BUSINESS FINANCE

BFIN 300

PREPARED AND COMPILED BY:

ALWIYA AHMED AL-BEITY

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1.AN INTRODUCTION TO FINANCIAL MANAGEMENT

Financial management is concerned with the creation of economic value or wealth. A number of decisions are undertaken including:

When to introduce a new product. When to invest in new assets. When to replace existing assets. When to borrow from banks. When to issue stocks or bonds. When to extend credit to a customer, and How much cash to maintain.

The goal of the firm

Profit Maximization

Economists identify profit maximization as the goal of the firm. Profit maximization stresses the efficient use of capital resources, but it is not specific with respect to the time frame over which profits are to be measured whether a year or a longer period of time. A financial manager could easily increase current profits by eliminating research and development expenditures and cutting down on routine maintanace. In the short run this might result in increased profits, but this is clearly not in the best long-run interests of the firm. If we are to base financial decisions on a goal, that goal must be precise, not allow for misinterpretation and deal with all the complexities of the real world.

Limitations of the Profit Maximization Goal

1. Economists ignore risk and uncertainty in presenting this theory. Projects and investment alternatives are compared by examining their expected values or weighed average profits instead of examining the riskiness of a project compared to another.

2. It ignores timing of the project’s returns. A dollar in hand now is much better than two in a year’s time.

3. Accounting profits fail to recognize one of the most important costs of doing business. When we calculate accounting profits, we consider interest expense as a cost of borrowing money, but we ignore the cost of the funds provided by the firm’s shareholders (owners).

Maximization of Shareholder Wealth

This is the maximizing of the market value of the existing shareholders’ common stock. Investors react to poor investment or dividend decisions by causing the total value of the firm’s stock to fall and they react to good decisions by pushing up the price of the stock. Under this goal, good decisions are those that create wealth for the shareholder.

In the short run their night be problems with this goal such as share price decreasing for no reson but in the long run price equals value.

Legal Forms of Business Organizations.

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Sole-proprietorship: is generally the simplest way to set up a business. A sole proprietor is fully responsible for all debts and obligations related to his or her business. A creditor with a claim against a sole proprietor would normally have a right against all of his or her assets, whether business or personal. This is known as unlimited liability.

Partnership: A partnership is an agreement in which two or more persons combine their resources in a business with a view to making a profit. In order to establish the terms of the business and to protect partners/shareholders in the event of disagreement or dissolution of the business, a partnership/shareholders agreement should be drawn up, usually with the assistance of a lawyer. Partners share in the profits according to the terms of the agreement. There are two types of partnerships:

a) General partnership: each partner is fully responsible for the liabilities incurred by the partnership. Any partner’s faulty conduct even having the appearance of relating to the firm’s business renders the remaining partners liable as well.

b) Limited partnership: some states permit one or more of the partners to have limited liability restricted to the amount of capital invested in the partnership. Several conditions must be met to qualify as a limited partner e.g

at least one partner must remain in the association for whom the privilege of limited liability does not apply.

The names of the limited partners may not appear in the name of the firm. The limited partners may not participate in the management of the business.

If one of these conditions is violated, all partners forfeit their right to limited liability.

Corporations: A corporation is a legal entity that is separate from its owners, the shareholders. No shareholder of a corporation is personally liable for the debts, obligations or acts of the corporation. Directors, officers and insiders can bear some liability for their involvement with the corporation. A corporation can be formed at either the federal or provincial level.

Co-operative: A co-operative is a corporation organized by people with similar needs to provide themselves with goods or services, or to make joint use of their available resources to improve their income. Their business structure ensures:

all members have an equal say (one vote per member, regardless of the number of shares held); open and voluntary membership; limited interest on share capital; surplus is returned to members according to amount of patronage.

Advantages and disadvantages of the types of business entities

Sole-proprietorship

AdvantagesDisadvantages

ease of formation unlimited liability

low start-up costs difficulty raising capital

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less administrative paperwork than some other organizational structures (such as incorporation)

lack of continuity in business organization in the absence of the owner

owner in direct control of decision making

minimal working capital required

tax advantages to owner

all profits to owner

2. PartnershipAdvantages Disadvantages

ease of formation unlimited liability (for general partners)

low start-up costs lack of continuity

additional sources of investment capital divided authority

broader management base hard to find suitable partners

possible development of conflict between partners

3. CorporationAdvantages Disadvantages

limited liability closely regulated

specialized management most expensive form to organize

ownership is transferable charter restrictions

continuous existence extensive record keeping necessary

separate legal entity double taxation of dividends

possible tax advantage (if you qualify for small business tax rate)

easier to raise capital

4. Co-operativeAdvantages Disadvantages

owned and controlled by members longer decision making process

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democratic control: one member, one vote requires members to participate for success

limited liability extensive record keeping necessary

The Role of a Financial Manager in a Corporation

A firm can have an organization structure such as:

The Vice President for Finance, also known as the Chief Financial Officer (CFO) who serves under the corporation’s Chief Executive Officer (CEO) and is responsible for overseeing financial planning, corporate strategic planning, and controlling the firm’s cash flow.

A Treasurer and a Controller serve under the CFO. In a smaller firm the same person may fill both roles, with just one office handling all duties. The Controller is responsible for managing the firm’s accounting duties, including producing financial statements, cost accounting, paying taxes, and gathering information necessary to oversee the firm’s financial well-being. The treasurer generally handles the firm’s financial activities including, cash and credit management, making capital expenditure decisions, raising funds, financial planning and managing any foreign currency received by the firm.

The Interaction between Corporations and the Financial Markets.

A corporation can interact with the financial markets in the following ways:

Initially, the corporation raises funds in the financial markets by selling securities and bonds. This happens in the primary market where only securities are traded through an initial public offering (IPO). An IPO is the first time a firm’s stocks are issued.

The corporation then invests this cash in return-generating assets- new projects. The cash flow from those assets is either reinvested in the corporation, given back to the

investors, or paid to the government in the form of taxes. The company can raise more funds by offering more stock in the secondary market. The

secondary market is the market in which stock previously issued by the firm trades. Shareholders can also trade their shares in the secondary market.

The principles of Financial Management

a) The Risk-Return Trade-off: i.e. we won’t take additional risk unless we expect to be compensated with additional return. Investors demand a minimum return for delaying consumption that must be greater than inflation. Investments also have different amounts of risks and expected returns. Investors sometimes choose to put their in risky investments because these investments offer higher expected returns.

b) The Time Value of Money: i.e. a dollar received today is worth more than a dollar received in the future. Because we can earn interest on money received today, it is better to receive money earlier rather than later.

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c) Cash not profit is king: in measuring wealth, cash flows not accounting profits are used as measuring tool i.e. Financial managers will be concerned with when the money hits our hands, when they can invest it and start earning interest on it, and when they can give it back to the shareholders in the form of dividends. Cash flows and accounting profits may not be the same because cash flows are actually received by the firm and are reinvested while accounting profit appear when they are earned rather than when money is in hand.

d) Incremental cash flows- its only what changes that counts i.e. the incremental cash flows is the difference between the cash flows if the project is taken versus what they will be if the project is not taken.

e) The curse of competitive markets- why it’s hard to find exceptionally profitable projects. The key to locating profitable investment projects is to first understand how and where they exist in competitive markets. Then the corporate philosophy must be aimed at creating or taking advantage of some imperfection in these markets either through product differentiation or creation of a cost advantage, rather than looking to new markets or industries that appear to provide large profits. Any perfectly competitive industry that looks too good to be true won’t be for long.

f) Efficient capital markets- the markets are quick and the prices are right. An efficient market is a market in which the values of all assets and securities at any instant in time fully reflect all available public information. The implications of an efficient market to financial managers include:

The price is right. Stock prices reflect all publicly available information regarding the value of the company. This means that financial managers can implement the firm’s goal of maximizing shareholder’s wealth by focusing on the effect each decision should have on the stock price if everything else were held constant i.e. overtime good decisions will result in higher stock prices and bad ones, Lower prices.

