20X2   20X1

$140    $107                                                                       $213    $197

 

Current assets:                                                                     Current Liabilities:

Cash and equivalents                                                           Accounts payable

50         53

 

Accounts receivable                                294       270          Notes payable

$486    $455

 

223      205

 

Inventories                                                269       280          Accrued expenses

Other                                                            58         50               Total current liabilities

Deferred taxes                                  $117    $104

 

Total current assets                         $761    $707        Long-term liabilities:

471        458

Fixed assets:

Property, plant, and equipment         $1,423 $1,274

Less accumulated depreciation          -550      -460


Long-term debt

Total long-term liabilities

Stockholder's equity:


$588    $562

Net property, plant, and equipment      873       814

Intangible assets and other                    245       221


Preferred stock                                   $39       $39

347       327

 

Common stock ($1 per value)            55         32

Total fixed assets                            $1,118 $1,035


Capital surplus

390       347

 

Accumulated retained earnings

$805    $725

 

Less treasury stock                          -26        -20

Total equity

 

Total assets


$1,879 $1,742        Total liabilities and                         $1,879 $1,742

stockholder's equity

 

 

Balance Sheet Analysis

 

  • When analyzing a balance sheet, the financial manager should be aware of three concerns:
  • Accounting liquidity
  • Debt versus equity
  • Value versus cost

 

Accounting Liquidity

 

  • Refers to the ease and quickness with which assets can be converted to cash.
  • Current assets are the most liquid.
  • Some fixed assets are intangible.
    • The  more  liquid  a  firm’s  assets,  the  less  likely  the  firm  is  to  experience  problems  meeting short-term obligations.
    • Liquid assets frequently have lower rates of return than fixed assets.

The Balance Sheet of the XYZ Corporation

XYZ CORPORATION

Balance Sheet

$252m = $707- $455


20X2 and 20X1

(in $ millions)

 

Liabilities (Debt)

Assets                         20X2      20X1                    and Stockholder's Equity          20X2      20X1

Current assets:                                                                    Current Liabilities:

Cash and equivalents                         $140       $107            Accounts payable                                   $213      $197

Accounts receivable                            294         270           Notes payable                                            50           53

Inventories                                         269         280           Accrued expenses                                      223        205

Other                                                    58           50               Total current liabilities                       $486      $455

Total current assets                     $761       $707

LHonegr-teerwmeliasbeielitNiesW:


C grow to $275 million in

Fixed assets:


2D0eXfe2rrefdrotamxes$252 million in 20X1.$117      $104

Property, plant, and equipment      $1,423    $1,274          Long-term debt                                         471        458

Less accumulated depreciation          -550       -460              Total long-term liabilities                   $588      $562

Net property, plant, and equipment    873         814

Intangible assets and other                  245         221        Stockholder's equity:

Total fixed assets                       $1,118    $1,035


$P2re3femrreidllisotonck                                        $39         $39

Common stock ($1 par value)                    55          32

$275m = $761m- $486m


TChaispiitanlcsrueraplsues of $23 million is an

Acthcuemfuirlamte.d retained earnings


347         327

inv39e0stmen3t47

of Less treasury stock                                  -26         -20

Total equity                                       $805      $725

Total assets                                      $1,879   $1,742          Total liabilities and stockholder's equity  $1,879   $1,742

 

 

 

 

 

 

Debt versus Equity

  • Generally, when a firm borrows it gives the bondholders first claim on the firm’s cash flow.
  • Thus shareholder’s equity is the residual difference between assets and liabilities.

Shareholders’ Equity = Assets – Liabilities

  • The Use of debt in a firm’s capital structure is called “Financial Leverage”
    • The more debt a firm has (as a percentage of assets) the greater is the degree of financial leverage
    • Debt acts as a lever in the sense that it magnifies both gains and losses

 

Value versus Cost

  • The true value of any asset is its market value, which is simply the amount of cash we would get if

we actually sold it.

  • The values shown on the balance sheet for the firm’s assets are book values and generally are not what the assets are actual worth.
  • Under the Accounting standards audited financial statements of firms carry assets at historical cost.
    • For current assets, market value and book value might be somewhat similar since they are bought and converted into cash over a relatively short span of time.
  • For fixed assets, its very unlikely that the actual market value of an asset is equal to its book value.
  • Example: Land purchased for railroads a century ago
    • Similarly the owner’s equity figure on the balance sheet and the true market value of the equity need not be related.
    • For Financial Managers, accounting value of the equity is not a matter of concern rather it is the market value of the shares that matters.

 

Market vs. Book Value

  • K Corporation has fixed assets with a book value of $700 and an appraised market value of $1,000
    • Net  working  capital  is  $400  on  the  books  but  approx.  $600  would  be  realized  if  the  current accounts were liquidated
    • K has $500 in long-term debt, both book & market value
    • What is the book value of the equity?
    • What is the market value?

 

K Corporation

Balance Sheet

Market Value vs. Book Value

 

Liabilities and

Assets                                                           Shareholders’ Equity

 

Book   Market                                            Book    Market

Net working Capital  $400    $600                      Long-term debt             $500       $500

Net Fixed Assets       700    1,000                       Shareholders’ equity         600       1,100

$1,100 $1,600                                                           $1,100     $1,600

THE INCOME STATEMENT

 

  • If we think of the balance sheet as a snapshot then we can think of income statement as a video recording covering before and after the picture.
  • The income statement measures performance over a specific period of time.
  • The accounting definition of income is
    • Revenue – Expenses ≡ Income

 

 

 

 

 

 

 

 

 

The operations

section of the income statement reports the firm’s revenues and expenses from principal operations


XYZ Corporation Income Statement

 

XYZ CORPORATION

Income Statement

20X2

(in $ millions)

 

Total operating revenues

Cost of goods sold

Selling, general, and administrative expenses

Depreciation Operating income Other income

Earnings before interest and taxes

Interest expense Pretax income Taxes

Current: $71

Deferred: $13

Net income

Retained earnings:                                             $43

Dividends:                                                        $43


 

 

 

 

 

 

$2,262

- 1,655

- 327

- 90

 

$190

29

$219

- 49

 

$170

- 84

 

 

 

$86

 

XYZ Corporation Income Statement

 

 

 

 

 

 

 

The non-operating section of the income statement includes all financing costs, such as interest expense.


XYZ CORPORATION

Income Statement

20X2

(in $ millions)

 

Total operating revenues

Cost of goods sold

Selling, general, and administrative expenses

Depreciation Operating income Other income

Earnings before interest and taxes

Interest expense Pretax income Taxes

Current: $71

Deferred: $13

Net income

Retained earnings:                                             $43

Dividends:                                                        $43


 

 

 

 

$2,262

- 1,655

- 327

- 90

 

$190

29

$219

- 49

 

$170

- 84

 

 

 

     $86

 

 

 

 

XYZ Corporation Income Statement

 

XYZ CORPORATION

Income Statement

20X2

(in $ millions)

 

 

 

 

 

 

 

 

 

 

 

Usually a separate section reports as a separate item the amount of taxes levied on income.


Total operating revenues

Cost of goods sold

Selling, general, and administrative expenses

Depreciation Operating income Other income

Earnings before interest and taxes

Interest expense Pretax income Taxes

Current: $71

Deferred: $13

Net income

Retained earnings:                                             $43

Dividends:                                                        $43


$2,262

- 1,655

- 327

- 90

 

$190

29

$219

- 49

 

$170

- 84

 

 

 

     $86

 

XYZ Corporation Income Statement

 

XYZ CORPORATION

Income Statement

20X2

(in $ millions)

 

Total operating revenues

Cost of goods sold

Selling, general, and administrative expenses

Depreciation Operating income Other income

Earnings before interest and taxes

Interest expense

Net income is the “bottom Pretax income


$2,262

- 1,655

- 327

- 90

 

$190

29

$219

- 49

$17

 

line”.


Taxes

Current: $71

Deferred: $13

Net income

Retained earnings:                                             $43

Dividends:                                                        $43


- 84

 

 

 

$86

 

Income Statement Analysis

  • There are three things to keep in mind when analyzing an income statement:
  • Generally Accepted Accounting Principles (GAAP)
  • Non Cash Items
  • Time and Costs

 

Income Statement Analysis

  • Generally Accepted Accounting Principles (GAAP)
    • “The  Realization  principle”  is  to  recognize  revenue  when  the  earning  process  is  complete,  i.e. revenue is recognized at the time of sale, which need not be the same as time of collection.
    • “The  matching  principal”  of  GAAP  dictates  that  revenues  be  matched  with  expenses.  Thus, income is reported when it is earned, even though no cash flow may have occurred.

