financial management teaching material1

Chapter OneAn over view of Financial Management

1.1 The nature and scope of financial managementDefinition: Financial management is an art and science of managing money.

As an art it requires some skills which can be used by professionals. As a science it involves some study and research used to come up with standards and principles. Financial management includes the process and transfer of money among and between individuals,

business and government. It is also used as mediator between who want to save their money & who want to invest money of

others. Scope of financeA firm secures whatever capital it needs and employs it (finance activity) in activities which generate returns on invested capital (production and marketing activities).

Financial Management Vs Economics & Accounting Economics

Financial managers need to have a good understanding of the economic environment. Some economic concepts are used by financial management such as:

o Demand & Supply concept o Profit maximization principle (i.e. MR = MC)o Pricing concept

Accounting Focuses on providing financial information to the user group. Accounting relies on past events, whereas the financial management focuses on the future. Accounting deals on preparing financial statement, this must be changed to other in understandable

form by the financial manager.Accounting Financial management

Incomes statement Analysis of F/S Capital statement Eg. -Ratio analysis

Balance sheet Common size statements Statement of cash flows

1.2 The goals of financial managementThe goals of managerial finance are:

1. Profit maximization2. Stockholder wealth maximization3. Managerial reward maximization: when the firms make a profit management give a bonus for

their employees. 4. Behavioral goal: change employees mind to think for the advancement of the organization.

5. Social responsibility: keep the environment in well manner. Avoid environmental pollutions.

1. Profit maximization. Objective: - to get large amount of profits in short period of time.

- It is short term goal

GEBRIE WORKU, AAUCC 1

- A firm may maximize its short-term profits at the expense of its long term profitability and still realize this goal. In contrast, stockholder wealth maximization is a long term goal, since stockholders are interested in future as well as present profits.

- You can attain maximum profit through selling a portion of your assets but you are endangering the existence of the business.

Advantages- easy to calculate profits - easy to determine the link between financial decisions and profits.

Disadvantages- emphasis only on short-term - ignores risk and uncertainty

2. Stockholder wealth maximizationObjective: is attained when highest market value of common stock is maintained. AdvantagesWealth maximization is generally preferred because:

- emphasis on long-term- recognizes risks and uncertainty

Disadvantages - offers no clear link between financial decisions and stock price- Leads to anxiety of management and frustrations.

The roles of financial managersThe financial manager performs the following functions:

1. Financial analysis, forecasting and planning - Monitoring the firms financial position - Determines the proper amount of funds to employ in the firm

2. Investment decisions- Make efficient allocations of funds to specific assets- Make long-term capital budget & expenditure dictions

3. Financing and capital structure decisions- Determines both the mix of short-term and long-term financing and equity/debt financing.- Raises funds on the most favorable terms possible.

4. Management of financial resources- Manages working capital- Maintains optimal level of investment in each of the current assets.

5. Risk management -As future is uncertain, the financial manager should consider/expectation of risk and protect the resources.

1.3 Financial management decisionsFinance functions or decisions include:

- investment or long-term asset mix decision


- financing or capital mix decision- dividend or profit allocation decision - liquidity or short-term asset mix decision

A firm performs finance functions simultaneously and continuously in the normal operation. Finance functions used to skilful planning, control and execution of a firm’s activities.

Investment decisions Investment decisions or capital budgeting involves the decision of allocation of capital or commitment

of funds to long term assets that would yield benefits in the future. Investment process should be evaluated in terms of both expected return and risk

Financing decisions Financing decisions is the second important function to be performed by the finance manager Deals with when, where, and how to acquire funds to meet the firm’s investment needs The mix of debt and equity is known as the firm’s capital structure. The financial manager

must strive to obtain the best financing mix or the optimum capital structure for his or her firm. The firm’s capital structure is considered to be optimum when the market value of shares is

maximized. The use of debt affects the return and risk of shareholders, it may increase the return on equity

funds but it always increases risk. A proper balance will have to be struck between return and risk.

Dividend decisions The financial manager must decide whether the firm should distribute all profits or

retain them or distribute a portion and retain the balance Like the capital structure policy, the dividend policy should be determined in terms of

its impact on the shares holders’ value. The optimum dividend policy is one that maximizes the market value of the firm’s shares.

Liquidity decisions Current assets must be managed efficiently for safeguarding the firm against the dangers of illiquidity

and insolvency. An investment in current assets affects the firm’s profitability, liquidity and risk. A conflict exists

between liquidity and profitability while managing current assets. Example, if the firm does not invest sufficient funds in current assets, it may become illiquid. But it would lose profitability as idle current assets would not earn any thing. Therefore, a proper tradeoff must be achieved between profitability and liquidity.

In order to ensure that neither insufficient nor unnecessary funds are invested in current assets, the financial manager should develop sound techniques of managing current assets.

Financial manager should estimate firm’s needs for current assets and make sure that funds would be made available when needed.

1.4 Financial Markets and InstitutionsFinancial Institutions:Financial institutions are financial intermediaries which include insurance companies, pension funds and investment banks.


Financial Market:Financial markets include primary markets, where new securities are sold, and secondary markets, where existing securities are traded.

Primary Markets Vs Secondary MarketsA primary markets is one in which a borrower issues new securities in exchange for cash from an investor (buyer). New sales of treasury bills, stock or bonds all take place in the primary markets. The issuers of these securities receive cash from the buyers of these securities, who in turn receive financial claims that previously did not exist.Secondary markets: markets where existing securities are traded among investors. Once new securites have been sold in the primary market, an efficient mechanism must exist for their resale if investors are to view securites as attractive opportunities. Secondary markets give investors the means to trade existing securities.Financial assetsMajor types of financial assets are:

1. Non marketable2. Money markets3. Capital market4. Derivative market

1. Non marketable financial assets: assets that represent personal transactions between the owner and the issuer. That is, you as the owner of a savings account at a bank must open the account personally, you must deal with the bank in maintaining the account or in closing it. In contrast, marketable securities trade in impersonal markets-the buyer (seller) does not know who the seller (buyer) is, and does not care. It includes:

Saving accounts: saving account are held at commercial banks or institutions such as saving and loan association and credit unions. Saving accounts in insured institutions offer a high degree of safety on both the principal and the return on that principal. Liquidity (which can be defined as the ease with which an asset can be converted to cash) is taken for granted.

Nonnegotiable certificate: commercial banks and other institutions offer a variety of savings certificate known as certificate of deposits (CDs). These certificates are available for various maturities, with higher rates offered as maturity increases.

Money markets deposit accounts: financial institutions offer money market deposit accounts with no interest rate ceilings. Money markets accounts, with a required minimum deposit to open, pay competitive money market rates and insured up with some amount.

2. Money markets: include short term, highly liquid, relatively low risk debt instrument sold by governments, financial institutions, and corporations to investors with temporary excess funds to invest. Some of these instruments are negotiable and actively traded, and some are not. It includes:

Treasury bills: the premier money market instrument, a fully guaranteed, very liquid IOU from the government. They are sold on auction basis.

Negotiable certificate of deposit ( CDs): issued in exchange for a deposit of funds by most banks, the CD is a marketable deposit liability of the issuer, who usually stands ready to sell new CDs on demand. The deposit is maintained in the bank until maturity, at which the time holder receives the deposit plus interest. However, these CDs are negotiable, meaning that they can be sold in the open market before maturity.

Commercial paper: a short term, unsecured promissory note issued by large, well known, and financially strong corporations (including finance companies). Commercial paper usually sold at a discount either by the issuer or indirectly through a dealer, with rates comparable to CDs.


Eurodollars: dollar denominated and developed in Europe. Major international banks transact among themselves with other participants including multinational corporations and government. Maturities mostly short term, often less than six months.

Repurchase agreement (RPs): an agreement between a borrower and a lender (typically institutions) to sell and repurchase government securities. The borrower initiates a RP by contracting to sell securities to a lender and agreeing to repurchase these securities at a prespecified price on a stated date. The effective interest rate is given by the difference between the purchase price and the sale price. The maturity of RPs is generally very short, from three days to 14 days, and some times overnight.

Banker's acceptance: a time draft drawn on a bank by a customer, whereby the bank agrees to pay a particular amount at a specified future date. Banker's acceptances are negotiable instruments because the holder can sell them for less than face value.

3. Capital Markets: encompass fixed income and equity securities with maturities greater than one year. Risk is generally much higher than in the money market because of the time to maturity and the very nature of the securities sold in the capital markets. Marketability is poor in some cases. The capital markets include both debt and equity securities, with equity security having no maturity date. It includes:

Fixed income securities Treasuries bonds agencies Municipal bonds corporate bonds

Equities Preferred stock common stock

5. Derivative Markets: securities that derive their value in whole or in part by having a claim on some underlying security. It includes

Forward options futures swaps caps floor

Derivative markets are important to investors because they provide a way for investors to manage portfolio risk.


Chapter Two

Evaluation of Financial Performance Financial statement analysis2.1 An over view of financial analysisDefinition: financial analysis is an evaluation of a firm's past performance and prospects for the future. The focus of financial analysis is on key figures in the financial statements and the significant relation

ships that exist between them. The analysis of financial statements is a process of evaluating relationship b/n component parts of f/s to

obtain a better understanding of the firm's financial condition and performance. Financial analysis helps users understand the numbers presented in financial statements and serve as a

basis for financial decision making. Financial analysis consists of three major stages. These are:1. Preparation and selection: - the preparatory steps include establishing the objective of the analysis and assembling the financial statements and other financial data. Objectives depend on the prospective of the financial statement user and the questions to be answered by

the analyst. For instance, management analysis financial statements to help in planning and decision making. The analysis providing answers to such questions as: How has the firm performed in the past? What are the firm's strengths and weaknesses? What changes are needed to improve future performance?

2. Computation and relation: - arrange it in a way that will bring about significant relationship. It involves the application of various tools and techniques to gain a basic understanding of the firm's financial condition and performance. The most frequently used techniques in analyzing f/s are:

a. Ratio analysis: converts birr amounts in to ratios.b. Common- size statements: express individual statement accounts as percentage of a base amount.

3. Evaluation and interpretation: involves the determination of the meaningfulness of the analysis and to develop conclusions, inferences, and recommendations about the firm's performance and financial condition. Financial statement analysis focuses primarily on the balance sheet and the income statement. How ever, data from the following two statements may also be used:

- the statement of retained earnings, and - the statement of changes in cash flow

2.2 ways of financial analysis: There are three ways of financial analysis:1. Horizontal analysis /trend analysis /: - as the name indicates in horizontal analysis, we compare financial

statement of a firm for different accounting periods. it gives an indication of the direction of change and refects whether the firm's financial performance

has improved, deteriorated or remained constsnt over time. Making use of comparative financial statement. e.g. I/S or balance sheet of period 2 with period 1 Note It is important to show both the dollar amount of change and the percentage of change because either one

alone might be misleading. In case where analysis of financial statements of large number of years is to be made, the horizontal

analysis becomes cumbersome. As result, it is recommendable to use trends relative to a certain base year. (the base year is 100% )


2. Vertical analysis /common size statement/ Analysis of financial statements where a significant item on a financial statement is used as a base value and other all items ate compared to it. Example in the case of balance sheet, total asset as abases value. Each asset account expressed in terms of total asset

- In the case of income statement, net sales as abase value. All expenses and net income are expressed in terms of net sales.

the primary objective of vertical analysis is to highlight relationship b/n components of financial statements ,not to assess trends in individuals components over time

it helps us to disclose the internal structure of an enterprise it indicates the existing relationship between each income statement account and revenue shows the mix of assets that produce income and the mix of the source of capital it also helps us to further assess financial status of a firm in the industry

Example Firm A Firm B Asset: Current asset 40% 60% Fixed asset 60% 40% Total 100% 100% Note: firm B is more liquid than firm A

3. Ratio analysis "A single figure by itself has no meaning but when expressed in terms of a related figure, it yields significant inferences".

Ratio analysis standardizes financial data by converting birr figure in the financial statements into ratios. A financial ratio is a mathematical relationship among several numbers usually stated in the form of percentage or times

Ratio analysis helps us to draw meaningful conclusions and make interpretations about a firm's:

-Financial conditions, and - Performance 2.3 Basis of comparisons:-Ratio, as yardsticks or financial flags of a firm’s overall performance, is meaningful only when compared with other information.Comparisons can be made in the following ways:1. Industry standards /comparisons: are standards used to compare a firm’s financial conditions to that of the industry average as a whole and reflects its performance in relation to its competitors. E.g. Comparison of Ethiopian air lines performance with air lines industry average2. Historical standards/trend analysis/: are standards used to compare current performance to past trends with in the same firm and indicate the direction of change in performance. It helps us to determine whether the firm’s financial conditions is improving or deteriorating.3.Management goals for key ratios: are standards or plans set in advance for specific ratios or financial statement accounts and serve as to assess the status of financial position and as a basis for evaluating actual performance.Examples, Management may se a net profit margin of 20 percent at the beginning and evaluate the actual performance.


2.4 Types of financial ratios Financial ratio classified into five categories. These are:

1. Liquidity ratios2. Activity ratios 3. Leverage ratios4. Profitability ratios5. Market value ratio

Example, ABC Company Balance sheet As of December, 31 (In thousands) yr2001 yr2000Assets: Current assets:Cash 675 450A/R 1,050 700Marketable securities 975 650Inventory 1,900 950Total current asset 4,600 2,750Plant assets (net) 3,125 1,250Total assets 7,725 4,000Liabilities Current liability 900 450Ling term liability 1,800 800Total liabilities 2,700 1250Stockholders’ equityCommon stock (100par) 2,000 2,000Retained earning 3,025 750Total liabilities &SHE 7,725 4,000


ABC Company Income statement For the year ended, December 31 (in thousands) yr2001 yr2000Sales 2250 1800Sales returns 375 300Net sales 1875 1500CGS 1000 850GP 875 650Operating expense:Selling expense 300 200General expense 105 60Total expense 405 260Income from operation 470 390Other income 130 80Earning before interest and tax (EBIT) 600 470Interest expense 100 55Earning before tax (EBT) 500 415Income tax(40%) 200 166Net income 300 249

1.liquidity ratios “are a firm’s current assets sufficient to pay its current liability “ Liquidity ratios measure the ability of a firm to meet its short term obligations and reflect the short term financial strength/solvency of a firm. Two commonly used ratios are:A. Current ratio:- measures a firm’s ability to satisfy or cover the claims of short term creditors by using only current assets. That is, it measures a firm’s short term solvency or liquidity.

Current ratio =Current assets Current liabilitiesCurrent ratio for ABC (for yr2000)= 2750 450 =6.1 timesInterpretation: ABC has birr 6.1 in current assets available for every one birr in current liabilities.