Earning manipulations through accounting changes will not result in price changes. Stock splits and other changes in accounting methods that do not affect cash flows are not reflected in prices. Market prices reflect expected cash flows available to shareholders.

g. The Agency Problem- managers won’t work for owners unless it’s in their best interest. Agency problems involve problems resulting from conflicts of interest between the manager (the stockholder’s agent) and the stockholders. Managers may make decisions that are not in line with the goal of maximization of shareholder’s wealth; instead they ay approach work less energetically and attempt to benefit themselves in terms of salary and benefits at the expense of the shareholder. Managers can be monitored by auditing financial statements and managers’ compensation packages. The managers and shareholders’ interest can be aligned by establishing management stock options, bonuses, and benefits that are directly tied to how closely their decisions coincide with the interest of shareholders.

h. Taxes bias Business Decisions- when a company is analyzing the possible acquisition of a plant or equipment, the returns from the investment should be measured on an after-tax basis. Otherwise the company will not be truly evaluating the true incremental cash flows generated by the project. The government also realizes taxes can bias business decisions and uses taxes to encourage spending in certain ways. If the government wanted to encourage spending on research and

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development projects,, it might offer an investment tax credit for such investments. This would have the effect of reducing taxes on research and development projects, which would in return increase the after-tax cash flows from those projects. The increased cash flows would turn some otherwise unprofitable research and development projects into profitable projects.

i. All risk is not equal- some risk can be diversified away some cannot. Diversification allows good and bad events to cancel each other out, thereby reducing total variability without affecting expected return. A project’s risk changes depending on whether you measure it standing alone or together with other projects the company may undertake.

j. Ethical Behavior- means doing the right thing. A difficulty arises however in attempting to define ethics. The problem is that everyone has his or her own set of values which forms the basis for our personal judgments about what is the right thing to do. However, every society adopts a set of rules or laws that prescribe what it believes to be doing the right thing. As a result, we have ethical dilemmas everywhere in finance.

2. UNDERSTANDING FINANCIAL STATEMENTS, TAXES AND CASH FLOWS.

INCOME STATEMENT

It is also known as profit and loss account. It is the statement of profit and loss for the period, comprised of revenues less expenses for the period. It reports the following information:

1. Revenues (sales)- money derived from selling the company’s products or service.2. Cost of Goods Sold- the cost of producing or acquiring the goods or services to be sold.3. Operating Expenses- expenses related to marketing and distributing the product or service

and administering the business.4. Operating Income- also known as earnings before interest and tax.it is calculated from sales

minus total operating expenses.5. Financing Costs of Doing Business- is the interest paid to the firm’s creditors and the

dividends paid to preferred shareholders (but not dividends paid to ordinary/common shareholders). A firm’s interest is tax deductible.

6. Earnings before Taxes- it is calculated by subtracting interest expanse from operating profit.

7. Tax Expanse- the amount of taxes owed by a company based on its taxable income.8. Net Income- a figure representing the firm’s profit or loss for the period. It also represents

the earnings available to the firm’s common stockholders.

NOTE:

Operating Income- is not affected by how the firm is financed, whether with debt or equity. Operating income is the firm’s profits from all of its assets regardless of whether the assets are financed from debts or stock.

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Interest Expense- is subtracted from income before computing the firm’s tax liability, which is not true for dividends. Interest is a tax deductible expense i.e. for every dollar a company spends on interest; its tax expense is reduced proportionally. Dividends are not tax deductible as they are computed from net income which is earnings before taxes minus taxes.

BALANCE SHEET

Is a statement of financial position at a particular date. The form of the statement follows the balance sheet equation:

Assets = Liabilities + Owner’s Equity

Assets

Assets on a balance sheet are listed in the order of the length of time necessary to converted into cash in the ordinary course of business. Assets can be divided into:

a) Current Assets- also known as gross working capital are assets that are expected to be converted into cash within a year, consisting primarily of:

Cash: every firm must have cash for current business operations. A reservoir of cash is needed because of the unequal flow of funds into (cash receipts) and out of (cash expenditures) the business. The amount of the cash balance is determined not only by the volume of sales, but also by the predictability of cash receipts and cash payments.

Accounts Receivables: is a promise to receive cash from customers who purchased goods from the firm on credit.

Inventories: consists of raw materials, work in progress, and finished goods held by the firm for eventual sale.

Prepaid Expenses: consists of expenses that have been in advance. These assets are recorded on the balance sheet and expenses on the income statement as they are incurred.

b) Fixed Assets: include machinery and equipment, buildings and land. Some businesses are more capital-intensive than others, for example, a manufacturer would typically be more capital-intensive than a wholesale operation and therefore have more fixed assets.

c) Other Assets: are all assets that are not current or fixed assets, for example, patents, copyright, and goodwill.

Assets should be reported on their accounting book value i.e. the value of an asset as shown on a firm’s balance sheet. It represents the historical cost of the asset rather than its current market value or replacement cost.

Types of Financing

Financing comes from:

a) Debt Capital/Liabilities: is financing provided by a creditor. It consists of such sources as credit extended by suppliers or a loan from a bank. It can be divided into:

Current or Short Term Debt: debts due to be paid within 1 year and includes:

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Accounts Payable: also known as trade credit. It is the liability of the firm for goods purchased from suppliers on credit. A purchasing firm may have 30 or 60 days before paying for inventory that has been purchased.

Other Payables: include interest payable and income taxes payable that are owed and are to be paid within a year.

Accrued Expenses: expenses that have been incurred but not yet paid in cash such as accrued wages.

Short-term Notes: represents amount borrowed from a bank or other lending source that are due and payable within a year

Long-term Debt: are loans from banks or other sources that lend money for longer than a year.

b) Equity: are stockholders’ investment in the firm and the cumulative profits retained in the business up to the date of the balance sheet. These include:

Preferred Stockholders: are investors who own a firm’s preferred stock. They receive a fixed dividend. In the event of liquidation of the firm, these stockholders are paid after the firm’s creditors, but before the common stock.

Common Stockholders: are the residual owners of a business. They own a firm’s ordinary stock. They receive whatever is left over whether bad or good after the creditors and preferred stockholders are paid. The amount of a firm’s common equity as reported in a balance sheet is equal to:

The net amount the company received from selling stock to investors less stock the firm has repurchased from shareholders (par value and paid in capita).

The firm’s retained earnings. Are the cumulative earnings that have been retained and reinvested in the firm over its life (cumulative earnings-cumulative dividends).

These amounts may be offset by any stock that has been repurchased by the company, which is typically shown as treasury stock.

COMPUTING A COMPANY’S TAX

Sole proprietors report their income in their personal tax returns and pay the taxes owed. Partnerships report income from the partnership but do not pay taxes. Each partner reports his or

her portion of the income and pays the corresponding taxes. The corporation, as a separate legal entity, reports its income and pays taxes rlated to these

profits. The owners/stockholders of the corporation do not report these earnings in their personal tax returns, except when all or a part of the profits are distributed in the form of dividends.

The taxable income for a corporation is based on the gross income from all resources less any tax deductible expenses. Tax deductible expenses include:

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Operating expenses e.g. marketing expenses, administrative expenses, and depreciation expense.

Interest expenses.

Marginal tax rate is the tax rate that would be applied to the next dollar of taxable income.

Average tax rate is taxes owed by the firm divided by the firm’s taxable income.

For financial decision making, it is the marginal tax rate, rather than the average tax rate, that matters because it is the marginal rate that is applied to any additional earnings resulting from a decision. Thus when making financial decisions involving taxes, always use the marginal tax rate in your calculations and not the average tax rate.

International tax rates can vary substantially and the job of the financial manager is to minimize the firm’s taxes by reporting as much income as legally allowed in the low tax-rate countries and as little as legally allowed in the high tax rate countries.

MEASURING FREE CASH FLOWS

Free cash flows are the amount of cash available from operations after paying for investments in net operating working capital and fixed assets. This cash is available to distribute to the firm’s creditors and owners. Free cash flows can be calculated using:

1. An asset perspective: the procedure for computing a firm’s free cash flows on an asset basis involves the following steps:

Convert the income statement from an accrual basis to a cash basis (compute after-tax cash flows from operations). This is done by:

Operating income (earnings before interest and taxes)

+ Depreciation

= earnings before interest, taxes, depreciation, and amortization.

- Cash payments = after-tax cash flows from operations.

Calculate the investment in net operating working capital. Compute investments made in fixed assets and other assets ( investment activities).

2. Financing perspective: a firm can either receive money from or distribute money to its investors. This is called financing cash flows. Cash flows between investors and the firm occur in one of 4 ways. The firm can:

Pay interest to creditors. Pay dividends to stockholders. Increase or decrease outstanding debt. Issue or repurchase stock from current investors.

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The cash flows from the assets, if positive, will be the amount distributed to the investors, and if the cash flows from the assets is negative, it will be the amount that the investors had to provide to the firm to cover the shortage in asset free cash flows.