 

Income Statement Analysis

  • Non Cash Items
    • The primary reason that accounting income differs from cash flow is that income statement contain non-cash items
    • Depreciation is the most apparent. No firm ever writes a check for “depreciation”.
    • The depreciation deduction is simply an application of the matching principle in accounting.
    • Another noncash item is deferred taxes, which does not represent a cash flow.

 

Income Statement Analysis

 

  • Time and Costs
    • In the short run, certain equipment, resources, and commitments of the firm are fixed, but the firm can vary such inputs as labor and raw materials.
    • In the long run, all inputs of production (and hence costs) are variable.
      • Financial accountants do not distinguish between variable costs and fixed costs. Instead, accounting costs usually fit into a classification that distinguishes product costs from period costs.

Income Statement Analysis

  • Time and Costs
    • Product cost include such things as raw materials, direct labor and manufacturing overhead and are reported  on  the  income  statement  as  the  cost  of  goods  sold,  but  they  include  both  fixed  and variable costs.
    • Period  costs  include  selling,  general,  and  administrative  expenses  which  may  be  fixed  as  well  as variable.

Taxes

  • One of the largest cash outflows that a Corporate firm experiences.
  • The size of tax is determined through the tax schedule issued by the Central Board of Revenue.
  • Taxes for partnerships and proprietorship are computed using the personal income tax schedules.

Model Tax Rates

Taxable Income                         Tax Rate      .

$0   -       50,000                                     15%

50,001   -   75,000                                    25

75,001   -  100,000                                   34

100,001   -  335,000                                  39

335,001   - 10,000,000                              34

10,000,001   -  15,000,000                          35

15,000,001   -  18,333,333                         38

18,333,334+                                             35

 

Average vs. Marginal Tax Rates

  • Average tax rate is tax bill divided by the taxable income or the percentage of the income that goes

to pay taxes

  • Marginal tax rate is the extra tax you would pay if you earn one more dollar.
  • Suppose a Corporation has a taxable income of $200,000. So the Tax calculation will be:

 

$ 50,000

x 15%

=

($ 75,000 – 50,000)

x 25%

=

($ 100,000 – 75,000)

x 34%

=

($ 200,000 – 100,000)

x 39%

=

$ 61,250

 

 

 

 

$  7,500

6,250

8,500

  39,000

 

  • Our total tax is $61,250
  • Average tax rate is $61,250 / 200,000 = 30.625%
  • Marginal rate is 39%

 

Flat Tax rate

  • There is only one tax rate and this rate is same for all income levels.
  • With such a tax, the marginal tax rate is always same as the average tax rate.
    • The model tax rate schedule presented earlier represents a modified flat-rate tax, which becomes a true flat rate for the highest incomes.
    • Lets take another view

 

Average vs. Marginal Tax Rates

 

Taxable Income           Marginal Tax Rate     Total Tax                  Average tax Rate

 

$      45,000                 15%                         $       6,750                15.00%

 

70,000

25

12,500

17.86

 

95,000

 

34

 

20,550

 

21.63

250,000

39

80,750

32.30

 

1,000,000

 

34

 

340,000

 

34.00

 

17,500,000

 

38

 

6,100,000

 

34.86

 

50,000,000

 

35

 

17,500,000

 

35.00

 

100,000,000

 

35

 

35,000,000

 

35.00

 

 

 

Average vs. Marginal Tax Rates

  • We see that the more a corporation makes, the grater is the percentage of taxable income paid in taxes.
  • So the average tax rate never goes down, even though the marginal rate does.
    • It will normally be the marginal tax rate that is relevant for financial decision making, since any new cash flows will be taxed at the marginal rate

Cost of a Tax Deductible Expense

  • The  businesspersons  often  say  that  a  tax-deductible  item,  such  as  interest  on  loans,  travel expenditures, or salaries, costs substantially less than the amount spent on after-tax basis.
  • Lets examine two corporations - one pays $100,000 in interest, while other has no interest expense.

 

Cost of a Tax Deductible Expense


Corporation A     Corporation B

 

 

 

Earnings before interest and taxes                                 $400,000               $400,000

 

- Interest Expense                                                           100,000                      0

 

Earning before taxes (taxable income)                           300,000                 400,000

 

- Taxes @35%                                                       ... 105,000                     140,000

 

 

Earning after taxes

$195,000

$260,000

Difference in earning after taxes

$65,000

 

It can also be computed as: Interest Expense (1 – Tax rate)

=$100,000 (1 – 35%)

= $65,000

 

Cost of a Tax Deductible Expense

  • Interest is deducted from earnings before determining taxable income, thus saving $35,000 in taxes

and costing only $65,000 on a net basis.

  • Because a dividend on common stock is non tax-deductible, we say it cost 100% of amount paid.

From a  purely  corporate cash flow point of  view, the firm would be indifferent between paying

$100,000 in interest and $65,000 in dividends.

 

 

 

 

 

LESSON 6

DEPRECIATION AS A TAX SHIELD

 

  • Although depreciation is not a new source of funds, it provides the important function of shielding part

of our income from taxes.

  • Again, we take the same two corporations – one   charges off $100,000 in depreciation, other charges

off none.

Depreciation as a Tax Shield

 

Corporation A      Corporation B

 

 

Earnings before depreciation & taxes                             $400,000               $400,000

 

- Depreciation                                                                  100,000                      0

 

Earning before taxes (taxable income)                            300,000                400,000

 

- Taxes @35%                                                              105,000                    140,000

 

Earning after taxes

$195,000

$260,000

+ Dep. charged without cash outlay

  100,000

            0

Cash flow

$295,000

$260,000

Difference

$35,000

 

It can also be computed as: Depreciation x Tax rate

$100,000 x 35%

= $35,000

Depreciation as a Tax Shield

 

Corporation  A  enjoys  $35,000  more  in  cash  flow,  since  depreciation  shielded  $100,000  from  taxation  in

Corporation A and saved $35,000 in taxes, which eventually appeared in cash flows.

 

Financial Cash Flow

  • In finance, the most important item that can be extracted from financial statements is the actual cash flow of the firm.
  • Since there is no magic in finance, it must be the case that the cash received from the firm’s assets must equal the cash flows to the firm’s creditors and stockholders.

Cash Flows to creditors

Cash Flow from Assets ≡                          +

Cash flow to stockholders

 

Cash Flow from Assets

 

  • Cash flow from assets involves three components
  • Operating Cash flow
  • Capital Spending
  • Change in Net Working capital

 

Operating Cash Flow

  • This  refers  to  the  cash  flow  that  results  from  the  firm’s  day-to-day  activities  of  producing  and selling.
  • Expenses  related  to  firm’s  financing  of  its  assets  are  not  included  since  they  are  not  operating expenses.
  • To calculate OCF, we calculate revenues minus costs (including taxes being paid in cash), but don’t include
  • depreciation since it is not a cash out flow
  • Interest because it is a financing expense
    • OCF  is  very  significant  as  it  tells  whether  or  not  the  firm’s  cash  inflows  from  its  business operations are sufficient to cover its everyday cash outflows.
    • So, a negative operating cash flow is a sign of trouble.

 

Financial Cash Flow of the XYZ Corporation

XYZ

Financial Cash

2

(in $

 

 

CashFlowof the Firm

 

Operating cash flow                                     $238

 

Capital spending                                           (173) Additions to net working capital                   (23)

Total                                                                $42

CashFlowof Investorsin the Firm

 

Debt                                                             $36

 

Equity                                                               6

 

 

Total                                                                $42


Operating Cash Flow:

EBIT                $219

Depreciation       $90

Current Taxes    ($71)

OCF                          $238

 

 

Capital Spending

  • Some portion of the firm’s cash flow is reinvested in the firm. Capital spending refers to the net spending on fixed assets (Purchases of fixed assets less sale of fixed assets).
  • Net Capital Spending could be negative if the firm sold off more assets than it purchased.
  • Depreciation of the respective assets is accounted for in this regard.

Financial Cash Flow of the XYZ

 

XYZ CORPORATION

Financial Cash Flow

20X2

(in $ millions)

 

CashFlowof the Firm

Operating cash flow                                   $238

 

Capital spending                                         (173) Additions to net working capital           (23)

Total                                                              $42

CashFlowof Investorsin the Firm

 

Debt                                                            $36

 

Equity                                                             6

 

 

Total                                                              $42


 

Capital Spending

Purchase of fixed assets        $198

Sales of fixed assets                    (25)

Capital Spending                        $173

 

 

Change in Net Working Capital

 

It  is  the  amount  spent  on  Net  Working  Capital,  and  represents  the  net  increase  in  current  assets  over current liabilities.