Low ratio-suggests that a firm may face difficulty in paying its short term obligations. High ratio- indicates that too much capital is tied up in current assets and a firm may be

sacrificing some return.Note: the ratio highly exceeds the industry average (i.e. 2 times) so that ABC is able to pay its debts when they are due.

A reasonable higher (moderate)the ratio,- the larger the amount of birr availability in current assets per birr of current liability- the more the firm’s liquidity position- the greater the safety of funds of short term creditors (i.e. less risk to creditors)


A very lower current ratio results opposite from current ratio out lined as above. A low current ratio could be improved by:

-long term borrowing to increase current assets -liquidating current liabilities using long term financing

A very high current ratio may indicate, -excessive cash due to poor cash management -excessive A/R due to poor credit management -excessive inventories due to poor inventory management

- A firm is not making full use of its current borrowing capacity There fore, a firm should have a reasonable current ratio.B. Acid –test or quick – ratio: - measures the short term liquidity by removing the least liquid assets such as:

- Inventories: are excluded because they are not easily and readily convertible in to cash. More over, losses are most likely to occur in the event of selling inventories

- Prepaid expenses: are excluded because they are not available to pay off current debts. Prepaid expenses include prepaid rent, prepaid insurance, prepaid advertising, supplies

Quick assets are: cash marketable securities receivables

Quick Ratio = Quick Asset Current liabilities or = Current Assets- (Inventory+ prepaid expenses) Current liabilitiesQuick Ratio for ABC (for yr.2000) = 450+700+65 = 4 times 450 Or

2750-950 = 4 times 450Interpretation: ABC has birr 4 in quick assets for every birr in current liabilities.

The current ratio is a crude measure of a firm’s liquidity position as it takes into account all current assets with out any distinction in their composition.

2) Activity ratios These ratios are also called. Efficiency ratios or Asset- utilization ratios

Activity ratios are employed to evaluate the efficiency with which the firm manages and utilizes its assets. These ratios are also called turnover ratios because they indicate the speed with which assets are being converted or turned over into sales.

i.e Merchandise A/RCash


Overall liquidity ratios generally do not give an adequate picture of company’s real liquidity due to differences in the kinds of current assets & liabilities the company holds. Thus, it is necessary to evaluate the activity ratio.

Example:- ABC Café XYZ Café (Birr) (Birr)

Cash 0 7000Marketable security 0 17,000AIR 0 5,000Inventories 35,000 6,000 Total current asset 35,000 35,000Current Liabilities A/P 0 6,000N/P 14,000 6,000Accruals 0 2,000 Total current liability 14,000 14,000

The two cafeterias have the same liquidity (current ratio) but their composition is different.CR = CA CR = CA

CL CL=35000 =35000 14,000 14,000= 2.5 times = 2.5 times

Activity (Asset utilization) Ratios include 1) A/R turnover ratio 2) A/P “ “3) Inventory “ “4) FA “ “5) Total Asset “ “

1) A/R turnover ratio : - measures the liquidity if a firm’s accounts receivable. That is, it indicates how many times or how rapidly A/R is converted into cash during a year. Financial analysts apply two tools to judge he quality or liquidity of A/R. A/R turnover Collection period A/R turnover = Net credit sales (Total sales)

Average A/RA/R turnover for ABC (yr 2000) = 1500

700 = 2.14 times

AIR turnover for (yr 2001)= 1875 875*

= 2.14 times*To compute average A/R sum up the last year A/R ( i.e beginning of this year) and the A/R of the current year and divide by two .


Interpretation :- ABC’s A/R are converted into cash 2.14 times in year. A reasonably high A/R turnover is preferable.

A ratio substantially lower than the industry average may suggest that a firm has: More liberal credit policy (i.e longer time credit period), poor credit selection, and inadequate

collection effort or policy which could lead. A/R to be too high Bad debts or uncorrectable Receivables

More restrictive cash discount (i.e no or little cash discount) that could make sales to be too low. A/R turnover = Net sales

A/R

Note: - As result of the above factors, The firm could have poor profitability position. The firm’s funds would be tied-up in receivable as payments by customers are delayed.

A ratio substantially higher than the industry average may suggest that a firm has: More restrictive credit policy (i.e. short term credit period) More liberal cash discount offers (i.e. larger discount and sale increase) More restrictive credit selection. More rigorous collection effort or policy

Note: the outcomes of a higher A/R turnover could be avoidance of the risk of bad debts Increase the firm’s profitability position. Small funds tied-up in A/R Customers pay quickly

A reasonable High ratio is required for a firm to be efficient in converting its A/R into cash.If available, only credit sales should be used in the numerator as A/R arises only from credit sales.

Average collocation period (ACP ) Represents the average length of time a firm must wait to receive cash after making a sale. That is, it indicates how many days a firm takes to convert receivable into cash or number of days sales are tied up in A/R

= 360 days Net sales

Average A/R

=360 x Average A/R Net sales

= 360 x average A/R Net sales


ACP= 360 day A/R turnover

ACP= Receivables Average sales per day

= 1 X Average A/R net sales

360 1 X Average A/RAverage sales per day= Average A/R Average sales per day

ACP= 360 days Receivable A/R turnover or Average sales per day = 360 days = 700 = 700

2.14 1500 4.16=168 days 360 =168 days

Assume, the credit term of ABC is 2/10 ,n/75.Interpretation: - Customer of ABC, on the average, is not paying their bills on time as the ACP greater than the credit term (75 days). In general, a reasonably short collection period is preferable.ABC takes about 168 days to collect its A/R and this lengthy collection period suggests that the firm might have potential problems in that:

It isn’t effective in collecting its A/R It may give credit to marginal customers Thus, the firm’s profitability is adversely affected.

2) A/P turnover ratio :- measures how rapidly creditors are paid. That is, how rapidly or how many times A/P are paid during a year.

Example, Assume for XYZ café net purchase (on credit) =150,000A/P- Dec 31, 2000 30,000A/P turnover = net purchase

A/P= 150,000 30,000=5 times

Interpretation :- Assume that industry average of A/P turnover is 6 times.XYZ cafe pays its creditors lower times a year (i.e 5 times). Thus, it may be rated a risky borrower. Average payment period (APP):- measures the average length of time creditors must wait to receive their

cash or simply the average time needed by a firm to pay its A/P to creditiors or suppliers from which purchase made.

APP for XYZ cafe = 360 days 5 times = 72 days


APP= 360 daysA/P turnover over

A/P Average purchase per day

Assume, suppliers on the average extend, say 60 days credit terms.Interpretation: - XYZ café would be given a low credit rating (low credit worthiness). That is XYZ is a risky borrower.3. Inventory turn over: the frequency at which inventory is converted into sales/ A/R. That is how fast inventory is sold or turned over?

Inventory turn over= CGS Average inventory

Inventory turnover for ABC ( 2001) = 1000950 + 1900 2

= 0.7 times

Note:- The average inventory is the average of beginning and ending balances of inventory.Interpretation:- ABC’s inventory is sold out or turned over 0.7 times per year. It general, a high inventory

turnover ratio is better than a low ratio. An Inventory turnover significantly higher than the industry average indicates:

Superior selling practices Improved profitability as less money is tied-up in inventory.

Possible problems of high inventory turnover Very low level of inventory (i.e under investment in inventory) Lost sales due to insufficient inventory (i.e risk of out of stock) Stoppage of production process for manufacturing firms.A very low inventory turn over suggests: Excessive inventory or over investment in anticipation of strike or price decreases. Inferior quality goods, stock of un salable / obsolete goods. Possible problems of a very low inventory turnover

- Cost of funds locked-up or tied up in inventory (opportunely cost)- Deterioration- Rental of space- Insurance cost, properly tax, and other inventory carrying costs.

Average age of inventory (AAI):- The number of days inventory is kept before it is sold to customers.AAI = 360 days

Inventory turnover360 days 0.7= 514 days

Interpretation: - ABC carries its inventory for 514 days.The lengthening of the holding period shows a potently greater risk of obsolescence.Operating Cycle: - is the number of days it takes to convert inventory and receivables to cash.

Inventory A/R Cash AAI ACP

Operating cycle = AAI + ACP where, AAI, Average Age of Inventory ACP, Average Collection Period


Operating cycle for ABC= 514 days +168 days= 682 days

Interpretation :- ABC takes 682 days to convert inventory and receivables to cash. A short operating cycle is desirable.4) Fixed Asset turnover: - measures the efficiency of a business firm with which the firm has been using its fixed assets to generate revenue

Fixed Assert turnover = Net salesNet fixed asset.

Fixed Asset turnover = 1500ABC (for 2000) 1250

=1.2 timesInteroperation:-ABC generated birr 1.20 in net sales for every birr invested in fixed assets.Other things being equal, a ratio substantially below the industry average:-Shows underutilization of available fixed assets. (i.e presence of idle capacity) relative to the industry.-Indicates possibility to expand activity level without requiring additional capital investment. Shows over investment in fixed assets, low sales, or both.-helps the financial manager to reject funds requested by production managers for new capital investments.Suggests that sales should be increased, some fixed asses Should be disposed of , or both. Other things being equal, a ratio higher than the industry average:

- Requires the firm to make additional capital investments to operate a higher level of activity.- Shows more efficiency in managing and utilizing fixed assets.

A firms fixed asset turnover is affected by: - The cost of the assets.

- The time elapsed since their acquisition.- The depreciation methods used

5. Total Asset turnover:- measures a firms efficiency in managing its total assets to generate sales. =Net sales Net total assets

(For year 2000) =1500 4000= 0.375 times

Net total assets = Net fixed assets + Current Asset. Depreciation is excluded.Interoperation: - ABC generates birr 0.375 in net sales for every birr invested in total assets. A high ratio suggests greater efficiency in using assets to produce sale A low ratio suggests that ABC is not generating a sufficient volume of sales for the size of its investment

in assets. Therefore, ABC should take steps to :--increase sales-Dispose of some of its investment in assets or both.

Caution has to be taken in making comparison b/n Asset turnover ratio of different organization because the initial cost of fixed asset differs from one organization to another. Moreover, the method of depreciation has its own impact on total asset turnover. Inflation has an impact. Comparing an old firm which had acquired many of its fixed assets at low prices with a new company which had acquired at high price may lead misleading.


Firm A (Meta Brewery) Firm B (Dashen Brewery) Old and well established company - New company Old fixed assets recorded at lower historical cost -New fixed assets purchased at higher prices Tend to have higher fixed asset turnover -Tend to have lower fixed asset turnover

These differences could result from:- Differences in net cost of fixed assets but not from differences operational

efficiencies. Thus, the analyst should consider these facts while comparing Firm A and Firm B

3. Leverage, solvency and long term debt ratioSolvency is a firm’s ability to pay long term debt as they come due.Leverage shows the degree of indebtness of a firm.There are two debt measurement tools. These areA. Financial leverage ratio: measures degree of indebtnessB. Coverage ratio: measures ability to pay debtA) Financial leverage. These ratios examine balance sheet ratios and determine the extent to which borrowed funds have been used to finance the firm. It is the relationship of borrowed funds and owner’s capital. This can be:

a) Debt ratiob) Debt equity ratio

a) Debt ratio: the percentage of assets financed through debtDebt ratio = Total Liability for ABC (yr 2000) 1250/4000=31.25% Total AssetsInterpretation: creditors have financed ABC about 31 cents of every birr assets. It is obviously implies that owners have financed 68.75 percent of total assets.Higher ratio shows- more of a firm’s asset are provided by creditors relative to owners

- The firm may face some difficulty in raising additional debt.- Further creditors may require a higher rate of return( interest rate) for taking higher

riskCreditors prefer moderate or low debt ratio, because low debt ratio provides creditors more protection in case

a firm experiences financial problems.

b) Debt –equity ratio: expresses the relationship between the amounts of a firm’s total assets financed by creditors (debt) and owners (equity). Thus, this ratio reflects the relative claims of creditors and shareholders’ against the asset of the firm/

For ABC ( yr 2000)=1250/2750=45.45%Interpretation: Lenders’ contribution is 0.45 times of stock holders’ contributions. That is. 0.3125/0.6875=0.4545=Debt ratio Equity ratio=Total liability = Total liability X Total assets = Total Liability Total assets Total assets Stockholders equity Stockholders equity Stock holders equity


Debt-equity ratio= Total Liability Stockholders equity

Total assetsB) Coverage ratio: these ratio measures the risk of debt by income statement ratios designed to determine the number of times fixed charges are covered by operating profits. Hence, they are computed from information available in the income statement.. It measures the relationship between what is normally available from operations of the firm’s and the claims of outsiders. The claims of a firm are normally met from the earnings or operating profits of the firm. These claims include loan principal and interest, lease payment and preferred stock dividends.The coverage ratios include:

A. Times Interest Earned Ratio: measures the ability of an a firm to pay interest on a timely basis. = EBIT Interest expense For ABC ( yr 2001)=600/100= 6 timesInterpretation: ABC earning can cover 6 times its interest expense.A low ratio suggests:- Creditors are at more risk in receiving interest due.-failure to meet interest payment can bring legal action by creditors possibly resulting in bankruptcy.- The firm may face difficulty in raising additional financing through debt as it is more than similar firms.A high ratio suggests the firm has sufficient margin of safety to cover its interest charges.B. Fixed Charge coverage ratio: measures the firm’s ability to meet all fixed payment obligation, such as

loan principal, interest, lease payment and preferred stock dividends. It helps to assess the business organization ability to meet all fixed payments.

Fixed charge coverage ratio= EBIT + Lease payments Interest+ Lease Payment+( principal pmt+ P/stock dividend) 1-T Where, T is tax rate.Note: a firm’s fixed charges are examined on a before tax basis. Interest payments and lease payments are

made on a before tax basis, so no need of adjustment. Principal payments and preferred stock dividend are not tax deductible and are paid from after tax earnings, a tax adjustment is necessary. That is, the payment grossed up by dividing (1-T) to find the before tax income.

Example, assume, Interest expense: 100000 Lease payment: 50,000 Principal payment: 10,000 Preferred stock dividend: 20,000 Tax rate: 40 percentFixed charge coverage ratio= 600+50 100+50+(10+20/1-0.4) 3.25 timesInterpretation: ABC is able to cover its fixed charges 3.25 times.If the ratio is lower:

- The firm may be unable to meet its fixed charges if earnings decline and may be forced into bankruptcy.

- Creditors and preferred stockholders see the firm as more risky.A high ratio suggests a good protection in the event of worsening financial position

4. Profitability ratio


These ratios are used to measure the management effectiveness. Besides management of the company, creditors and owners are also interested in the profitability of the company. Creditors want to get interest and repayment of principal regularly. Owners want to get a required rate of return on their investment. The ratio includes:

A. Gross profit marginB. Operating profit marginC. Net profit marginD. Return on investmentE. Return on equityF. Earning per share

A. Gross profit marginThis ratio indicates management effectiveness in pricing policy, generating sales and controlling production costs.

