The Financial Manager and the Firm CHAPTER 1 The Financial Manager and the Firm Unit Slides by UK Versity

Legal Forms of Business Organizations Quick Links The Role of the Financial Manager Legal Forms of Business Organizations Managing the Financial Function The Goal of the Firm Agency Conflicts: Separation of Ownership and Control

The role of financial manager The financial manager is responsible for making decisions that are in the best interests of firm owners or maximize the owner’s wealth. Stakeholder is someone other than an owners. The managers, employees, suppliers, government, creditors.

The Role of the Financial Manager It is all About Cash Flows A firm generates cash flows by selling the goods and services produced by its productive assets and human capital. The firm is successful when these cash inflows exceed the cash outflows needed to pay operating expenses, creditors, and taxes. The firm can pay the remaining cash, called residual cash flows, to the owners as a cash dividend, or reinvest the cash in the business.

Exhibit 1.1: Cash Flow Diagram

The Role of the Financial Manager It is all about cash flows A firm is unprofitable when it fails to generate sufficient cash flows. Firms that are unprofitable over time will be forced into bankruptcy by their creditors. In bankruptcy, the company will either be reorganized, or the company’s assets will be liquidated.

The Role of the Financial Manager Three Fundamental Decisions in Financial Management The capital budgeting decision: Which productive assets should the firm buy? A good capital budgeting decision is one in which the benefits are worth more for the firm than the cost of the assets. The financing decision: How should the firm finance or pay for assets?

The Role of the Financial Manager Three Fundamental Decisions in Financial Management Financing decisions involve trade-offs between advantages and disadvantages of debt and equity financing. Working capital management decisions: How should day-to-day financial matters be managed? The mismanagement of working capital can cause the firm to go into bankruptcy even though the firm is profitable.

Exhibit 1.2: How Financial Manager’s Decisions Affect the Balance Sheet

Legal Forms of Business Organizations Sole Proprietorship No legal distinction between personal and business income for a sole proprietor. All business income is taxed as personal income. A sole proprietorship has unlimited liability for all business debts and other obligations of the firm.

Legal Forms of Business Organizations Partnership Has the same basic advantages and disadvantages as a sole proprietorship. When a transfer of ownership takes place, the partnership is terminated and a new partnership is formed. The problem of unlimited liability can be avoided in a limited partnership.

Legal Forms of Business Organizations Corporation In a legal sense, it is a “person” distinct from its owners. The owners of a corporation are its stockholders, or shareholders. A major advantage of the corporate form of business is that stockholders have limited liability.

Legal Forms of Business Organizations Corporation The owners of corporations are subject to double taxation first at the corporate level and then at the personal level when dividends are paid to them. Public corporations can sell their debt or equity in the public securities markets. Private corporations are held by a small number of investors.

Legal Forms of Business Organizations Hybrid Forms of Business Organization Limited liability partnerships (LLPs) combine the limited liability of a corporation with the tax advantage of a partnership. Limited liability companies (LLCs) Professional corporations (PCs)

Managing the Financial Function Chief Executive Officer (CEO) Ultimate management responsibility and decision-making power in the firm. Reports directly to the board of directors, which is accountable to the company’s owners.

Managing the Financial Function Chief Financial Officer (CFO) Responsible for the best possible financial analysis that is presented to the CEO. Positions that report to the CFO: The Controller prepares financial statements, oversees the firm’s cost accounting systems, prepares taxes, and works closely with the firm’s external auditors.

Managing the Financial Function Chief Financial Officer (CFO) CFO’s Key Financial Reports The Treasurer looks after the collection and disbursement of cash, invests excess cash, raises new capital, handles foreign exchange, and oversees the firm’s pension fund managers.

Managing the Financial Function Chief Financial Officer (CFO) CFO’s Key Financial Reports The Internal Auditor is responsible for in-depth risk assessments, performing audits of high-risk areas. The Risk Manager manages the firm’s risk exposure in financial markets and the relationships with insurance providers.

Managing the Financial Function External Auditors (big Four) Provide an independent annual audit of the firm’s financial statements. Ensure that the financial numbers are reasonably accurate, and accounting principles have been consistently applied.

Managing the Financial Function Audit Committee Approves the external auditor’s fees and engagement letter. The external auditor cannot be fired or terminated without the audit committee’s approval. Compliance and Ethics Director Oversees the compliance program, ethics program, and the compliance hotline and reports directly to the audit committee.

Exhibit 1.3: Simplified Corporate Organization Chart

The Goal of the Firm What Should Management Maximize? Minimizing risk or maximizing profits without regard to the other is not a successful strategy.

The Goal of the Firm What Should Management Maximize? Why not maximize profits? Profit maximization does not tell us when cash flows are to be received. Profit maximization ignores the uncertainty or risk associated with cash flows.

The Goal of the Firm Maximize the Value of the Firm’s Stock Price When analysts and investors determine the value of a firm’s stock, they consider. The size of the expected cash flows. The timing of the cash flows. The riskiness of the cash flows.

The Goal of the Firm Maximize the Value of the Firm’s Stock Price An appropriate goal for financial management is to maximize the current value of the firm’s stock. For private corporations and partnerships, the goal is to maximize the current value of owner’s equity.