 

 

 

 

 

 

 

 

CashFlowof the Firm


Financial Cash Flow of the XYZ

 

XYZ CORPORATION

Financial Cash Flow

20X2

(in $ millions)


 

 

 

 

 

 

NWC grew to $275 million in

Operating cash flow                                   $238

 

Capital spending                                         (173) Additions to net working capital              (23)

Total                                                              $42

CashFlowof Investorsin the Firm

 

Debt                                                            $36

 

Equity                                                              6

 

 

Total                                                              $42


20X2 from $252 million in 20X1. This increase of $23 million is the addition to NWC.

 

 

 

 

 

 

 

 

CashFlowof the Firm


Financial Cash Flow of the XYZ

 

XYZ CORPORATION

Financial Cash Flow

20X2

(in $ millions)

 

Operating cash flow                                         $238

 

Capital spenading


(173)

 

Additions to net working capital                          (23) Total         $42

CashFlowof Investorsin the Firm

 

Debt                                                                 $36

 

Equity                                                                    6

 

 

Total                                                                    $42

 

 

 

Cash Flow to Creditors

 

Cash flow to creditors is calculated as interest paid less net new borrowing

 

 

 

 

 

 

 

CashFlowof the Firm


Financial Cash Flow of the XYZ

 

XYZ CORPORATION

Financial Cash Flow

20X2

(in $ millions)


 

 

 

 

 

CashFlowto Creditors

Interest                         $49

Operating cash flow                                      $238

 

Capital spending                                           (173) Additions to net working capital                       (23) Total                                                                               $42

CashFlowof Investorsin the Firm

 

Debt                                                              $36

 

Equity                                                                6

 

 

Total                                                                 $42


Retirement of debt

73

Debt service                  122

Proceeds from

new debt sales              (86)

Total                             36

 

 

Cash Flow to Stockholders

 

Cash flow to stockholders is calculated as dividends paid less net new equity raised.

 

 

 

 

 

 

 

 

CashFlowof the Firm


Financial Cash Flow of the XYZ

 

XYZ CORPORATION

Financial Cash Flow

20X2

(in $ millions)

 

CashFlowto Stockholders

Dividends                             $43

Operating cash flow                                     $238

 

Capital spending                                           (173) Additions to net working capital              (23)

Total                                                                $42

CashFlowof Investorsin the Firm

 

Debt                                                             $36

 

Equity                                                                6

 

 

Total                                                                $42


Repurchase of  stock

6

Cash to Stockholders            49

Proceeds from new stock issue

(43)

Total

$6

 

 

 

Financial Cash Flow of the XYZ

 

XYZ CORPORATION

Financial Cash Flow

20X2

(in $ millions)

CashF

 

Cash Flow of the Firm

low of the Firm

Operating cash flow                                   $238

 

Capital spending                                         (173) Additions to net working capital              (23)

Total                                                              $42

CashFlowof Investorsin the Firm

 

Debt                                                            $36

 

Equity                                                              6

 

 

Total                                              $42


The cash from received from the firm’s assets  must equal the cash flows to the firm’s creditors and stockholders:

 

 

 

 

 

 

 

 

CF ( Assets) º

CF (Creditors) +  CF (Stockholders)

 

 

 

 

 

Cash Flow Summary

 

Cash Flow identity

 

Cash flow from Assets = Cash Flow to creditors

+Cash flow to Stockholders

 

 

Cash flow from Assets

Cash flow from assets = Operating Cash Flow

- Net Capital Spending

- Change in Net Working Capital Where

 

Operating cash flow = Earnings before Interest and taxes

+ Depreciation – Taxes

Net Capital Spending = Ending Net Fixed Assets

- Beginning Net Fixed Assets    + Depreciation

Change in NWC = Ending NWC – Beginning NWC

 

 

Cash flow to creditors (bondholders)

Cash flow to creditors = Interest paid – Net new borrowings

 

Cash flow to stockholders (owners)

Cash flow to stockholders = Dividends Paid – Net new equity raised

THE STATEMENT OF CASH FLOWS

 

  • There is an official accounting statement called the statement of cash flows.
  • This helps explain the change in accounting cash,
  • The three components of the statement of cash flows are
  • Cash flow from operating activities
  • Cash flow from investing activities
  • Cash flow from financing activities

 

The Balance Sheet of the XYZ Corporation

XYZ CORPORATION

Balance Sheet

20X2 and 20X1

(in $ millions)

 

 

Assets                          20X2  20X1

$140    $107

 

Current assets:

Cash and equivalents

Accounts receivable                       294       270

Inventories                                   269       280

Other                                            58         50

Total current assets                 $761    $707

 

Fixed assets:

 

Property, plant, and equipment   $1,423 $1,274

873       814

 

Less accumulated depreciation     -550      -460

Net property, plant, and equipment

Intangible assets and other              245       221

Total fixed assets                    $1,118 $1,035

 

 

 

 

Total assets


$1,879 $1,742

 

The Balance Sheet of the XYZ Corporation

XYZ CORPORATION

Balance Sheet

$213    $197

 

50         53

 

20X2 and 20X1

(in $ millions)

 

Liabilities (Debt)

and Stockholder'sEquity              20X2   20X1

Current Liabilities:

Accounts payable

223      205

 

Notes payable

$486    $455

 

Accrued expenses

Total current liabilities

$117    $104

 

Long-term liabilities:

471       458

 

Deferred taxes

$588    $562

 

Long-term debt

Total long-term liabilities

$39       $39

 

Stockholder's equity:

55         32

 

Preferred stock

347       327

 

Common stock ($1 per value)

390       347

 

Capital surplus

Accumulated retained earnings

$805    $725

 

Less treasury stock                          -26        -20

Total equity

Total liabilities and stockholder's equity


$1,879 $1,742

 

XYZ Corporation Income Statement

 

XYZ CORPORATION

Income Statement

20X2

(in $ millions)

 

 

Total operating revenues

Cost of goods sold

Selling, general, and administrative expenses

Depreciation Operating income Other income

Earnings before interest and taxes

Interest expense Pretax income Taxes

Current: $71

Deferred: $13

Net income

Retained earnings:                                             $43

Dividends:                                                        $43


$2,262

- 1,655

- 327

- 90

 

$190

29

$219

- 49

 

$170

- 84

 

 

 

 

      $86   

 

 

 

XYZ Corporation Cash Flow from Operating Activities

 

XYZ CORPORATION

Cash Flow from Operating Activities

20X2

 

To calculate cash flow from operations, start with net income, add back noncash items like depreciation and adjust for changes

in current assets and liabilities (other

than cash).


 

Operations Net Income Depreciation

Deferred Taxes


(in $ millions)


 

 

 

$86

90

13

Changes in Assets and Liabilities

Accounts Receivable

Inventories Accounts Payable Accrued Expenses Notes Payable Other

 

Total Cash Flow from Operations


(24)

11

16

18 (3)

(8)

 

$199

 

XYZ Corporation Cash Flow from Investing Activities

 

XYZ CORPORATION

Cash Flow from Investing Activities

20X2

(in $ millions)

Cash flow from investing activities

involves changes in capital assets:

acquisition of fixed assets and sales oAfcquisition of fixed assets


 

 

$(198)

fixed assets (i.e. net capital

expenditures).


Sales of fixed assets

 

Total Cash Flow from Investing Activities


25

 

$(173)

 

 

XYZ Corporation Cash Flow from Financing Activities

 

XYZ CORPORATION

Cash Flow from Financing Activities

20X2

(in $ millions)

 

Cash flows to and from

creditors and owners include changes in equity and debt.


Retirement of debt (includes notes) Proceeds from long-term debt sales Dividends

Repurchase of stock

Proceeds from new stock issue

 

Total Cash Flow from Financing


$(73)

86 (43)

(6)

43

 

  $7     

 

 

 

XYZ Corporation Statement of Cash Flows

 

Operations


 

$86

The statement of cash flows is the

addition of cash flows from operations, cash flows from investing activities, and cash flows from financing activities.


Net Income Depreciation Deferred Taxes

Changes in Assets and Liabilities Accounts Receivable Inventories

Accounts Payable Accrued Expenses Notes Payable

Other

Total Cash Flow from Operations

Investing Activities

Acquisition of fixed assets

Sales of fixed assets

Total Cash Flow from Investing Activities

Financing Activities

Retirement of debt (includes notes)

Proceeds from long-term debt sales

Dividends

Repurchase of stock

Proceeds from new stock issue

Total Cash Flow from Financing


90

13

 

 

(2141)

16

18

(3)

  $1(989)

 

$(12958)

$(173)

 

$(8763)

(43)

4(63)

   $7    

Change in Cash (on the balance sheet)                 $33

Significance of Financial Statements

 

A good Working Knowledge of financial Statements is desirable simply because these statements   are the primary means of communicating financial information both within and outside the firm.

 

External Uses of Statement Analysis

 

  • Trade Creditors -- Focus on the liquidity of the firm.
  • Bondholders -- Focus on the    long-term cash flow of the firm.
  • Shareholders -- Focus on the profitability and long-term health of the firm.