For ABC( yr 2000) = 650/1500=43.3%Interpretation: The company profit is 0.43 cents for each birr of sales.A high gross profit margin ratio is a sign of good management. A gross margin ratio may increase by the following factors:

Higher sales price, CGS remaining constant Lower CGS, sales prices remaining constant

A low gross profit margin may reflect higher CGS due to the firm’s: Inability to purchase raw materials at favorable terms Inefficient utilization of plant and machinery Over investment in plant and machinery, resulting higher cost of productionThe ratio also low due to a fall in prices in the market or marked reduction in selling by the firm in an attempt to obtain large sales volume.B. Operating profit margin: measures the percentage of operating profit to sales.

For ABC( yr 2000)=470/1500=31.3%Interpretation: ABC generates 31 cents operating profits for each of birr sales.

C. Net profit Margin: measures the percentage of net income to sales.

For ABC (yr 2000) =249/1500=16.6%Interpretation: ABC generates nearly 17 cents in net income for each of birr net sales.


Gross profit margin= Gross profit Net sales

Operating profit margin= EBIT Net sales

Net profit margin= Net income Net sales

D. Return on investment (ROI): measures the overall effectiveness of management in utilizing assets in the process of generating revenue. It reflects how effectively and efficiently the firm’s assets are used. This ratio is also called Return on Asset (ROA).

Or using Dupont formula: ROA= net profit margin X Total asset turnover = Net income X Net sales Net sales Total assets

= 249/4000=6.225% or =0.06225x0.375=6.225% Interpretation: ABC generates little more than 6 cents for every birr invested in assets. E. Return on equity( ROE): measures the rate of return realized by stockholders on their investment.

Or

Leverage ratio measures how the firm finances its assets. Basically, firms can finance with either debt or equity. ROA= ROE, with only equity financing that asset is equal to stockholders equity and leverage multiplier is 1.For ABC (yr 20000=249/2750=9.05%Interpretation: ABC generates about 9 cents for every birr in shareholders equity.F. Earning per share (EPS) represents the amount of birr earned on behalf of each outstanding shares of

common stock.

For ABC (2000) 249/20=12.45Interpretation: ABC earns birr 12.45 for each shares outstanding.

5. Market Value ratio: these ratio are primarily used for investment decisions and long range planning and include:

A, Price/ Earning ratio(P/E ratio): shows the amount investors are willing to pay for each birr of the firm’s earnings.

Or


ROA= Net income Total assets

ROE= Net income Stockholders equity

ROE= ROA X Equity multiplier Where, Equity multiplier= Total assets Stockholder equity

EPS= Net income No. of C/stock shares outstanding

P/E ratio= Current Market price per share Earning per share

P/E ratio= D1/E1 k-gWhere, D1/E1, is the expected dividend payout ratio K, is the required rate of return for the stock g, is expected growth rate in dividends.

Assume, that ABC year end Dec 31, 2000 market price of common stock is birr 115 per share.P/E ratio=115/12.45=9.24 times.Interpretation: the market is willing to pay 9.24 birr for every birr in earnings. A high P/E multiplier often reflects the market’s perception of the firm’s growth prospects. Thus, if investors believe that a firm’s future earnings potential is good and they may be willing to pay a higher price for the stock.B. Book value per share: is the value of each share of common stock based on the firm’s accounting records.

For ABC (yr 2000) =2750-0/20=137.50 birr/shareC. Dividend Ratios. These can be: i) Dividend payout ratio ii) Dividend yieldi) Dividend Payout ratio: shows the percentage of earnings distributed at the end of the accounting period. It is the birr amount of dividend paid on a share of common stock outstanding during the reporting period.

Assume that ABC dividend per share is birr 2.49 Dividend payout ratio = 2.49/12.45=20%Interpretation: ABC paid 20 percent of its earning as dividend. The higher the ratio may reflect the firms lower growth opportunities.ii) Dividend yield: shows the rate earned by shareholders from dividends relative to the current price of the stock. Dividend yield is part of a stock’s total return.

For ABC Dividend yield = 2.49/115=2.17%Limitation of Ratio analysis

The ratio analysis is a widely used technique to evaluate the financial position and performance of a business. But there are certain problems in using ratios. The analysts should be aware of these problems. The following are some of the limitations of the ratio analysis.

1. Many large firms operate different divisions in different industries, and for such enterprises it is difficult to develop a meaningful set industry average.

2. Most firms want to be better than industry average approximations. So merely attains average performance is not sufficient.

3. Non recognition of inflation in financial statement makes a ratio analysis difficult4. Firms can employ a “ window dressing” technique to make their financial statement more stronger5. Different accounting methods are employed by different enterprises.


Book value per share= Total stockholders equity- Preferred stock No. of common shares outstanding

Dividend payout ratio= Dividend Per share Earning per share

Dividend yield= Dividend per share Market price per share

Chapter Three

FUNDAMENTAL FINANCIAL CONCEPTS3.1 Time value of Money

The recognition of the time value of money and risk is extremely vital in financial decision -making. The welfare of owner's would be maximized when net worth or net present value is created form making a financial decision. What is net present value? It is a time value concept.

If an individual behaves rationally, he would not value the opportunity to receive a specific amount of money now equally with the opportunity to have the same amount at some future date. Most individuals value the opportunity to receive money now higher than waiting for one or more years to receive the same amount. Three reasons for this are

Risk Preference for consumption Investment opportunities

Risk:- we live under risk or uncertainty. As an individual is not certain about future cash receipts, he prefers receiving cash now.

Preference for consumption: most people have subjective preference for present consumption over future consumption of goods and services either because of the urgency of their present wants or because of the risk of not being in a position to enjoy future consumption that may be caused by illness or death, or because of inflation.Investment Opportunities: - Most individuals prefer cash to day to future cash because of the available investment opportunities to which they can put present cash to earn additional cash.

Future Values Interest: When A borrows money from B, then A has to pay certain amount to B for the use of the money. The amount paid by A is called Interest.Principal:- The amount borrowed by A from B is called principal.Amount :( Total Amount):- the sum of the interest and principal is usually called the amount.A). Simple Interest and the future Value:-

When interest is payable on the principal only, it is called simple interest.E.g. Simple interest on birr 100 at 5% per annum will be birr 5 each year. i.e. at the end of one year, total amount will be birr 105, at the end of second year, it will be birr 110 and so on. When money is put out at simple interest, the interest is payable for each year, but is not added to the

principal.Let P be the principal and n, the number of years for which the principal is lent, r, the rate of interest per annum.

Example 1. Find the future value if birr 20, 000 is borrowed at 6 percent simple interest for 3 months.Here, 3 months is 3/12 = 1/4 of a year, so n = 1/4Hence, Fv = p+pnr


Fn= P+ Pnr P (1 +nr)

=20,000 + 20,000 (3/12x 6%) = 20,000+300 = birr 20,300

Example 2 Mamush has placed birr 500 in an employees’ savings account that pays 8% simple interest. How long will it be, in months, until the investment amount to birr 530?

Fv= P (1+nr)530 =500(1+nx8%)530= 500(1+0.08n) n=0.75 Years

N= 0.75x12 months= 9 month

Example 3 At what annual rate of simple interest will an investment of birr 1000 for 2 years grow to the amount of birr 1100?

F= p (1+nr)1100= 1000 (1+2r) r=5%

Simple Discount: present value

Example 1 How much will Mimi have to invest now in the 8% simple interest savings account in order to have birr 600 a year from now ?

P = F (1+nr)= 600 (1+ 1x8%) = birr 555.56

Example 2 Find the present value of birr 1000 at 9% simple interest due 8 months from now.P = F (1+nr) = 1000 (1+ 8/12 x 9%) = birr 943.40

B). Compound Interest and the future value If the money is lent at compound interest, the interest is added each year to the principal and for the following year the interest is calculated on their sum.Let p be the principle and n, the number of years for which the principal is lent at i, percent per annum

compound interest.Example 1 If you deposited birr 10,000 in NIB bank which was paying a 6% rate of interest compounded annually on a ten year time deposit, how much would the deposit grow at the end of ten years?

Fv = P (1+) n = 10000(1.06)10

= 10000(1.7908)

=Birr 17,908.48Example 2


P= F (1+ nr)

Fn =P (1+i) n

If Sara deposited birr 10,000 in Awash Bank which was paying a 6 percent rate of interest compounded semiannually, on a ten year time deposit, How much would the deposit grow at the end of ten years?I=6%/2= 3%, since it is compounded semiannually, n= 10x2 =20Fv= p (1ti) n

= 10,000 (1.03)20

= 10,000(1.8061) =birr 18,061.11 Exercise If Fekadu deposited birr 8,000 in Dashen Bank which was paying a 4% rate of interest compounded quarterly on an 8 year time deposit ,how much the deposit grow at the end of 8 years? Fn =10,999.53Example 3

A sum of money may double itself in n years, compounded at 12 percent interest annually. Find n ?Fv= p(l+i)n

2P= P(l+i)n

2=(l+0.12)n

2=(1.12)n

log 2 = log 1.12n

log2= n log 1.12n= log2 log 1.12n= 0.301029 0.049218= 6 years

Exercise At 8% compounded annually, how many years will it take far birr 2,000 to grow to birr 3,000

F= p(l+i)n

3000=2000(1.08) n

3000 =1.08 n

20001.5 =1.08n

log 1.5 = log 1.08n

log 1.5=n log 1.08n= log1.5 log1.08n=0.17609 n=5.27 0.03342Example 4, IF Ato Gebru Tsehayneh deposited birr 11,000 in commercial Bank of Ethiopia at i, rate of interest compounded annually, on a 5 years time deposit, the deposit would be birr 14,720.48. Find the interest rate?

Fv = p (l+i) n

14720.48= 11,000(l+i)5

14720.48 = (l+i) 5

11,000


1.338225 =(l+i)5

(1.338225)1/5= (l+i) =1.05999= l+i i=1.05999-1 i=6%

Exercise Find the rate of interest that, compounded annually, will result in tripling a sum of money in 10 years.Solution i=11.61%Compound Discount: present Value

F= P (l+i) n

Dividing both sides of the future value formula by (l+i) n leads to F = P(l+i) n

By The definition of negative exponent,

Example 1 Suppose that an investor wants to find out the present value of birr 20,000 to be received after 5 years. Her interest rate is 12% compounded annually. Find the present value?

P= F (l+i) -n

= 20,000(1.12)-5 20,000(0.5674) Birr 11,348.54

Example 2 How much must be deposited now in an account paying 8% compounded monthly in order to have just enough in the account 5 years from now to make a birr 10,000 down payment on a home?

P= F (l+i)-n i=8/12= 0.00666 =10,000(1+8/12%)-60 n= 5x12= 60=10,000(0.671210)= 6,712.10Exercise 6 What sum of money deposited now at 8% compounded quarterly will provide just enough money to pay a birr 1,000 debit due 7 years from now?Solution =birr 574.37

Effective RateBecause of lack of comparability, it is hard to judge whether interest quoted at 8 percent compounded

semiannually results in more or less interest than would be the case if the rate was 7.9 percent compounded monthly. To make the comparison possible, we change both to their equivalent annual rates, there equivalents are called effective rate.

Example: Birr 1 at 8 % compounded quarterly for one year would amount to F= P(l+i) n

=1(1+8/4%) 4

= 1(1.02)4

=1.08243


P=F (l+i)-n

Which is the same as, the amount of birr 1 at a rate of 0.08243, or 8.243% for one year.F= 1(1.08243)1

= 1.08243Similarly, Birr at 7.9% compounded monthly for one year would amount to

F= P(l+i)n

=1(1+7.9%) 12

12=1.08192

Which is equivalent to the amount of birr 1 at a rate of 8.192 percent for one year.

Effective rate of i compounded m times a year

Example 1 find the effective rate of 24% compounded monthly.i = 24% = 2% 12m= 12 months in a year.re= (1+ 0.02)12-1 = 1.26824-1 = 0.26824 = 26.824%

Example 2 Find the effective rate of 15 percent compounded annually, semiannually, quarterly and weekly.Annually: 15%, re =15%Semiannually: re =15.563%Quarterly: re = 15.865%Weekly: re = 16.158%

Annuity Payments An Annuity is a series of fixed payment (or receipt) in which each payment is made at the end / beginning of the period. Annuity can be:i) Ordinary Annuity ii) Annuity Due

i) Ordinary Annuities: Future Value

An ordinary Annuity is a series of equal periodic payments in which each payment is made at the end of the period. Periods

0 1 2 3 n


re= (l+i)m – l, where i = J m

Where, J= nominal (annual rate)m= compounded times a year

re= effective rate

Fv=R [(1+i) n -1 ] Where n=Number of periods i i=Interest rate per period

p=Payment per period Fv= future value of the annuity

Example. Supposes Martha deposits birr 1000 at the end of each year for 3 years at 6 % rate of interest. How much would this annuity accumulate at the end of the third year?

Fu= R[(1+i)n-1] i

=1000[(1.06)3-1] 0.06

=1000(3.1836) Fv =birr 3183.60Example 2: If birr 100 is Deposited in an account at the end of every quarter for the next 5 years, how much will be in the account at the time of the final deposit if interest is 8 % compounded quarterly?

i=8%=2% 4

n=5x4=20Fv=100[(1.02) 20 -1 0.02

=100[24.2974 = 2429.74 Exercise: When Derartu was born, her parents decided to deposit birr 500 every 6 months at the end for 15 years in an account earning 6% compounded semiannually. How much will be in account after the last deposit is made?F=R[1+i)n-1] i=6%/2=3%

i n=15X2=30=500[(1.03)30-1] 0.03=birr 23787.71 Ordinary Annuities : Sinking fund A sinking fund is fund in to which periodic payments are made in order to accumulate a specified amount at point in the future.

F= R [l+i) n -1 ] iR= F [(1+i)n-1]

i

Example: How much should be deposited in a sinking fund at the end of each quarter for 5 years to accumulate birr 10,000 if the fund earns 8 % compounded quarterly?

N=5x4=20i= 8%/2=2%


R=F[ i ] (1+i)n-1

R=F[ i ] (1+i)n-1R=10,000 [ 0.02 ] (1.02)20-1=10,000(0.0411567) = birr 411.57

Ordinary Annuities: Present ValuePresent value annuity calculations arise when we wish to determine what lump sum must be deposited in an account now if this sum and the intersect it earns are to provide equal payments for a stated number of periods, with the last payment making the account balance zero.