Exhibit 1.4: Major Factors Affecting Stock Prices

The Goal of the Firm Can Management Decisions Affect Stock Prices? YES!!!

Agency Conflicts: Separation of Ownership and Control For large corporations, the ownership of the firm is spread over huge number of shareholders and the firm’s owners may effectively have little control over management . Management may make decisions that benefit their self-interest rather than those of the stockholders.

Agency Conflicts: Separation of Ownership and Control Agency Relationships An agency relationship arises whenever one party, called the principal, hires another party, called the agent. The relationship between stockholders (principals) and management (agents) is an agency relationship.

Agency Conflicts: Separation of Ownership and Control Do Managers Really Want to Maximize Stock Price? Shareholders own the corporation, but managers control the money and have the opportunity to use it for their own benefit. Agency Costs The costs of the conflict of interest between the firm’s owners and its management.

Agency Conflicts: Separation of Ownership and Control Aligning the Interests of Management and Stockholders Management Compensation A significant portion of management compensation should be tied to firm performance (e.g. stock price).

Agency Conflicts: Separation of Ownership and Control Aligning the Interests of Management and Stockholders Managerial Labor Market Firms with unethical behavior have difficulty hiring top managers. Executives with poor performance or criminal convictions can rarely secure good positions in the future.

Agency Conflicts: Separation of Ownership and Control Aligning the Interests of Management and Stockholders Board of Directors Lack of board independence is a key factor in the misalignment between board members’ and stockholders’ interests Other Managers Large Stockholders The Takeover Market The Legal and Regulatory Environment

Financial Statements, Cash Flows, and Taxes CHAPTER 3 Financial Statements, Cash Flows, and Taxes

Quick Links The Balance Sheet The Income Statement Statement of Retained Earnings Cash Flows

The Balance Sheet This financial statement identifies all the assets and liabilities of a firm at a point in time. Left side of the balance shows all assets the firm owns and uses to generate revenues. Right side represents the liabilities of the firm – money that the firm has borrowed from both creditors and shareholders. Total assets = Total liabilities+Total stockholders’ equity (3.1)

The Balance Sheet Balance sheet also lists the capital raised from its shareholders. Assets listed in order of their liquidity. Liabilities listed in order in which they must be paid. Shareholders of the firm’s common equity are listed last. Shareholders will be paid with whatever remains after paying all other suppliers of funds.

The Balance Sheet Current Assets and Liabilities Current assets include all assets likely to be converted to cash within a year (or within an operating cycle). These include cash and marketable securities, accounts receivables, and inventory.

The Balance Sheet Current Assets and Liabilities Current Liabilities include all liabilities that have to be paid within a year. Bank loans and other borrowings with less than a year’s maturity, accounts payables, accrued wages and taxes Net working capital= Total current assets - Total current liabilities (3.2)

The Balance Sheet Net working capital example - Diaz Manufacturing Total current assets = $1,039.8 million Total current liabilities = $377.8 million Net working capital =?

The Balance Sheet Inventory Accounting Inventory (least liquid of current assets) usually reported in one of two ways on balance sheet. FIFO (First in first out) refers to practice of recognizing a sale as being made up of inventory purchased earlier. LIFO (Last in first out) calls for firm to attribute any sale made to the most recently acquired. Book Example?

The Balance Sheet Inventory Accounting During rising prices, FIFO reporting leads to higher current asset value and higher net income. Firms may switch from one to another only under extraordinary circumstances and not frequently.

The Balance Sheet Long-Term Assets Real assets firm acquires to produce its products and generate cash flows. Land, buildings, plant and equipment. Intangible assets also listed here. Goodwill, patents, copyrights, etc.

The Balance Sheet Long-Term Assets All long-term real assets that deteriorate with use are depreciated. Intangible assets are amortized. Depreciating assets allow a firm to lower taxable income and reduce taxes. Firms are allowed to depreciate assets using straight line method or accelerated depreciation method allowed by IRS.

The Balance Sheet Long-Term Liabilities Long-term debt of the company. Includes bank loans, mortgages, and bonds with a maturity of one year or longer.

The Balance Sheet Equity – There are two sources of equity funds Common Equity Common equity represents the true ownership of the firm. Preferred Equity Has features that make it a combination of a fixed income security and an equity security.

The Balance Sheet More Balance Sheet Accounts Retained earnings Results from funds the firm has reinvested from its earnings. These funds are not cash–they already have been put to work. Treasury stock This account reflects the value of the shares that the firm has repurchased from investors.

The Income Statement The Income Statement: Overview Measures the profitability of a firm for any reporting period. Revenues represent value of products and services sold by firm–include both cash and credit sales. Expenses range from cost of producing goods for sale and asset utilization costs- depreciation or amortization. Net income = Revenues – Expenses (3.3)

The Income Statement Net Income example – Diaz Manufacturing Revenues = $1,563.7 million Expenses = $1,445.2 million Net Income = ?

The Income Statement The Income Statement: Depreciation The cost of any physical asset, such as plant or machinery, is written off over its lifetime. This is called depreciation and is a non-cash expense. Firms use one of these for depreciating an asset: Straight line method Accelerated depreciation method Firms allowed to use one for internal purposes and another for tax purposes.

