Investing in Bonds: Go to the FINRA Bonds Quick Search Link: http://finra-markets.morningstar.com/BondCenter/Screener.jsp • • Click the Corporate check box under Bond Type then click Show Results. Choose any bond. Assume interest rates for bonds today is 5% for an AAA rated bond. Calculate the price of the bond you have selected relative to the 5%. Is the bond selling at a premium or a discount? Why? Be sure to show how you arrived at your answer. What other factors may influence the value of a bond? Utilize the reading materials to support your claims. 3 Polka Dot/Thinkstock Financial Forecasting Learning Objectives Upon completion of Chapter 3, you will be able to: • Construct a pro forma income statement using the percent of sales method. • Construct a pro forma balance sheet. • Complete a cash budget. byr80656_03_c03_043-076.indd 43 3/28/13 3:21 PM Introduction CHAPTER 3 F inancial management is forward-looking. Financial decisions almost always require predicting how the decision will affect the future value of the firm. Therefore, we need to have tools that will help us forecast the financial performance and financial position of the company. In this chapter we introduce two financial forecasting tools—pro forma (or projected) financial statements and the cash budget. Pro forma statements use the basic format of accounting statements to make financial forecasts. These projected (or pro forma) financial statements will be important as you progress through this textbook. The cash budget is similar to the register in your checkbook. It records cash receipts and outlays, and then shows when the company will have a cash surplus or a cash deficit. A cash surplus is cash in excess of the minimum amount required to keep the business operating on a day-to-day basis. As the feature box that follows illustrates, the cost of a cash surplus is great. Efficient firms invest this surplus to earn interest income. A cash deficit requires the company to arrange the appropriate amount and timing of funding through a credit line or short-term bank loan. Forecasting is necessary if a company is going to effectively invest its surplus cash or arrange for appropriate financing to cover deficits. Financial forecasting tools are not limited to predicting cash surpluses or shortages. They are much more versatile than that. These tools can be used to try out new policies and strategies before implementing them. By forecasting the financial impact of a new product, strategy, or policy before implementing it, a company can avoid costly mistakes. Moreover, forecasting helps show managers what steps need to be taken to help make the new plans or policies successful. Financial forecasting is an important part of the corporate planning process. The tools introduced in this chapter will be valuable as you pursue your business career. All companies should do financial forecasting, but it is particularly important for small, fast-growing companies with limited cash reserves. In the Web Resources at the end of Chapter 2, we list a New York Times article about why small firms fail. The top 10 reasons include too much growth, lack of a cash cushion, and poor accounting. This chapter introduces some tools that will help you avoid those three problems. Without some idea of where a company is heading financially, it is impossible to choose policies, plan new products, or determine how much to grow. Much of this chapter is about collecting, organizing, analyzing, and interpreting data. As you go through the chapter, think about where in a company the data might come from. For example, sales growth estimates require input from sales and marketing departments and may need to be modified based on economic information. Costs can come from many places in an organization—human resources, production, marketing, etc. We hope that as you progress through this textbook you will see that financial management doesn’t operate in a vacuum. It is woven into the fabric of the entire company and relies on other departments as much as those areas rely on finance. Financial forecasting may depend more than most other finance topics on an interchange between functional areas, but we should always be aware that we are part of a larger team, and we all need each other. byr80656_03_c03_043-076.indd 44 3/28/13 3:21 PM Section 3.1 Constructing Pro Forma Financial Statements CHAPTER 3 3.1 Constructing Pro Forma Financial Statements P ro forma financial statements (or projected finance statements) are powerful tools for the financial manager or analyst. They help the financial manager forecast how changes in policies will affect the company’s financial situation. For example, how will changing a company’s credit policy change the size of its short-term bank loan? One of our students who became an investment banker doing leveraged buyouts of companies says that he used pro forma statements more than any other financial tool. In this section we first show the mechanics of creating a pro forma income statement and balance sheet, and then we discuss where an analyst would get the information required for these statements. A Closer Look: The Cost of Holding Too Much Cash As odd as it sounds, having too much cash can be a problem. Why? Poor use of resources: In most firms cash keeps things going but does not add to earnings. Companies make money by investing their cash in whatever product or service they sell. Holding large cash balances (i.e., more than is needed to carry out the day-to-day transactions of the company) means that part of a company’s resources are not being used efficiently. One of the authors of this textbook has a relative who keeps a large part of his savings (about $10,000) in a coffee can buried in his garden. He has done this for years, occasionally adding some iStockphoto/Thinkstock money, sometimes raiding the can when he needs some cash. Over the past 10 years that money has earned Keeping too much cash on hand can nothing, while the stock market (the Dow Jones Indusactually cause problems for companies. trial Average) has gone from 3,000 to over 11,000—a 250% increase. Even a bank account paying 5% would have grown by 60% or 70% over that period. Having cash sit around is a waste. It needs to be put to work. If a company does not have good investment opportunities, the cash should be distributed to shareholders so they can invest it. Agency costs: A prominent financial economist, Michael Jensen, has argued that when companies have too much cash, managers tend to make poor decisions. His theory is that most managers want to run a large company. The bigger the company, the higher their pay, the more colleagues they can promote (and thereby the more loyalty they earn), the more prestige they attain, and so on. Excess cash (which he calls free cash flow) lets managers grow their companies without much monitoring to assure the growth makes sense. Jensen cited examples of companies with excess cash that entered markets they knew nothing about, made acquisitions that were later reversed, or used the cash to buy fancy offices, private jets, and other executive perks. He called such wasteful or misdirected spending agency costs of free cash flow to recognize that the source of the waste was often having too much cash on hand. (continued) byr80656_03_c03_043-076.indd 45 3/28/13 3:21 PM Section 3.1 Constructing Pro Forma Financial Statements CHAPTER 3 A Closer Look: The Cost of Holding Too Much Cash (continued) In July of 1999, the New York Society of Security Analysts (NYSSA) began studying how companies could enhance shareholder value. One of their first projects was an evaluation of National Presto, a housewares manufacturing company with headquarters in Eau Claire, Wisconsin. One of the NYSSA committee’s concerns was that National Presto held too much cash: 80% of its assets were in cash or cash equivalents. The committee’s analysts recommend paying a large cash dividend or using the cash to make an acquisition that would contribute to earnings. As it stands, cash and cash equivalents earn a very low return, especially when compared to the rise in the stock market over the last several years. The Income Statement A standard method for constructing pro forma income statements is to use historical percent of sales for many categories, supplementing with additional information when