Example 1What sum deposited now in an account earning 8% interest compounded quarterly will provide quarterly payments of birr 1000 for 10 years, the first payments to be made 3 months from now?

n=10x4=40i=8%=2% 4p=R[1-(1+i) - n]

i=1000[1-(1.02)-40]

0.02=1000(27.35548)=birr 27355.48

Example 2.a) The directors of a company have voted to establish a fund that will pay a retiring accountant, birr 1000 per month for the next 10 years , the first payment to be made a month from now. How much should be placed in the fund if it earns interest at 12% compounded monthly?b) How much interest will the fund earn during its existence?a) p=R[1-(1+i)-n] n=10x12=120 i i=12%/12=0.01 =1000[1-(1+0.01)-120

0.01 =69,700.52b) We have 120 payment X birr 1000=birr 120,000Interest earned= 120,000-69700.52

=50299.48Example. Ato Ayalkebet borrowed birr 5,000 to buy a television. He will amortize the 1000 by monthly payments of birr R each over a period of 3 years. The payment is made at the end of each month.

a) Find the monthly payment if interest is 12% compounded monthly.b) Find the total amount Ato Ayalkebet will pay. a) P=R[1-(1+i)-n] I=12%=1%

i 125,000=R[1-01)-36 n=3x12=36


P=R[1-(1+i)-n] i

0.01 5,000=R[30.107505]

R=5,000 30.107505 R= 166.07

b) Ato Ayailkebet pays birr 166.07 a month for 36 months. The total paid will be= 36x166.07 =5978.52 of which interest is 5978.52-5000=978.52

Exercise: A birr 70,000 car is to be purchased by paying birr 10,000 in cash and mortgage for 30 years at 12% compounded monthly. The payment is made at the end of each month.a) Find the monthly payment on the mortgageb) What will be the total amount of interest paid?

a) P=R[ 1-(1+i)-n] i=12%/12=1% i n=30x12=36060,000=R[1-1.01)-360]

0.01 R=617.17

b) The total amount paid in 360 months will he 360x617.17=222,181.20Interest paid will be 222,181.20-60,000

=162,181.20 ii. Annuity due: future valueAnnuity due is a series of equal periodic payments in which each payment is made at the beginning of the period.

_____________ Periods 0 1 2……..n

Example, suppose Daniel deposits birr 1000 at the beginning of each year for 3 years at 6% rate of interest How much would this annuity accumulate after the third year payment is made? Fv=R[1+i) n -1 ](1+i)

i =1000[(1.06) 3 -1](1.06) 0.06 =birr 3374.62Example 2. If birr 100 is deposited in an account at the beginning of every quarter for the next 5 years, how much will be in the account at the time of the final deposit if interest is 8% compounded quarterly?Solution

Fv=R[(1+i) n -1 ] (1+i) n=5x4=20 i i=8%/4=2%

=100[(1.02) 20 -1(1.02) 0.02

=birr 2478.33Annuity Due: present value

P=R[1-(1+i)-n](1+i)i


Fv=R[(1+i) n -1] (1+i) i

Example. What sum deposited now in an account earing 8% interest compounded quarterly will provide quarterly payments of birr 1000 for 10 years, the first payment to be made now? n=10x4=40 i=8%/4=2%

P=R[1-(1+i) - n](1+i)

i =1000[1-(1.02) - 40](1.02)

0.02=27,902.59

Example 2:On September 1,2002 Zerfie borrowed birr 5,000 to buy a house. She will amortize the loan by monthly payment of birr R starting from September 1,2001each over a period of 3 years. Find the monthly payment if interest is 12% compounded monthly?

i=12%=1% n=3X12=36 12

P=R[1-(1+i) - n](1+i) i

5000=R[1-(1.06) - 36](1.01)0.01

5000=R[30.40858]R=164.43

Present value of a mixed streamABC company has been offered an opportunity to receive the following mixed stream of cash flows over the next five years. Year Cash flows

1 Birr 4002 8003 5004 4005 300

If the firm earn 9 Percent on its investment, A) what is the future value for this opportunityB) what is the present value for this opportunityA) Future value

Year Cash flows 1. Birr 400x(1.09)1=

2 800x(1.09)2=3. 500x(1.09)3=4 400x(1.09)4=5 300x(1.09)5= Future value =

B) Present value Year Cash flows

1. Birr 400x(1.09)1=366.80 2 800x(1.09)2=673.60


3. 500x(1.09)3=386.004 400x(1.09)4=283.205 300x(1.09)5=195.00

Present value =1904.60Example 2, Assume that you can choose between receiving birr 3000 either as an ordinary three years, birr 1000 annuity or receiving birr 1500, birr 1000 and birr 500 at the end of years 1,2 and 3, respectively. Which alternative would you prefer assume the annual interest rate was 10 percent?Solution: To compare, you should compute the present value of each alternative and select the alternative which result in higher amount of present value?Alternative 1(Present value of ordinary annuity)PV=R[ 1-(1+i)- n ] i =1000[1-(1.1)-3 =2487 0.1 Alternative 2( Mixed stream)Year Cash flow PV1 1500 1500(1.1)-1=1363.52 1000 1000(1.1)-2=8263 500 500(1.1)-3=375.50 Present value =2565, therefore, the second alternative is better.A mixed stream with embedded annuityExample1 A cash flows in the following years and interest of 12 percent per annum. Year Cash flow Present value

1 100002 10000 10000[1-(1.12)-4 ] =303733 10000 0.124 100005 15000 15000(1.12)-5 =85116 16000 16000(1.12)-6 =81067 17000 17000(1.12)-7 =7690 Present value =54680

Example2, Year Cash flow Present value 1 5000 5000(1.12)-1=4464.29 2 6000 6000(1.12)-2=4783.16 3 8000 4 8000 8000[1-(1.12)-3] (1.12)-2=15317.80 5 8000 0.12 6 9000 9000(1.12)-6=4559.68 Present value 29125


Perpetuities: Perpetuity can be defined as an annuity that has an indefinitely long life. Any perpetuity can be discounted by dividing the value of one payment by the required rate of return. An important special case of an annuity arises when the level stream of cash flow continues forever. Perpetuities are also called Consol.Perpetuity present value X Rate = Cash flow Pv x r = CTherefore, given a cash flow and a rate of return, we can compute the present value very easily.

Example, An investment offers a perpetual cash flow of birr 500 every year. The return you require on such an investment is 8 percent, what is the value of this investment? The value of this perpetuity is:Pv = C/r = 500/0.08=6250

Loan AmortizationLoan amortization refers to the determination of equal periodic loan payments necessary to provide a lender with a specified interest return and repay the loan principal over a specified period.Loan amortization schedule is a schedule of equal payments to repay loan . It shows the allocation of each loan payment to interest and principal.Example,An individual borrow birr 6,000 at 10 percent and agree to make equal annual end of year payments over four years.Required: Prepare loan amortization schedule?]

Present value formula should apply to find the periodic loan payment.Pv=R[1-(1+i) - n]

i6000=R[1-(1.1) - 4]

0.1R= 6000 3.170R= 1892.74

Loan Amortization schedule1.End of year 2. Loan

payment Payments3. Interest Principal 4=2-3

End of YearPrincipal 5=5-4

0 - - - 6,0001 1,892.74 6,000x10% =600 1292.74 4,707.262 1,892.74 4,707.26 x10%=470.73 1422.01 3,285.25


Pv for a perpetuity = C r

3 1,892.74 3,285.25x 10%=328.53 1,564.21 1,721.044 1,892.74 1,721.04x10%=172.10 1720.64 0

Chapter FourRisk, Return and Financial Asset Portfolios

Return: if you buy an asset of any sort, your gain (or loss) from that investment is called the return on your investment. This return will usually have two components: income component and capital gain or capital loss on the investment.The rate of return can be calculated with the following formula:

Example, End of year Price of asset Dividend1 birr 21 02 19 13 18 14 21 1.055 24 1.056 26 1.10Required: calculate rate of return?Year Pt Pt-1 D Kt1 21 - 0 -2 19 21 1 19-21+1/21= -0.04763 18 19 1 18-19+1/19= 04 21 18 1.05 21-18+1.05/18= 0.2255 24 21 1.05 24-21+1.05/21= 0.19296 26 24 1.10 26-24+1.10/24 = 0.1292

Mean: The mean of rate of return is calculated as follows:

Example,


Kt= Pt – Pt-1 + D Pt-1

Where, kt, required rate of return Pt, Price of asset at time t Pt-1, Price of asset at time t-1

D, dividend paid

Mean=∑r n

The mean for the above example is 0.0476+0+0.225+0.1929+0.1292 5 =0.0999 =10%

Probabilities: Probabilities can be used to more precisely assess an asset’s risk. The probability of a given outcome is its chance of occurring.The expected value of a return: is the most likely return on a given asset

Standard Deviation: The most common statistical indicator of an asset’s risk is the standard deviation. It measures the dispersion around the expected value. The expression for the standard deviation of returns, حk, is given as:

Expected values of returns for assets A and B Example Asset APossible outcomes Probability (1) Return (%) (2) Weighted value (3) =(1)X(2)

Pessimistic 0.25 13 3.25

Most likely 0.50 15 7.50

Optimistic 0.25 17 4.25

Expected return = 15

Asset B

Possible outcomes Probability (1) Return (%) (2) Weighted value (3) =(1)X(2)

Pessimistic 0.25 7 1.75

Most likely 0.50 15 7.50

Optimistic 0.25 23 5.75


nk= ∑(Ki-K)2 X Priح

- nK=∑ ki X Pri i=1Where, Ki= return for the ith outcome Pri= probability of occurrence of the ith out come n= number of out comes considered K= the expected value of a return

Expected return 15

Standard deviation of the returns for Assets A and B

Example,

Asset A

i ki k ki-k (ki-k)2 Pri (Ki-k) 2 X Pri

1 13 15 -2 4 0.25 1

2 15 15 0 0 0.50 0

3 17 15 2 4 0.25 1

∑ (ki –k)2 X Pri = 2

Therefore, حkA= 2 =1.41%

Asset B

i ki k ki-k (ki-k)2 Pri (Ki-k)2 X Pri

1 7 15 -8 64 0.25 16

2 15 15 0 0 0.50 0

3 23 15 8 64 0.25 16

∑ (ki –k)2 X Pri = 32

Therefore, حkA= 32 =5.66%

In general, the higher the standard deviation, the greater the risk. The higher risk of asset B is clearly reflected

in its higher standard deviations.

Variance: shows how far the actual return deviates from the average in a typical year. It is the average squared difference between the actual return and the average return.

Coefficient of variation

It is a measure of relative dispersion used in comparing the risk of assets with differing expected returns.

Example, Coefficient of variation for asset A is 1.41/15=0.094


Cv= حk K Where, حk is standard deviation K is expected value of return.

Coefficient of variation for asset B is 5.66/15=0.377

Asset B has the higher coefficient of variation and is therefore more risky than asset A. The higher the

coefficient of variation is, the greater the risk.

Note: since both assets have the same expected return, the coefficient of variation has not provided any more

information than the standard deviations. The real utility of the coefficient of variation is in comparing assets

that have different expected returns.

Example,

Asset X Asset Y

Expected return 12% 20%

Standard deviation 9% 10%

Coefficient of variation 9/12=0.75 10/20=0.5

If the firm were to compare the assets only with standard deviations, it would prefer asset X, since asset X has

a lower standard deviation than asset Y. However, using coefficient of variations, risk is lower in asset Y than

asset X. Therefore, the use of the coefficient of variation to compare asset risk is effective because it also

considers the relative size, or expected return of the assets.

Covariance: statistical representation of the degree to which the returns on two assets move together over

time; calculated as the sum of the product of each asset’s deviation from its expected value over time divided

by the number of time periods. The covariance of asset A and B can be computed as follows:

Correlations

Correlation is a statistical measure of the relationship, if any, between series of numbers representing data of

any kind. If two series move in the same direction, they are positively correlated. If the series move in

opposite directions, they are negatively correlated. Correlation is a statistical representation of the degree to

which returns on two securities vary together over time, with a maximum value of +1 (perfect positive

correlation) and a minimum value of -1 (perfect negative correlation)

Correlation coefficient: a measure of the degree of correlation between two series.


AB= ∑ (rA-rA) (rB-rB)ح

n

Perfectly positively correlated: describes two positively correlated series that have a correlation

coefficient of +1

Perfectly negatively correlated: describes two negatively correlated series that have a correlation

coefficient of -1

Uncorrelated: describes two series that lack only relationship or interaction and therefore have a

correlation coefficient close to zero.

Example, For positively correlated

- cyclical business, i.e having high sales when the economy is expanding and low

sales during rescission

For negatively correlated

- Counter cyclical business: having low sales during economic expansion and high sales

during recession

Risk PreferenceThe three basic preference behaviors are

Risk averse: the attitude toward risk in which an increased return would be required for an increase in risk.

Risk indifferent: the attitude toward risk in which no change in return would be required for an increase in risk.

Risk seeking: the attitude toward risk in which a decreased return would be accepted for an increase in risk

Risk and time

The variability of the returns and the risk increases with the passage of time.

Risk of a portfolio

The risk of any single proposed asset investment should not be views independent of other assets. New

investments must be considered in light of their impact on the risk and return of the portfolio of assets. The

financial manager’s goal for the firm is to create efficient portfolio. Efficient portfolio is a portfolio that

maximizes return for a given level of risk or minimizes risk for a given level of return. The statistical concept

of correlation is useful in the process of diversification that is used to develop an efficient portfolio.


Coefficient correlation= Covariance

(Sd) (Sd)

A Portfolio is a collection of securities held by a single investor, whether an individual or institution. The

main incentive for forming portfolios is diversification, which is the allocation of investable funds to a variety

of sources.

A perfect market is a market without any impediments to trading, such as transaction costs or costly

information. The assumptions are:

1. Securities markets operate with no transaction costs

2. All investors have free access to the complete body of information about everything relevant to the pricing

of securities.

3. All investors appraise this information in a similar way; that is, they have homogeneous expectations

4. Investors are interested only in the risk and expected return characteristics of securities. They seek

securities with higher expected returns and try to avoid risk.

5. All investors in the marketplace have the same one period time horizon.

The concept of dominance

When an investor has investment opportunities in which this risk/return trade off is not confronted, one

investment opportunity “dominates” the other. In establishing a definition of dominance, one security

dominates another if it meets at least one of the following three conditions:

A. One security offers greater expected return, but the same risk, than another security

B. One security offers the same expected return, but lower risk, than another security

C. One security offers greater expected return, but lower risk, than another security

Portfolio return and standard deviation

The return on a portfolio is calculated as a weighted average of the returns on the individual assets.