The Income Statement The Income Statement: Amortization Amortization expenses are related to the writing off of the value of intangible assets, such as: Goodwill, Patents, Licenses, etc. It is also a non-cash expense like depreciation.

The Income Statement Extraordinary Items Extraordinary Items refer to income or expenses associated with events that are not expected to happen on a regular basis.

The Income Statement Bottom Line Accounts Earnings before interest, taxes, depreciation and amortization (EBITDA) . Earnings generated from operations prior to payment of expenses not directly connected to production of products. After netting out the expenses related to depreciation and amortization, we arrive at earnings before interest and taxes (EBIT).

The Income Statement Bottom Line Accounts Earnings before taxes (EBT) represents the taxable income for the period. Subtracting taxes from EBT yields net income or net income after taxes. This amount tells us amount available to management to pay dividends, pay off debt, or reinvest in firm.

Statement of Retained Earnings This financial statement shows the changes in the retained earnings account from one period to the next. This account will show changes whenever a firm reports a loss or profit and when a cash dividend is declared.

Exhibit 3.3: Diaz Mfg Statement of Retained Earnings

Cash Flows Net Cash Flow versus Net Income While accountants focus on net income, shareholders would be more interested in net cash flows. These two are not the same, because of the presence of non-cash revenues and expenses.

Cash Flows Net Cash Flow versus Net Income We can estimate the net cash flow from operating activities (NCFOA) as: NCFOA = Net income + Depreciation and Amortization (3.5)

Cash Flows NCFOA example – Diaz Manufacturing Net Income = $118.5 million Depreciation and Amortization = $83.1 million NCFOA = ?

Cash Flows The Statement of Cash Flows Helps to measure cash outflows and cash inflows generated during any period. Indicates cash flows resulting from Operating activities, investing activities, and financing activities. Sum of cash flows measures net cash flows of firm during a given period. Net cash flows is the bottom line of this financial statement.

Cash Flows Organization of the Statement of Cash Flows Operating Activities Cash inflows result from producing and selling goods and services. Cash outflows are tied to the purchase of raw materials, inventory, salaries and wages, utilities, rent, interest and other related expenses.

Cash Flows Organization of the Statement of Cash Flows Investing Activities Cash inflows and outflows arise out of the acquisition and selling of long-term assets necessary to operate the business. investing activities. Also result from Buying and selling financial assets (bonds, stocks). Making and collecting loans. Selling and settling insurance contracts.

Cash Flows Organization of the Statement of Cash Flows Financing Activities Cash Inflows–when a firm issues debt or equity securities, or borrows money from banks or other lenders. Cash Outflows–if they pay interest or dividends on the investor’s funds, pay off debt, or purchase treasury stock.

Exhibit 3.5: Interrelations among the Financial Statements

In-class discussion End of chapter questions Group selection

Analyzing Financial Statements CHAPTER 4 Analyzing Financial Statements

Quick Links Ratio Analysis Financial Statement Analysis The DuPont System, ROA, ROE Benchmarks Limitations of Ratio Analysis

Perspectives on Financial Statement Analysis A firm’s financial statements can be analyzed from the perspective of different stakeholders. Important perspectives: Stockholder Manager Creditor

Perspectives on Financial Statement Analysis Stockholders’ perspective Centers on value of stock held. Interest in the financial statement is to gauge cash flows firm will generate from operations. Allows determination of firm’s profitability, return for that period, and likely dividends.

Perspectives on Financial Statement Analysis Manager’s perspective Interest in firm’s financial statement is similar to stockholders’. Manager’s job security depends on firm’s performance. Management gets feedback on investing, financing, and working capital decisions by identifying trends in various accounts reported in financial statements.

Perspectives on Financial Statement Analysis Creditors’ perspective Focus on getting loans repaid and receiving interest payments on time. A firm’s creditors closely monitor Amount of debt firm has. Ability to meet short-term obligations. Ability to generate sufficient cash flows to meet all legal obligations, debt repayment, and interest payments.

Guidelines for Financial Statement Analysis Main Concern From whose perspective firm analysis is done. Management, shareholder or creditor. Use only audited financial statements if possible. Perform analysis over 3-5 year period–time-trend analysis.

Guidelines for Financial Statement Analysis Main Concern (cont.) Compare firm’s performance to direct competitors’ performance. Example? Perform a benchmark analysis comparing it to most relevant competitors – Vietnam Airlines to Indochina or Jetstar

Common-Size Financial Statements Common-Size Balance Sheets Each asset and liability item on balance sheet is standardized by dividing by total assets. Accounts are then represented as percentages of total assets.

Exhibit 4.1: Common-Size Balance Sheets

Common-Size Financial Statements Common-Size Income Statement Each income statement item standardized by dividing it by dollar amount of net sales. Each income statement item now indicated as percent of sales.