3: EVALUATING A FIRM’S FINANCIAL PERFORMANCE.

Financial Ration Analysis

It is restating accounting data in relative terms to identify some of the financial strengths and weaknesses of a company. The objective in using ratio analysis is to standardize the information being analyzed so that comparisons can be made between ratios of different firms or possibly the same firm at different points in time.

Financial ratio analysis tries to answer the following questions:

How liquid is the firm? Is management generating adequate operating profits on the firm’s assets? How is the firm financing its assets? Are the owners (stockholders) receiving an adequate return on their investments?

1. Liquidity Ratios: there are two approaches to measure the liquidity of a firm:a) Approach 1: the first approach compares current assets and current liabilities. These include:

Current Ratio: indicates a firm’s liquidity, as measured by its liquid assets (current assets) relative to its liquid debt (short-term or current liabilities).

Current ratio= current assetsCurrent liabilities

Acid- test Ratio: also known as quick ratio, it indicates a firm’s liquidity, as measured by its liquid assets, excluding inventories, relative to its current liabilities.

Acid- test ratio= current assets – inventoriesCurrent liabilities

b) Approach 2: it examines the firm’s ability to convert accounts receivable and inventory into cash on a timely basis. Average Collection Period: indicates how rapidly a firm is collecting its credit, as measured by the average number of days it takes to collect its account receivable.

Average collection period= accounts receivable Daily credit sales

Accounts Receivable Turnover Ratio: indicates how rapidly the firm is collecting its credit, as measured by the number of times its accounts receivable are collected or rolled over during the year.

Accounts receivable turnover= credit sales Accounts receivable

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Inventory Turnover Ratio: it indicates the relative liquidity of inventories, as measured by the number of times a firm’s inventories are replaced during the year.

Inventory turnover ratio= cost of goods sold Inventory

2. Profitability Ratios: tells whether the firm’s profits are sufficient relative to the assets being invested or not. These include:Operating Income Return on Investment (OIROI): indicates the effectiveness of management at generating operating profits on the firm’s assets, as measured by operating profits relative to the total assets.Operating income return on investment = operating income

Total assetsThe firm’s OIROI is a multiple of the following two ratios:Operating profit margin: indicates management’s effectiveness in managing the firm’s income statement, as measured by operating profits relative to sales.Operating profit margin = operating income

SalesThe driving forces of the operating profit margin include:

The number of units of product sold. The average selling price for each product unit. The cost of manufacturing or acquiring the firm’s product. The ability to control general and administrative expenses. The ability to control expenses in marketing and distributing the firm’s products.

Total asset turnover: indicates management’s effectiveness at managing a firm’s balance sheet as indicated by the amount of sales generated per one dollar of assets.

Total asset turnover = sales

Total assets.

Net profit margin: it measures the net income of the firm as a percent of sales.

Net profit margin = net profit

Sales.

Fixed asset turnover: indicates the management effectiveness in managing its fixed assets as indicated by the amount of sales generated by one dollar of fixed assets.

Fixed assets turnover = sales

Net fixed assets

3. financial ratios: tells us how the firm is financed whether its by debt or credit. They include:

Debt ratio: indicates how much debt is used to finance a firm’s assets.

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Debt ratio = total debt

Total assets

Times interest earned: indicates a firm’s ability to cover its interest expense, as measured by its earnings before interest and taxes relative to the interest expense.

Times interest earned = operating income

Interest expense

4. investment ratios: measures return on common equity. Are the investors receiving adequate return on their investment or not? These ratios include:

Return on common equity: indicates the accounting rate of return on the stockholders’ investment, as measured by net income to common equity.

Return on common equity = net income

Common equity including par, paid-in capital and retained earnings.

Limitations of ratio analysis

It is sometimes difficult to identify the industry category to which a firm belongs when the firm engages in multiple lines of business. Thus, we frequently must select our own set of peer firms and construct tailor- made norms.

Published industry averages are only approximations and provide the user with general guidelines rather than scientifically determined averages of the ratios of all or even a sample of the firms within an industry.

Accounting practices differ widely among firms and can lead to differences in computed ratios. An industry average may not provide a desirable target ratio or norm. at best , an industry average

provides a guide to the financial position of the average firm in the industry. It does not mean it is the ideal or best value for the ratio. Thus, we may choose to compare our firm’s ratios with self-determined peer group or even a single competitor.

Many firms experience seasonality in their operations. Thus, balance sheet entries and heir corresponding ratios will vary with the time of the year when the statements are prepared.

QUESTIONS

Q1) complete the following balance sheet using the following information provided:

Cash accounts payable 100,000

A/c receivables long-term debt

Inventory total liabilities

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Current assets common equity ________

Net fixed assets 1,500,000 total 2,100,000

2,100,000

Current ratio = 6.0 total asset turnover = 1.0

Inventory turnover = 8.0 average collection period= 30 days

Debt ratio = 20% gross profit margin = 15%

Solution

Current ratio = current assets 6= current assets

current liabilities 100,000

Current assets = 6×100,000 = $600,000

Debt ratio = total debt ×100 20% = total debt ×100

Total assets 2,100,000

Total debt = 2,100,000×20 = 420,000

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Long-term debt = 420,000-100,000 = 320,000

Total asset turnover = sales/ total assets 1.0 = sales/2,100,000

Sales = 1×2,100,000 = 2,100,000

Average collection period = accounts receivable/daily average sales

30 = accounts receivables/(2,100,000/365)

Accounts receivables = (30×2,100,000)/365 = $172,603

Gross profit margin = gross profit ×100/sales

15% = gross profit/2,100,000 = $315,000

Gross profit = sales –cost of goods sold

2,100,000-315,000 = $1,785,000

Inventory turnover = cost of goods sold / inventory

8 = 1,785,000/inventory

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Inventory = $223,125.

Cash = current assets – (accounts receivables +inventory)

= 600,000 –(172,603+223,125) = $204,272

Q2) the Mitchen Marble Company has a target current ratio of 2.0 but has experienced some difficulties financing its expanding sales in the past few months. The firm has a current ratio of 2.5 with current assets of $2.5 million. If Mitchen expands its receivables and inventories using its short-term line of credit, how much additional short-term funding can it borrow before its current ratio standard is reached?

Solution

Current ratio = current assets/current liabilities

2.5 = 2,500,000/current liabilities

Current liabilities = $1,000,000

2= 2,500,000/current liabilities

Current liabilities = 2,500,000/2 = $1,250,000

Additional short-term funding = $1,250,000-$1,000,000= $250,000

Q3) the R.M Smithers Corporation earned n operating profit margin of 10% based on sales of $10 million and total assets of $5million last year.

a) What was Smither’s total asset turnover?b) During the coming year, the company president has set a goal of attaining a total assets turnover

of 3.5. How much must firm sales rise, other things being the same, for the goal to be achieved?c) What was Smither’s operating income return on investment last year? Assuming the firm’s

operating profit margin remains the same, what will the operating income return on investment be next year if the total asset turnover goal is achieved?

Solution

a) Total asset turnover = sales /total assets

=10m/5m = 2

b) 3.5 = sales/5m = 3.5×5m = 16.5 million

Increase in sales = 16.5m – 10m = 6.5 m

%increase in sales = 6.5×100/10 = 65%

c) Operating income return on investment = operating income/total assets

Operating profit margin = operating income/sales

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Operating income = 10%×10,000,000 = $1,000,000

Operating income return on investment = 1,000,000×100/5,000,000 = 29%

If the total asset turnover is achieved, the total sales will be $16.5 million.

Operating income = 10%×16.5 m = $1.65 m

Operating income return on investment = 1.65×100/5 = 33%

Q4) the Brenmar Sales Company had a gross profit margin (gross profit/sales) of 30% and sales of $9m last year. 75% of the firm’s sales are on credit and the remainder are cash sales. Brenmar’s current assets equal $1.5m, its current liabilities equal $300,000, and it has $100,000 in cash plus marketable securities.

a) If Brenmar’s accounts receivable are $562,500, what is its average collection period?b) If Brenmar reduces its average collection period to 20 days, what will be its new level of accounts

receivables?c) Brenmar’s inventory turnover ratio is 9 times. What is the level of Brenmar’s inventories?