Example,

A portfolio is to be constructed by investing birr 100,000 in three financial assets. The birr amounts

committed to each asset, the return value are as follows:

Asset Birr investment Return

A 20,000 9%

B 30,000 11%

C 50,000 14%

Total 100,000


Kp= (w1 X k1) + (w2 X k2) + ……+ (wn X kn) Where, Kp is portfolio return Wn= the proportion of the portfolio total value Kn = the return on asset

Required: Calculate the expected return for portfolio?

The proportion (W) of each asset can be obtained as follows: Asset A (w1)= 20000/100000=0.2 and similarly

you can calculate for asset B and C. The proportion for asset B and C is 0.3 and 0.5, respectively.

Kp= (w1 X k1) + (w2 X k2) + ……+ (wn X kn) = 0.2(9%)+0.3(11%)+0.5(14%) =12.1%Exercise:If security A has an expected return of 10% and security B has an expected return of 15%, how should you weight your holdings to get an expected return of 12%?SolutionThe sum of investment in security A and B must be 100%, therefore , we can write as A +B =1……………..Equation 1With the formula of expected return on portfolio 0.1A +0.15B =0.12…………..Equation 2Solve the two equations simultaneously; the proportion security A and B is 60% and 40 %Example,

Return

Year Asset A Asset B

1 14% 7%

2 9% 12%

3 12% 6%

4 4% 10%

5 11% 5%

Required: Compute

1. Variance and standard of asset A

2. Variance of asset B

3. Covariance of asset A and B

4. Coefficient of correlation between asset A and B

Solution:

Year rA rB ( rA-rA) (rB-rB) (rA-rA) (rB-rB) (rA-rA) 2 (rB-rB) 2

1 0.14 0.07 (0.14-0.1)=0.04 (0.07-0.08)=-0.01 -0.0004 0.0016 0.0001

2 0.09 0.12 (0.09-0.1)=-0.01 (0.12-0.08)=0.04 -0.0004 0.0001 0.0016

3 0.12 0.06 (0.12-0.1)=0.02 (0.06-0.08)=-0.02 -0.0004 0.0004 0.0004

4 0.04 0.10 (0.04-0.1)=-0.06 (0.10-0.08)=0.02 -0.0012 0.0036 0.0004

5 0.11 0.05 (0.11-0.1)=0.01 (0.05-0.08)=-0.03 -0.0003 0.0001 0.0009

∑ =-0.0027 0.0058 0.0034


1) The variance of asset A is 2) The variance of asset B is

=0.0058 =0.0012 0.0034 =0.0007

5 5

3) The covariance of asset A and B is حAB= ∑ (rA-rA) (rB-rB)

n

=-0.0027/5= -0.0005

A positive covariance indicates that the values of two variables tend to increase and decrease together. A

negative covariance indicates that the two variables tend to move in opposite directions.

4) The coefficient correlation of asset A and B are computed as follows:

Exercise

ABC corporation owns a portfolio which consists of two common stocks: stock M and stock E. The amount

invested in each stock is birr 120,000 and birr 280,000, respectively. The rates of returns on each stock in

three economic conditions are given below.

Economic condition Probability Return on stock M Return on stock E

Recession 0.2 7% 6%

Stagnant 0.5 9% 10%

Expanding 0.3 12% 15%

Required:1) calculate expected rate of return on stock M and E?

2) The portfolio returns of stocks M and E?


A2=(rA-rA) 2ح

n B2 = (rB-rB) 2ح

n

Coefficient correlation= Covariance

(Sd) (Sd)

CAB= ح AB

(Bح )(Aح )

= -0.0005

(0.0346)(0.0265)

= -0.54

Solution:

1) The expected return for stock M= 0.2(7%)+0.5(9%)+0.3(12%)

=9.5%

The expected return for stock E= 0.2(6%)+0.5(10%)+0.3(15%)

=10.7%

2) The portfolio returns of stock M and E

Stock Amount invested Proportion Return

M 120,000 0.3 9.5

E 280,000 0.7 10.7

Therefore, the portfolio return is 0.3(9.5%)+0.7(10.7%)

=10.34%

The formula for the variance of a two asset portfolio using the correlation coefficient is:

Example, you are trading in a market that has only two securities available. Security A has an expected return

of 8 % and a standard deviation of 40 %. Security B has an expected return of 20% and a standard deviation

of 120%.

1. If you place 40 % of your money in A and the remaining 60% in B, what is your expected return?

2. If the correlation between the returns of securities A and B is 0.8, what is the variance and the standard

deviation of the portfolio?

Solution

1. The expected return on any portfolio depends on the percentage invested in each stock and the expected

return of the stock:

Expected return= 0.4(8%)+0.6(20%) =15.2%

2. The problem provides almost all of the information necessary to solve the formula for the variance of a

portfolio of imperfectly correlated assets:


2ح P=Where wl and w2 are the proportion of the components of asst 1 and asset 21ح and 2ح are standard deviations of the components of asset 1 and 2 r1,2 is the correlation coefficient between the returns of component assets 1 and 2

You must remember that the variance of a security’s return is the square of the standard deviation so:

2ح A=(0.4)2=0.16 and 2ح B=(1.2)2=1.44

and the proportion wl =40% and w2=60%

Therefore, Variance of portfolio= (0.4)2(0.16)+(0.6)2(1.44)+2(0.4)(0.6)(0.4)(1.2)(0.8)

=0.0256+0.5184+0.1843=0.7283

Standard deviation= square root of variance

= (0.7283)1/2=0.853=85.3%

Diversification and risk reduction

Increasing the number of financial assets in a portfolio is referred to as diversification. The portion of a

portfolio’s risk that can be reduced or eliminated by diversification is called diversifiable risk.( unsystematic

risk). It is unique to a particular firm and/or the industry in which it operates. The goods and services provided

by the industry, action of competitors, the quality of the firm management, operating leverage, capital

structure, financial leverage, and marketing strategies are some of the factors that combine to produce

unsystematic risk.

The portion of a portfolio’s risk that can not be eliminated by diversification is called non- diversifiable risk

(Systematic risk). It represents portion of total portion risk caused by factors that affect the prices of all

securities. Example, national economic and political development, business cycle, inflation, unemployment,

fiscal and monetary policy.

A portfolio that contains a large number of securities exhibits only systematic risk. An investor’s expected

rate of return holding a portfolio of risky financial assets is thus based on the expected rate of return and the

systematic risk contained in the portfolio and not on the risk-return characteristics of individual assets.

The beta coefficient

It is the slope of the security characteristic line, which shows the volatility of a security’s returns relative to

that of the market portfolio. It is index of systematic risk. This index measures the amount of systematic risk

contained in individual securities and portfolio relative to financial markets. This index also is used to

determine the rate of return that an investor expects from individual securities and portfolios. Systematic risk

is often referred to as market risk. Beta coefficient can be obtained for actively traded stocks form published

sources such as value line investment survey. The beta coefficient for the market is considered to be equal to

1.0, all other betas are viewed in relation to this value. Asset betas make take on values that are either positive

or negative, but positive beta is the norm. One important point for beta is beta tend to change in particular

ways over time.


Beta and their interpretation

Asset’s Beta Interpretation

Positive Move in same direction as market

Zero Unaffected by market movement

Negative Move in opposite direction to market

Example, the following presents estimates of market returns and hypothetical security A.

Year Market risk (rm) Return of asset A (rA)

1 0.0830 0.115

2 0.2216 0.24

3 0.0089 0.0975

4 0.0306 -0.0652

5 0.1275 0.1123

6 0.2057 0.1879

7 0.13 0.1443

8 -0.007 0.1234

Required: compute

A. Variance of the market and asset A

B. Covariance of asset A and market

C. Beta coefficient

Solution:

Year (rm) (rA) (rA-rA) (rm-rm) (rm-rm)2 (rA-rA) (rm-rm)

1 0.0830 0.115 -0.0044 -0.0170 0.0003 0.0001

2 0.2216 0.24 0.1206 0.1216 0.0148 0.0147

3 0.0089 0.0975 -0.0219 -0.0911 0.0083 0.0020

4 0.0306 -0.0652 -0.1846 -0.0694 0.0048 0.0128

5 0.1275 0.1123 -0.0071 0.0275 0.0008 -0.0002

6 0.2057 0.1879 0.0685 0.1057 0.0112 0.0072

7 0.13 0.1443 0.0249 0.0300 0.0009 0.0007

8 -0.007 0.1234 0.0040 -0.1070 0.0114 -0.0004


Beta= Covariance of security with market Market variance BA= ح AM 2ح m

∑ 0.8003 0.9552 0.0525 0.0369

Mean (rA )= ∑rA = 0.9552 =0.1194

n 8

Mean (rm) = ∑rm = 0.8003 =0.10

n 8

Variance of market ( 2ح m)= ∑(rm-rm) 2 = 0.0525 = 0.0066

n 8

Covariance (حAm)= 0.0369 = 0.0046

8

Beta (BA) = ح AM =0.00462ح m 0.0066 =0.6970

Note: a beta of 1.0 means that a security contains the same degree of systematic risk as found in the market. In

actual practice, all corporate beta coefficients have a value that is greater than zero and less than 3.0

Portfolio Betas

The beta of a portfolio can be easily estimated by using the beta of the individual assets it includes. Let wi, the

proportion of the portfolio’s total birr value represented by assets and bi, the beta of asset i, the portfolio beta,

Bp using Bi and wi as defined as:

It states that the weighted average of the financial asset beta contained in portfolio.

Example, four financial assets are purchased with birr 50,000. The percentage composition of the portfolio

and its corresponding betas are:

Financial assets Birr investment Xi Bi

A 20,000 40% 1.3

B 15,000 30% 1.1

C 10,000 20% 1.0

D 5,000 10% 0.8

Required: 1) compute the portfolio beta (Bp)?

2) Suppose that asset A is sold for birr 30,000 and the proceeds are invested as asset E with a beta


Bp= ∑wi X Bi iWhere, wi is the proportion of security Bi is the beta value of each security

of 1.4, compute the new portfolio beta?

1. Portifolio beta(Bp)= = ∑wiBi = wa X b1+wb X b2+wc X b3 i = 0.4(1.3)+ 0.3(1.1) + 0.2(1.0) + 0.1(0.8) = 1.13

2. Financial assets Birr investment Xi Bi

B 15,000 25% 1.1

C 10,000 17% 1.0

D 5,000 8% 0.8

E 30,000 50% 1.4

Total 60,000 100%

Bp= 0.25(1.1)+0.17(1.0)+0.08(0.8)+0.5(1.4)

=1.21

Risk and Return: The Capital Asset Pricing Model (CAPM)

The most important aspect of risk is the overall risk of the firm as viewed by investors in the market place.

Overall risk significantly affects investment opportunities and the owner’s wealth. The basic theory that links

together risk and return for all assets is called the William Sharp’s Capital Asset Pricing Model (CAPM)

Types of risk

1. Diversifiable risk (unsystematic risk): is the portion of an asset’s risk that is attributable to firm specific,

random causes, can be minimized through diversification. It is unique risk or asset specific risk.

Example, A firm specific event such as strikes, lawsuits, regulatory action and loss of a key account.

3. Non diversifiable risk (systematic risk): is the relevant portion of an asset’s risk attributable to market

factors that affect all firms, can not be eliminated through diversification. It is also said to be market risk.

Example, war, inflation, international incidents and political events.

4. Total risk: is the combination of a security’s non diversifiable and diversifiable risk.

Total security risk= Non diversifiable + Diversifiable risk

Diversifiable risk


Risk

Non diversifiable risk Total risk

No of securities (Assets) in portfolio.

Any investor can create a portfolio of assets that will eliminate all diversifiable risk, the only relevant risk is

non diversifiable risk. Therefore, any investor must concern only with non diversifiable risk.

The required return on an asset, Ki, is an increasing function of beta, bi, which measures non diversifiable risk. In other words, the higher the risk, the higher the required return, and the lower the risk, the lower the required return. The model can divide in to two parts:

1) the risk fee rate, RF and2) the risk premium, bi(km-Rf)

The (km-Rf) portion of the risk premium is called the market risk premium, since it represents the premium the investor must receive for taking the average amount of risk associated with holding the market portfolio of assets.Example, ABC corporation wishes to determine the required return of an asset Z that has a beta bZ if 1.5. The risk free rate of return is 7 %, the return on the market portfolio of assets is 11%.Required: Determine1. Required return of asset Z2. The market risk premium3. The risk premiumSolutionKz = Rf + [bi (km- Rf)] 7+[1.5 (11- 7)] 7+6 13Market risk premium= km-Rf = 11- 7 =4%Risk premium= bi (km- Rf) =1.5(11-7) =6%

The security Market line (SML)When the capital asset pricing model (CAPM) is depicted graphically, it is called the security market line (SML). The SML reflects for each level of non diversifiable risk (beta) the required return in the market place.


William Sharp CAPM ModelKi = Rf + [bi (km- Rf)] Where, Ki is required return of asset i Rf is risk free rate of return Bi is beta coefficient Km is market return; the return on the market portfolio of assets.

SML 13 …………………………. 11 …………………Return 7 ……Market risk…………Risk Premium…… premium 0 1 1.5 2 Beta(risk)


Chapter FiveValuation of Financial Assets

Valuation concept is the process that links risk and return to determine the worth of an asset.Bond ValuationWhen a corporation or government wishes to borrow money from the public on a long term basis, it usually does so by issuing or selling debt securities that is generally called bonds. A bond is normally an interest only loan, meaning that the borrower will pay the interest every period, but none of the principal will be repaid until the end of the loan.TerminologiesCoupon: is the stated interest payments made on a bondFace value: is the principal amount of a bond that is repaid at the end of the term. It is also called par value.Coupon rate: is the annual coupon divided by the face value of a bond.Maturity: is specified date at which the principal amount of a bond is paidExample,ABC corporation borrow birr 1000 for 10 years at interest of 8 percent. The corporation will pay 0.08x1000 =80 birr interest for 10 years. The birr 80 regular interest payments that the corporation promises to make are called the bond’s Coupon. The par value is the amount repaid at the end and in this example it is birr1000. The annual coupon divided by the face value is the coupon rate and it is 80/1000=8%.Example,Suppose that an investor purchases a four year debt instrument with the following payments promised by the borrower.Year Interest payment Principal payment Cash flow1 birr 120 0 1202 120 0 1203 140 0 1404 150 1000 1,150Assume that the one year rates for the next four years are: r1=7%, r2=8%, r3=9%, r4=10%,Required: Determine the current value or price of this debt instrument today?Solution:

Po= 100 + 120 + 140 + 1,150 . (1.07) (1.07)(1.08) (1.07)(1.08) (1.09) (1.07)(1.08) (1.09) (1.10) =1,138.43


Po= a1 + a2 + a3 +…. An . (1+r1) (1+r1)(1+r2) (1+r1)(1+r2) (1+r3) (1+r1)(1+r2) (1+r3)…..(1+rn)

ExerciseA birr 1000 face, 8% annual payment coupon bond with three years to maturity has a yield of 12%.Required:

1) What is its price?2) If the yield on the bond changes to 10% , which way do you expect its price to move? Why?Solution:1. The price is the present value of the three years worth of coupon payments plus the present value of the face amount in three years discounted at 12%.