 

Internal Uses of Statement Analysis

 

  • Plan -- Focus on assessing the current financial position and evaluating potential firm opportunities.
  • Control -- Focus on return on investment for various assets and asset efficiency.
  • Understand -- Focus on understanding how suppliers of funds analyze the firm.

 

Significance of Financial Statements

 

  • The  reason,  we  rely  on  accounting  figures  for  much  of  our  financial  information  is  that  we  are almost always unable to obtain all of market information we want.
  • The  only  meaningful  yardstick  for  evaluation  business  decisions  is  whether  or  not  they  create economic value.
  • Clearly,  one  important goal  of  the  accountant  is  to report  financial  information  to the  user  in  a form useful for decision making.
  • But the financial statements don’t come with a user’s guide.
  • We will try to fill up this gap through learning a comprehensive analysis of financial statements.

 

Standardized Financial Statements

 

  • One obvious thing we want to do with a company’s financial statements  is to compare  them to those of other.
  • It is almost impossible to directly compare the financial statements for two companies because of differences in size. So we will try to standardize the financial statements.

 

Common-Size Statements

 

  • One very common and useful way of standardized comparison is to work with percentages instead

of dollars.

  • So, a standardized financial statement presenting all items in percentages is called a common-size statement.
  • Balance  sheet  items  are  shown  as  a  percentage  of  total  assets  and  income  statement  items  as  a percentage of sales.

COMMON-SIZE STATEMENTS


LESSON 8

 

  • One very common and useful way of standardized comparison is to work with percentages instead

of dollars.

  • So, a standardized financial statement presenting all items in percentages is called a common-size statement.
  • Balance  sheet  items  are  shown  as  a  percentage  of  total  assets  and  income  statement  items  as  a percentage of sales.

 

A2Z Inc., Balance Sheet

 

A2Z Inc.

Balance Sheet as of December 31 ($ in millions)

Assets                          20X1                 20X2

Current Assets

Cash                             $  84                 $  98

Accounts receivable          165                   188

Inventory                                    393                   422

Total                                 $ 642                   $708

Fixed assets

Net plant and equipment   2,731       2,880

Total assets                               $3,373      $3,588

 

A2Z Inc., Balance Sheet

 

Liabilities and equity                             20X1     20X2

Current liabilities

Accounts payable                                   $  312   $  344

Notes payable                                           231       196

Total                                                            $  543   $  540

 

Long-term debt                                        531       457

Stockholders’equity

Common stock and paid-in surplus            500      550

Retained earnings                                     1,799  2,041

Total                                                     $2,299     $2,591

Total liabilities and equity                      $3,373     $3,588

 

A2Z Inc., Common-Size Balance Sheet

 

Assets                                                  20X1                 20X2

Current Assets

Cash                                                     2.5%       2.7% Accounts receivable       4.9                                                                      5.2

Inventory                                              11.7                   11.8

Total                                                            19.1%    19.7% Fixed assets

Net plant and equipment            80.9%    80.3% Total assets       100.0%                                                 100.0%

 

 

 

 

A2Z Inc., Common-Size Balance Sheet

 

Liabilities and equity                                       20X1                20X2

Current liabilities

Accounts payable                                                 9.2%     9.6%

Notes payable                                                    6.8                    5.5

Total                                                                        16.0%   15.1%

Long-term debt

15.7%

12.7%

Stockholders’equity

 

 

Common stock and paid-in surplus

14.8%

15.3%

Retained earnings                                               53.3                  56.9

Total                                                                        68.1                  72.2

Total liabilities and equity                                 100.0%      100.0%

 

A2Z Inc., Common-Size Balance Sheet

 

More on Standardized Statements

Suppose we ask: “What happened to A2Z’s net plant and equipment (NP&E) over the period?”

  • Based on the 20X1 and 20X2 B/S, NP&E rose from $2,731 to $2,880, so NP&E rose by $149.
  • Did the firm’s NP&E go up or down? Obviously, it went up, but so did total assets. In fact, looking

at the standardized statements, NP&E went from  80.9% of total assets to 80.3% of total assets.

 

More on Standardized Statements

  • If we standardized the 20X2 numbers by dividing each by the 20X1 number, we get a common base

year statement. In this case, $2,880 / $2,731 = 1.0545, so NP&E rose by 5.45% over this period.

  • If we standardized the 20X2 common size numbers by dividing each by the 20X1 common size number, we get a combined common size, common base year statement. In this case, 80.3%/ 80.9% =

99.26%, so NP&E almost remained the same as a percentage of assets.

  • (. .)        In absolute terms, NP&E is up by $149 or 5.45%, but relative to total assets, NP&E fell by

2.6%.

 

More on Standardized Statements

  • Current assets rose from 19.1% in 20X1 to 19.7% in 20X2
  • Current liabilities declined from 16.0% to 15.1% of total liabilities and equity over the same time.
  • Total equity rose from 68.1% of total liabilities and equity to 72.2%.
    • Overall, A2Z’s liquidity as measured by current assets compared to current liabilities, increased over the year. Also, A2Z’s indebtness diminished as a percentage of total assets.
    • So we may conclude that balance sheet as grown stronger

 

A2Z Inc., Income Statement

For the Year 20X2 ($ in millions)

Net sales                                                           $2,311

Cost of goods sold                                              1,344

Depreciation                                                          276

Earnings before interest and taxes            $   691

Interest                                                      141

Taxable income                                          550

Taxes                                                                    187

Net income                                                       $   363

Dividends                                                $121

Retained earnings                                     242

 

A2Z Inc., Common-Size Income Statement

 

Net sales                                                           100.0 % Cost of goods sold                                                                          58.2

Depreciation                                                      11.9

Earnings before interest and taxes              29.9

Interest                                                     6.1

Taxable income                                       23.8

Taxes                                                                    8.1

Net income                                                        15.7 % Dividends       5.2%

Retained earnings                        10.5

A2Z Inc., Common-Size Income Statement

 

  • This statement tells us what happened to each dollar in sales.
  • For A2Z interest expense eats up 6.1% of sales, while taxes take another 8.1% of sales figure.
    • Following this, 15.7% of revenues  from sales flow down  to bottom as net income; one-third of which is paid in dividends and remainder two-thirds is taken as retained earnings for business.
  • As far as cost is concerned, 58.2% of revenues are spent on the goods sold

 

Standardized Financial Statements

 

Although an organization’s common-size statements provide a better analytical insight into the it’s strength and standing, yet it’s performance and efficiency can be better judged by comparing these with those of the firm’s competitors.

 

Ratio Analysis

 

  • Another way of avoiding the problems involved in comparing companies of different sizes, is to calculate and compare financial ratios.
  • One problem with ratios is that different people and different sources frequently don’t compute them in exactly the same way.
  • While using ratios as a tool for analysis, you should be careful to document how you calculate each one, and, if you are comparing your numbers to those of another source, be sure you know how their numbers are computed.

 

For each of the ratios we discuss, several questions come to mind:

  • How is it computed?
  • What is it intended to measure, and why might we be interested?
  • What is the unit of measurement?
  • What might a high or low value be telling? How might such values be misleading?
  • How could this measure be improved?

 

Financial ratios are traditionally grouped into the following categories:

  • Short-term solvency, or liquidity, ratios
  • Ability to pay bills in the short-run
  • Long-term solvency, or financial leverage, ratios
  • Ability to meet long-term obligations
  • Asset management, or turnover, ratios
    • Intensity and efficiency of asset use
    • Profitability ratios
    • Ability to control expenses
    • Market value ratios
    • Going beyond financial statements

Short-Term Solvency, or Liquidity Measures

  • The primary concern to which these ratios relate, is the firm’s ability to pay its bills over the short run without undue stress. So these ratios focus on current assets and current liabilities.
  • Liquidity  ratios  are  particularly  interesting  to  short-term  creditors.  Since  financial  managers  are constantly  working  with  banks  and  other short-term  lenders,  an understanding  of  these ratios  is essential

 

Current assets and liabilities

  • Their book values and market values are likely to be similar.
  • They can and do change fairly rapidly, hence unpredictable

 

Current Assets

Current Ratio= ------------------------ Current Liabilities

 

  • Because  current  assets  and  liabilities  are  converted  into  cash  over  the  following  12  months,  the current ratio is a measure of short run liquidity.
  • The unit of measurement is either dollars or times.

Current Ratio

 

For A2Z Corporation, the 20X2 current ratio is

 

 

 

 

 

We can say that


$708

Current Ratio= ---------- = 1.31 times

$540

•A2Z has a $1.31 in current assets for every $1 in current liabilities OR

•A2Z has its current liabilities covered 1.31 times over.

 

•To a creditor (particularly a short-term creditor like supplier), the higher the current ratio, the better

•To firm, high current ratio indicates liquidity, but it may also indicate an inefficient use of cash and other short-term assets.