Solution

a) Average collection period= accounts receivables/daily credit sales =

562,500/(75%×9/365) = 30.4

b) 20=accounts receivables/ (75%×9/365)

Accounts receivables = 20×(75%×9/365)=$369,863.

c) Inventory turnover = cost of goods sold/inventory

Gross profit margin = gross profit/sales

Gross profit = 30%×9,000,000=$2,700,000

Cost of goods sold= 9,000,000-2,700,000=$6,300,000

inventory = 6,300,000/9 = $700,000

4: TIME VALUE OF MONEY

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Time value of money means that a Dollar today is worth more than a Dollar received from now because a Dollar can be invested and earn interest. In making decisions using this concept, one has to know:

The present value of money, and The future value of money.

Compound Interest and Future Value

Compound interest is the interest that occurs when interest paid on the investment during the first period is added to the principal, then, during the second period , interest is earned on this new sum.

The formula used in calculating compound interest is:

FVn = PV(1+i)n where

FVn= the future value of investment at the end of n years.

n = the number of years during which the compounding occurs.

i = the annual interest (or discount ) rate.

PV=the present value or original amount invested at the beginning of the first year.

The future value interest factor (FVIFi,n) is the value (1+i)n used as a multiplier to calculate an amount’s future value. It is the compound sum of $1 for n years at i% interest rate.

Example 1

What amount will $5000 invested for 10 years at 10% compounded annually accumulate to?

Solution

PV=$5000 n=10 i=10%

FV10 = 5000 (1+0.1)10

=5000×2.594

=$12970

Solving for N

The formula to solve for N periods is:

FVn ÷ PV = FVINi,n

Check in the FVINi,n table to find the number of years.

Example 2

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How many years will $500 take to grow to $1039.50 if invested at 5% compounded annually?

Solution

PV=$500 FV=$1039.50 i=5%

1039.50 = 500(1+0.05)n

1039.50 = (1.05)n

500

(1.05)n = 2.079

N = 15 years.

Solving for I

This is the same as for calculating for N but instead of checking for the number of years in the FVINi,n table , you check for the interest rate.

Example3

At what annual rate would $500 have to be invested to grow to $1948.00 in 12 years?

Solution

FV = $1948.00 PV=$500 n=12years

1948 = 500(1+i)12

1948 = (1+i)12

500

(1+i)12 = 3.896

I = 12%

Compound interest with non-annual periods.

Compounding interest is not always annual, sometimes it is monthly, quarterly, semi-annually and so on. The formula to calculate compound interest for non-annual periods is :

FVn = PV (1+ i/m)mn where

FVn = the future value of the investment at the end of N years.

N = the number of years during which the compounding occurs.

i = the annual interest (or discount rate)

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PV= the present value or original amount invested at the beginning of the first year.

Example

If we place $100 in a savings account that yields 12% compounded quarterly, what will our investment grow to at the end of five years?

Solution

N= 5 m= 4 i=12% PV=$100

FV5 = $100(1+0.12/4)4×5

= 100×(1.03)20

= 100(1.806)

= $180.60

Present Value

It is the current value of a future sum. The formula used in calculating the present value is :

PV = FVn (1÷(1+i)n)

(1÷(1+i)n)= PVIF

PVIF= the present value interest factor. These are given in the PVIF tables.

FVn= the future value

PV = the present value

Example

What is the present value of $500 to be received in 10years from today if our discount rate is 6%?

Solution

FV= $500 n=10% i=6%

PV= $500(1÷(1+0.06)10)

=500(1÷(1.791)

= 500×0.558

=$279

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OR

PV= $500(PVIF6%,10)

=500×0.558

=$279

Present value of multiple uneven cash flows

The concept of present value allows us to bring those future cashflows back to the present and view them in terms of todays dollars. Moreover, because all present values are comparable since they are all measured in dollars of the same time period, we can add and subtract the present value of inflows and outflows to determine the present value of an investment.

Example

What is the present value of an investment that yields $500 to be received in 5 years and $1000 to be received in 10 years if the discount rate is 4%?

Solution

PV= $500(PVIF4%,5) + $1000(PVIF4%,10)

= (500×0.822) + (1000×0.676)

= $411 + $676

= $1087

Q1) To what amount will the following investment accumulate?

a. $21,000 invested for 5 years at 5% compounded annually.b. $775 invested for 12 years compounded annually at 12%.

Solution

a. p=21,000 n=5 i=5%

FV= 21,000(1+0.05)5

=21,000×1.158=$24,318

b. P=775 N=12 I=12%

FV= 775(1+0.12)12

=775×3.498=$2710.95

Q2) How many years will the following have to be invested

20

a. $100 to grow to $298.60 if invested at 20% compounded annually.b. $35 to grow $c. 53.87 if invested at 9% compounded annually.

Solution

P=100 fv=298.60 i=20%

298.60/100= (1+0.20)n

2.986= (1+0.20)n

N=6years

b. p= 35 fv=53.87 i=9%

53.87/35= (1+0.09)n

1.5391= (1+0.09)n

N=5years

Q3) At what annual rate would the following have to be invested?

a. $300 to grow o $422.10 in 7 years.b. $50 to grow to $280.20 in 20 years.

Solution

P=300 FV=422.1 N=7years

422.1/300= (1+i)7

1.407= (1+i)7

I=5%

b. p=50 fv=280.20 n=20

280.2/50= (1+i)20

5.604= (1+i)20

I=9%

Q4)

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a. Calculate the future sum of $5000 given that it will be held in the bank for 5 years at an annual interest rate of 6%.

b. Recalculate part a using a compounding period that is: Semi-annual Bi-monthly

c. Recalculate parts a and b for a 12% annual interest rate.d. Recalculate part a using a time horizon of 12 years (annual interest rate of 6%)e. With respect to the effect of changes in the stated interest rate and holding periods on future

sums on part c and d, what conclusions do you draw when you compare these figures with the answers found in parts a and b.

Solution

a. p=$5000 n=5 i=6%

FV= 5000(1+0.06)5

5000×1.338=$6690

b. p=5000 n=10 i=3%

FV = 5000(1+0.03)10

=5000×1.344=$6720

P=$5000 n=30 i=1%

FV=5000×(1+0.01)30

=5000×1.348=$6740

c. p=$5000 n=5 i=12%

FV=5000(1+0.12)5

=5000×1.791=$8810

P=5000 N=10 I=6%

FV= 5000(1+0.06)10

5000×1.791= $8955

P=$5000 N=30 I=2%

FV=5000(1+0.02)30

5000×1.811=$9055

d. P=5000 N=12 I=6%

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FV=5000(1+0.06)12

5000×2.012=$10,060

Q5) What is the present value of the following amounts?

a. $1000 to be received in 8 years from now discounted back to the present at 20%b. $300 to be received 5 years from now discounted back to the present at 5%

Solution

a. FV=$1000 N=8 I=20%

P=1000×(PVIF20%,8)

=1000×0.233

=$233

b. FV=$300 N=5 I=5%

PV= 300(PVIF5%,5)

=300×0.784

=$235.20

Q6) What is the accumulated sum of each of the following streams of payments?

a. $35 a year for 7 years compounded annually at 7%b. $25 a year for 3 years compounded annually at 2%

Solution

a. PMT=$35 N=7 I=7%

FVa= 35(FVIFA7%,7)

= 35 × 8.654 = $302.89

b. PMT=$25 N=3 I=2%

FVa=25(FVIF2%,3)

= 25×3.06

=$76.5

Q7) What is the present value of the following annuities?

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a. $280 a year discounted back to the present at 6%b. $70 a year for 30 years discounted back to the present at 3%

Solution

a. PMT=$280 N=7 I=6%

PVa=280(PVIFA6%,7)

= 280×5.582

=$1562.96

b. PMT = $70 N=3 I=3%

PVa=70×2.829

=$198.03

Q8) Mr. Bill S. Pearson purchased a new house for $80,000. He paid $20,000 down and agreed to pay the rest over the next 25 years in 25 equal annual payments that include principal payments plus 9% compound interest on the unpaid balance. What will these equal payments be?

Solution

PV = $60,000 N=25 I=9%

60,000=PMT(PVIF9%,25)

PMT=60,000/9.823

=$6108.11

Q9) What is the present value of the following?

a. $100 perpetuity discounted back to the present at 9%b. $95 perpetuity discounted back to the present at 5%

Solution

a) 100/0.09 = $1111.11

b) 95/0.05 = $1900

Q10) You are given 3 investments alternatives to analyze. The cash flows from these 3 investments are as follows:

End of year A B C

1 2000 2000 5000

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2 3000 2000 5000

3 4000 2000 -5000

4 -5000 2000 -5000

5 5000 5000 15000

What is the present value of each of these investments if 10% is the appropriate discount rate?