Po= a1 + a2 + a3 +…. An . (1+r1)1 (1+r1)2 (1+r3)3 (1+rn)n

po= 80 + 80 + 80 + 1000 (1.12)1 (1.12)2 (1.12)3 (1.12)3 =903.92 Or

P= 80 [1-(1.12) -3 ] +1000(1.12)-3

0.12=903.922. Price with a 10% yield

Po= 80 + 80 + 80 + 1000 (1.1)1 (1.1)2 (1.1)3 (1.1)3

=72.73+66.12+60.11+751.31 =950.27

The prices of coupon bonds with fixed payments are inversely related to their yields. As one discounts (divides) the fixed payments by a smaller yield, a larger price results. Notice that the present value of each coupon payment has risen as the discount factor has fallen. A coupon bond’s nominal yield could fall because the real rate of interest has fallen or, more likely, because the market’s opinion of expected inflation has fallen. Changes in bond prices are directly related to time to maturity and inversely related to bond yield.ExerciseA birr 1000 face value, 10% coupon bond with semi annual payments and two years to maturity has a yield to maturity of 8%.Required:

a) Compute its price.


Po= a1 + a2 + a3 +…. An . (1+r1)1 (1+r1)2 (1+r3)3 (1+rn)n

Price of a Bond can be computed using annuity formula asPo= R [1-(1+i) -n ] +F(1+i)-n

i Where, R is coupon paid each period i is rate per period n is number of periods F is bond’s face value

Solution,The price is the present value of the actual payments. With semi annual payments, the investor will receive an annual payment of 0.1(1000)=100 as two payments of 100/2=50 birr every six months. The annual yield of 8% must also be converted to a semi annual basis for a semi annual yield of (0.08/2)=0.04 Po= 50 + 50 + 50 + 1050 (1.04)1 (1.04)2 (1.04)3 (1.04)4

=48.04+46.23+44.45+897.54 =1,036.26

Exercise,You are trying to decide between purchasing birr 1000 face value bonds with 10% annual coupons and one year or two years to maturity. The expected real rate of interest is 3% and the expected inflation rate is 6%.Required:1. Compute the nominal yield for the one year bond2. What is its price?3. Compute the nominal yield for the two year bond4. What is its price?Solution,1. The nominal interest rate is determined by the expected real rate and the expected inflation rate:(1+R)= (1+r)(1+h)(1+R)=(1.03)(1.06)R=9.18%

2. The price of the one year bond is just the present value of the terminal payments, 0.1(1000)=100 in interest, plus the face value: P= 1100 =1,007.51 (1.0918)1

3. The two year nominal rate is determined by compounding the annual relationships:(1+R)2= (1+r)2(1+h)2

(1+R)2=(1.03)2(1.06)2

(1+R)= (1.192)1/2=9.18%Notice that this is identical to the nominal one year yield since the same interest rates are expected to hold ove the two year interval.4. The price of the two year bond is the present value of the two payments discounted at 9.18%P= 100 + 1100 (1.0918)1 (1.0918)2

=91.59+922.80=1014.39

Common stock ValuationA share of common stock is more difficult to value in practice than a bond for the following reasons:

The promised cash flow are not known in advance The life of the investment is essentially forever since common stock has no maturity. There is no way to easily observe the rate of return that the market requires.


However, there are cases under which we can come up with the present value of the future cash flows for a share of stock and thus determine its value.

A corporation doesn’t make a definite or explicit commitment to pay dividends to common stock holder. However, when common stockholders invest their funds in a corporation, they also expect returns in the form of dividends. Common stockholders assume the highest degree of financial risk because they have residual rights on dividends and up on liquidations. Because of these, common stockholders expect a higher return and that is why cost of common stock is the most expensive.On common stock, dividends:

- are never granted- are not legally required, and- are not fixed as in the case of preferred stock

Therefore, common stock dividends can increase, decrease, or remain constant.Common stock cash flowsCommon stockholders expect to be awarded through the receipt of periodic cash dividends and an increasing or at least non declining share value. Like current owners, prospective owners and security analysts frequently estimate the firm’s value. They choose to purchase the stock when they believe that it is undervalued ( i.e that its true value is greater than its market price) and to sell it when they feel that it is overvalued ( i.e that its market price is greater than its true value)

Common stock valuation modelLike bonds, the value of a share of common stock is equal to the present value of all future benefits it is expected to provide. Simply, the value of a share of common stock is equal to the present value of all future dividends it is expected to provide over an infinite time horizon. Although by selling stock at a price above that originally paid, a stockholder can earn capital gain in addition to dividends, what is really sold is the right to all future dividends. Therefore, from a valuation viewpoint, only dividends are relevant. The basic valuation model is given as follows:

The equation can be simplified somewhat by redefining each yea’s dividend, Dt, in terms of anticipated growth. The growth can be seen into three cases:1. Zero growthThe simplest approach to dividend valuation, the zero growth model, assumes a constant, non growing dividend stream. D1=D2=D3=…=Doo


Po = D1 + D2 + . . . .+ Doo (1+ks)1 (1+ks)2 (1+ks)oo

where, po= value of common stock Dt= per share dividend expected at the end of year t Ks= required return on common stock

Po= D1 Ks

The equation shows that with zero growth the value of a share of stock would equal the present value of perpetuity of D1 birrs discounted at a rate KsExample,The dividend of ABC company is expected to remain constant at birr 3 per share indefinitely. If the required return on its stock is 15 percent.Required: Determine the value of the stock? Po= D1/ks= 3/0.15=birr 20Since preferred stock typically provides its holders with a fixed annual dividend over its assumed infinite life. This equation can be used to find the value of preferred stock.2. Constant growthThe most widely cited dividend valuation approach, the constant growth model,assumes that dividends will grow at a constant rate, g, that is less than the required return, ks (g<ks). Letting Do represent the current dividend the equation can be rewritten as follows:Po= Do(1+g) 1 + Do(1+g) 2 + …+ Do(1+g) oo (1+ks)1 (1+ks)2 (1+ks)oo

If we simplify the equation it can be rewritten as follows:

The constant growth model is commonly called the Gordon Model.Example,A firm’s earnings for the next period are expected to be birr 2.50 per share. The firm follows a constant payout policy, retaining 60% of all earnings for future investment. This reinvestment should generate a 6% rate of growth in earnings. If the cost of capital for this firm is 11%, what share price should prevail?SolutionFirst we must find the dividend for the next period. With a constant payout policy of paying 40% of earnings and projected earnings of birr 2.50, the dividend for the next period is:D1=0.4(2.50)=1.0Using constant growth model,Po = D1 Ks-g = 1 =20 birr (0.11-0.06)The cost of common stock is calculated as follows:

Example,ABC company issued common stock to investors for birr 20 per share and incurs a selling expense of birr 1 per share. The current dividend is birr 1.50 per share and is expected to grow at a 6% annual rateRequired: Compute the specific cost of this common stock?Solution:Po= birr 20 per shareF= birr 1 per shareDo= birr 1.50 per shareg = 6%Nps= Po-f=20-1=19


Po = D1 Ks-g

Ks= D1 + g NpsWhere, Nps is net proceeds of the new common stock ( Nps=Po-f) Po is current market price of the common stock F is flotation cost

D1=1.5(1.06)=1.59Ks= D1 +g = 1.59 +0.06 Nps 19 =0.0837+0.06=14.37%Example,Dividend per share on a firm’s common stock is expected to be birr 1 in next year and is expected to grow at 6% per year perpetually. Assuming the market price per share is birr 25 and no flotation costs, compute the cost of common stock to the firm.Solution:D1=1G= 0.06 Nps=Po=25, because no flotation costs.Ks= D1 + g Nps =1 +0.06 =0.04+0.06 =10% 2ExerciseRefer the above example and compute the expected market value per share assuming the current dividend per share is birr 1 (D0=1)

A. at the end of year 1B. at the end of year 3C. at the end of year 7

Solution,Po= Dt Ks-g

A) Po at the end of year 1Po= Dl = Do(1+g) 1 = 1(1.06) 1 =26.50 birr Ks-g ks-g 0.10-0.06B) Po at the end of year 3Po= D3 = Do(1+g) 3 = 1(1.06) 3 =29.79 birr Ks-g ks-g 0.10-0.06

C) Po at the end of year 7Po= D7 = Do(1+g) 7 = 1(1.06) 7 =37.40 birr Ks-g ks-g 0.10-0.06

3. Variable growth (Multiple growth case)Many firms grow at a rapid rate for a number of years and then now down to an “average” growth rate. Other companies pay no dividends for a period of years, often during their early growth period. The constant growth model is unable to deal with these situations therefore; the multiple growth model is needed.Multiple growth is defined as a situation in which the expected future growth in dividends must be described using two or more growth rates. Although any number of growth rates is possible, most stocks can be described using two or possibly three.A well known multiple growth rates model is the two stage growth rate model. This model assumes near term growth at a rapid rate for some period (typically, 2 to 10 years) followed by a steady long term growth rate that is sustainable ( i.e a constant growth rate). This can be described in equation form as


Conceptually, the valuation process is summing up the present values.Po= Discounted value of all dividends through the unusual growth period n + the discounted value of the constant growth model which covers the period n+1 to ooExample,ABC Corporation has been undergoing rapid growth for the last few years. The current dividend of birr 2 per share is expected to continue to grow at the rapid rate of 20 percent a year for the next three years. After that time ABC is expected to slow down, with the dividend growing at a more normal rate of 7 percent a year for the indefinite future. Because of the risk involved in such rapid growth, the required rate of return on this stock is 22 percent. Required: calculate the implied price for ABC company stocks?Solution:To solve for the value of this stock, it is necessary to identify the entire stream of future dividends from year 1 to infinity, and discount the entire stream back to time period zero. After the third year a constant growth model can be used which accounts for all dividends from the beginning of year 4 to infinity.We first calculate the dividends for each individual year of the abnormal growth period. And we discount each of these dividends at the required rate of return. Present valueD1=2(1.2)1=2.40 x(1.22)-1=1.97D2=2(1.2)2=2.88 x(1.22)-2=1.94D3=2(1.2)3=3.46 x(1.22)-3=1.91Present value of the first three years of dividends=5.82P3=3.46(1.07) =24.68 x(1.22)-3=13.60 0.22-0.07Present value of the stock at time period zero 19.42

Preferred stock valuationThe cost of preferred stock is the minimum rate of return required by preferred stockholders to purchase a firm’s preferred stock. When a corporation sells preferred stock, it expects to pay dividend to investors in return for their money capital. Dividend payments on preferred stock are made after interest payment on debt and before dividend payment on common stock. Thus, both the risky ness of preferred stock to investor and the resulting cost of issuing preferred stock fall some where between debt and common stock. It is hybrid security, sharing features of both bonds and common stock.


Po = n Do(1+g1)t + Dn(1+gc) 1 ∑ (1+k)t k-g (1+k)n

t=1 Where, Po= the estimated value of the stock today Do= the current dividend g1= the supernormal ( or subnormal) growth rate for dividends gc= the constant growth rate for dividends k= required rate of return n= the number of periods of supernormal (or subnormal) growth Dn= the dividend at the end of the abnormal growth period

Chapter six

Long term Investment Decisions (Capital budgeting decisions)The capital budgeting decision processThe capital budgeting process involves generating long term investment proposals; reviewing, analyzing, and selecting them; and implementing and following up on those selected. Why do financial managers give these long term investment decision so much attention? Because long term investment represent sizable outlays of funds that commit a firm to some course of action, procedures are needed to analyze and select applying appropriate decision techniques. Attention must be given to measuring relevant cash flows and applying appropriate decision techniques.

Capital budgeting: is the process of evaluating and selecting long term investments that are consistent with the firm’s goal of owner wealth maximization. Capital budgeting and financing decisions are treated separately. Once a proposed investment has been determined to be acceptable, the financial manager then chooses the best financing method.Capital expenditure motives A capital expenditure is a plan for an outlay of funds by an enterprise that is expected to provide benefit over a period more than one year, such as purchase of fixed assets. A current expenditure is an outlay resulting in benefits received within one year. Fixed asset outlays are capital expenditures, but not all capital expenditures are classified as fixed assets. Example. A 100,000 birr outlay for advertising that produces benefit over a long period is a capital expenditure. How ever, it is not a fixed asset.The basic motives for capital expenditure are to expand, replace, or renew fixed assets or to obtain some other less tangible benefit over a long period.

- These expenditures have long- term effects and, once made, are not easily reversed.- Sound capital investment decisions can lead to higher earnings and stock prices, which help the firm to

achieve its goal of maximizing share holder wealth. Capital budgeting is a dynamic process because the firm’s changing environment may affect the desirability of current or proposed investments.

The capital budgeting process involves five major steps:1. Generating project proposalsProposals for capital expenditures are made by people at all levels with in the organization.Investment proposals may be classified in to four distinct types

a) Expansion projects:- to increase existing capacity or to make new products or enter new markets.

b) Replacement projects:- replacing worn out or obsolete facilities or equipments with new ones. c) Renewal:- to upgrade or improve existing fixed assets such as rebuilding an existing machine.d) Safety or environmental projects:- It is mandatory or non-revenue producing projects to

maintain good working condition required by government, labor unions, or insurance companies such as expenditure on pollution control devices and ventilator.

2). Review and AnalysisThe proposals are reviewed:

To assess their appropriateness in light of the firm’s overall objectives and plans and, more important,


To evaluate their economic validity. The proposed costs and benefits are estimated and then converted into a series of relevant cash flows to which various capital budgeting techniques are applied to measure the investment merit of the potential outlay. Evaluating project proposals using

a) Unsophisticated or traditional techniques eg. PBP, ARRb) Sophisticated or time adjusted or discounted cash flow techniques eg. NPV, IRR

Estimating cash flowsNet cash flow = cash inflows – cash out flows. Non-cash expenses are added to net income.Selecting projects which depends on:

Project types:-Independent projects-Mutually exclusive projects

Availability of funds Decision Criteria: - ranking projects according to a prescribed rate or minimum acceptable rate of

return.

3) Decision making.The actual birr outlay and the importance of a capital expenditure determine the organizational level at which the expenditure decisions is made.4). ImplementationOnce a proposal has been approved and funding has been made available, the implementation phase begins. Implementing and reviewing projects

Implementation stage- involves developing formal procedures for authorizing the expenditure of funds for capital projects

5). Follow up Involves monitoring the results during the operating phase of a project. The comparisons of actual outcomes in terms of costs and benefits with those expected and those of previous projects are vital. When actual outcomes deviate from projected out comes, action may be required to cut costs, improve benefits, or possibly terminate the project.