Exhibit 4.2: Common-Size Income Statements

Liquidity Ratios Measures ability of firm to meet short-term obligations with short-term assets, without endangering the firm. Two commonly used ratios to measure liquidity Current ratio Quick ratio

Liquidity Ratios Current ratio is calculated by dividing current assets by current liabilities. Amount of current assets firm has per dollar of current liabilities. Higher number = more liquidity

Liquidity Ratios Quick (acid-test) ratio calculated by dividing most liquid current assets by current liabilities. Inventory subtracted from total current assets determines most liquid assets. Amount of liquid assets firm has per dollar of current liabilities. Higher number = more liquidity

Liquidity Ratios Quick ratios typically smaller than current ratios for manufacturing firms Service firms see no different between current and quick ration

Efficiency Ratios Sometimes called asset turnover ratios. Measure how efficiently firm’s management uses assets to generate sales.

Efficiency Ratios Used by management to identify areas of inefficiency. Used by creditors to determine speed of converting inventory to receivables. Receivables convert to cash to help firm meet debt obligations. Efficiency ratios focus on inventory, receivables and use of fixed and total assets.

Efficiency Ratios Inventory turnover ratio–measures how many times inventory turned over into saleable products. In general, more often a firm can turn over inventory, the better. Too high or too low a turnover could be warning sign.

Efficiency Ratios Days’ sales in inventory ratio also builds on inventory turnover ratio. Measures number of days firm takes to turn over inventory. The smaller the number, the faster the firm turns over inventory, more efficient it is.

Efficiency Ratios Accounts receivable turnover ratio measures how quickly firm collects on its credit sales. The higher the frequency of turnover, the faster it converts credit sales into cash flows

Efficiency Ratios Days Sales Outstanding (DSO) measures number of days firm takes to convert receivables into cash. The fewer the days, the more efficient the firm. Note: an overzealous credit department may offend firm’s customers.

Asset Turnover Ratios Total asset turnover ratio measures level of sales firm generates per dollar of total assets. The higher the turnover, the more efficiently management is using total assets. More relevant for service industry firms.

Asset Turnover Ratios Fixed asset turnover ratio measures level of sales firm generates per dollar of fixed assets. Higher the fixed asset turnover, the more efficiently management uses plant and equipment. More relevant for equipment intensive firms (e.g. mfg).

Leverage Ratios Leverage ratios reflect ability of firm and owners to use equity to generate borrowed funds. Financial leverage refers to use of debt in firm’s capital structure.

Leverage Ratios Use of debt increases shareholders’ returns; tax benefits from interest payments on debt. Two sets of ratios can analyze leverage: Debt ratios quantify use of debt in capital structure; Coverage ratios measure firm’s ability to meet debt obligations.

Leverage Ratios Total debt ratio is calculated using short-term and long-term debt. The higher the amount of debt, the higher the firm’s leverage, and the more risky it is.

Leverage Ratios Debt to equity ratio is a second leverage ratio, measuring amount of debt per dollar of equity.

Leverage Ratios Equity multiplier or leverage multiplier reveals amount of assets firm has for every dollar of equity. Best measure of firm’s ability to leverage shareholders’ equity with borrowed funds.

Other Leverage Relationships Equity multiplier = 1 + Debt to equity ratio

Coverage Ratios Times interest earned measures number of dollars in operating earnings firm generates per dollar of interest expense.

Coverage Ratios Cash coverage ratio measures amount of cash firm has to meet its interest payments.

Profitability Ratios Gross profit margin measures amount of gross profit generated per dollar of net sales.

Profitability Ratios Operating profit margin measures the amount of operating profit generated by firm for each dollar of net sales.

Profitability Ratios Net profit margin measures amount of net income after taxes generated by firm for each dollar of net sales. In each case, the higher the ratio, the more profitable the firm. Management and creditors likely to focus on these profitability measures; shareholders likely to concentrate on two others.

Profitability Ratios Return on assets (ROA) ratio measures amount of net income per dollar of total assets. There are two approaches to calculate the return on assets. This ratio reveals how efficiently management utilized assets under their command.

Profitability Ratios Some analysts calculate return on assets as:

Profitability Ratios Return on equity (ROE) ratio measures dollar amount of net income per dollar of shareholders’ equity. For firm with no debt, ROA = ROE For firm with debt, ROE >ROA

Market Value Ratios The following ratios reveal how market views company’s liquidity, efficiency, leverage, profitability. Earnings per share (EPS) ratio measures income after taxes generated by firm for each share outstanding.

Market Value Ratios Price-earnings (P/E) ratio ties firm’s earnings per share to price per share. P/E ratio reflects investors’ expectations of firm’s future earnings growth.

The DuPont System Diagnostic Tool Set of related ratios that links balance sheet and income statement. Diagnostic tool for evaluating firm’s financial health. Used by management and shareholders to understand factors that drove firm’s ROE. Based on two equations that relate firm’s ROA and ROE.

The ROA Equation Return on assets (net income/total assets) can be broken down into two components: Profit margin and total assets turnover ratio Net profit margin measures management’s ability to generate sales & manage operating expenses.

The ROA Equation Total asset turnover reveals how efficiently management uses assets under its command; how much output can be generated with a given asset base. Thus, asset turnover measures asset use efficiency. The ROA equation says if management wants to increase firm’s ROA, it can increase profit margin, asset turnover, or both. Management can examine a poor ROA and determine whether the problem is operating efficiency or asset use efficiency.