Solution

Date PVIF 10% A PV of A B PV of B C PV of C12345Total

0.9090.8260.7510.6830.621

200030004000-50005000

181824783004-341531056990

20002000200020005000

181816521502136631059443

50005000-5000-500015000

45454130-3755-3415931510822

ANNUITIES

An annuity is a series of equal dollar payments for a specified number of years. Types of annuities include:

Ordinary annuity which is an annuity in which the payments occur at the end of each period. Annuity due which is an annuity in which the payments occur at the beginning of each period. Compound annuity which involves depositing an equal sum of money at the end of each year for

a certain number of years and allowing it to grow.

The formula used to calculate the future value of an annuity is:

FVn= PMT(FVITAi,n) where

FVn= the future value of the annuity at the end of the nth year.

PMT= the annuity payment deposited or received at the end of each year.

FVITAi,n= the future value interest factor for an annuity. This is available in the FVITA tables.

Example

To provide for a college education, we are going to deposit $500 at the end of each year for the next five years in a bank where it will earn 6% interest, how much will we have at the end of 5 years?

25

Solution

PMT= $500 i= 6% n=5years

FVn= $500(FVITA6%,5)

=$500 × 5.637

=$2818.50

Solving for payment

Given the future value of an annuity, interest rate and the time period, the payment can be calculated using the following formula:

PMT= FVn÷FVITAi,n

Example

How much must we deposit in an 8% savings account at the end of each year to accumulate $5000 at the end of 10 years?

Solution

FV10=$5000 i=8% n=10years PMT=?

PMT=5000÷(FVITA8%,10)

=5000÷14.487

=$345.14

Present Value of an Annuity

The present value of an annuity can be calculated a follows:

PV = PMT (PVIFAi,n)

Example

What is the present value of a 10 year $1000 annuity discounted back to the present at 5%?

Solution

PV= 1000 (PVIFA5%,10)

= 1000×7.722

= $7222

ANNUITIES DUE

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Because an annuity due merely shifts the payments from the end of the year to the beginning of the year, we now compound the cash flows for one additional year. Therefore, the compound sum of an annuity due is:

FVn (annuity due) = PMT (FVIFAi,n)(1+i)

Example

5: RISK AND RATES OF RETURN

RATES OF RETURN IN THE FINANCIAL MARKETS

In the financial markets where stocks and bonds are sold, net users of money, such as companies that make investments, have to compete with one another for capital. To obtain financing for projects that will benefit a firm’s stockholders, a company must offer investors a rate of return that is competitive with the next best investment available to the investor. This rate of return on the next best alternative to the saver is known as the investor’s opportunity cost of funds.

As managers we need to understand the investor’s opportunity cost of investing so as to understand whether the shareholders are receiving a fair return on their investments. Also, from an investor’s perspective, there is a need to know the historical experience of other investors in the capital markets, otherwise, there is no basis for knowing what can be reasonably expected in terms of rates of returns.

The relationship between risk and rate of return.

Types of investment securities include:

Common stocks of small firms. Common stocks of large companies. Long-term corporate bonds. Long-term government bonds. Treasury bills.

The portfolios in order of the less risky to the high risky are:

a) Treasury bill is the least risky of the five portfolios, because, it has a short maturity date, the price is less volatile (less risky) than the price of a long-term government bond.

b) Long-term corporate bonds because in government securities, the chance of default is non-existent. It is risky than treasury bills because of the length of time.

c) Long-term corporate bonds because there is a chance of default.d) Common stock of large companies.e) Common stock of small companies.

Common stock of small companies i.e. the smallest companies listed in the stock exchange are more risky than common stock of large companies because:

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Smaller businesses experience greater risk in their operations-they are more sensitive to business downturns, and some operate in niche markets that can quickly appear and disappear.

They rely more heavily on debt financing than do larger firms.

With this in mind, we should expect different rates of return to the holders of these varied securities. If the market rewards an investor for assuming risk, the average annual rates of return should increase as risk increases.

Annual rates of return 1926-2002

securities Nominal Average Annual Returns.

Standard Deviation of Returns.

Real Average Annual Returns (a).

Risk Premium (b).

Small Company StockLarge-Company StockLong-Term Corporate Bonds.Long-tem Government Bonds.U.S Treasury bills.

16.9%12.26.25.83.8

33.2%20.58.79.43.2

13.8%9.13.12.70.7

13.1%8.42.42.00.0

a) Real rate equals the nominal return less the average inflation rate from 1926 -2002 of 3.1%.

b) Risk premium equals the nominal return less the average risk-free rate (treasury bills) of 3.8%.

Standard deviation of returns measures the volatility or riskiness of the portfolios.

The return information in the table, demonstrates that common stock has been the investor’s primary inflation hedge (returns are greater than the inflation rate) in the long run- the average inflation has been 3.1%- and offered the highest risk premium. However, it is equally apparent that the common stock holder is exposed to sizable risk, as demonstrated by a 20.5% standard deviation for large companies and 33.2% for small companies stock.

The effects of Inflation on Rates of Return and the Fisher Effect.

The Nominal Rate of Return or the Observed Rate of Return is the quoted interest rate. The Real Rate of Interest is the Nominal Rate of Interest minus the expected rate of inflation over the maturity of the fixed-income security. This represents the expected increase in actual purchasing power to the investor.

We can express the relationship among the nominal interest rate (K r f), the rate of inflation (IRP), and the real rate of interest (K *) as follows:

1 + k r f = (1 + k*) ( 1 + IRP)

K r f = (1 + k*) (1 + IRP) – 1

K r f = 1 + k* + IRP + (K* × IRP) – 1

K r f = K* + IRP + (K* × IRP)

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Consequently, the nominal rate of interest is equal to the sum of the real rate of interest, the inflation rate and the product of the real rate and the inflation rate. This relationship is known as the Fisher Effect. It means that the observed nominal rate of interest includes both the real rate and an inflation premium.

Example

What is the real rate of interest, given the rate of inflation as 5% and the nominal rate as 11.3%

Solution

K r f = K* + IRP + ( K* × IRP)

O.113 = K* + 0.05 +(K* × 0.05)

0.113 = K* + 0.05 + 0.05K*

1.5K* = 0.113 – 0.05

K* = 0.108

K* = 0.06 = 6%

The term structure of interest rate (the yield to maturity).

Is the relationship between a debt security’s rate of return and the length of time until the debt matures.

The term structure of interest rate

Percentage

14

10

0

5 10 15 20 25

Years to maturity.

The curve above is upwards slopping, indicating that longer terms to maturity command higher returns, or yields. In this hypothetical term structure, the rate of interest on a five –year note or bond is 11.5%, whereas the comparable rate on a 20 year bond is 13%.

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The term structure of interest rate changes over time, depending on the environment. The particular term structure observed today may be quite different from the term structure a month ago and different still from the term structure one month from now. An example of the changing term structure or yield curve was witnessed during the period around the September 11, 2001 attack on the World Trade Centre and the Pentagon. Investors quickly developed fears about the prospect of increased inflation caused by the crisis and consequently increased their required rates of return.

Expected Return

The expected return from an investment, either by an individual investor or a company, is determined by the different possible outcomes that could occur from making the investment. The expected benefits or returns that an investment generates come in the form of cash flows. Cash flows, not accounting profits, should be used to measure returns. This principle holds true regardless of the type of security, whether it is a debt instrument, preferred stock, common stock or any mixture of these such as convertible bonds.

In an uncertain world, an accurate measurement of expected future cash flows is not easy for an investor to ascertain. The uncertainty of making an investment is apparent any times you buy stock and watch the price of the stock fluctuate. At the firm level, uncertainty comes to play in almost any decision made, but particularly when investing in new product lines or entering a new geographical market.

Expected return could be measured using two methods:

Expected cash flows, and Expected rate of return.

An expected cash flow is simply the weighted average of the possible cash flows outcomes such that the weights are the probabilities of the occurrence of the various states of the economy. The formula is as follows:

X = x 1 p (x 1) + x 2p (x2)………. X n p(x n) where x is the possible cash flow and P is the probability of X occurring.

The expected rate of return is the weighted average of all possible returns where the returns are weighted by the probability that each will occur. The formula to calculate this is as follows:

K = K1 P (K1) + K2 P (K2)…………… K n P (K n) where k is the possible rate of return and P is the probability of the possible rate of return.

State of the Economy. Probability of the State.

Cash Flows from the Investment.

Percentage Return (cash flow ÷ investment cost).

Economic recession.Moderate economic growth. Strong economic growth.