it is available. The approach is as follows: a. Obtain next year’s projected sales or the estimated sales growth for the coming year. b. Compute cost of goods sold, as a percent of sales based on historical data. If information is available about possible changes in the cost structure, this can be used to modify the estimate. c. Compute gross margin (sales minus cost of goods sold). d. Determine general, administrative, and sales expense; depreciation expense; and other expenses, based on historical patterns from previous years, or cost estimates from other departments. e. Compute taxable income by subtracting the expenses in (d) from the gross margin. f. Compute taxes using the companywide rate or rates from tax tables, then subtract taxes from taxable income to arrive at net income. Pro Forma Income Statement Example We will use the ACME Inc. income statements for 2011 and 2012 to construct a pro forma income statement for 2013 based on some assumptions about how the business will perform during 2013. The historical income statements for the company are given in Table 3.1. Here are our assumptions for 2013: • • • • • • byr80656_03_c03_043-076.indd 46 Sales will increase by 10% in 2013 from 2012 levels. COGS and SG&A will be the average percent of sales for the last 2 years. Depreciation expense will increase to $1,800. Interest expense will be $840. The tax rate is 25%. Dividend payout will remain at $650. 3/28/13 3:21 PM CHAPTER 3 Section 3.1 Constructing Pro Forma Financial Statements Table 3.1: ACME Inc. actual income statements 2011 2012 Revenue 45,000 48,000 COGS 32,400 34,560 12,600 13,440 SG&A expense 5,850 6,240 Depreciation expense 1,500 1,600 5,250 5,600 750 800 4,500 4,800 Taxes 1,125 1,200 Net income 3,375 3,600 600 650 2,775 2,950 Gross margin EBIT Interest expense Taxable income Dividends To retained earnings Sales will increase by 10% in 2013, so 1.10 3 $48,000 5 $52,800. In 2011 and 2012 COGS values were 72% of sales. We will assume that COGS remains 72% of sales in 2013. SG&A expense was 13% of sales in both 2011 and 2012, so we will use that percent of sales in 2013. We have the information we need to begin building the pro forma income statement, as shown in Table 3.2. Table 3.2 2011 (Actual) 2012 (Actual) 2013 (Projected) Source Revenue 45,000 48,000 52,800 10% growth COGS 32,400 34,560 38,016 72% of sales 12,600 13,440 14,784 Subtraction SG&A expense 5,850 6,240 6,864 13% of sales Depreciation expense 1,500 1,600 1,800 Given 5,250 5,600 6,120 Subtraction 750 800 840 4,500 4,800 5,280 Subtraction Taxes 1,125 1,200 1,320 25% of taxable income Net income 3,375 3,600 3,960 Subtraction 600 650 650 2,775 2,950 3,310 Gross margin EBIT Interest expense Taxable income Dividends To retained earnings byr80656_03_c03_043-076.indd 47 Given Given Subtraction 3/28/13 3:21 PM Section 3.1 Constructing Pro Forma Financial Statements CHAPTER 3 Starting with sales, we enter the information we have, subtract items to get gross margin, EBIT, and taxable income. We compute taxes at 25% and subtract them from taxable income to get net income. We subtract dividends from net income to determine how much money will be reinvested in the firm by adding it to retained earnings on the balance sheet. Notice that if the company wanted to retain more money for reinvestment on behalf of shareholders, it could do so by reducing dividends. This shows the two ways that shareholders earn a return on their investment: dividend payments and company growth through investment of earnings. The Balance Sheet Pro forma or projected balance sheets are often useful when analyzing the effect of corporate decisions on the company’s financial condition. One of the most common uses for a pro forma balance sheet is estimating future financial need, so a company can make arrangements for loans or lines of credit. Before a balance sheet can be constructed, the appropriate pro forma income statement must already be completed. Constructing a simple pro forma balance sheet usually requires four steps: Step 1: Fill in all of the values that don’t change, are known, or that change in a definite manner. These include items such as long-term debt and the common stock accounts. Step 2: Compute accumulated depreciation (or net fixed assets) and retained earnings that depend on values from the income statement. For example, accumulated depreciation at the end of 2013 will be the sum of accumulated depreciation at the end of 2012 plus depreciation expense during 2013 (sometimes if assets are sold during the year, further adjustment is necessary. Similarly, retained earnings at the end of 2013 will be the sum retained earnings at the end of 2012 plus net income retained (i.e., not paid out as dividends) during 2013. Step 3: Fill in all values that are projected according to company policy or that represent target policy values. These include inventory; accounts receivable; accounts payable; and property, plant, and equipment. Some of these will change as a percent of sales. Often the cash account is set at some minimum based on sales. Step 4: Add up the asset side of the balance sheet, and transfer that total to the liabilities and equity side. Balance the asset and liabilities by adjusting a plug figure, usually bank loans or notes payable, on the liabilities side of the balance sheet. If the bank loan is negative, make it zero, add up the liabilities, move that total to total assets, and adjust the asset side, with the cash account taking up whatever slack is necessary to balance things. We will go through the four steps with an example that builds on the pro forma income statement we just completed for ACME. The actual balance sheet for 2012 is shown in Table 3.3. We will construct the balance sheet for 2013 using the following assumptions: byr80656_03_c03_043-076.indd 48 3/28/13 3:21 PM CHAPTER 3 Section 3.1 Constructing Pro Forma Financial Statements • • • • • • The minimum cash balance is 3% of sales Working capital accounts (accounts receivable, accounts payable, and inventory) will be the same percent of sales in 2013 as they were in 2012. $4,000 of new PP&E will be purchased in 2013. Other current liabilities (CL) will remain at 2% of sales in 2013. There will be no changes in the common stock or long-term debt accounts. The plug figure (the last number entered that makes the balance sheet balance) is bank loan. Table 3.3 Assets as of December 31, 2012 Cash 1,440 Accounts receivable 3,840 Inventory 7,200 Total current assets 12,480 Property, plant, & equipment (PP&E) 24,570 Accumulated depreciation 8,900 Net PP&E 15,670 Total assets 28,150 Liabilities & equity as of December 31, 2012 Accounts payable 1,728 Bank loan (10%) 4,102 Other CL    960 Total current liabilities 6,790 Long-term debt (12%) 5,600 Common stock 1,000 Retained earnings 14,760 Total liabilities & equity 28,150 Step 1: Fill in all of the values that don’t change. The assumptions tell us that there will be no changes in the common stock or long-term debt accounts, so we can enter those numbers. Table 3.4 shows only the liability side of the balance sheet to highlight these two accounts. byr80656_03_c03_043-076.indd 49 3/28/13 3:21 PM CHAPTER 3 Section 3.1 Constructing Pro Forma Financial Statements Table 3.4 Liabilities & equity as of December 31, 2012 Accounts payable 1,728 Bank loan (10%) 4,102 Other CL as of December 31, 2013 (pro forma)    960 Total current liabilities 6,790 Long-term debt (12%) 5,600 5,600 Common stock 1,000 1,000 Retained earnings 14,760 Total liabilities & equity 28,150 Step 2: Move values from the income statement. Accumulated depreciation at the end of 2013 will be the sum of accumulated depreciation at the end of 2012 plus depreciation expense during 2013. This will be $1,800. Net income not paid out as dividends during 2013 will be $3,310. Table 3.5 shows the results. Table 3.5 Assets as of December 31, 2012 Property, plant, & equipment (PP&E) 24,570 Accumulated depreciation 8,900 Net PP&E 15,670 Liabilities & equity as of December 31, 2012 Long-term debt (12%) 5,600 Common stock 1,000 Retained earnings 14,760 Total liabilities & equity 28,150 as of December 31, 2013 (pro forma) 10,700 18,070 Step 3: Fill in values determined by company policy. The assumptions tell us that the cash account needs to be at least 3% of sales. We will start with this amount ($1,584) and adjust