The ROA Equation This equation is simply a restatement of equation 4.19. ROE is determined by firm’s ROA and its use of leverage. Firm with small ROA can increase ROE by using higher leverage.

The DuPont Equation Shows that a firm’s ROE is determined by three factors: Net profit margin, which measures firm’s operating efficiency. Total asset turnover, which measures firm’s asset use efficiency. The equity multiplier, which measures firm’s financial leverage.

Exhibit 4.5: Relations in the DuPont System of Analysis

Selecting a Benchmark A ratio analysis becomes relevant only when compared against a benchmark. Financial managers can create a benchmark for comparison in three ways: 1. Time-trend 2. Industry average 3. Peer group

Selecting a Benchmark Time-trend analysis Based on firm’s historical performance. Allows management to examine each ratio over time, determine whether trend is good or bad for firm.

Selecting a Benchmark Industry average analysis Another way of developing benchmark. Firms in same industry grouped by size, sales, and product lines, to establish benchmark ratios. Example

Selecting a Benchmark Peer group analysis Instead of selecting an entire industry, management may select firms similar in size or sales, or who compete in same market. Average ratios of this peer group would then be used as benchmark. Peer groups can be only 3 or 4 firms, depending on industry.

Limitations of Ratio Analysis Ratio analysis depends on accounting data based on historical costs. No theoretical backing in making judgments based on financial statement and ratio analysis. When doing industry or peer group analysis, one often encounters large, diversified firms that do not fit into any financial statement. Example comparing Apple to Apple, Vinashin example

Limitations of Ratio Analysis Time trend analysis could be distorted by financial statements affected by inflation. Multinational firms deal with many accounting standards. (GAAP, IFRS) Difficult to compare financial reports. Even among domestic firms, differences in accounting practices make comparisons difficult. FIFO versus LIFO

CHAPTER 5 The Time Value of Money

Time Value of Money Time Value of Money Future Value and Compounding Present Value and Discounting Finding the Interest Rate Rule of 72 Compound Growth Rates

The Time Value of Money Consuming Today or Tomorrow TVM is based on the belief that people prefer to consume goods today rather than wait to consume similar goods tomorrow. People have a positive time preference. Money has a time value because a dollar today is worth more than a dollar tomorrow.

The Time Value of Money Consuming Today or Tomorrow Today’s dollar can be invested to earn interest or spent. Value of a dollar invested (positive interest rate) grows over time. Rate of interest determines trade-off between spending today versus saving. Example: Inflation 18%, saving 14%, which is better, spend now or save now, spend later?

The Time Value of Money Timelines as Aids to Problem Solving Timelines are an easy way to visualize cash flows. Cash outflows as negative values. Cash inflows as positive values.

Exhibit 5.1: Five-year Timeline for $10,000 Investment

The Time Value of Money Future Value versus Present Value Financial decisions are evaluated either on a future value basis or present value basis. Future value measures what one or more cash flows are worth at the end of a specified period. Present value measures what one or more cash flows that are to be received in the future will be worth today (at t=0).

The Time Value of Money Future Value versus Present Value Compounding is the process of earning interest over time. Discounting is the process of converting future cash flows to their present values. Discounting rate

Exhibit 5.2: Future Value & Present Value Compared

Future Value and Compounding Single Period Investment We can determine the value of an investment at the end of one period if we know the interest rate to be earned by the investment. If you invest for one period at an interest rate of i, your investment, or principle, will grow by (1 + i) per dollar invested. The term (1+ i) is the future value interest factor, often called simply the future value factor.

Future Value and Compounding Two-Period Investing A two-period investment is simply two single-period investments back-to-back. After the first period, interest accrues on original investment (principle) and interest earned in preceding periods.

Future Value and Compounding Two-Period Investing The principal is the amount of money on which interest is paid. Simple interest is the amount of interest paid on the original principal amount only. Compounding interest consists of both simple interest and interest-on-interest.

Future Value and Compounding The Future Value Equation General equation to find the future value after any number of periods. The term (1 + i)n is the future value factor. We can use financial calculators or future value tables to find the future value factor at different interest rates and maturity periods.

Future Value and Compounding The general equation to find the future value is: where: FVn = future value of investment at the end of period n PV = original principle (P0) or present value i = the rate of interest per period, which is often a year n = the number of periods

Future Value and Compounding Future value example You leave your $100 invested in the bank savings account at 10 percent interest for five years. How much would you have in the bank at the end of five years?

Exhibit 5.4: How Compound Interest Grows

Future Value and Compounding Compounding More Frequently Than Once a Year The more frequently the interest payments are compounded, the larger the future value of $1 for a given time period. where: m = number of compounding periods in a year

Future Value and Compounding Non-annual compounding example You invest $100 in a bank account that pays a 5 percent interest rate semiannually for two years. How much would you have in the bank at the end of two years?

Future Value and Compounding When interest is compounded on a continuous basis, we can use the equation below. where: e = exponential function which is about 2.71828

Future Value and Compounding Continuous compounding example Your grandmother wants to put $10,000 in a savings account at a bank. How much money would she have at the end of five years if the bank paid 5 percent annual interest compounded continuously?