20%30%50%

$100012001400

10% (= 1000/10000)12% (= 1200/10000)14% (= 1400/10000)

X = 0.2 (1000) + 0.3 (1200) + 0.5 (1400) = $1,260.

K = 0.2 (10%) + 0.3 (12%) + 0.5 (14%) = 12.6%

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RISK AND A SINGLE INVESTMENT

It is the possibility of losing something. It is the prospect of an unfavorable outcome. This concept has been measured operationally as the standard deviation or beta.

Standard deviation is a measure of the spread or dispersion about the mean of a probability distribution. We calculate it by squaring the differences between each outcome and its expected value, weighting each squared difference by its associated probability, summing over all possible outcomes, an taking the square root of this sum.

Σ ={ (k i – k) 2 P (K i) +…………….. (K n – k) 2 P (K n) } ½ where

k is the expected rate of return.

K I is the value of the ith possible rate of return.

P k I is the probability of ith outcome or return will occur.

The standard deviation as a measure of risk can be interpreted in 2 ways as follows:

Two – thirds of the time, an event will fall within plus or minus one standard deviation of the expected value. Thus given a 15% expected return and a standard deviation of 12.85% we may reasonably anticipate that the actual returns will fall between 2.15% and 27.85% (15% + 12.85%) two thirds of the time – not much certainty within this investment.

Compare the investment with other investments. The attractiveness of a security with respect to its return and risk cannot be determined in isolation. Only by examining other available alternatives can we reach a conclusion about a particular investment’s risk. For example an investment in a firm that owns a radio station has the same expected return of 15% as the publishing firm but with a standard deviation of 7%, we would consider the risk associated with the publishing firm 12.85% to be excessive. That is, the radio company investment has the same expected results but it less risky than the publishing firm.

N/B the best investment is the one with a higher expected return but with a low standard deviation.

RISK AND DIVERSIFICATION

Risk can be reduced by diversifying. Diversifying means the investing in more than one project. If we diversify our investments across different securities rather than invest in only one stock, the variability in the returns of our portfolio should decline. The reduction in risk will occur if the stock returns within our portfolio do not move precisely together over time. The reduction occurs because some of the volatility in returns of a stock is unique to that security. The unique return variability of a single stock tends to be countered by the unique variability of another stock.

Risk can be divided into:

Firm – specific risk or company – unique risk (diversifiable risk or unsystematic risk): is the portion of the variation in investment returns that can be eliminated through investor

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diversification. This diversifiable risk is the result of factors that are unique to the particular firm.

Market – related risk (non – diversifiable risk or systematic risk): is the portion of variations in investment returns that cannot be eliminated through investor diversification. This variation results from factors that affect all stock.

Example

Types of Securities A B CShort-term Government Securities (Treasury Bills).Long- Term Government Bonds.Large- Company Stocks.

0%

100%0%100%

63%

12%25%100%

34%

14%52%100%

Average Annual Return 5.5% 5.5% 8.0%Risk (Standard Deviation) 11.3% 6.1% 11.3%

From the table, we can see that:

1. Portfolio A, which consists entirely of long-term government bonds, had an average annual return of 5.5% with a standard deviation of 11.3%.

2. In portfolio B, we have diversified across all three security types, with the majority of the funds 63% now invested in Treasury Bills and a lesser amount 25% in stocks. The effects are readily apparent. The average returns of the two portfolios A & B are identical but the risk associated with portfolio B is almost half that of portfolio A – standard deviation of 6.1% for portfolio B compared to 11.3% for portfolio A. risk has been reduced in portfolio B even though stocks a far more risky security have been included in the portfolio because stocks behave differently than both government bonds and treasury bills with the effect being a less risky portfolio.

3. Portfolio B demonstrates how an investor can reduce risk while keeping returns constant and portfolio C, with its increased investment in stocks (52%), shows how an investor can increase average returns while keeping risk constant. This portfolio has a risk level identical to that of long-term government bonds alone (portfolio A), but achieves a higher average return of 8% compared to 5.5% for the government bonds portfolio.

Measuring market risk

Kt = (pt/(pt – 1)) – 1 where

Kt = the holding period return in month t or the return on market portfolio.

Pt = a firm’s stock price at the end of month t.

Average return = the sum of the holding period return/ number of months

(Standard deviation)2 = (return in month 1 – average return) 2 + (return in month n – average return) 2

Number of months – 1 number of months – 1

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We can also measure the market risk or non-diversifiable risk by drawing a graph of returns for a firm against the market return. The characteristic line is the line of ‘best fit’ through a series of returns for a firm’s stock relative to market return. The slope of this line frequently known as beta represents the average movement of the firm’s stock returns in response to a movement in the market’s return.

In measuring the beta of a portfolio, we take the sum of the percentage of each stock multiply by its beta value.

Example

Ahmed bought 8 stocks with the same beta of 1 and 12 stocks with the same beta of 1.5. what is the value of the 20 stock portfolio beta?

Solution

Β portfolio = (8 ÷ 20 × 1) + (12 ÷ 20 × 1.5)

= 1.3

Measuring the investors required rate of return.

The investor’s required rate of return is the minimum rate of return necessary to attract an investor to purchase or hold a security. It is also the discount rate that equates the present value of the cash flows with the value of the security.

K = k r f + k r p where

K = the investor’s required rate of return.

K r f = the risk free return.

K r p = the risk premium.

The capital asset pricing model is an equation stating that the expected rate of return on an investment is a function of:

The risk – free rate. The investor’s systematic risk, and The expected risk premium for the market portfolio of all risky securities.

K j = k r f + β (k m – k r f)

Example

Standard and poor’s estimate General Electric’s beta to be 1.05. The risk free rate of return in 2003 is about 1.8% and the risk premium for large companies is 8.8%. What is the investor’s expected return?

Solution

KGE = k r f + β GE(km – k r f)

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= 1.8% + 1.05 (8.8)

= 1.8% + 9.24%

= 11.04%

Questions

Q1) what would you expect the nominal rate of interest to be if the real rate is 4.5% and the expected inflation rate is 7.3%.

k r f = k*+ IRP + (k*× IRP) where

K r f = nominal rate

K* = real rate, and

IRP = anticipates inflation

K r f = 0.045 + 0.073 + (0.045 × 0.073)

= 0.118 + 0.03285

= 0.121285 = 12.1285%

Q2) Assume the expected inflation rate is 3.8%. If the current real rate of capital is 6.4%, what should the nominal rate of interest be?

K r f = k* + IRP + (k* × IRP)

= 0.064 + 0.038 + (0.064 × 0.038)

= 0.102 + 0.002432

= 0.104432 = 10.4432%

Q3) Pritchard Press Inc. is evaluating a security. One-year Treasury bills are currently paying 3.1%. Calculate the following investment’s expected return and its standard deviation. Should Pritchard invest in this security?

probability return0.150.300.400.15

-1%2%3%8%

K* = (0.15)(-1%) + (0.30)(2%) + (0.40)(3%) + (0.15)(8%)

= - 0.15 + 0.6 + 1.2 + 1.2

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= 2.85%

σ ={ (-1% - 2.85%) 2 (0.15) + (2% - 2.85) 2 (0.30) + (3% - 2.85) 2 (0.40) + (8% - 2.85) 2 (0.15)} ½

= { 2.223375 + 0.21675 + 0.009 + 3.978375 } ½

= {6.4194} ½

= 2.53

Q4) Syntex, Inc is considering an investment in one of two common stocks. Given the information that follows, which investment is better, based on risk (as measured by standard deviation) and return?

Common stock A common stock B

probability return probability return0.300.400.30

11%15%19%

0.200.300.300.20

-5%6%14%22%

Common stock A

K* = (o.30)(11%) + (0.40)(15%) + (0.30)(19%)

= 3.3% + 6% + 5.7%

= 15%

σ = {(11% - 15%) 2(0.30) + (15% - 15%) 2 (0.40) + (19% - 15%) 2 (0.30)} ½

= {4.8% + 0 + 4.8} ½

= {9.6}1/2

= 3.09

Common stock B

k* = (0.20)(-5%) + (0.30)(6%) + (0.30)(14%) + (0.20)(22%)

= -1% + 1.8% + 4.2% + 4.4%

= 9.4%

σ = {(-5% -9.4%) 2(0.20) + (6% -9.4%) 2 (0.30) + (14% -9.4%) 2(0.30) + (22% - 9.4%) 2(0.20)}1/2

= {41.472 + 3.468 + 6.348 + 31.752}1/2

= {83.04} ½

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= 9.1

Q5) Johnson Manufacturing Inc is considering several investments. The rate on Treasury Bills is currently 6.75% and the expected return for the market is 12%. What should be the required rates of return for each investment? (Using CAPM)

security betaABCD

1.500.820.601.15

K j = k r f + β j (k m – k r f) where

K j = the required rate of return.