Basic terminologiesSome of the basic terminologies areIndependent versus mutually exclusive projectsThe two most common project type are: 1) Independent projects and2) Mutually exclusive projects.Independent projects are projects whose cash flows are unrelated or independent of one another, the acceptance of one does not eliminate the others from further consideration. If a firm has unlimited funds to invest, all the independent projects that meet its minimum investment criteria can be implemented.Mutually exclusive projects are projects that have the same function and therefore compete with one another. The acceptance of one of a group of mutually exclusive projects eliminates all other projects in the group from further consideration.Capital rationing means that there is only limited birr available for capital expenditure and that numerous projects will compete for these limited birrs. The firm must therefore ration its funds by allocating them to projects that will maximize share value.Conventional versus non conventional cash flow


Conventional cash flow patterns consist of an initial outflow followed by a series of inflows. For example, a firm may spend 100,000 birr today and expect to receive cash inflow of birr 3000 each year for the next 40 years. A non conventional cash flow is any pattern in which an initial outflow is not followed by a series of inflow. For example, the purchase of a machine may require an initial cash outflow of birr 20, 000 and may generate cash inflows of birr 4000 each year for 5 years and in the sixth year an outflow of 6000 may be required to overhaul the machine , after which it generates inflow of 4000 each year for five years.

Cash flow principles Estimating cash flaws is the most difficult task. The difficulty in estimating cash flows arises because of uncertainty and accounting ambiguities. Mostly accounting data form the basis for estimating cash flows. If care is not taken in adjusting the accounting data errors could be made in estimating cash flows.Cash flow is a simple and objectively defined concept. It is simply the difference between birr received and birr paid out. Cash flow should not be confused with profits. Changes in profits do not necessarily mean changes in cash flaws. It is not uncommon in practice that firms experience cash shortages in spite of increasing profits. Cash flow is not the same thing as profit, for two reasons: first, profit, as measured by an accountant, is based on accrual concept- revenue is recognized when it is earned, rather than when cash is received, and expense is recognized when it is incurred rather than when cash is paid. In other words, profit includes cash revenues as well as receivables and excludes cash expenses as well as payables. Second, for computing profit, only revenue expenditures are entirely charged to profits while capital expenditures are capitalized as assets and depreciated over their economic life. Only annual depreciation is charged to profit. Depreciation is an accounting entry and does not involve any cash flow. Thus, the measurement of profit excludes some cash flaws such as capital expenditures and includes some non-cash items such as depreciation. Cash flow ignores depreciation since it is a non cash item

Types of Cash Flows The relevant cash flows used to make capital budgeting decisions include the initial investment, operating cash inflows, and a terminal cash flow.A typical investment will have three components of cash flows

1) Initial investment2) Incremental cash flow (operating cash inflows)3) Terminal cash flow.

All projects whether for expansion, replacement, renewal or some other purpose have the first two components. Some, however, lack the terminal cash flow.1) Initial investment Initial investment is the net cash outlay in the period in which an asset is purchased. It refers to the relevant cash out flows at time zero to be considered when evaluating a prospective capital expenditure. It includes:-

Installed cost of the new assets which comprises purchasing price (including accessories & spare parts) insurance, transportation & installation costs.

After tax proceeds from sale of old assets .(In case of replacement decisions ) Change in net working capital. (when an asset is purchased for expanding revenues)


Initial investment= Installed cost – after tax proceeds ± Change in Net working capital

Installed cost= cost of new asset+ installation costsAfter tax proceeds = proceeds from the sale of old asset ± Tax on sale of old asset.Change in working capital= Current asset- current liability

ExampleABC Company is considering the purchase of a new grading machine to replace the existing one. The existing machine was purchased three years ago at installed cost of birr 50,000; it was being depreciated by the straight line method using an economic life of 5 years and scrap value of birr 3,000. The new machine costs Birr 60,000 and requires birr 5,000 in installation costs is expected to have a useful life of 6 years and scrap value of birr 2,000. And with this new machine the firms current asset and current liabilities will rise by birr 6500 and birr 4000, respectively. The old machinery could be sold at birr 25,000. The firm is under 40% tax bracket. Determine initial investment?

Solution Initial investment = Installed cost- after tax proceeds + Net working capital.

Old machineCost =50,000Scrap value = 3,000ELF= 5 years Depreciation = 50,000-3000

5 = 9400

Accumulated depreciation = 9400x 3 28,200

Book value= 50,000 -28,200=21,800

Sale 25,000Book value 21,800Gain 3200Tax (40%) 1280After tax gain 1920

After tax proceeds = Book valve + after tax gain = 21800 + 1920= 23,720

or Net working capital = current Asset- current liability.

= 6500- 4000=2500

Initial investment =60,000+5000 – 23,720+2500 = 43,780 birr


After tax proceeds form sale of existing plant Assets.Case i) Selling price greater than original cost

Capital gain=proceeds- original costAssume selling price 100,000Original cost 80,000Capital gain 20,000

Note: tax rate for capital gain and ordinary gain may be different.

Case ii) Selling price is less than original cost but greater than book value Gain = proceeds- Book valueAfter tax proceeds from sales of P/A = BV+ After tax gain

Case iii) selling price equal to Book valueAfter tax proceeds= Book value (or proceeds), since no gain or no loss.

Case iv) selling price less than Book valueAfter tax proceeds= proceeds + tax shieldAssume, Book value= 40,000

Selling price = 30,000Tax = 40%

Loss= 30,000-40,000(10,000)

Tax shield = 40 % x 10,000 =4,000

After tax proceeds= 30,000 +4,000=34,000

Note: if the net proceeds from the sale are expected to exceed the book value, a tax payment shown as an outflow (deduction from sale proceeds) would occur. When the net proceeds from the sale are below book value, a tax rebate shown as a cash inflow (addition to sale proceeds) would result.

2. Incremental Cash flow The incremental cash flows represent the additional cash flows-outflows or inflows that are expected to result from a proposed capital expenditure. Given estimates of the revenue, expenses, and depreciation associated with both the old and new asset, it is possible to estimate the operating cash flows for a replacement decision.

Accounting Income Vs cash flowDepreciation expense is considered when we determine the net income but it is not out lay of cash on the business organization.

Sunk cost:- out lay of a firm that have already been committed and hence, is not affected by the accept / reject decisions under consideration. Sunk costs are not incremental costs & should not be included in the analysis.

Method 1 To compute incremental (relevant) cash flow :1) Compute after tax cash flows of each proposal by adding back non- cash charges.


=NI after tax + Depreciation exp.

2) Deduct the cash inflows after tax result from the old asset from the cash inflow generated by the new asset.Or

Method 2

Example 1A new plant Asset:Original cost = 80,000 with a useful life of 10 years Annual revenue = 60,000Annual operating cost = 25,000An old plant Asset:-Annual Depreciation expense = 7,000Annual revenue = 50,000Annual operating cost & expense = 30,000Tax= 40%Required: Determine incremental cash flow?Method 1

New P/A Old P/ARevenue 60,000 Revenue 50,000Cost 25,000 Cost 30,000Depreciation exp 8,000 33,00 Depreciation 7,000 37,000EBT 27,000 EBT 13,000Income tax (40%) 10,800 Tax (40%) 5,200Net Income 16,200 Net income 7,800Add: Depreciation exp 8,000 Add: Depreciation exp 7,000Cash inflow from new Asset=24,200 Cash inflow from old Asset 14,800

Incremental cash flow =24,200-14,800

= 9,400Method 2Incremental = (Increase in Revenue – increase in cash charge) (1-Tax) + (increase in deprecation exp) (Tax)Cash flow = [(60,000- 50,000) - (25,000-30,000)] (1-40%) + (8000-7000) (40%)

= [(10,000) - (-5000)] (60%) + (1,000) (40%)= (15,000) (60%) + (1000) (40%)= 9,000 +400= 9,4003) Terminal cash Flows

It is the after tax nonoperating cash flow occurring in the final year of the cash flow resulting from termination and liquidation of a project at the end of its economic life.Cash flows associated with a project’s termination generally include the disposal value of the project plus or minus any taxable gains or losses associated with its sale. In most case, the disposal value at the end of the projects useful life results in a taxable gain since its book value is usually zero. The terminal cash flow must include the recapture of working capital investments required in the initial out lay.


Incremental cash flow = (Increase in Revenue – Increase in cash charge) (1-Tax) + (increase in depreciation expense) (Tax rate)

After tax proceeds from sale of new asset= proceeds from sale of new asset ± tax on sale of new assetAfter tax proceeds from sale of old asset= proceeds from sale of old asset ± tax on sale of old asset

Example 1A company expects to be able to liquidate a new office equipment at the end of its useful life at birr 60,000. The office equipment will have a book value of birr 25,000.The old machine can be liquidated at the end of the year to net zero because it will completely obsolete. The firm expects to recover its birr 15,000 net working capital investment up on termination of the project. Assume a tax rate is 40%. Required: Determine terminal cash flow?Solution After tax proceeds from sale of new Equipment Birr 60,000

Less: Book value 25,000Taxable income (gain) 35,000

Tax (40%) 14000 After tax proceeds from new equipment 46,000

Less: After tax proceeds from sale of old Equipment 0Add: Recovery net working capital 15,000

Terminal cash flow 61,000

Capital budgeting techniquesCapital budgeting techniques are used by firms to select projects that will enhance owner wealth.It can be: A) Traditional methods 1) Pay back periods (Non-discounted methods) 2) Accounting rate of return B) Discounted methods 3) net present value

4) Internal rote of return.A) Traditional method( non-discounted method)1) Pay back period (PBP)i) Even cash in flow (annuity)-is to measure the expected number of years to recover the original investment. If the project generates constant annual cash in flows, the PBP is computed by dividing the initial investment by the cash inflow through increased revenue or cost saving.

: Example 1: Assume that initial investment of a project is 120,000 birr and yields after tax cash inflow of 25,000 for 10 years and the maximum pay back period set by firm’s managements is 5 years. The pay back period of the project is

PBP= 120,000


Terminal cash flow= after tax proceeds from sale of new asset – After tax proceeds from sale of old asset ± Change in net working capital

PBP= Initial Investment Annual cash inflow

25,000=4.8 Years

Accept Reject RuleAccept the project if the actual or computed pay back period is less than the maximum payback period

set by the firm otherwise the project is rejected. In ranking two projects having the same maximum allowable payback, the project with shorter pay back period should be chosen because it pays for itself more quickly.Therefore, accept the project because the payback period (4.8 years) is less than the Maximum allowable payback period (5 years).

ii) Uneven cash in flow (mixed stream)In case of unequal cash inflows, the payback period can be found out by adding up the cash inflows until the total is equal to the initial investment.

Example 2Compute the pay back period for the following cash flows, assuming a net investment of birr 25,000 and target payback period of 3 years?Year Net investment Cash in flows0 25000 01 100002 70003 60004 20005 2000Solutions Year Net cash inflows Commutative net cash inflows1 10,000 10,0002 7,000 17,0003 6,000 23,0004 2,000 25,0005 2,000 27,000 Payback period= 4 yearsReject the project as the computed payback period of 4 years is greater than the target payback period of 3 years.Example 3Melat pvt ltd.co is evaluating two projects with the following cash inflows.Year Cash inflows

Project A Project B0 (56,000) (56,000)1 14,000 22,0002 16,000 20,0003 18,000 20,0004 20,000 14,0005 25,000 17,000Requited: - Compute the PBP for each project and, show which one is more desirable?Solution

Cumulative net cash inflows


Year Project A Project B1 14,000 22,0002 30,000 42,0003 48,000 62,0004 68,000 76,0005 93,000 93,000PBP for project A=3 years +56,000-48,000

68,000-48,000 = 3Years +8,000

20,000 = 3Years +0.4

= 3.4 YearsPBP for project B= 2 Years + 56,000-42,000 62000-42000

= 2 Years +14,000 20,000

= 2 Years + 0.7 Years= 2.7 Years

Melat should prefer project B over project X because it has a shorter payback period of 2.7 Years Advantage of payback period

1) It is easy to understand and easy to calculate.2) It costs less than most of the sophisticated techniques which requires a lot of the analyses time & the

use of computers.3) It provides a crude measure of risk because it considers projects with shorter payback period as less

risky. 4) It measures the time required for a project to recover the initial investment & there fore, it provides a

measure of liquidity.Disadvantage 1) It doesn’t measure the profitability of investment because it ignores cash inflows earned after the

payback period.For example, consider the following project X&Y

Project x Project yInitial Investment 15,000 15,000Cash InflowsYear 1 5,000 4,000

2 6,000 5,000 3 4,000 6,000

4 0 8,000 Ignored 5 0 9,000 “

6 0 3,000 “PBP: project X=3 years

Project Y=3 years As per the payback rule both the projects are equally desirable since both return the initial investment in 3 years. However, from profitability point of View, project Y is more attractive than project X.

2. It ignores the time value of money for it fails to consider the magnitude and timing of cash inflows. Project x Project y


Project cost 15,000 15,000Cash inflow year

1 10,000 1,0002 4,000 4,0003 1,000 10,000

Total cash inflows 15,000 15,000Both projects have the same PBP, but project X would be more acceptable because of the time value of money. Cash today is better than cash tomorrow.

3. It biases capital budgeting decisions in favor of short- term projects and against long term projects.

2. Accounting Rate of Return (ARR):- measure profitability of the capital investment from conventional accounting stand point by relating or associating accounting NI with initial investment.

- Tells us the percentage of net income that has already generated a result of commitment of certain money.

- It is based on accounting information rather than on cash flows.- Depreciation is a non-cash flow expense, so, it should be added with net income to come up with the

cash flow(NI=CF- Depreciation )

.Example 1,

Anwar Company is considering an investment in x- project based on the following information:Initial Investment= 15,000Annual net income = 3,000Useful life= 5 years Target ARR= 30 %

ARR= NI Average investment = 3,000 15,000 Average

2ARR= 40%Accept Reject Rule: Accept the project if the computed ARR is Greater than the minimum target ARR set by the firm otherwise the project is rejected. Anwar company should accept the investment in x- project because the actual ARR (40%) is greater than the target ARR of 30 % Example 2Asteway co is considering an investment in project X based on the following information. Initial investment= 15,000 Annual cash inflow= 4,500 Useful life= 5 years (straight line method of depreciation is used) Target ARR= 30 %Required: Determine ARR?