Using Excel: Time Value of Money

Using Excel: Time Value of Money Excel also has the following functions for time value of money problems. PV: PV(RATE, NPER, PMT, FV) FV: FV(RATE, NPER, PMT, PV) Discount Rate: RATE(NPER, PMT, PV, FV) Payment: PMT(RATE, NPER, PV, FV) Number of Periods: NPER(RATE, PMT, PV, FV)

Present Value and Discounting Present value calculations state the current value of a dollar in the future. This process is called discounting, and the interest rate i is known as the discount rate. The present value (PV) is often called the discounted value of future cash payments. The present value factor is more commonly called the discount factor.

Present Value and Discounting The equation below gives us the general equation to find the present value after any number of periods.

Present Value and Discounting Present value example Suppose you are interested in buying a new BMW 330 Sports Coupe a year from now. You estimate that the car will cost $40,000. If your local bank pays 5 percent interest on savings deposits, how much will you need to save to buy the car?

Present Value and Discounting The further in the future a dollar will be received, the less it is worth today. The higher the discount rate, the lower the present value of a dollar. Show formula

Finding the Interest Rate A number of situations will require you to determine the interest rate (or discount rate) for a given stream of future cash flows. For an individual investor or a firm, it may be necessary. to determine the return on an investment. to determine the interest rate on a loan. to determine a growth rate.

Examples Buy government bond price $90 each, in next 20 years, you receive $1000 value each bond. What is interest rate?

The Rule of 72 Rule of 72 is used to determine the amount of time it takes to double an investment. It says that the time to double your money (TDM) approximately equals 72/i, where i is expressed as a percentage. Rule of 72 is fairly accurate for interest rates between 5% and 20%.

Compound Growth Rates Compound growth occurs when the initial value of a number increases or decreases each period by the factor (1 + growth rate). Examples include population growth, earnings growth.

Compound Growth Rates Compound growth rate example Because of an advertising campaign, a firm’s sales increased from $20 million in 2007 to more than $35 million three years later. What has been the average annual growth rate in sales?

Discounted Cash Flows and Valuation CHAPTER 6 Discounted Cash Flows and Valuation

Level Cash Flows: Annuities and Perpetuities Quick Links Multiple Cash Flows Level Cash Flows: Annuities and Perpetuities Cash Flows That Grow at a Constant Rate The Effective Annual Interest Rate

Future Value of Multiple Cash Flows Solving future value problems with multiple cash flows. 1. Draw timeline to ascertain each cash flow is placed in correct time period. 2. Calculate future value of each cash flow for its time period. 3. Add up the future values.

Exhibit 6.1: Future Value of Two Cash Flows

Exhibit 6.2: Future Value of Three Cash Flows

Multiple Cash Flows Present Value of Multiple Cash Flows Many business situations call for computing present value of a series of expected future cash flows. Determining market value of security. Deciding whether to make capital investment Process similar to determining future value of multiple cash flows.

Multiple Cash Flows Present Value of Multiple Cash Flows First, prepare timeline to identify magnitude and timing of cash flows. Next, calculate present value of each cash flow using equation 5.4 from the previous chapter. Finally, add up all present values. Sum of present values of stream of future cash flows is their current market price, or value.

Exhibit 6.3: Present Value of Three Cash Flows

The Value of a Gift to the University Suppose that you made a gift to your university, pledging $1,000 per year for four years and $3,000 for the fifth year, for a total of $7,000. After making the first three payments, you decide to pay off the final two payments of your pledge because your financial situation has improved. How much should you pay to the university if the interest rate is 6 percent?

Buying a Used Car For a student—or anyone else—buying a used car can be a harrowing experience. Once you fi nd the car you want, the next diffi cult decision is choosing how to pay for it—cash or a loan. Suppose the cash price you have negotiated for the car is $5,600, but that amount will stretch your budget for the year. The dealer says, “No problem. The car is yours for $4,000 down and payments of $1,000 per year for the next two years. Or you can put $2,000 down and pay $2,000 per year for two years. The choice is yours.” Which offer is the best deal? The interest rate you can earn on your money is 8 percent.

The Investment Decision You are thinking of buying a business, and your investment adviser presents you with two possibilities. Both businesses are priced at $60,000, and you have only $60,000 to invest. She has provided you with the following annual and total cash flows for each business, along with the present value of the cash flows discounted at 10 percent: Cash flow ($ thousands) Business 1 2 3 Total A $50 $30 $ 20 $100 B $ 5 $ 5 $100 $110 Which business should you acquire?

Annuities and Perpetuities Level Cash Flows Annuities and Perpetuities Many situations exist where businesses and individuals would face either receiving or paying constant amount for a length of period. Individual investors may make constant payments on home or car loans, or invest fixed amount year after year saving for retirement.

Level Cash Flows Annuities and Perpetuities Annuity: any financial contract calling for equally spaced level cash flows over finite number of periods. Perpetuity: contract calling for level cash flow payments to continue forever. Ordinary annuities: constant cash flows occurring at end of each period.

Level Cash Flows Present Value of an Annuity Can calculate present value of annuity same way present value of multiple cash flows is calculated. Instead, simplify equation 5.4 in chapter 5 to obtain annuity factor. Results in equation 6.1 that can be used to calculate the annuity’s present value.