K r f = the risk free rate.

Β j = beta

K m = expected return for the market.

K a = 6.75 + 1.5(12 – 6.75) = 14.625%

K b = 6.75 + 0.82(12 – 6.75) = 11.055%

K c = 6.75 + 0.60(12-6.75) = 9.9%

K d = 6.75 + 1.15(12 – 6.75) = 12.7875%

Q6)

a) Given the following holding-period returns, compute the average returns and the standard deviations for the Zemin Corporation and for the market.

month Zemin Corp. Market123456

6%31-350

4%2-1-222

Average return = sum of holding period returns/number of months

For Zemin = ( 6 +3 + 1 – 3 + 5 + 0)/6 = 2%

For the market = (4 + 2 – 1 – 2 + 2 + 2)/6 = 1.17%

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Standard deviation = {(return in month t – average return) 2 + {return on month n – average return) 2 }1/2

No. of months -1 no. of months -1

For Zemin = {(6-2)/5) 2 + (3 – 2)/5) 2 + (1-2)/5)2 + (-3-2)/5)2 + (5-2)/5)2 }1/2

= {0.64 + 0.04 + 0.04 + 1 + 0.36}1/2

= {2.08]1/2

= 1.44

For the market = {(4-1.17)/5) 2 + (2-1.17)/5)2 + (-1-1.17)/5)2 + (-2-1.17)/5)2 + (2-1.17)/5)2 + (2-1.17)/5)2}1/2

= {0.32 + 0.028 + 0.188 + 10.05 + 0.028 + 0.028}1/2

= {1.642}1/2

= 1.28

b) If Zemin’s beta is 1.54 and the risk free rate is 8%,what would be an appropriate required rate of return for an investor owning Zemin?( Note: because the preceding returns are based on monthly data, you will need to annualize the returns to make them comparable with the risk free rate. For simplicity, you can convert from monthly to yearly returns by multiplying the average monthly returns by 12)

K j = k r f + β j (k m – k r f) where

K j = the required rate of return.

K r f = the risk free rate.

Β j = beta

K m = expected return for the market.

Monthly market rate = 1.17%

Annual market rate = 1.17 × 12 = 14.04%

K j = 8 + 1.54 (14.04 – 8)

= 17.3%

c) How does Zemin’s historical average return compare with the return you believe to be a fair return, given the firm’s systematic risk?

Historical average return = 2 × 12 = 24%

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The historical average rate (24%) is higher than the fair return (17.3%) since the firm’s systematic risk (1.44) is higher than the market systematic risk of 1.28. investments with a higher risk, usually have higher returns than the ones with lower risk.

Q7) Jones Corporation has collected information on the following three investments. Which investment is the most favorable based on the information presented?

Stock1 stock2 stock3

probability return probability return probability return0.150.40.30.15

2%7%10%15%

0.250.50.25

-3%20%25%

0.10.40.30.2

-5%10%15%30%

Rate of return

Stock 1

(0.15)(2) + (0.4)(7) + (0.3)(10) + (0.15)(15) = 8.35%

Stock 2

(0.25)(-3) + (0.5)(20) + (0.25)(25) = 15.5%

Stock 3

(0.1)(-5) + (0.4)(10) + (0.3)(15) + (0.2)(30) = 14%

Standard deviation

Stock 1

σ ={ (2-8.35)2(0.15) + (7-8.35)2(0.40 + (10-8.35)2(0.3) + (15-8.35)2(0.15)}1/2

= 3.77

Stock 2

σ ={(-3-15.5)2(0.25) + (20-15.5)2(0.5) + (25-15.5)2(0.25)}1/2

= 10.88

Stock 3

σ = {(-5-14)2(0.1) + (10-14)2(0.4) + (15-14)2(0.3) + (30-14)2(0.2)}1/2

= 12.88

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The best investment is the one with a higher return but a lower standard deviation. Each investor has a different reaction towards risk – some opt for higher risk investments but with a high returns while others are risk averse and try to avoid risk. For the risk averse investor stock 1, is the best since it has a low risk. For investors who are not risk averse stock 2 is the best since it has the highest return with a lower risk compared to stock 3.

Q8) Whitney common stock has a beta of 1.2. The expected rate of return for the market is 9% and the risk free rate is 5%.

a) Compute a fair rate of return based on this information.b) What would be a fair rate if the beta were 0.85?c) What would be the effect on the fair rate if the expected return for the market improved to 12%?

a) K j = 5% + 1.2(9% - 5%) = 9.8%

b) K j = 5% + 0.85(9% - 5%) = 8.4%

c) K j = 5% + 1.2(12% - 5%) = 13.4%

The fair rate of return increases to 13.4% from 9.8%.

6: VALUATION AND CHARACTERISTICS OF BONDS

A bond is a type of bond or a long-term promissory note, issued by the borrower, promising to pay its holder a predetermined and fixed amount of interest each year.

Types of bonds

a) Debentures: is any unsecured long-term debt. They are riskier than secured binds and as a result must provide investors with a higher yield. Sometimes, customers can be protected when the firm is prohibited from issuing more long-term debt that would further tie up the firm’s assets and leave the bondholders less protected. To the issuing firm, the major advantage of debentures is that no property has to be secured by them which allow the firm to issue debt and still preserve some future borrowing power.

b) Subordinated debentures: these are debentures whose claims are honored only after the claims of secured debt and unsubordinated debentures have been satisfied.

c) Mortgage bonds: is a bond secured by real property. The value of real property is higher than that of the mortgage bond issued. This provides the bondholder with a margin of safety in the event the market value of the secured property declines. In the event that the proceeds from the sale of the property do not cover the bonds, the bondholders become general creditors, similar to debenture holders, for the unpaid portion of the bonds.

d) Eurobonds: these are bonds issued in a country different from the one in whose currency the bond is denominated- for instance, a bond issued in Europe or in Asia by n American company that pays interest and principal to the lenders in U.S Dollars.

e) Zero and very low coupon bonds; are bonds issued at a substantial discount from their $1,000 face value that pay no or little interest.

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f) Junk bonds (high-yield bonds): these are bonds that offer a high interest rate and they have a lower chance of default.

Terminology and characteristics of bonds

a. Claims on assets and income: in the case of insolvency, claims of debt in general, including bonds are honored before those of common and preferred stock. Bonds also have aa claim on income that comes ahead of common and preferred stock.

b. Par value: the bonds face value that is returned to the bondholder at maturity, usually $1,000.c. Coupon interest rate: indicates what percentage of the par value of the bond will be paid out

annually in the form of interest.d. Maturity: the length of time until the bond issuer returns the par value to the bond holder and

terminates the bond.e. Indenture: the legal agreement or contract between the firm issuing the bonds and the bond

trustee who represents the bondholders.f. Current yield: the ratio of the annual interest payment to the bond’s market price.it is calculated

as follows:

Current yield = annual interest paymentMarket price of the bond

g. Bond ratings: these involve a judgement about the future risk potential of the bond. They are favourably affected by:

A greater reliance on equity as opposed to debt in financing the firm, Profitable operations, A low variability in past earnings, Large firm size, and Little use of subordinated debt.

Definitions of value

a. Book value: is the value of an asset as shown on a firm’s balance sheet. It represents the historical cost of the asset rather than its current market value or replacement cost.

b. Liquidation value: the amount that could be realized if an asset were sold individually and not as part of a going concern.

c. Market value: the observed value for the asset in the market value.d. Intrinsic or economic value: the present value of the asset’s expected future cash flows. This

value is the amount the investor considers to be a fair value, given the amount, timing and riskiness of future cash flows.Determinants of value

These include:

a) Asset characteristics which include: amount of expected cash flows. Timing of expected cash flows. Riskiness of expected cash flows.

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b) Investor attributes which include: investor’s assessment of the riskiness of the asset’s cash flows. Investor’s willingness to bear risk.

c) Investor’s required rate of return which is used to calculate the present value of the asset.Bond valuation

Bonds can be valued as follows:

V = c1 + c2 + c3 + ---- + c n

(1 + k)1 (1 + k)2 (1+k)3 (1+k)n or

V = (I × PVIFA i n) + (P × PVIF I n) where

I = interest per annum i.e. coupon rate multiply by the par or face value.

i = interest rate per annum.