Solution


ARR = NI . Average investment

Deprecation exp =15,000 5 years = 3,000

NI=CF- Depreciation EXP=4,500-3,000=1,500

NI .ARR= Average Investment

=1500 15,000 Average 2=15,000 7,500 ARR= 20%

Asteway co should reject the investment in project X because the actual ARR (20%) is less than the target ARR of 30%ExerciseA project will cost 60,000 birr. Its stream of earnings before deprecation and taxes during first year through five years is expected to be birr 20,000, 22,000, 25,000, 27,000& 29,000, respectively. Assume estimated life and salvage value is 5 years & 500 birr, respectively. Again assume income tax rate is 55% .Target ARR is 15%. Depreciation is to be computed on straight line method.Required: Determine ARR?

Solution Year Profit before deprn & tax Deprn.exp Profit after deprn Tax (55%) NI1 20,000 11,000 9,000 4950 40502 22,000 11,000 11,000 6050 49503 25,000 11,000 14,000 7,700 6,3004 27,000 11,000 16,000 8,800 7,2005 29,000 11,000 18,000 9,900 8,100

Total Net income 30,600 Average Annual net income=30600

5 = 6120

Deprn Exp= 60,000-5000 5 Average net investment= (cost of machine-Salvage) +Salvage

2 =11,000 = (60,000-5,000) +5000

2=32,500

ARR= NI . Average investment = 6120 =18.83% 32,500

There fore, the project is accepted because the computed ARR is greater than the target ARR.Advantages of ARR


1. It is easy to calculate. 2. It is understandable 3. It considers the entire stream of income in calculating the project’s profitability.

Disadvantages of ARR1. It uses accounting income rather than cash flows.2. It ignores the time value of money3.

B) Discounted methods3) Net present Value (NPV)It is one of the discounted cash flow (DCF) techniques explicitly recognizing the time value of money. NPV should be found out by subtracting initial investment from present Value of cash inflows.Steps in the calculation of NPV

1. Net cash flows of the investment project should be forecasted based on realistic assumptions.2. Appropriate discount rate should be identified to discount the forecasted cash flows. The

appropriate discount rate is the firms opportunity cost of capital which is equal to the required rate of return expected by investors on investments of equivalent risk.

3. Compute the present value of net cash flows & summing up to come up the present value of the net cash flows generated by the project

4. Compute the excess of sum of present value over the initial investment.

Accept Reject Rule. Accept if NPV>0(i.e. NPV is positive). Reject if NPV<0(i.e. NPV is negative). Project may be accepted if NPV=0

Example 1A company is considering the following investment projects. Net cash in flows:Year Project A Project B1 12,000 5,4002 10,000 8,0003 8,000 10,0004 5,400 12,000Total 35,400 35,400Assume initial investment is 25,000 and discount rate is 12% .Determine NPV of project A& project B?Project AYear NCF Pvat 12% Pv of cash inflows1 12,000 (1.12)-1 = 10714.32 10,000 (1.12)-2 =7971.933 8,000 (1.12)-3 = 5694.244 5,400 (1.12)-4 = 3431.79

Present Value= 27812.26 Less: Initial Investment= 25,000

NPV= 2812.26


NPV=∑ of PV- Initial Investment.

Project BYear NCF PVAT 12% Pv of cash inflows1 5400 (1.12)-1= 4,821.432 8,000 (1.12)-2= 6,377.553 10,000 (1.12)-3= 7117.804 12,000 (1.12)-4= 7626.22

Present Value= 25943 Less: Initial invest=25,000

NPV= 943Therefore, both project A & B are acceptable since their NPV Positive.

Mutually exclusive DecisionsTwo or more investment are said to be mutually exclusive when accepting one of them excludes all others from being accepted. Mutually exclusive decisions occur whenever a corporation receives competitive bids for a given project. The bids are mutually exclusive because the winning bid exclude all other bids from being accepted.

4) The Internal Rate of ReturnThe internal rate of return (IRR) of an investment proposal is defined as the discount rate that produces a zero NPV. Thus, the actual rate of return that a project earns profits and the time value of money are taken into account. i) When cash flows are in Annuity formWhen the cash flows of an investment are in annuity form, its IRR can be computed very easily.Example,A project that required a net investment of birr 100,000 produces annual cash flows for 16 years each of birr 14,000 and a required rate of 10%. The IRR for this project is found by dividing the value of one cash flow into the net investment and locating the resulting quotient in the present value annuity table100,000/14,000=7.143Table value IRR7.379 11%6.974 12%Thus, the IRR for this project is between 11% and 12 % and computed as follows:

1. Identify the closest rates of return 2. compute the NPV for each of these two closest rates

NPV at 11% = 14,000/(7.379)-100,000=3,306NPV at 12%=14,000/(6.974)-100000= -2,364

3. Compute the sum of the absolute values of the NPVs obtained in step24. Divide the sum obtained in step3 into the NPV of the smaller discount rate identified in

step 1. Then add the resulting quotient to the smaller discount rate3,306/5670=0.58IRR=11%+0.58=11.58%

Accept if IRR is greater than the cost of capital. Therefore accept the project.When cash flows are not in Annuity form


When the cash flows of an investment are not in annuity form, the computation of its IRR can become tedious. In order to minimize the difficulty, it is necessary to make a good first guess at the project’s IRR and apply interpolation methods.Example,A project with a net investment of birr 60,000, a required rate of return of 13 %, and the following cash flows: Year CF

1 20,0002 200003 200004 150005 150006 15000

Required: Calculate the IRR?Guess at 20 % and compute the Npv, the Npv=405 At 21% the Npv= -940Then the IRR with interpolation computed as follows:Interest NPV20% 405IRR 021% -940There fore, IRR=20%+(0-405) (21-20)% -940-405 20%+405 (1)% 1345 20%+0.3% IRR= 20.3%Conflicting rankingConflicting ranking using NPV and IRR result from differences in the magnitude and timing of cash flows. Which approach is better NPV or IRR? On a purely theoretical basis, Npv is the better approach to capital budgeting but evidence suggests that in spite of theoretical superiority of Npv, financial manager prefer to use IRR. The preference for IRR is attributable to the general disposition of business people toward rates of return rather than actual birr amounts.Capital Rationing DecisionsCapital rationing happens when a situation in which a corporation is unable to finance its entire capital budget.Example,Assume that a corporation is considering three independent capital budgeting projects. The corporation advertises for competitive bids on each project. One bid is received on project A, three bids are received on project B, and two bids are received on project C. the corporation’s financial managers then calculate the following net investments and NPV coefficients on all the bids for each project: Net investment NPVProject ABid A-1 3,000,000 250,000Project BBid B-1 3,000,000 200,000Bid B-2 3,500,000 250,000


Bid B-3 4,000,000 225,000Project CBid C-1 5,000,000 300,000Bid C-2 6,000,000 325,000Since only one bid is available for project A, it is evaluated on accept /reject basis. The bid is acceptable because its NPv is positive.The three bids on project B are mutually exclusive B-2 is chosen because it shows the largest positive Npv. The two bids on project C are also mutually exclusive. C-2 is chosen.In the absence of capital rationing, the capital budget would consist of alternatives A-1,B-2 and C-2. The total investment required in order to adopt this budget is 3 million+3.5 million+6 million=12.5 million. If 12.5 million is available, the capital budget can be adopted. However, if only 12 million is available, capital rationing exists because the funds needed for the capital budget exceed the amount of funds available.The decision rule for capital rationing problems selects a capital budget from sets of feasible investment alternatives. A group of investments alternatives is called a feasible set when it meets the following conditions:

1. The set contains no mutually exclusive alternatives.2. The total net investment required for the set does not exceed the net investment

constraint, or capital constraint.3. When all the feasible sets have been identified, choose the set of feasible investment

alternatives that contains the largest totalFeasible sets for projects A,B,C for a capital rationing Examples,Feasible set Net investment NPVA-1,B-1,C-1 11 million 750,000A-1,B-1,C-2 12 million 775,000A-1,B-2,C-1 11.5 million 800,000A-1,B-3,C-1 12 million 775,000The feasible project with capital rationing is A-1,B-2, and C-1.

Methods for incorporating risk in to capital budgetingExpected cash flows and expected net present valueUnder conditions of risk, a separate probability distribution is used to summarize the possible net investments or cash flows for each year. The first step in evaluating the desirability of a risky project is to compute the expected value of each probability distribution. This is obtained by multiplying each possible cash value by its probability of occurrence and adding the resulting products.

Example, Expected values of cash flow and probability distributions are as follows: Cash flow Probability Year1 2000 0.3

4000 0.46000 0.3


Et=(fi) (pi) IWhere, fi is possible cash value i for year t Pi is probability of occurrence of fi Et is expected value

Year 2 1000 0.13000 0.57000 0.4

El= 0.3x2000+0.4x4000+0.3x6000 =4000E2=0.1x1000+0.5x3000+0.4x7000=4400Expected Net present valueThe expected net present value of a capital budgeting alternatives, ENpv, is computed as follows. Let k* represent the risk free rate of return, then:ENPV= . Et t=0 (1+k*)t

Example,Possible Net Investment Probability(4,000) 0.3 (5,000) 0.4 (6,000) 0.3 The bracket (negative) values indicate that a net investment is a cash outflow. This probability distribution has an expected value of (5,000)

EtYear 0 (5,000)Year 1 4,000Year 2 4,400

If the risk free-rate of return is 8 percent, the NPV statistics for this project are calculated as follows. The expected NPV is computed

ENPV = -5,000 + 4,000 + 4,4000(1+0.08)0 (1 +0.08)1 (1 +0 .08)2

=-5000+3703.70+3772.09 = 2,076


Sensitivity and scenario analysisTwo approaches for dealing with project risk to capture the variability of cash inflows ans NPVs are sensitivity analysis and scenario analyses.Sensitivity analysis is a behavioral approach that uses a number of possible values for a given variable, such as cash inflows, to asses its impact on the firm’s return, measured by NPV. In capital budgeting, one of the most common sensitivity approaches is to estimate the NPVs associated with pessimistic, most likely, and optimistic cash inflow estimates. By subtracting the pessimistic outcome NPV from the optimistic outcome NPV, the range can be determined.Example, Assume ABC Company’s financial manager made pessimistic, most likely and optimistic estimates of the cash inflows for each project. The cash inflow estimates and resulting NPVs in each case are summarized as follows.Sensitivity analysis of ABC’s projects X and Y Project X Project YInitial investment Birr 10,000 Birr 10,000 Annual cash inflowsOutcomePessimistic Birr 1,500 Birr 0Most likely 2,000 2,000Optimistic 2,500 4,000Range 1,000 4,000 Net present values*OutcomePessimistic Birr 1,409 Birr -10,000Most likely 5,212 5,212Optimistic 9,015 20,424Range 7,606 30,424

* The values were calculated by using the corresponding annual cash inflows. A 10 percent cost of capital and a 15 year life for the annual cash inflows were used.Comparing the ranges of cash inflows (birr 1000 for project X and 4000 for project Y) and, more important, the ranges of NPVs (birr 7,606 for project X and birr 30,424 for Y) makes it clear that project X is less risky than project Y. Given that both projects have the same most likely NPV of birr 5,212, the assumed risk averse decision maker will take project X because it has less risk and no possibility of loss.Scenario analysis, which is a behavioral approach similar to sensitivity analysis but broader in scope, is used to evaluate the impact of various circumstances on the firm’s return. Rather than isolating the effect of a change in a single variable, scenario analysis is used to evaluate the impact on return of simultaneous change in a number of variables, such as cash inflows, and the cost of capital, resulting from differing assumptions relative to economic and competitive conditions. For example, the firm could evaluate the impact of both high inflation (scenario 1) and low inflation (scenario 2) on a project’s NPV. Each scenario will affect the firm’s cash inflows, cash outflows, and cost of capital, thereby resulting in different levels of NPV. The decision maker can use these NPV estimates to roughly assess the risk involved with respect to the level of inflation.Certainty Equivalent


One of the most direct and theoretically preferred approaches for risk adjustment is the use of certainty equivalents, which represents the percent of estimated cash inflow that investors would be satisfied to receive for certain rather than the cash inflow that investors would be satisfied to receive for certain rather than the cash inflows that are possible for each year. The basic expression for NPV when certainty equivalents are used for risk adjustment is as follows:

The equation is shows that the project is adjusted for risk by first converting the expected cash inflows to certain amounts, etXCFt, and discounting the cash inflows at the risk free rate, Rf.Example, ABC Company wishes to consider risk in the analysis of two projects, A and B. The cost of capital is 10 percent when considering risk. The project cash flows are as follows

Project A Project BInitial investment Birr 42,000 Birr 45,000Year Cash flows1 14,000 28,0002 14,000 12,0003 14,000 10,0004 14,000 10,0005 14,000 10,000By ignoring risk differences and using net present value at 10 percent cost of capital, project A is preferred over project B, since its NPV of birr 11074 is greater than N’s NPV of birr 10,914. Assume however, that on further analysis the firm found that project A is actually more risky than project B. to consider the deferring risks; the firm estimated the certainty equivalent factors for each project’s cash inflows for each year.Certainty equivalent for project A and B are as follows:Year Project A Project B1 0.90 1.002 0.90 0.903 0.80 0.904 0.70 0.805 0.60 0.70Upon investigation, ABC’s management estimated the prevailing risk free rate of return, Rf, to be 6 percent.Required: calculate the NPV.Project Ayear Cash

flowsCertainty equivalent factor

Certainty cash inflows

Present value

1 14,000 0.90 12,600 X(1.06)-1=11,8822 14,000 0.90 12,600 X(1.06)-2=11,2143 14,000 0.80 11,200 X(1.06)-3=9,4084 14,000 0.70 9,800 X(1.06)-4=7,7625 14,000 0.60 8,400 X(1.06)-5=6,275 Present value of cash inflows=46,541 Less: initial investment =42,000


NPV=∑et X CFt - I (1+Rf)t

Where, et is certainity equivalent factor in year t (0≤ et≤1) CFt is relevant cash inflow in year t Rf is risk free rate of return

NPV =4,541

Project Byear Cash flows Certainty equivalent

factorCertainty cash inflows

Present value

1 28,000 1.00 28,000 X(1.06)-1=26,4042 12,000 0.90 10,800 X(1.06)-2=96123 10,000 0.90 9,000 X(1.06)-3=75604 10,000 0.80 8,000 X(1.06)-4=63365 10,000 0.70 7,000 X(1.06)-5=5229 Present value of cash inflows=55141 Less: initial investment =45,000 NPV =10,141Note that as a result of the risk adjustment, project B is now preferred. The usefulness of the certainty equivalent approach for risk adjustment should be quite clear, the only difficulty lies in the need to make subjective estimates of the certainty equivalent factors.


financial management teaching material1

Documents

financial decisions

financial statement

financial analysis

goals of financial management

view of financial management

financial information

firms financial position

profit management