•We would expect to see a current ratio of at least 1, because a current ratio of less than 1 would mean

that net working capital is negative

 

•Like any other ratio, current ratio is effected by various transactions.

•If a firm borrows over long-term,

The short run effect would be an increase in cash as well as in long term liabilities.

Current liabilities would not be affected, so the current ratio would rise.

•An apparently low current ratio may not be a bad sign for a company with a large reserve of unlimited borrowing power.

 

Current Events

A firm wants to payoff some of its suppliers and creditors. What would happen to current ratio?

•Current ratio moves away from 1. if it is greater than 1 it will get bigger. But if it is less than 1, it will get smaller.

•Suppose a firm has $4 in current assets and $2 in current liabilities for a current ratio of 2. and uses $1 in

cash to reduce current liabilities, then new current ratio is ($4-2) / ($2-1) = 3

•Reversing the situation to $2 in current assets and $4 in current liabilities, the change will cause current ratio to fall to 1/3 from 1/2

 

Suppose a firm buys some inventory. What would happen in this case?

•Nothing  happens  to  current  ratio.  Because  in  this  scenario,  one  current  asset  (cash)  goes  down  while another current asset (inventory) goes up. Total current assets are unaffected.

 

What happens if a firm sells some merchandise?

•Current  ratio  would  usually  rise  because  inventory  is  shown  at  cost  and  sale  would  normally  be  at something greater than cost (difference is markup).

•So, the increase in either cash or receivables is greater  than the decrease in inventory.

•This increases current assets and current ratio rises.

 

Quick (or Acid-Test) Ratio

  • Inventory is often the least liquid current asset. And its book values are least reliable as measures of market value since the quality of inventory isn’t considered. Some of the inventory may turn out to be damaged, obsolete or lost.
  • Relatively large inventories are often a sign of short-term trouble.
    • The firm may have overestimated sales and overbought or overproduced as a result, hence tied up a substantial portion of its liquidity in slow moving inventory

 

It is computed just like current ratio, except inventory is omitted.

 

Current Assets – Inventory

Quick Ratio= ------------------------------------ Current Liabilities

For A2Z, this ratio in 20X2 was

 

$708 – 422

Quick Ratio= ----------------- = 0.53 times

$540

 

  • The quick ratio here tells a somewhat different story than the current ratio, because inventory accounts

for more than half of A2Z’s current assets

  • If the same figure is for an aircraft manufacturing corporation, then this would certainly be a cause for a

BIG concern.

 

Cash Ratio

A very short-term creditor may be interested in the cash ratio

Cash

Cash Ratio= ----------------------- Current Liabilities

 

Current ratio for A2Z in 20X2 was 0.18

RATIO ANALYSIS A2Z Inc., Balance Sheet

A2Z Inc.

Balance Sheet as of December 31 ($ in millions)


LESSON 9

Assets

20X1

20X2

Current Assets

 

 

Cash

$  84

$  98

Accounts receivable

165

188

Inventory

 

  393                   422

Total                                $ 642                   $708

Fixed assets

Net plant and equipment 2,731       2,880

Total assets                                      $3,373               $3,588

A2Z Inc., Balance Sheet

Liabilities and equity                             20X1    20X2

Current liabilities

Accounts payable                                   $  312   $  344

Notes payable                                           231       196

Total                                                      $  543         $  540

Long-term debt                                         531      457

Stockholders’equity

Common stock and paid-in surplus             500      550

Retained earnings                                    1,799   2,041

Total                                                    $2,299      $2,591

Total liabilities and equity                      $3,373     $3,588

 

A2Z Inc., Income Statement

For the Year 20X2 ($ in millions)

Net sales

 

$2,311

Cost of goods sold

 

1,344

Depreciation

 

 276

Earnings before interest and taxes

$   691

 

Interest

 141

 

Taxable income

550

 

Taxes

 

  187

Net income

 

$   363

Dividends

$121

 

Retained earnings                                     242

 

Current Ratio

 

Current Events

•Suppose a firm buys some inventory. What would happen in this case?

•Nothing  happens  to  current  ratio.  Because  in  this  scenario,  one  current  asset  (cash)  goes  down  while another current asset (inventory) goes up. Total current assets are unaffected.

 

What happens if a firm sells some merchandise?

•Current  ratio  would  usually  rise  because  inventory  is  shown  at  cost  and  sale  would  normally  be  at something greater than cost (difference is markup).

•So, the increase in either cash or receivables is greater  than the decrease in inventory.

•This increases current assets and current ratio rises.

 

Current Ratio

 

A firm wants to payoff some of its suppliers and creditors. What would happen to current ratio?

•Current ratio moves away from 1. if it is greater than 1 it will get bigger. But if it is less than 1, it will get smaller.

•Suppose a firm has $4 in current assets and $2 in current liabilities for a current ratio of 2. and uses $1 in

cash to reduce current liabilities, then new current ratio is ($4-1) / ($2-1) = 3

•Reversing the situation to $2 in current assets and $4 in current liabilities, the change will cause current ratio to fall to 1/3 from 1/2

 

Long Term Solvency Measures

 

  • These ratios are intended to address the firm’s long-run ability to meet its obligations, or its financial leverage.

 

Total Debt Ratio

This ratio takes into account all debts of all maturities to all creditors. It is computed as

 

Total Assets – Total Equity

Total Debt Ratio=   ------------------------------------ Total Assets

For A2Z Corporation

 

$3,588 – 2,591

Total Debt Ratio=   ---------------------- = 0.28 times

$3,588

  • So A2Z uses 28% debt. Whether this is high or low, or whether it even makes any difference depends

on whether or not capital structure matters.

  • A2Z has 28% debt against total assets, thus there is 72% equity against total assets.
  • Here we draw two variations out of total debt ratio

•Debt-equity ratio

•Equity multiplier

 

  • Debt–Equity ratio = Total Debt / Total Equity

= 28% / 72% = 0.39 times

  • Equity Multiplier = Total Assets / Total Equity

= 100% / 72% = 1.39 times

OR

= 1 + Debt-Equity ratio = 1.39 times

Interest Coverage Ratio

  • Also known as Times Interest Earned (TIE) ratio, refers to the ability of the firm to cover is interest obligations.

 

Earning before Interest & Taxes

Interest Coverage ratio = ----------------------------------------- Interest

For A2Z corporation:


= $691 / $141 = 4.9 times

 

 

 

Cash Coverage Ratio

  • A  problem  with  Interest  Coverage  Ratio  is  that  it  is  based  on  Earnings  before  Interest  and  Taxes

(EBIT) which is not really a measure of cash available to pay interest.

  • The reason is that depreciation, a non-cash expense has been deducted out. So we use:

 

 

 

EBIT + Depreciation

Cash Coverage ratio = ----------------------------------------- Interest

 

=  $691 + 276 =  $967 =  6.9 times

$141          $141

 

Asset Management or Turnover Measures

 

The measures in this section are sometimes called Asset Utilization Ratios. These are intended to describe how efficiently or intensively a firm uses its assets to generate sales.

 

Inventory Turnover Ratio

 

Inventory turnover can be calculated as:

 

Cost of goods Sold

Inventory Turnover ratio = -------------------------------- Inventory

For A2Z, ITR would be:


$1,344

= ---------------- = 3.2 times

$422

So A2Z sold off or turned over the entire inventory 3.2 times. As long as stock-out and foregoing sales situation doesn’t arise, the higher this ratio is, the more efficiently inventory is being managed

 

Days’ Sales in Inventory

 

If we know sales were turned over 3.2 times during the year, we can calculate easily how long it took to turnover on average.

365 days

Days’ Sales in Inventory = -------------------------------- Inventory Turnover

For A2Z:


365

= ----------- = 114 days

3.2

So inventory stays for just less than 4 months before being sold or it would take 114 days to sell off current inventory.

 

Receivables Turnover

 

Now we take a look on how fast we collect on the sales of inventory.

Sales

Receivables Turnover = ------------------------------- Accounts Receivables

For A2Z:

 

 

$2,311

= ----------  = 12.3 times

$188

So  A2Z  collected  its  outstanding  credit  accounts  and  reloaned  the  money  12.3  times  during  the  year.

(Assuming all the sales are credit sales. If not, we use only credit sales for this ratio)

 

Days’ Sales in Receivables


 

365 days

Days’ Sales in Receivables = ------------------------------- Receivables Turnover

 

 

 

 

For A2Z:


 

365

= ----------- = 30 days

12.3

 

So A2Z collects on its credit sales in a month, or the firm has 30 days’ worth of sales uncollected. This ratio

is also called Average Collection Period

 

A Variation: Payables Turnover

 

It describes a how long does the firm take to pay its bills, and is computed as: Cost of Goods Sold

Payables Turnover = ------------------------------- Accounts payables

 

$1,344

= ------------   = 3.9 times

$344

So days it took to turnover the payables are:

365

= -----------   = 94 days

3.9

This figure is very significant to the current as well as potential creditors of A2Z.