it later if necessary. Other current liabilities (CL) will remain at 2% of sales, which is $1,056 5 0.02 3 $52,800. byr80656_03_c03_043-076.indd 50 3/28/13 3:21 PM CHAPTER 3 Section 3.1 Constructing Pro Forma Financial Statements Working capital accounts (inventory, accounts receivable, accounts payable) will be the same percent of sales in 2013 as in 2012. We compute those numbers by dividing each of the 2012 balances for these accounts by $48,000, the sales for 2012. We find that accounts receivable is 8% of sales, inventory is 15%, and accounts payable is 3.6%. To find the 2013 values for these accounts, we multiply 2013 projected sales of $52,800 by the appropriate percent. The value of accounts receivable in 2013 will be $4,224. The value of inventory in 2013 will be $7,920. The value of accounts payable in 2013 will be $1,900.80. The final policy assumption or plan is that $4,000 of new property, plant, and equipment (PP&E) will be purchased. Putting these items into the balance sheet results in Table 3.6. Table 3.6 Assets as of December 31, 2012 as of December 31, 2013 (pro forma) Cash 1,440 1,584 Accounts receivable 3,840 4,224 Inventory 7,200 7,920 Total current assets 12,480 Property, plant, & equipment (PP&E) 24,570 28,570 8,900 10,700 Accumulated depreciation Net PP&E 15,670 Total assets 28,150 Liabilities & equity as of December 31, 2012 Accounts payable 1,728 Bank loan (10%) 4,102 Other CL    960 as of December 31, 2013 (pro forma) 1,901 1,056 Total current liabilities 6,790 Long-term debt (12%) 5,600 5,600 Common stock 1,000 1,000 Retained earnings 14,760 18,070 Total liabilities & equity 28,150 Step 4: Add up the asset side of the balance sheet and transfer that total to the liabilities & equity side. Balance the asset and liabilities by adjusting a plug figure (bank loan). We do this in Table 3.7. We include an explanation for each of the entries. byr80656_03_c03_043-076.indd 51 3/28/13 3:21 PM CHAPTER 3 Section 3.1 Constructing Pro Forma Financial Statements Table 3.7 Assets as of December 31, 2012 as of December 31, 2013 (pro forma) Explanation Cash 1,440 1,584 3% of sales Accounts receivable 3,840 4,224 8% of sales Inventory 7,200 7,920 15% of sales Total current assets 12,480 13,728 Sum Property, plant, & equipment (PP&E) 24,570 28,570 Plus $4,000 purchased in 2013 8,900 10,700 2012 value plus 2013 depreciation expense Net PP&E 15,670 17,870 Subtraction Total assets 28,150 31,598 Current assets plus net PP&E Liabilities & equity as of December 31, 2012 as of December 31, 2013 (pro forma) Explanation Accumulated depreciation Accounts payable 1,728 1,901 5% of COGS Bank loan (10%) 4,102 3,971 Subtraction: total current liabilities – other CL – accounts payable    960 1,056 2% of sales Total current liabilities 6,790 6,928 Subtraction: TL&E – long-term debt – common stock – retained earnings Long-term debt (12%) 5,600 5,600 No change Common stock 1,000 1,000 No change Retained earnings 14,760 18,070 2012 value 1 2013 earnings retained from income statement Total liabilities & equity 28,150 31,598 From total assets Other CL byr80656_03_c03_043-076.indd 52 3/28/13 3:21 PM CHAPTER 3 Section 3.1 Constructing Pro Forma Financial Statements More on Pro Forma Statements There are several aspects of pro forma statements that are worth discussing in further detail. These include interest expense, negative bank loan plug figures, differences in intrayear and end-of-year financing needs, and using the “days” approach instead of the point-of-sales method. Interest Expense The pro forma financial statements we just completed give an initial estimate of a company’s profitability and financing needs. In this example the interest expense for 2013 was given as $840, but if you look at the balance sheet, you see that it should be higher. With $5,600 of long-term debt at 12% and $3,971 of short-term debt (bank loan) at 10%, the interest is then $1,069 5 12% 3 $5,600 1 10% 3 $3,971 To develop a more precise and accurate forecast, we should replace the $840 of interest expense with the calculated value of $1,069. Doing this would reduce net income and the amount added to retained earnings on the balance sheet. This effect would filter up the liabilities, eventually making the short-term loan need greater. We would then have a new interest expense value and would have to complete this process a second time. Usually one or two such iterations get to a bank loan and interest expense combination that doesn’t change very much. That is, we converge on an answer that has acceptable accuracy. Table 3.8 shows just the key items that change as the new interest expense is inserted into the income statement. From $840, interest expense increases to $1,069. This decreases net income, so less money is retained, making the bank loan larger. The larger bank loan balance requires more interest ($1,086), as shown in the bottom row under Iteration 2. Iteration 3 shows that the loan and interest have again increased. By Iteration 4, interest expense no longer changes, so we have converged on our final bank loan amount and interest expense. Table 3.8: Finding the interest rate 2013 (Projected) Iteration 1 2013 (Projected) Iteration 2 2013 (Projected) Iteration 3 2013 (Projected) Iteration 4 6,120 6,120 6,120 6,120 840 1,069 1,086 1,087 Taxable income 5,280 5,051 5,034 5,032 Taxes 1,320 1,263 1,258 1,258 Net income 3,960 3,788 3,775 3,774 650 650 650 650 3,310 3,138 3,125 3,124 EBIT Interest expense Dividends To retained earnings (continued) byr80656_03_c03_043-076.indd 53 3/28/13 3:21 PM CHAPTER 3 Section 3.1 Constructing Pro Forma Financial Statements Table 3.8: Finding the interest rate (continued) 2013 (Projected) Iteration 1 2013 (Projected) Iteration 2 2013 (Projected) Iteration 3 2013 (Projected) Iteration 4 Accounts payable 1,901 1,901 1,901 1,901 Bank loan (10%) 3,971 4,143 4,156 4,157 Other CL 1,056 1,056 1,056 1,056 Total current liabilities 6,928 7,100 7,113 7,114 Long-term debt (12%) 5,600 5,600 5,600 5,600 Common stock 1,000 1,000 1,000 1,000 Retained earnings 18,070 17,898 17,885 17,884 Total liabilities & equity 31,598 31,598 31,598 31,598 Corrected interest expense (10% 3 bank loan 1 12% 3 long-term debt) 1,069.10 1,086.28 1,087.57 1,087.67 You might ask why we cannot program our spreadsheet to compute this final solution for us. If you create a spreadsheet in which interest expense is a function of debt amounts, and debt amounts rely on net income (which is determined by interest expense), then you have a circular system. Spreadsheets can’t cope with circular arguments. Excel- has a feature that addresses this problem. It is called “Calculate Iterations” and can be switched on under “Preferences.” Negative Bank Loan Plug Figure The plug figure is the number that varies so the balance sheet balances. Usually this is a short-term loan account. Sometimes the plug figure will be negative. We cannot have a negative loan amount, so we need to adjust the balance sheet so that the loan is zero. We will need to add the amount of the negative loan to cash, as a positive number (e.g., if the loan is 227, you would add 27 to cash), and then make all of the adjustments down the asset side of the balance sheet (total current assets and total assets both increase). Then we use the new total assets as the total liabilities & equity and work up that side of the balance sheet until the loan plug figure becomes zero. End-of-Year Versus Intrayear Financing Need The pro forma statements we created showed that the company needed a certain bank loan at the end of the fiscal year. If a company has relatively level sales or constant sales growth, the end-of-the-year estimate is appropriate. However, if the company has seasonal sales, the end-of-the-year estimate could be far from the company’s real financing need. In a company with seasonal sales, the greatest financial need is almost always at the byr80656_03_c03_043-076.indd 54 3/28/13 3:21 PM Section 3.1 Constructing Pro Forma Financial Statements CHAPTER 3 start of the high season. Production in preparation for the high sales period requires large outlays, but money hasn’t started coming in. When doing financial forecasting it is important to do the forecast when the need is likely to be greatest, even if this doesn’t coincide with the company’s fiscal year. Days Versus Percent of Sales We have used the