N = number of years to maturity, and

P = par value of the bond.

If the interest is paid semi-annually, the following is done:

Divide the interest per annum and the interest rate per annum by 2. Multiply the number of years by 2.

Questions

Q1) Calculate the value of a bond that matures in 12 years and has a $1000 face value. The coupon interest rate is 8% and the investor’s required rate of return is 12%.

I = 8% × 1000 = $80 i = 12% n =12 p = 1000

V = (80 × PVIFA 12%,20) + (1000 × PVIF12%,20) = 637 + 1040 = $1677

Q2) Enterprise Inc, bonds have a 9% coupon rate. The interest is paid semi-annually and the bonds mature in 8 years. Their par value is $1000. If your required rate of return is 8%, what is the value of the bond? What is its value if the interest is paid annually?

I = 9% × 1000 = 90 i = 8% n = 8 p = 1000

If interest is paid semi-annually, then I = 45 n = 16 i = 4%

V = ( 45 × PVIFA4%,16) + (1000 × PVIF4%,16) = 524.34 + 534 = $1058.34

If interest is paid annually

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V = (90 × PVIFA8%,8) + (1000 × PVIF8%,8) = 517.23 + 540 = 1057.23

Q3) You own a bond that pays $100 in annual interest, with a $1000 par value. It matures in 15 years. Your required rate of return is 12%.

a. Calculate the value of the bond.b. How does the value change if your required rate of return (i) increases to 15% or (ii) decreases to

8%.c. Assume that the bond matures in 5 years instead of 15 years. Recomputed your answers in part

(b).

Answer.

a. I = 100 n = 15 i = 12% p = 1000

V = (100×PVIFA12%,15) + (1000×PVIF12%,15) = 681+1830 = $2511

b. V = (100 ×PVIFA15%,15) + (1000 × PVIF15%,15) = 587.47 + 1230 = 1817.47V = (100 × PVIFA8%,15) + (1000×PVIF8%,15) = 856 + 315 = 1171

c. V = (100×PVIFA15%,5) + (1000×PVIF15%,5) = 335.2+497 = 832V = (100×PVIFA8%,5) + (1000×PVIF8%,5) = 399.3+650 = 1049.3

7: STOCK VALUATION

Preferred stock

This is a hybrid security with characteristics of both common stock and bonds. It is similar to common stock because it has no fixed maturity date, the nonpayment of dividends does not bring on bankruptcy, and dividends are not deductible for tax purposes. Preferred stock is similar to bonds in that dividends are limited in amount.

Features and types of preferred stock

a) Multiple classes: if a company desires, it can issue more than one series of preferred stock, and each class can have different characteristics. In fact it is quite common for firms that issue preferred stock to issue more than one series. These issues can be differentiated in that some are convertible into common stock and others are not, and they have varying priority status regarding assets in the event of bankruptcy.

b) Claim on assets and income: preferred stock has a priority over common stock with regard to claims on assets in the case of bankruptcy. If a firm is liquidated, the preferred stock claim is honored after that of bonds and before that of common stock. Multiple issues of preferred stock may be given an order of priority. Preferred stock also has a claim on income prior to common stock. That is, the firm must pay its preferred stock dividends before it pays common stock dividends. Thus, in terms of risk, preferred stock is safer than common stock because it has a

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prior claim on assets and income. However, it is riskier than long-term debt because its claims on assets and income come after those of bonds.

c) Cumulative features: requires all past unpaid preferred stock dividends to be paid before any common stock dividends are declared. This feature provides some degree of protection for the preferred shareholder.

d) Protective provisions: these re protective provisions for preferred stock that are included in the terms of the issue to protect the investor’s interest. Theseprovisions generally allow for voting rights in the event of non-payment of dividends, or they restrict the payment of common stock features included with preferred stock are similar to the restrictive provisions included with long-term debt.

e) Convertibility: convertible preferred stock allows the preferred stockholder to convert the preferred stock into a predetermined number of shares of common stock, if he or she chooses.

f) Adjustable rate preferred stock: preferred stock intended to provide investors with some protection against wide swings in the stock value that occur when interest rates move up and down. The dividend rate changes along with prevailing interest rates.

g) Participating preferred stock: allows the preferred stockholder to participate in earnings beyond the payment of the stated dividend.

h) PIK Preferred stock: investors receive no dividends initially, they merely get more preferred stock, which in turn pays dividends in even more preferred stock.

Valuing preferred stock

The owner’s of preferred stock generally receives a constant income from the investment in each period. however, the return from preferred stock comes in the form of dividends rather than interest. Inaddition, whereas bonds generally have a specific maturity, most preferred stock are perpetuities(nonmaturing).

Finding the value (present value) of preferred stock is like finding the present value of a perpetuity.

V p s = annual dividend ÷ required rate of return = D/K p s

Example

What is the value of a preferred stock that pays an annual dividend of $5 and the investor’s required rate of return is 6%?

V p s = 5/6% = $83.33

Characteristics of common stock

Common stock shares represent the ownership in a corporation.

a) Claim on income: as the owners of the corporation, the common shareholders have the right to the residual income after bondholders and preferred stockholders have been paid. This income may be paid directly to the shareholders in the form of fdividends or retained and reinvested by the firm. Although it is obvious the shareholder benefits immediately from the distribution of income in the form of dividends, the reinvestment of earnings also benefits the

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shareholder. Plwing earnings back to the firm should result in an increase in the value of the firm, in its earning power, and in its future dividends. This action in turn results in an increase in the value of the stock. Ineffect, residual income is distributed directly to shareholders in the form of dividends or indirectly in the form of capital gains (a rising stock price) on their common stock. The right to residual income has both advantages and disadvantages for the common stockholder. The advantage is that the potential return is limitless. Once the claims of the more senior securities (bond and preferred stock) have been satisfied, the remaining income flows to the common stockholders in the form of dividends or capital gains. The disadvantage is that if the bond and preferred stock claims on income totally absorb earnings, common shareholders receive nothing. In years when earnings fall, it is common shareholders who suffers first.

b) Claims on asset: just as common stock has a residual claim on income, it also has a residual claim on assets in the case of liquidation.

c) Voting rights: the common shareholders elect the board of directors and are in general the only security holders given a vote.

d) Preemptive rights: are certificates issued to shareholders giving them an option to purchase a stated number of new shares of stock at a specified price. It entitles the common shareholder to maintain a proportionate share off ownership in the firm.

e) Limited liability: although the common shareholders are the actual owners of the corporation, their liability in the case of bankruptcy is limited to the amount of their investment. The advantage is that investors who might not otherwise invest their funds in the firm become willing to do so.

Valuing common stock

Vo = D1/Kcs – g where

D1 = Do (1+g)

VO = value of the common stock

D1 = the next dividend to be received

Kcs = common holders required rate of return

G = growth rate

Do = last year’s dividend.

Example

What is the value of a share of common stock that paid a $2 dividend at the end of last year and is expected to pay a cash dividend every year from now until infinity. Ech year the dividends are expected to grow at a rate of 10%. Based on an assessment of the riskiness of the common stock, the investor’s required rate of return is 15%.

D1 = D0 (1+ g)

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= $2 (1+0.10)

=$2.20

V c s = D1/(K c s – g)

= 2.20/(0.15-0.10)

= $44

Stockholders required rate of return

Preferred stock

K ps = D/V p s

Common stock

K c s = (D1/V c s) + g

Questions

Q1) Calculate the value of a preferred stock that pays a dividend of $6 per share and your required rate of return is 12%.

V p s = 6/0.12 = $50

Q2) Made-Its common stock currently sells for $22.50 per share. The company’s executives anticipate a constant growth rate of 10% and an end-year dividend of $2

a. what is your expected rate of return if you buy the stock at $22.5?

b. if you require a 17% return, should you purchase the stock?

a. K c s = (2/22.5) + 0.1

= 0.089 + 0.1

= 0.189 = 18.9%

b. No. since the required rate of return on a security Is the required rate of return of investors who are willing to pay the present market price for the security but no more. Since the required rate of return is 17%, it means I cant pay more than 17%.

Q3) Header comp. paid a $3.5 dividend last year. At a constant growth rate of 5%, what is the value of the common stock if the investors require a 20% rate of return?

D1 = D0 (1+g)

= 3.5 (1+0.05)

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= 3.675

V c s = D1/(K C S – g)

= 3.675/(0.20-0.05)

= $24.50

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