RATIO ANALYSIS

 

A2Z Inc., Balance Sheet

A2Z Inc.

Balance Sheet as of December 31 ($ in millions)

Assets

20X1

20X2

Current Assets

 

 

Cash

$  84

$  98

Accounts receivable

165

188

Inventory

 

  393                   422

Total                                                            $ 642                $708

Fixed assets

Net plant and equipment            2,731       2,880

Total assets                                                    $3,373             $3,588

 

 

A2Z Inc., Balance Sheet

 

Liabilities and equity                             20X1     20X2

Current liabilities

Accounts payable                                   $  312   $  344

Notes payable                                           231       196

Total                                                            $  543   $  540

Long-term debt                                        531       457

Stockholders’equity

Common stock and paid-in surplus             500      550

Retained earnings                                    1,799   2,041

Total                                                    $2,299      $2,591

Total liabilities and equity                        $3,373      $3,588

 

A2Z Inc., Income Statement

For the year 20X2 ($ in millions)

Net sales                                                           $2,311

Cost of goods sold                                              1,344

Depreciation                                                         276

Earnings before interest and taxes            $   691

Interest                                                      141

Taxable income                                          550

Taxes                                                                     187

Net income                                                       $   363

Dividends                                                $121

Retained earnings                                        242

 

Total Asset turnover

 

Sales

Total Assets Turnover = --------------------

Total Assets

 

$2,311

= ------------  = 0.64 times

$3,558

In other words, for every dollar in assets, A2Z generated $0.64 in sales.

Capital Intensity Ratio

It is simply the reciprocal of total assets turnover, or: Total Assets

Capital Intensity Ratio =  -------------------- Sales

  • It  is  interpreted  as  the  dollar  investment  in  assets  needed  to  generate  $1  in  sales.  Higher  values represent capital intensive industries.
  • For A2Z, this ratio is computed to be 1.56, i.e. A2z has to invest $1.56 in assets to get $1 in sales.

Profitability Measures

  • In one form or the other, these ratios are intended to measure how efficiently the firm uses its assets and how efficiently the firm manages its operations.
  • The focus in this group is on the bottom line – net income.

Profit Margin

Every company, big or small, pays very close attention to their profit margin

Net income

Profit Margin=  -------------------- Sales

For A2Z company the profit margin will be:

$ 363

= ------------ = 15.7%

$2,311

  • So in accounting sense, A2Z generates a little less than 16 cents in profit for every dollar in sales.
    • Other Things being equal, a relatively high profit margin is obviously desirable, corresponding to low expenses vs. sales.
    • But Other Things are not always equal !
      • For  example,  lowering  the  sales  price  will  usually  increase  unit  sales  but  will  normally  cause  profit margin to shrink. Total Profit of operating cash flow may go up or down.

Return on Assets

Return on Assets (ROA) is a measure of profit per dollar of assets: Net income

Return on Assets =  -------------------- Total Assets

For A2Z:


$ 363

ROA = ---------- = 10.12%

$3,588

 

Return on Equity

  • Return on equity  (ROE) is a measure of how the stockholders fared during the year.
    • Since  benefiting  the  shareholders  is  the  goal  of  corporation,  ROE  is  a  true  bottom  line  measure  of performance.

Net income Return on Equity =  -------------------- Total Equity

For A2Z ROE figure is:


$ 363

ROE = ---------- = 14%

$2,591

Therefore,  for every  dollar in equity,  A2Z generated  14 cents in  profit.  But  this is  correct  in accounting terms only.

 

ROA and ROE

  • Because ROA and ROE are most widely used and commonly cited numbers, so it should be kept in mind that these are accounting rates of return.
  • That is why these are called return on book assets and return on book equity
  • ROE is sometimes called return on Net Worth

 

Market Value Measures

  • This  group  of  measures  is  based,  in  part,  on  information  not  necessarily  contained  in  financial

Statements, like market price per share.

  • These measures can be calculated directly only for publicly traded companies.

 

Earnings Per Share

Assuming,

•A2Zhas 33 million shares outstanding and

•stock sold for $88 per share at the end of year. So the Earnings per Share (EPS) will be:

 

Net income              $363

EPS =  ---------------------------  = --------- = $11

Shares Outstanding        33

 

Price-Earning Ratio

Price-earnings or PE ratio is defined as: Price per share

PE ratio =   -------------------------- Earnings per share

For A2Z,


$ 88

PE ratio = --------- = 8 times

$11

  • So A2Z shares sell for eight times earnings or it carries a PE multiple of 8.
  • Since PE ratio measures how much investors are willing to pay per dollar of current earnings, higher

PEs are often taken to mean that the firm has significant prospects for future growth.

  • If a firm had no or almost no earnings, its PE would probably be quite large; so careful interpretation is required.

Book Value per share

Book Value is calculated as:

Total equity

Book Value = ------------------------------------

No. of shares outstanding

 

$ 2,591

Book Value = ------------- = $78.5

33

Since book value per share is an accounting number, it reflects historical costs.

 

Market-to-Book ratio

It is defined as:


 

Market value per share

Mark-to-Book ratio = ------------------------------------

Book value per share

 

 

 

For A2Z,


 

$ 88

= --------- = 1.12 times

$78.5

  • The market-to-Book ratio compares the market value of the firm’s investment to their costs.
    • A value less than 1 could mean that the firm has not been successful overall in creating value for its stockholders.

 

The Du Pont Identity

 

  • The difference between the two profitability measures, ROA and ROE, is the use of debt financing , or financial leverage.
  • The relationship between these measure can be illustrated by decomposing ROE into its component parts.

Recall,

Net Income

ROE =  -------------------- Total Equity

 

Multiplying it by Assets / Assets (without changing anything)

 

Net Income     Net Income     Assets

ROE =  -------------------- = ---------------- x ----------- Total Equity                       Total Equity      Assets

 

Net Income        Assets

= ---------------- x ---------------- Assets          Total Equity

 

 

Net Income      Assets

ROE = ---------------- x ----------------

Assets                 Total Equity

 

So, we have expressed ROE as a product of two other ratios – ROA and the equity multiplier

 

ROE = ROA x Equity multiplier

= ROA x (1 + Debt-Equity ratio)

THE DU PONT IDENTITY

 

  • The difference between the two profitability measures, ROA and ROE, is the use of debt financing , or financial leverage.
  • The relationship between these measure can be illustrated by decomposing ROE into its component parts.

 

Recall,


 

Net Income

ROE =  -------------------- Total Equity

 

Multiplying it by Assets / Assets (without changing anything)

Net Income     Net Income     Assets

ROE =  -------------------- = ---------------- x ----------- Total Equity                       Total Equity      Assets

 

Net Income      Assets

= ---------------- x ---------------- Assets         Total Equity

 

 

Net Income      Assets

ROE = ---------------- x ----------------

Assets                 Total Equity

 

  • So, we have expressed ROE as a product of two other ratios – ROA and the equity multiplier

 

ROE = ROA x Equity multiplier

= ROA x (1 + Debt-Equity ratio)

 

•Looking back at A2Z:

•Debt-Equity Ratio = 0.39

•ROA = 10.12%

•while ROE calculated previously = 14%

 

•Now, using the decomposition method:

ROE = 10.12% x 1.39 = 14%

We can further decompose ROE by multiplying the top and bottom by total sale: Sales     Net Income           Assets

ROE = --------  x ---------------- x ----------------

Sales        Assets            Total Equity

Rearranging a bit,

 

Net Income     Sales          Assets

ROE = ---------------  x ----------- x ----------------

Sales             Assets          Total Equity

 

Return on Assets

=  Profit      x     Total Assets   x             Equity

Margin          Turnover                 Multiplier

 

                        ROE            =  Profit      x  Total Assets   x       Equity                                                                              

Margin          Turnover                 Multiplier

 

This last Expression is called Du Pont  identity after the Du Pont Corporation, which popularized its use. Now for A2Z:

ROE     =  15.7%   x   0.64   x   1.39

=   14%

 

  • The Du Pont identity tells us that ROE is affected by three things:
  • Operating efficiency (as measured by profit margin)
  • Asset use efficiency (as measured by total assets turnover)
  • Financial Leverage (as measured by equity multiplier)

 

Considering the Du Pont identity,

  • it appears that a firm could leverage up its ROE by increasing its amount of debt
  • this will only happen if ROA exceeds interest rate on debt.
    • The  decomposition  of  ROE  is  a  convenient  way  of  systematically  approaching  the  financial statements analysis.
    • If ROE is unsatisfactory by some measure, then Du Pont identity tells you where to start looking

for the reasons.