percent-of-sales method to construct pro forma financial statements in this chapter. Another, equivalent, approach, is using “days” or activity ratios. In our example accounts receivable were computed as 8% of sales. We could have said that number of accounts receivable days was 29.2 days (8% of 365 days) and arrived at the same dollar amount of accounts receivable. Accounts receivable days is also called days sales outstanding. Inventory and accounts payable can also be expressed in terms of days. In accounting these are referred to as activity or efficiency ratios. The “days” approach works well sometimes because it immediately shows whether a company is following its stated policy. If the number of accounts receivable days is 47, but the company’s stated credit policy is payment within 30 days, then either the collection system isn’t working or the company is extending credit to higher-risk customers than it should. Similarly, a company could have a policy of paying its suppliers on time, but the activity ratio might show that it is, on average, late. This could harm the company’s relationship with the supplier. In fact, if it occurs too often the supplier could sever the relationship or require cash on delivery. If you are given days, you need to be aware that the value of the accounts receivable account is based on sales, but the values of inventory and accounts payable are based on costs. Thus, a 30-day payable period would translate into accounts payable as 30/365 3 (credit purchases) or 30/365 3 COGS. Here are the standard formulas for activity ratios, which should allow you to make the translation from days to percent of sales, and then to dollars: Accounts Receivable Days 5 365 3 Accounts Receivable/Sales Accounts Payable Days 5 365 3 Accounts Payable/COGS Inventory Days 5 365 3 Inventory/COGS See Demonstration Problem 3.1 for an example. Sometimes you will see accountants using 360 days instead of 365. The important thing is to be consistent. The 5 fewer days usually won’t have a huge impact on forecasts. For a more accurate result if a company is growing (or shrinking), average the balance sheet items from the start of the period and the end of the period. For example, if the values of accounts receivable at the end of 2013 and 2014 were, respectively, $500 and $700, the average would be $600. This average better matches the sales from the income statement, which is measured over the entire year. byr80656_03_c03_043-076.indd 55 3/28/13 3:21 PM CHAPTER 3 Section 3.2 The Cash Budget Demonstration Problem 3.1: The Days Model During 1999 Taylor Enterprises had sales of $358,920 and associated cost of goods sold of $241,481. The average accounts receivable balance for 1999 was $27,534, while the average inventory balance was $43,003. Accounts payable averaged $15,127 during 1999. Use these data to compute Taylor Enterprises’s financing gap in days and in dollars. Solution: First compute the following three activity ratios: receivable days 5 5 inventory turnover days 5 5 accounts payable days 5 5 average accounts receivable 3 365 days annual credit sales 27,534 3 365 5 28 days 358,920 average inventory 3 365 days cost of goods sold 43,003 3 365 5 65 days 241,481 average accounts payable 3 365 days cost of goods sold 15,217 3 365 5 23 days 241,481 We combine these activity ratios into the days model as follows: Financing Gap in Days 5 Receivables Days 1 Inventory Turnover Days 2 Accounts Payable Days 5 28 1 65 2 23 5 70 days We transform days into dollars by multiplying the financing gap in days by the cost of goods sold per day. This gives us a rough estimate of how much money is required to see the company through until it begins collecting cash from customers. Thus Financing Gap in Dollars 5 Financing Gap in Days 3 Cost of Goods Sold per Day 5 70 days 3 5 $46,311 COGS 241,481 3 365 days 365 Thus, the firm needs a cash buffer of approximately $46,311 to support its activities until cash arrives from the collection of accounts receivable. 3.2 The Cash Budget C ompanies use many types of budgets: production budgets, capital budgets, marketing budgets, and more. All budgets are planning tools. They show what the company plans to do in the future in some activity area. Production budgets show the number of units of each product that the company manufactures and the costs of that production. Capital budgets determine what long-lived assets will be purchased and thereby define how the company operates. We discuss capital budgeting in much more detail in Chapter 7. The marketing budget ensures that potential customers hear about your products. We have included a short article about creating a marketing budget in the Web Resources section at the end of this chapter. byr80656_03_c03_043-076.indd 56 3/28/13 3:21 PM Section 3.2 The Cash Budget CHAPTER 3 The budget we focus on in this chapter is the cash budget. The cash budget is the primary planning tool for short-term finance. Its purpose is to predict shortages and surpluses of cash. The cash budget is especially important as an early warning of insolvency or periods of cash shortages. It gives the firm time to accumulate cash reserves, reduce the period of its cash cycle, or arrange for credit. For example, a firm with seasonal sales may generate a large cash surplus during its busy season, but operate at a deficit during its low season. Knowing how much of the surplus cash it must keep to get through the following low period helps managers plan. For many companies creating a monthly cash budget for the next 6 months or a year is very effective. This schedule matches many business transactions, which occur on a monthly schedule (e.g., employees are paid every 2 weeks or monthly, bills are paid monthly, credit terms are often 30 days, etc). A company with potentially large fluctuations in cash, such as a casino, might prepare cash budgets on a weekly basis, or update the cash budget whenever a large cash outlay occurs (when someone wins big!). Because distant cash flows are difficult to forecast on a weekly basis, it makes sense to use monthly budgets for the year ahead, and then weekly budgets for the immediately upcoming 1 or 2 months. A common practice is to use rolling budgets. Each month, a new month is added, and each week a new week is added. In this way, the company always has a budget for 12 months and 8 weeks ahead, for example. Donald Reilly/The New Yorker Collection/www.cartoonbank.com Creating a Cash Budget The cash budget involves virtually all elements of the firm. The budget hinges on sales forecasts from the marketing and sales staff and possibly economic consultants. Credit policies determine collection periods. Purchasing, production, and human resources staff must provide essential information on inventory purchases and payments, labor costs, and production schedules. Support groups, such as information systems, the legal department, and engineering must forecast expenses. The capital budget (plans for purchases of large equipment or fixed assets) must be included. All of these functional elements in the corporation have a stake in the cash budget because they depend on money being available as needed. Poor cash planning could result in a cash shortage that would disrupt important business activities. Cash budgets always begin with a sales forecast. Cash receipts and many expenses are tied directly to sales activity, making an accurate sales forecast essential. Sales forecasts may come from two sources, the sales department and corporate, or outside, economists. Salespeople know their customers and competitors, but they may not understand demographic, economic, and industry trends that affect future sales. Forecasts from these two sources can be combined to produce the best available forecast. byr80656_03_c03_043-076.indd 57 3/28/13 3:21 PM Section 3.2 The Cash Budget CHAPTER 3 Most companies make at least some of their sales on credit. Therefore, the cash budget must reflect the timing of collection of these receivables. The forecast of cash receipts (when cash actually is collected) will be based on the historic pattern of collections. For example, 10% of sales might be for cash, so the money is collected at the time of the sale. Sometimes companies offer a small discount for cash sales, such as 2% below the list price. Another portion may be credit sales that