Exhibit 6.3: Present Value of Three Cash Flows

Level Cash Flows

Level Cash Flows Present Value of Annuity example A financial contract pays $2,000 at the end of each year for three years and the appropriate discount rate is 8% percent? What is the present value of these cash flows?

Level Cash Flows Finding Monthly or Yearly Payments Example You have just purchased a $450,000 condominium. You were able to put $50,000 down and obtain a 30-year fixed rate mortgage at 6.125 percent for the balance. What are your monthly payments?

Level Cash Flows Preparing a Loan Amortization Schedule Amortization: the way the borrowed amount (principal) is paid down over life of loan. Monthly loan payment is structured so each month portion of principal is paid off; at time loan matures, it is entirely paid off.

Exhibit 6.5: Amortization Table for a 5-Yr, $10K Loan

Level Cash Flows Preparing a Loan Amortization Schedule Amortized loan: each loan payment contains some payment of principal and an interest payment. Loan amortization schedule is a table showing: loan balance at beginning and end of each period. payment made during that period. how much of payment represents interest. how much represents repayment of principal.

Level Cash Flows Future Value of an Annuity Future value annuity calculations usually involve finding what a savings or investment activity is worth at some future point. E.g. saving periodically for vacation, car, house, or retirement. We can derive the future value annuity equation from the present value annuity equation (equation 6.1). This results in equation 6.2.

Level Cash Flows Future Value of an Annuity Equation

Exhibit 6.6: Future Value of 4-Yr Annuity

Level Cash Flows: Annuities and Perpetuities Finding the Interest Rate The present value of an annuity equation can be used to find the interest rate or discount rate for an annuity To determine the rate-of-return for an annuity, solve the equation for i Using a calculator is easier than a trial-and- error approach

Level Cash Flows Perpetuities A perpetuity is constant stream of cash flows that goes on for infinite period. In stock markets, preferred stock issues are considered to be perpetuities, with issuer paying a constant dividend to holders. Equation for present value of a perpetuity can be derived from present value of an annuity equation with n tending to infinity.

Level Cash Flows Perpetuities

Level Cash Flows Perpetuities - Example Suppose you decided to endow a chair in finance. The goal of the chair is to provide the chair holder with $100,000 of additional financial support per year forever. If the rate of interest is 8 percent, how much money will you have to give the university foundation to provide the desired level of support?

Exhibit 6.7: Ordinary Annuity versus Annuity Due

Level Cash Flows Annuity Due Annuity transformation method shows relationship between ordinary annuity and annuity due. Annuity due = Ordinary annuity value  (1+i) (6.4) Each period’s cash flow thus earns extra period of interest compared to ordinary annuity. Present or future value of annuity due is always higher than that of ordinary annuity.

Level Cash Flows Annuity Due Example The value of the annuity due shown in Exhibit 6.7B is: Annuity due = $3,312  (1.08) = $3,577

Cash Flows That Grow at a Constant Rate In addition to constant cash flow streams, one may have to deal with cash flows that grow at a constant rate over time. These cash-flow streams called growing annuities or growing perpetuities.

Cash Flows That Grow at a Constant Rate Growing Annuity Business may need to compute value of multiyear product or service contracts with cash flows that increase each year at constant rate. These are called growing annuities. Example of growing annuity: valuation of growing business whose cash flows increase every year at constant rate.

Cash Flows That Grow at a Constant Rate Growing Annuity Use this equation to value the present value of growing annuity (equation 6.5) when the growth rate is less than discount rate.

Growing Annuity Example Cash Flows That Grow at a Constant Rate Growing Annuity Example A coffee shop will be in business for 50-years. It produced $300,000 this year and the discount rate used by similar businesses is 15 percent. The cash flows will grow at 2.5 percent per year. What is the estimated value of the coffee shop?

Cash Flows That Grow at a Constant Rate Growing Perpetuity When cash flow stream features constant growing annuity forever. Can be derived from equation 6.5 when n tends to infinity and results in the following equation:

Growing Perpetuity Example Cash Flows That Grow at a Constant Rate Growing Perpetuity Example Your account reports that a firm’s cash flow last year was $450,000 and the appropriate discount rate for the club is 18 percent. You expect the firm’s cash flows to increase by 5 percent per year and that the business will have no fixed life. What is the value of the firm?

Effective Annual Interest Rate Interest rates can be quoted in financial markets in variety of ways. Most common quote, especially for a loan, is annual percentage rate (APR). APR represents simple interest accrued on loan or investment in a single period; annualized over a year by multiplying it by appropriate number of periods in a year.

Calculating the Effective Annual Rate (EAR) Effective Annual Interest Rate Calculating the Effective Annual Rate (EAR) Correct way to compute annualized rate is to reflect compounding that occurs; involves calculating effective annual rate (EAR). Effective annual interest rate (EAR) is defined as annual growth rate that takes compounding into account.

Calculating the Effective Annual Rate (EAR) Effective Annual Interest Rate Calculating the Effective Annual Rate (EAR) EAR = (1 + Quoted rate/m)m – 1 (6.7) m is the # of compounding periods during a year. EAR conversion formula accounts for number of compounding periods, thus effectively adjusts annualized interest rate for time value of money. EAR is the true cost of borrowing and lending.