Dividend Payout

We have seen earlier that the net income is divided into two pieces.

  • The first piece is cash dividend paid to stockholders
  • Leftover amount is the addition to retained earnings

A2Z’s Net Income was $363, of which $121 was paid out in dividends. As a percentage: Cash Dividends

Dividend Payout ratio = -----------------------

Net Income

$121

= --------- = 331/3%

$363

Retention Ratio

 

Anything A2Z does not pay out in form of dividends must be retained in the firm. So retention ratio is: Retained Earnings

Retention ratio = -----------------------

Net Income

$242

= ---------- = 662/3%

$363

  • So A2Z retains two-thirds of its net income.
    • The retention ratio is also known as the plowback ratio, as this is the amount which is plowed back into the business

 

Payout and Retention

 

Q:        LMN corporation pays out 40% of net income in  form of dividends. What is its retention ratio?

A:         If payout ratio is 40%, retention ratio is

1 – 40% = 60%

 

Q:        If net income of LMN is $800, how much did stockholders actually receive?

A:         Dividends are    $800 x 40% = $320

 

 

Internal and Sustainable Growth

 

  • Firm’s  Return  on  Assets  and  Return  on  Equity  are  frequently  used  to  calculate  two  additional numbers, both of which have to do with the firms ability to grow.
  • Investors and others are frequently interested in knowing how rapidly a firm’s sales can grow.
    • But the important thing to recognize is that if sales are to grow, assets have to grow as well, at least over the long run.
  • Further if assets are to grow, then the firm must somehow obtain money to pay for the purchases.

 

  • So, the growth has to be financed. And more so, a firm’s ability to grow depends on its financing policies.
  • A firm has two broad sources of financing:

 

Internal financing simply refers to what the firm earns and subsequently plows back into the business. External financing refers to funds raised by either borrowing money or selling stock.

 

Internal Growth Rate

 

A  firm  having  a  policy of  internal  financing,  won’t  borrow  funds and won’t  sell any  new stock. Internal growth rate represents how rapidly the firm grow.

ROA   x   b

Internal Growth rate = ------------------


(1 – ROA) x b

where ROA is return on assets and b is the retention ratio

For A2Z this rate is

0.1012 x 2/3

= -----------------------

(1 – 0.1012) x 2/3

 

= 7.23%

Relying solely on internal financing, A2Z can grow at a maximum rate of 7.23% per year

 

Sustainable Growth Rate

 

If a firm only relies on the internal financing , then through time, its total debt ratio will decline, because assets will grow but total debt will remain the same (or even fall if some is paid off). Frequently, firms have a particular total debt ratio or equity multiplier that they view as optimal.

With this in mind we now consider how rapidly a firm can grow if

it wishes to maintain a particular total debt ratio; and

it is unwilling to sell new stock

Given these assumptions, the maximum growth rate that can be achieved is called the Sustainable Growth

Rate:

 

Sustainable Growth rate = ------------------

 

For A2Z this rate is


ROE   x   b

 

(1 – ROE) x b

 

0.14 x 2/3

= --------------------

(1 – 0.14) x 2/3

 

= 10.29%

The reason for Sustainable Growth rate (10.29%) being larger than internal growth rate (7.23%) is that, as the firm grows, it will have to borrow additional funds if it has to maintain a constant debt ratio.

This new borrowing is an extra source of financing in addition to internally generated funds, so A2Z can expand more.

Determinants of Growth

Using Du Pont identity, we saw that ROE can be decomposed into its various components

Since  ROE  appears  so  prominently  in  determination  of  Sustainable  growth  rate,  the  factors determining ROE are also important determinants of growth.

We know that:

ROE            =    Profit      x    Total assets   x         Equity margin        turnover          multiplier

 

  • Anything  that  increases  ROE  will  increase  the  Sustainable  growth  rate.  Increasing  the retention ratio will have the same effect.
  • So putting it all together, the firm’s ability to sustain growth depends explicitly on the four factors:

 

Profit margin

 

An increase in profit margin will increase the firm’s ability to generate funds internally and thereby increase

its sustainable growth.

 

Total Assets Turnover

 

An  increase  in  firm’s  total  assets  turnover  increases  the  sales grow  and thereby  increases  the  sustainable growth rate. Increasing total assets turnover is the same thing as decreasing capital intensity.

 

Financial Policy

 

An increase in the debt-equity ratio increases the firm’s financial leverage. Since this makes additional debt financing available, it increases the sustainable growth rate.

 

Dividend Policy

 

A  decrease  in  the  percentage  of  net  income  paid  out  as  dividends  will  increase  the  retention  ratio.  This increases internally generated equity and thus increases internal and sustainable growth.

  • The sustainable growth rate illustrates the explicit relationship between the firm’s four major areas

of concern:

  • Operating efficiency (as measured by profit margin)
  • Asset use efficiency (as measured by total assets turnover)
  • Financial policy (as measured by the debt-equity ratio)
  • Dividend policy (as measured by the retention ratio)

If sales are to grow at a rate higher than the sustainable growth rate, the firm must

  • increase profit margins,
  • increase total assets turnover,
  • increase financial leverage,
  • increase earnings retention, or
  • Sell new shares

USING FINANCIAL STATEMENTS INFORMATION


LESSON 12

 

 

  • Now we take a look at some practical aspects of the financial statements analysis.
  • Reasons for doing financial statements analysis
  • Benchmarking the information
  • Problems arising in the process

 

Why Evaluate Financial Statements

  • Primary reason for looking at the accounting information is that we don’t have and cant expect to

get market value information. But if we have such information, we will use it instead of accounting data.

  • If there is a conflict between accounting and market data, market data would be preferred.
    • Financial  statements  analysis  is  an  application  of  management  by  exception  and  boils  down  to comparing ratios for one business with some average or representative ratios.
  • The ratios differing considerably from averages are studied further.

 

Internal Uses

Performance Evaluation

  • Profit margin and return on equity
  • Comparing the performance of different divisions
  • Planning for the future
  • Historical information used for generating projections
  • Checking the realism of assumptions for the projections

 

External Uses

 

Customers:

  • To evaluate the credit standing of a new customer
  • Large customers would eye on the sustainability of the firm
  • Suppliers:
  • Evaluate the financial worth of the supplier
  • Suppliers would be concerned about the creditworthiness of the firm

 

Competitors

  • Potential strength of the competitors in case of a new product launched by a firm
  • Acquisition of new firms
  • Identification of potential targets
  • What to offer.

 

Choosing a Benchmark

 

  • Benchmarking is to establish a standard to follow for comparison.
  • Some methods of benchmarking are:
  • Time-Trend analysis
  • Peer Group Analysis

 

Time-Trend Analysis

  • Based on the historical data of the firm
    • If the current ratio of a firm is 2.4 for the recent financial statements, we may compare it with the current ratios for last 10 years.
  • We may find that current ratio has declined over the years because of
  • More efficient usage of current assets
  • Change in the nature of business of the firm
  • Change in business practices of the firm

 

Peer Group Analysis

 

Identifying the firms

  • competing in the same markets,
  • Having similar assets,
  • Operate in similar ways

 

Benchmarking:

  • averages for this group of firms  OR
  • the top firms among the group

 

 

Problems with Financial Statements Analysis

 

  • No  underlying  theory  to  help  identify  the  items  or  ratios  to  look  at  or  to  guide  in  establishing benchmark
  • Very little help on value and risk
  • Which ratios matter the most?
  • What a high or low value might be?

 

•Firms with many diversified businesses

•Different accounting standards and procedures in different parts of the world

 

Time Value of Money

•It refers to the fact that a dollar in hand today is worth more than a dollar promised at some time in future.

•The trade-off between money today and money later depends on, among other things, the rate one can

earn by investing the money today for some interest income.

 

Simple Interest vs. Compound Interest

Its most basic form, interest is calculated by multiplying principal (amount invested) by rate (% of interest)

multiplied by time (number of periods the interest is calculated). This is called simple interest.

 

 

Where


I = P x r x t

 

P => principal amount r  => interest rate

t  => time periods (years) I  => simple interest

 

However, if interest is left in the account to accumulate for a longer period (usually longer than one year),

common  practice  requires  that  after  interest  is  earned  and  credited  for  a  given  period,  the  new  sum  of principal + interest must now earn interest for the next period, etc.  This is compound interest.

I = P x rt

 

Future Value

•It refers  to the amount  of  money an investment  will grow to  over  some period  of  time at some given interest rate.

•Alternatively, future vale is the cash value of an investment at some time in future.

Simple Interest is calculated as:

I = P x r x t

A $1,000 deposit at 8% per year for 3 years' simple interest:

I = 1000 x .08 x 3 = 240

A $1000 deposit at 8% simple interest for three years earns $240 interest.