will be paid within 1 month. These two parts of the pattern (2% discount for cash sales and payment at full price within 1 month) would be reflected in the credit terms 2% 10/Net 30, which translates as a 2% discount for payment within 10 days, and full payment (i.e., no discount), within 30 days. Finally, there may be some sales that are slow to collect, so the cash only arrives 2 months after the sale. If we want, we can include some small percentage for bad accounts. There maybe a pattern for purchasing raw materials or inventory for resale. Many of these expenses are tied to production, which may precede sales by several weeks or months. This payment pattern needs to be identified to ensure that the cash budget has the correct timing of cash expenditures. If the company purchases materials or inventory on credit, then the cash budget will reflect the payment schedule that the company uses. It may pay some bills immediately to obtain a discount or wait until the end of the 30-day or 45-day credit period, thereby postponing its outlay and getting more use of the cash. The company can often forecast its tax payments and any significant outlays for new equipment. Wage and salary expenses are usually paid in the month in which they are incurred. In some states businesses are required to pay hourly employees every 2 weeks, while salaried employees can be paid monthly or on an even longer schedule. Cash Budget Example Shining Star Manufacturing Inc. makes a variety of large metal seasonal decorations, such as snowflakes, reindeer, snowmen, etc., which are used in shopping malls and municipal parks. The business is highly seasonal, with revenues peaking in the late summer and fall, then dropping to very low levels the rest of the year. In the past the company has used a short-term bank loan to get through the last few months of the low season and to have the necessary cash to begin to produce inventory for the next high sales period. It is important that Shining Star estimate its cash needs, and the timing of those needs, so that it can make sure sufficient cash will be available from its bank. It is early July 2013. Shining Star Manufacturing is getting close to its next production cycle, and its cash surplus from the previous year is getting small. It needs to estimate its loan need for the upcoming season. Shining Star’s banker will need to know both the maximum amount and the timing of the need (e.g., when the credit line will be accessed and when it will be repaid). To determine the loan amount and timing, we will create a cash budget for the months July through December. Cash Receipts We begin by computing the cash receipts. This requires a pattern of collections. Historically, customers have paid as follows: • byr80656_03_c03_043-076.indd 58 The company offers customers a 5% discount if they pay at the time of sale. About 20% of the customers take advantage of this discount. This means that for every $100 of merchandise sold, Shining Star collects $19.00 in the sale month. 3/28/13 3:21 PM CHAPTER 3 Section 3.2 The Cash Budget • This represents 20% of the sales being sold at a 5% discount or at 95% of full price ($100 3 0.20 3 0.95 5 $19.00). Credit sales: 50% of each month’s sales are collected 1 month after the sale, and 30% are collected 2 months after the sale. Table 3.9 lists the sales forecasts for the next 7 months (and actual sales for May and June). Table 3.9: Shining Star sales forecasts Month May 2013 June 2013 July 2013 August 2013 September 2013 October 2013 November 2013 December 2013 January 2014 Sales ($000s) 200 200 250 500 650 700 500 250 200 The cash budget begins in July, so we need the cash receipts for July. These will come from three different sources: cash sales made in July, collection of credit sales made in June (customers paying in 30 days), and the collection of credit sales made in May (customers paying in 60 days). In July $50,000 of merchandise is sold for cash, but those customers receive a 5% discount, so the money received is $47,500. Credit customers from June send in $100,000. This is 50% of June sales. Finally, some late payers from May send in $60,000. This is 30% of May sales of $200,000. The total cash inflow for July 2012 is $207,500. This pattern is repeated for August through December. Figure 3.1 shows the details of the cash receipts for July and August 2012, and the totals for the other months through December. As a test of your understanding, make sure that you can reach the same totals for September through December. Figure 3.1: Shining Star cash receipts byr80656_03_c03_043-076.indd 59 Month May June July August September October November December Sales 200 200 250 500 650 700 500 250 Cash 47.50 95.00 30-day 100.00 125.00 60-day 60.00 60.00 Total 207.50 280.00 448.50 608.00 640.00 507.50 3/28/13 3:21 PM CHAPTER 3 Section 3.2 The Cash Budget Cash Expenditures Expenditures can have different payment patterns. Employee wages are usually paid every 2 weeks or monthly. Payments for materials depend on the credit terms offered by suppliers. Raw materials and employee wages depend on the quantity of items being produced, which in turn depends on sales. Some payments occur sporadically, such as quarterly tax payments or outlays for new equipment. The Shining Star Manufacturing example demonstrates several of these potential patterns. Raw Materials Raw materials comprise a significant portion of costs of goods sold for Shining Star. In fact, raw materials average 60% of sales. The cash outlay pattern for raw materials follows this pattern: Materials are ordered 2 months in advance and are paid for the following month. So, materials for July are ordered in May and paid for in June. Figure 3.2 shows this ordering and payment pattern for July and August sales. In July the company will pay for August’s raw materials. The outlay will be 60% of August’s sales, or 60% of $500,000, which is $300,000. September sales of $650,000 require $390,000 of raw materials, which are ordered in July and paid for in August. Figure 3.2: Shining Star raw materials purchases Month Raw Materials May July materials are ordered in May June July August July materials are paid for in June August materials are ordered in June August materials are paid for in July Other Expenditures As we mentioned earlier in the chapter, many states require that hourly employees be paid every 2 weeks and in a timely manner. Shining Star’s manufacturing process doesn’t take much time, so items are produced as orders arrive. The company pays its employees in the month of production, which is also the month of sales. Manufacturing labor is 20% of sales, so manufacturing wages in July will be 20% of July sales (0.20 3 $250,000 5 $50,000) and will be paid for in July. Similarly, manufacturing wages in August will be 20% of August sales (0.20 3 $500,000 5 $100.000) and will be paid for in August. Some expenditures are fixed, so they don’t vary from month to month. For example, managerial salaries ($30,000 per month) and rent and lease payments ($15,000 per month) are fixed costs. Other expenditures occur once or a few times a year. Quarterly tax payments are a good example of such a payment pattern. Shining Star will make tax payments of $25,000 in September and December. The company plans on buying a new fabricating byr80656_03_c03_043-076.indd 60 3/28/13 3:21 PM CHAPTER 3 Section 3.2 The Cash Budget machine in August for $100,000. We can now complete the expenditure portion of the cash budget. Figure 3.3 shows all expenditures for July through September and totals for October through December. Be sure that you can compute these totals. Figure 3.3: Shining Star cash expenditures Month July August September October November December January Sales ($000s) 250 500 650 700 500 250 200 Raw Materials 300 390 420 Manufacturing Labor 50 100 130 Salaries 30 30 30 Rent 15 15 15 485 295 240 25 Taxes New Machine Total Cash Outlays 100 395 635 620 Table 3.10 shows what we have completed so far. Table 3.10 Month Sales ($000s) Cash receipts May 2012 200 Jun 2012 200 Jul 2012 250 47.5 Aug 2012 500 95 Sep 2012 Oct 2012 Nov 2012 650 700 500 123.5 133 95 Dec 2012 250 100 125 250 325 350 250 60-day 60 60 75 150 195 210 Total receipts 207.5 280 448.5 608 640 507.5 Materials 300 390 420 300 150 120 Labor 50 100 130 140 100 50 Salaries 30 30 30 30 30 30 Rent/leases 