Effective Annual Rate (EAR) Example Effective Annual Interest Rate Effective Annual Rate (EAR) Example Your credit card has an APR of 12 percent (1 percent per month). What is the effective annual interest rate? EAR = (1 + 0.12/12)12 – 1 = (1.01)12 – 1 = 1.1268 – 1 = 0.1286 or 12.68%

Examples: Calculating EAR Lender A: 10.40% compound monthly Lender B: 10.90% compound annually Lender C: 10.50% compound quarterly Who will you chose to borrow?

CHAPTER 7 Risk and Return

Risk and Return Future Value vs. Present Value The greater the risk, the larger the return investors require as compensation for bearing that risk. Higher risk means less certainty.

Quantitative Measures of Return Holding Period Returns Total holding period return consists of two components: 1) capital appreciation and 2) income. Capital appreciation component of a return, :

Quantitative Measures of Return Holding Period Returns Income component of a return RI: Total holding period return is simply

Quantitative Measures of Return Holding Period Returns Example One year ago today, you purchased a share of Dell Inc. stock for $26.50. Today it is worth $29.00. Dell paid no dividend on its stock. What total return did you earn on this stock over the past year?

Quantitative Measures of Return Expected Returns Example You estimate that there is 30 percent chance that your total return on your Dell stock investment will be -3.45 percent, a 30 percent chance that it will be 5.17 percent , a 30 percent chance that it will be 12.07 percent and a 10 percent chance that it will be 24.14 percent. Calculate your expected return.

Quantitative Measures of Return Expected Returns Expected value represents the sum of products of possible outcomes, and probabilities that those outcomes will be realized. Expected return, E(RAsset), is an average of possible returns from an investment, where each of these returns is weighted by the probability that it will occur:

Quantitative Measures of Return Expected Returns If each of the possible outcomes is equally likely (that is, p1 = p2 = p3 = … = pn = p = 1/n), the expected return formula reduces to:

Variance and Standard Deviation as Measures of Risk Calculating the Variance and Standard Deviation The variance (2) squares the difference between each possible occurrence and the mean (squaring the differences makes all the numbers positive), and multiplies each difference by its associated probability before summing them up: Take the square root of the variance to get the standard deviation ().

Variance and Standard Deviation as Measures of Risk Calculating the Variance and Standard Deviation If all possible outcomes are equally likely, the formula becomes:

= > σ = 0.0838 or 8.38%

Variance and Standard Deviation as Measures of Risk Interpreting the Variance and Standard Deviation Normal distribution is a symmetric frequency distribution that is completely described by its mean (average) and standard deviation. Normal distribution’s left and right sides are mirror images of each other. The mean falls directly in center of distribution. Probability that an outcome is a particular distance from the mean is the same, whether the outcome is on the left or the right side of the distribution.

Risk and Diversification The concept of diversification By investing in two or more assets whose values do not always move in same direction at same time, investors can reduce risk of investments or portfolio.

Risk and Diversification Single-Asset Portfolios Returns for individual stocks from one day to next are largely independent of each other and approximately normally distributed. A first pass at comparing risk and return for individual stocks is coefficient of variation, CV.

  Stock A Stock B E(R) 0,08 0,24 σ 0,06 CV 0,75 0,33

Risk and Diversification Portfolios with More than One Asset Coefficient of variation has a critical shortcoming not quite evident when only a single asset is considered. Expected return of portfolio made up of two assets:

Risk and Diversification Portfolios with More than One Asset Expected return of portfolio made up of multiple assets:

Risk and Diversification Expected return of Portfolio Example You invested $100,000 in Treasury bills that yield 4.5 percent; $150,000 in Proctor and Gamble stock, which has an expected return of 7.5 percent; and $150,000 in Exxon Mobil Corporation stock, which has an expected return of 9.0 percent. What is the expected return of this $400,000 portfolio?

Risk and Diversification Expected return of Portfolio Example -continued

Risk and Diversification Portfolios with More than One Asset Expected return of each asset must be found before applying either of the two above formulas; fraction of portfolio invested in each asset must also be known. Prices of two stocks in a portfolio will rarely change by the same amount and in the same direction at same time.

Risk and Diversification Portfolios with More than One Asset When stock prices move in opposite directions, the change in price of one stock offsets at least some of the change in price of other stock. Level of risk for portfolio of two stocks is less than average of risks associated with individual shares. The risk can be calculated with the variance equation below:

Risk and Diversification Portfolio Variance Example The variance of the annual returns of CSX and Wal- Mart stocks in Exhibit 7.6 are 0.03949 and 0.02584 respectively. The covariance between the annual returns of these stocks is 0.00782. Calculate the variance of the portfolio that consists of 50 percent CSX stock and 50 percent Wal-Mart stock.

Risk and Diversification Portfolios with More than One Asset In order to ease interpretation of covariance, we divide it by the product of the standard deviations of returns for the two assets. This gives the correlation coefficient between the returns on the two assets:

Risk and Diversification Correlation Coefficient Example Find the correlation coefficient between the annual returns of CSX and Wal-Mart in Exhibit 7.6.