The future value (FV) of a simple interest calculation is derived by adding the original principal back to the interest earned.

$1,000 + $240 =  $1,240

Expressed as a formula:

 

FV =  P(1 + rt)

FV = 1000+(1000 x .08 x 3) = 1,240

In the one-period case, the formula for FV can be written as:

FV = C0×(1 + r)

 

Where C0  is cash flow today (time zero) and

r is the appropriate interest rate.

 

Future Value for a Lump Sum

If $100 are invested at 10% interest rate, the future value of this $100 in each proceeding year would be:

 

•1.

 

$110

 

= $100 x (1 + .10)

 

•2.

 

$121

 

= $110 x (1 + .10) = $100 x 1.10 x 1.10

= $100 x 1.102

 

•3.        $133.10 = $121 x (1 + .10) = $100 x 1.10 x 1.10 x .10

= $100 x (1.10)3

The Multiperiod

Case:

Future Value

Generalizing the future value of an investment over many periods:

FV = C0×(1 + r)t

Where

C0  is cash flow at date 0,

r is the appropriate interest rate, and

t is the number of periods over which the cash is invested.

The expression (1 + r)t is the future value interest factor.

The Multiperiod Case:Future Value

Year         Beginning Amount             Interest Earned     Ending Amount

 

 

 

1

$100.00

$10.00

$110.00

 

2

 

110.00

 

11.00

 

121.00

 

3

 

121.00

 

12.10

 

133.10

 

4

 

133.10

 

13.31

 

146.41

5               146.41                      14.64                      161.05

 

 

Total Interest     61.05

 

The Multiperiod Case:Future Value

 

 

Future

Value ($)

 

 

160

 

150

 

140

 

130

 

120


 

 

 

 

 

 

 

 

 

 

 

 

$121


 

 

 

 

 

 

 

 

 

$133.10


 

 

 

 

 

 

$146.41


 

 

 

$161.05


 

 

 

 

Future Value, Simple interest, and compound interest

 

110

 

100


$110

 

 

 

 

1            2            3            4            5


Time

(Years)

 

 

 

 

 

 

 

Future Value Projections

 

 

 

 

Future value

of $1 ($)

7

6

5

4

3

2

 

1


 

 

 

20%

 

 

 

15%

 

10%

5%

0%

 

 

1     2    3    4    5    6


7    8    9  10


Time

 

 

Future Value and Compounding


 

$1.10 ´


 

(1.40)5

 

$1.10 ´


(1.40)4

 

$1.10 ´


(1.40)3

 

$1.10 ´


(1.40)2

$1.10 ´


(1.40)

 

 

$1.10


$1.54


$2.16


$3.02


$4.23


$5.92

 

 

 

 

 

0            1            2            3            4            5

 

Future values of $1.10 at 40% rate of interest

 

 

 

Future Value Interest Factors (FVIF)

 

Numbe


Interest Rates

 

5%                     10%                    15%                    20%

1

1.0500

1.1000

1.1500

1.2000

 

 

r       of

Periods

 

 

 

 

 

2                        1.1025

 

 

1.2100

 

 

1.3225

 

 

1.4400

 

3                        1.1576

 

1.3310

 

1.5209

 

1.7280

 

4                        1.2155

 

1.4641

 

1.7490

 

2.0736

 

5                        1.2763

 

1.6105

 

2.0114

 

2.4883

FUTURE VALUE


LESSON 13

 

 

  • Usually simple interest is used in financial institutions for interest periods of less than one year.
    • If  the  rate  is  expressed  as  an  annual  rate  (normal  practice),  then  the  time  period  (t)  must  be  a fraction of a year.
  • By investing $10,000 in an 8%, 90-day certificate of deposit, total proceeds at the end of the CD

period will be:

  • FV = (10,000)+(10,000x.08x90/365) = $10,197.26

 

If you were to invest $10,000 at 5-percent interest for one year, your investment would grow to $10,500

 

$500            would be interest ($10,000 × .05)

$10,000 is the principal repayment ($10,000 ×1)

$10,500 is the total due. It can be calculated as:

 

$10,500 = $10,000×(1.05).

 

$10,000 today is worth $10,500 in one year, given that interest rate is 5%

 

  • It refers to the current value of the future cash flow discounted at the appropriate discount rate.
  • In other words, the amount one would need to invest today at some pre-determined interest rate to

get some desired amount in future is the present value of the desired money.

 

Present Value

 

  • Often, if a bank or other financial institution loans a sum for a short term, the lender will prefer to calculate the interest up front and loan out the discounted principal, or principal minus interest to be earned.
  • The  interest  to  be paid  up front  on  a  loan  is  called  discount  and  the discounted  principal,  or  the actual amount loaned is called the present value (PV)

 

PV =    FV

(1+rt)

 

  • Repeating the discount basic formula (simple interest): PV =        FV

(1+rt)

  • Example: If the bank loans out $10,000 for 90 days at 8% simple interest, the PV is: PV = 10000 / [1 + (.08)(90/365)]

= 10000/ 1.019726

= $9,806.56

 

Present Value

 

Suppose you need $400 to buy textbooks next year, You can earn 7% on your money. How much do you have to put up today? Now, ----------- Present value x 1.07 = $400. Solving for present value:

 

Present value =


$400 =


$373.83

                                                            1.07                                                       

© Copyright Virtual University of Pakistan                                             55

 

So investing $373.83 (present value) at 7 %will result in having $400 (future value) in one year.

 

If you were to be promised $10,000 due in one year when interest rates are at 5-percent, your investment be worth $9,523.81 in today’s dollars.

 

 

 

 

 

$9,523.81 =


$10,000

1.05

 

So, the amount that a borrower would need to set aside today to, be able to meet the promised payment of

$10,000 in one year is called the Present Value (PV) of $10,000.Note that ------- $10,000 = $9,523.81×(1.05)

 

In the one-period case, the formula for PV can be written as:

  • Where C1 is cash flow at date 1 and
  • r is the appropriate interest rate or discount rate.

PV  =     C1

 

 

 

Present Value for Multiple Periods


1 +  r

 

 

  • Calculating  present  value  for  multiple  periods  is  quite  similar  in  nature  as  was  in  case  of  future

value.

  • General formula for calculating present value of C cash flow in t periods time is:

PV  =  C ´        1

(1 +


r )t

 

 

  • 1 /(1 + r)t  is used to discount a future cash flow, so it is called the discount factor Or present

value interest factor (PVIF r,t),

 

Calculating  the  present  value  of  a  future  cash  flow  to  determine  its  worth  today  is  commonly  called

discounted cash flow (DCF) valuation

 

Present Value Interest Factors (PVIF)

 

 

 

 

Number           of

Periods

Interest Rates

5%

10%

15%

20%

1

0.9524

0.9091

0.8696

0.8333

2

0.9070

0.8264

0.7561

0.6944

3

0.8638

0.7513

0.6575

0.5787

4

0.8227

0.6830

0.5718

0.4823

5

0.7835

0.6209

0.4972

0.4019

 

Present Value for Multiple Periods

  • Do you want to be a millionaire? No problem!
  • Suppose you are currently 21 years old, and can earn 10 percent on your money.
  • How much you must invest today  in order to accumulate $1 million by the time you reach age 65?

 

 

First define the variables:

 

FV = $1 million

 

r = 10 percent

t = 65 - 21 = 44 years

PV =

?

 

Set this up as a future value equation and solve for the present value:

$1 million = PV x (1.10)44

PV = $1 million/(1.10)44 = $15,091.

Of course, we’ve ignored taxes and other complications, but stay tuned - right now you need to figure out where to get $15,000!

 

Present Value of $1 for Different Periods and Rates

Present                                                                                                                                        value

of $1 ($)

 

 

 

 

 

1.00

 

.90

 

.80

 

.70

 

.60

 

.50

 

.40

 

.30

 

.20


r = 0%

 

 

 

 

 

 

 

r = 5%

 

 

 

 

r = 10%

 

 

r = 15%

 

r = 20%

 

.10


 

1      2        3       4        5        6       7        8       9        10


Time

(years)

 

 

Present Value

 

How much would an investor have to set aside today in order to have $20,000 five years from now if the current rate is 15%?

PV                                                    $20,000

 

 

 

0           1            2            3            4            5

$9,943.53 =  $20,000

(1.15)5

 

 

Present Value vs. Future Value

 

  • What we called the present value factor is just the reciprocal of the future value factor.
    • Future value factor = (1 + r)t
    • Present value factor = 1/(1 + r)t

 

If we let FVt  stand for the future value after t periods, then the relationship between the future value and the present value is:

 

PV x (1 + r)t  = FVt

PV = FVt  / (1 + r)t  = FVt  x [1/ (1 + r)t]

 

This is also known as basic present value equation.

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