15 15 15 15 15 15 25 New machinery Total expenditures byr80656_03_c03_043-076.indd 61 200 47.5 30-day Taxes Jan 2013 25 100 395 635 620 485 295 240 3/28/13 3:21 PM CHAPTER 3 Section 3.2 The Cash Budget Changes in Cash, Loan Need, and Surpluses The final stage of creating a cash budget is like tracking your checking account balance. Shining Star has a cash balance of $110,000 at the beginning of July. This $110,000 is the last of the company’s cash surpluses from its previous high season of sales. The company needs at least $50,000 as a cash buffer or minimum cash balance. At the beginning of July there is no loan outstanding. The company has a cash surplus—the $110,000 cash balance exceeds its $50,000 minimum—so it has no need for a loan. For each month from July through December, we will calculate the change in cash due to cash collections and outlays. We will compare this to the cash balance and determine if the company has a cash surplus (cash balance greater than $50) or needs a loan to reach the $50,000 minimum cash balance amount. We will accumulate the loan amounts so that we can tell the banker the size of the loan the company will need at its maximum borrowing. Figure 3.4 shows this process for the months July through October. It also gives the final result (surplus or loan) for November and December. Be sure you can compute these results for those 2 months. Figure 3.4: Shining Star cash surpluses and loans (in thousands of dollars) Month July August September October November December Cash Receipts 207.50 280.00 448.50 608.00 640.00 507.50 Cash Outlays 395.00 635.00 620.00 485.00 295.00 240.00 –187.50 –355.00 –171.50 123.00 345.00 267.50 50.00 Change in Cash Beginning Cash 110.00 50.00 50.00 50.00 End Cash Without Loan –77.50 –305.00 –121.50 173.00 Loan 127.50 355.00 171.50 0.00 50.00 50.00 50.00 50.00 End Cash With Loan Loan Repayment Cumulative Loan Cash Surplus 123.00 127.50 482.50 654.00 531.00 186.00 0.00 81.50 The cash budget shows us that as the company begins to increase its spending in July (acquiring raw materials for August manufacturing), it quickly runs a cash shortage. This need grows through September, reaching a maximum loan of $654,000. As production slows and the company begins to collect cash from customers, the loan is paid down and eventually a surplus emerges in December. byr80656_03_c03_043-076.indd 62 3/28/13 3:21 PM Section 3.2 The Cash Budget CHAPTER 3 Recognize the Limitations of End-of-Month Accounting The cash budget suggests that if the company arranges for a loan of $654,000, then it will never have a cash shortage, but this is not quite true. The amounts in the cash budget are for the end of the month. We don’t know the timing of cash outlays and cash receipts within the month. If the company must pay its bills at the beginning of the month but only receives its cash at the end of the month, there could be a deficit. The $50,000 cash buffer was chosen to cover this deficit, but be aware that the cash budget reports only end-of-month balances, and we don’t know about the intramonth timing of cash flows. If this is a problem, the company may need to create a cash budget using 2-week intervals instead of the 1-month periods in this cash budget. This concern also applies to pro forma financial statements. Understand Your Assumptions Spreadsheet programs make creating forecasts with pro formas and cash budgets fairly easy. But you need to keep in mind that the mechanical structure of the forecast, while important, is less important than the content you enter into the model. There is a phrase from computer science that is applicable here: garbage in–garbage out (GIGO). If you build your forecast using unrealistic numbers, the result will be incorrect. It is crucial that you think about the assumptions you use in your forecasting model. As you prepare your forecasts, you need to ask yourself questions such as: Does the cost of goods sold number match cost data? Does sales growth match market and overall economic conditions? Are accounts receivable based on the company’s credit policy and customer mix? We have included two short articles about financial forecasting assumptions in the Web Resources at the end of the chapter. Here is an example of how constructing financial forecasts without paying close attention to the underlying assumptions can be costly. The owner and manager of a local business selling green and eco-friendly building supplies and home furnishings was raising money to expand her business, so a neighbor decided to invest in the business. The financial forecasts all looked great and supported expansion. At this time the first signs of the real estate crash were being felt in several U.S. states, but the market the store served was doing fine. A new location was found, the space was remodeled, new lines of inventory were purchased, and then the local real estate market softened. For the next 2 years only a handful of new houses were built in the multicounty region. Sales at the store eroded, and eventually it closed. The financial forecasts were based entirely on how the real estate market had behaved, not on what was likely to happen in the future. Had the pro forma statements been based on less optimistic growth forecasts, the expansion plan would have been postponed, and the store might have weathered the recession. That one key assumption about sales growth doomed the store to failure. Use Information from Other Company Departments We began this chapter by saying that financial forecasting requires information from throughout the firm. Sales forecasts come from marketing and salespeople as well as managers observing the overall economy. Costs come from across the company—human resources, production, inventory managers, and so on. We have to recognize that good byr80656_03_c03_043-076.indd 63 3/28/13 3:21 PM Summary CHAPTER 3 forecasts (i.e., accurate forecasts) depend on good information. Finance is just one of many important functional areas in a company. If your career takes you into financial management, be sure to get to know colleagues in other departments. In the Web Resources at the end of the chapter, there is a short article from the Financial Times that discusses how silo thinking (not going beyond one’s own narrow area) contributed to the fall of the investment banking firm Lehmann Brothers. To be effective in finance you have to get out of the finance silo! Financial Forecasting and Business Policy and Strategy While introducing the construction of pro forma financial statements and cash budgets, we focused on estimating cash need. But these tools, especially pro forma statements, can do much more. Forecasting lets you test policy changes before implementation to be sure that they will create value for the company. For example, new credit policies can be examined to see how the tradeoff between offering credit to more customers, thereby increasing sales, and enduring more bad debt expenses affects profits. As a company considers an expansion or the launch of a new product line, it can use pro forma statements to determine how much working capital and long-term funding it will need. Forecasting can be applied to any changes with financial ramifications. If the human resources department proposes a more generous family leave policy, pro forma financial statements can be used to estimate how higher employee retention, and lower recruiting and training costs, will offset anticipated costs of the program. Financial forecasting tools are quite versatile. Many of our students have commented that these are the financial tools they use most often once they join a business. Summary T his chapter introduced two financial forecasting tools—pro forma (or projected) financial statements and the cash budget. These forecasting tools will be important not only as you progress through this your study of finance, but also during your business career. All companies need to do financial forecasting, but it is particularly important for small, fast-growing companies with limited cash reserves. Forecasting can help companies avoid some of the problems that lead to business failure. Without forecasts managers are driving the company without a map. While the chapter focused primarily on the mechanics of pro forma statements and cash budgets, it also discussed the limitations of these tools. The results of a forecast are only as good as the inputs and assumptions used to create them—the garbage in–garbage out scenario. You can improve the quality of the forecasts by reaching out to people beyond the finance department for information. Financial forecasting is a great example of the interdependence among all of a company’s departments. byr80656_03_c03_043-076.indd 64 3/28/13 3:21 PM CHAPTER 3 Web Resources Key Terms activity ratios Ratios that express balance sheet items in terms of days rather than percent of sales. GIGO Garbage in–garbage out. capital budget Planned expenditures on long-lived assets such as machines and equipment. plug figure The balance sheet item that varies to make the balance sheet balance. It is often a short-term loan account but can vary depending on the needs of the analysis. cash budget An estimation of the cash inflows and outflows for a business or individual for a specific period of time. pro forma financial statements Projected or anticipated financial statements. They help the company plan for the future. cash surplus Cash balances in excess of the minimum required cash balance. Surplus cash can be invested to earn income. rolling budget A cash budget that drops the most recent month and adds a future month so the forecast always covers a given number of months. credit terms The payment terms given to customers, which often include the size of the discount for early payment, the length of the early payment period, and how many days after purchase before the bill is overdue. An example is 2% 10/Net 30, which translates as a 2% discount if paid within 10 days of the sale, but the full amount is due within 30 days of the sale. Web Resources This article discusses how the sales forecast drives much of financial forecasting: http://www.esmalloffice.com/SBR_template.cfm?DocNumber=PL10_0100.htm. This article from the U.S. government’s Small Business Administration, which has lots of resources for people thinking about or running their own small companies, discusses how to create a marketing budget: http://www.sba.gov/community/blogs/how-set-marketing-budget-fits-your-business -goals-and-provides-high-return-investmen. To find information for forecasts, follow links at the bottom of the first webpage for details on sales and expense forecasting: http://www.smallbusiness.wa.gov.au/financial-forecasts/. This article from the Financial Times discusses the dangers of silo thinking: http://digital.olivesoftware.com/Olive/ODE/FTUSEDU/LandingPage/LandingPage.aspx ?href=RklULzIwMDkvMTIvMTU.&pageno=MzM.&entity=QXIwMzMwMg. .&view=ZW 50aXR5. byr80656_03_c03_043-076.indd 65 3/28/13 3:21 PM Practice Problems CHAPTER 3 Critical Thinking and Discussion Questions 1. Evaluate the following statement: The best financial forecasts will come from forecasts developed entirely within the finance function. 2. Why it important to assess your firm’s cash needs within a period, even though you may have constructed pro forma financial statements? 3. What are the important limitations for financial forecasting? 4. What are activity ratios? Why are they important? 5. The cash budget is the primary planning tool for short-term finance. Why is the cash budget so important? Practice Problems Mini-Case: Specialty Hardwoods, Inc. It is early 2013 and Tim O’Dell, president and majority owner of Specialty Hardwoods Inc., is very worried about the firm’s short-term financing. His accountant has just brought the year-end 2012 financial statements to Tim. The statements show what Tim already knows, the $35,000 line of credit from First Interstate Bank is completely drawn down, and cash balances are well below the $10,000 minimum balance Tim feels is necessary. Tim started Specialty Hardwoods in 1997 with a family loan of $160,000 and $80,000 of Tim’s and his wife’s savings as equity. At the time, Tim had been very interested in making fine furniture but had problems finding rare hardwoods to use in his projects. To fill this void, he began a mail-order lumber business specializing in wood for craftsmen. He found sources in the United States for fine cherry, oak, walnut, and yew and began importing exotic woods such as ebony, cocobolo, tulipwood, ironwood, and many varieties of rosewood. Initially, the lack of competition allowed him to maintain a high profit margin. Annual sales growth of 15% to 25% was financed entirely by profits and the startup capital. Furthermore, operating expenses had been kept low because Tim did all of the firm’s marketing and purchasing himself. Besides Tim, the firm had six employees. These employees were primarily responsible for filling mail orders and billing customers. In 2005 several competitors emerged in the marketplace. Each year, in order to continue to increase sales, Tim had to lower prices slightly, or not raise them despite having to pay his suppliers more. Between 2005 and 2012, his gross margin fell from 28.6% to 26.2% of sales. In 2010, he had been forced to forgo the cash discounts his suppliers offered. By 2011, he was beginning to have trouble meeting his suppliers’ 30-day payment terms and was forced to arrange a line of credit for $10,000 with his bank. During 2012, the line of credit had to be increased to $35,000. In a recent conversation with his banker, Tim had been told that it would be difficult for the bank to grant further increases of the credit line. The banker was concerned about the amount of long-term debt outstanding and about Tim’s inability to pay down any of the $35,000 loan. The banker did say the $35,000 would continue to be available through 2013 but that the bank could not increase the loan amount. Tim thought that there were three possible strategies for 2013, but he was not sure how to analyze them. Tim would like you to analyze the three plans described below. Financial statements from 2010 through 2012 are included. Plan 2013A: Sales growth will be stimulated by offering low prices. Tim is uncertain whether the $35,000 credit line will be sufficient to finance this plan. (continued) byr80656_03_c03_043-076.indd 66 3/28/13 3:21 PM Practice Problems CHAPTER 3 Mini-Case: Specialty Hardwoods, Inc. (continued) Objectives: Sales growth of 25%. Gross margin 5 26% of sales. Pay suppliers in 30 days. Plan 2013B: Limit sales to exotic, high-profit-margin types of wood. Lower sales growth, with higher return and lower inventories, will reduce financing need. Objectives: Sales growth of 10%. Gross margin 5 30% of sales. Pay suppliers in 30 days. Plan 2013C: Follow plan B but take the cash discount offered by suppliers. This requires paying for inventory in 10 days, rather than 30, which may strain his available working capital. Objectives: Sales growth of 10%. Gross margin 5 32% of sales. Pay suppliers in 10 days. The Gross Margin of 32% of sales includes the 2% supplier discount. You have been asked to prepare 2013 pro forma income statements and balance sheets for each of Tim O’Dell’s plans. The actual financial statements from 2010 through 2012 are shown below. Base your pro forma analysis of all three plans, on the following assumptions: byr80656_03_c03_043-076.indd 67 • All sales are credit sales. • GA&S (including interest) 20% of sales. • All after-tax profits are retained in the firm. • A/R and inventory days of 45 and 90, respectively, based on a 365-day year. • Net fixed assets will be unchanged at $90,000. • Make the $8,000 long-term debt payment. • Other current liabilities will remain 2% of sales. • Cash balance minimum of $10,000. • The tax rate is 40%. (continued) 3/28/13 3:21 PM CHAPTER 3 Practice Problems Mini-Case: Specialty Hardwoods, Inc. (continued) Specialty Hardwoods, Inc. Income Statement (Actual) all numbers in thousands (000s) 2010 2011 2012 Sales $700 $860 $1,070 COGS $500 $620 $790 Gross margin $200 $240 $280 GA&S expense $150 $180 $210 Profit before taxes $50 $60    $70 Tax (40%) $20 $24    $28 Net income $30 $36   $42 2010 2011 2012 Cash $22    $7     $8 A/R $88 $108 $134 Inventory $125 $155 $198 Total current $235 $270 $340 $65 $80    $90 $300 $350 $430   $0    $9   $35 Accounts payable $42 $52    $68 Other CL $14 $17   $21    $8    $8     $8 Total CL $64 $86 $132 Long-term debt $56 $48   $40 Common stock $80 $80    $80 Retained earnings $100 $136 $178 Total liabilities & equity $300 $350 $430 Specialty Hardwoods, Inc. Balance Sheets (Actual) as of December 31 Assets: Net fixed assets Total assets Liabilities & equity: Bank loan Current portion long-term debt (continued) byr80656_03_c03_043-076.indd 68 3/28/13 3:21 PM CHAPTER 3 Practice Problems Mini-Case: Specialty Hardwoods, Inc. (continued) Specialty Hardwoods, Inc. Pro Forma Statements for 2013: Plans A, B, and C Plan A Plan B Plan C Sales ______________ ______________ ______________ COGS ______________ ______________ ______________ Gross margin ______________ ______________ ______________ GA&S expense ______________ ______________ ______________ Earnings before tax ______________ ______________ ______________ Taxes (40%) ______________ ______________ ______________ Net income ______________ ______________ ______________ Balance Sheets as of December 31 Cash ______________ ______________ ______________ Accounts receivable ______________ ______________ ______________ Inventory ______________ ______________ ______________ Total CL ______________ ______________ ______________ Net fixed ______________ ______________ ______________ Total assets ______________ ______________ ______________ N/P (bank) ______________ ______________ ______________ Accounts payable ______________ ______________ ______________ Other CL ______________ ______________ ______________ Current long-term debt ______________ ______________ ______________ Total CL ______________ ______________ ______________ Long-term debt ______________ ______________ ______________ Common stock ______________ ______________ ______________ Retained earnings ______________ ______________ ______________ Total liabilites & equity ______________ ______________ ______________ byr80656_03_c03_043-076.indd 69 (continued) 3/28/13 3:21 PM CHAPTER 3 Practice Problems Mini-Case: Specialty Hardwoods, Inc. (continued) Specialty Hardwoods Case Solution 2013 Pro Forma Income Statements 2012 actual Plan A Plan B Plan C Sales $1,070 1,338 1,177 1,177 COGS $790 990 824 800 Gross margin $280 348 353 377 GA&S expense $210 268 235 235 Profit before taxes    $70 80 118 141 Tax (40%)    $28 32 47 56 Net income   $42 48 71 85 2013 Pro Forma Income Statements as of December 31 2012 actual Plan A Plan B Plan C Assets: Cash    $8 10 22 10 Accounts receivable $134 165 145 145 Inventory $198 244 203 197 Total CL $340 419 370 352 $90 90 90 90 $430 509 460 442 Bank loan $35   55    0   13 Accounts payable $68    81    68   22 Other CL $21    27   24   24 Current Portion Long-term debt    $8     8     8     8 Total CL $132 171 100    67 Long-term debt $40 32   32   32 Common stock $80 80    80    80 Retained earnings $178 226 249 263 Total liabilites & equity $430 509 460 442 Net fixed assets Total assets Liabilities & equity: (continued) byr80656_03_c03_043-076.indd 70 3/28/13 3:21 PM CHAPTER 3 Practice Problems Mini-Case: Specialty Hardwoods, Inc. (continued) Notes on the solution Plan A: Accounts Receivable 5 45 3 Sales/365 5 45 3 1338/365 5 165 Inventory 5 90 3 COGS/365 5 90 3 990/365 5 244 Accounts Payable 5 30 3 COGS/365 5 30 3 990/365 5 81 Retained Earnings 5 178 1 2012 Net Income (A) 5 178 1 48 5 226 Total Current Liabilities 5 Total Liabilities 2 Retained Earnings 2 Common Stock 2 Long-term Debt 5 509 2 226 2 80 2 32 5 171 Plan B: Accounts Receivable 5 45 3 Sales/365 5 45 3 1177/365 5 145 Inventory 5 90 3 COGS/365 5 90 3 824/365 5 203 Accounts Payable 5 30 3 COGS/365 5 30 3 824/365 5 68 Retained Earnings 5 178 1 2012 Net Income (B) 5 178 1 71 5 249 With cash set at $10 the bank loan is 2$12. Add $12 to cash and recompute all affected accounts to get a zero balance in the bank loan account. Plan C: Accounts Receivable 5 45 3 Sales/365 5 45 3 1177/365 5 145 Inventory 5 90 3 COGS/365 5 90 3 800/365 5 197 Accounts Payable 5 10 3 COGS/365 5 30 3 800/365 5 22 Retained Earnings 5 178 1 2012 Net Income (C) 5 178 1 85 5 263 Discussion Plan A is not feasible. It requires the bank to increase the loan amount beyond $35,000, which the banker said the bank would not do. Plans B and C are both feasible. To choose between them, consider the differences in profit and loan amount. Under Plan C how long will it take to pay off the slightly larger loan? Is it worthwhile having a loan for this period of time given the additional profits that Plan C generates? It seems that the extra $14,000 per year would very quickly pay off the loan and become additional income for Tim O’Dell. The final decision between Plans B and C may also depend on other factors, but having completed the pro forma statements, the financial side of the decision is understood. byr80656_03_c03_043-076.indd 71 3/28/13 3:21 PM CHAPTER 3 Practice Problems Mini-Case: Two Season Mountain Sports Two Season Mountain Sports is a Colorado-based retailer specializing in mountaineering and backcountry skiing equipment. The company has exclusive distribution rights for several lines of European skis and bindings, so ski-related sales are about 75% of total revenues. Two Season Sports begins preparing for its winter season in March by ordering inventory. Summer sales will provide some cash flow, but in the past Two Seasons has had to arrange a short-term credit line with its bank to carry it through the fall and early winter. Each year, as part of the loan approval process, Hans Meersburg, co-owner of Two Seasons, prepares a monthly cash budget for the bank. It is now July 1, and Hans is putting together the loan application for the coming ski season. Use the following information to develop a cash budget for the months July through February for Two Seasons Mountain Sports. May (actual)   $36,000 June (Actual)   $44,500 July   $70,000 August   $80,000 September   $80,000 October   $90,000 November $140,000 December $180,000 January $120,000 February   $80,000 March   $60,000 April   $40,000 Determine the maximum short-term loan the company needs and when that loan can be repaid. Sales collection pattern: 60% of sales are cash sales. Of the remaining 40%, 34% arrive the month following the sale, 5% arrive 2 months after the sale, and 1% are not collected. The cash from July’s sales ($70,000) would be received as follows: $42,000 in July, $23,800 in August (34% of $70,000), and $3,500 in September (5% of $70,000). About $700 of July sales would be lost due to bad accounts. Inventory purchases: The cost of merchandise is 50% of sales. Merchandise is preordered up to 9 months early. Suppliers offer generous credit terms on preorders, with payment often not due for 6 or 7 months after the order is placed. European suppliers tend to be less generous that U.S. companies, resulting in a two-tier payment structure. Imported equipment makes up about 30% of sales and must be paid for 2 months before the sales month. The remaining 70% of merchandise comes from U.S. suppliers and is paid for 1 month before the sales month. Merchandise sold in July was ordered in the early spring. The cost was $35,000 (50% of $70,000) with 30% of that amount ($10,500) being paid in May and the remaining $24,500 being paid in June. (continued) byr80656_03_c03_043-076.indd 72 3/28/13 3:21 PM CHAPTER 3 Practice Problems Mini-Case: Two Season Mountain Sports (continued) Rent: Rent is $5,000 per month plus 2% of sales from the previous month. In July the rent payment will be $5,890 ($5,000 1 2% of $44,500). If July sales are $70,000 as forecast, August rent will be $6,400 ($5,000 1 2% of $70,000). Wages: The business has several full-time employees. As the store gets busier, part-time employees join the staff. Total wage expenses (wages, benefits, etc.) are $12,000 per month plus 10% of sales for part-time employees. Wage expenditures in July will be $19,000 ($12,000 1 10% of $70,000). Marketing: Two Seasons spends $3,000 on advertising each month except in November and December when it spends $6,000. Travel: Hans Meersburg and his partner feel it is important for employees (including themselves) to use the equipment they sell. Two Seasons budgets $1,500 per month for employee travel. The business has helped support employee trips to ski and climb in North America, South America, and Asia. It is a perk that employees love, and employee turnover is correspondingly low because of it. Other outlays: Other expenses average $2,000 per month. Taxes: Tax payments of $6,000 will be made in August, October, and December. Equipment purchase: A new base grinder will be purchased and paid for in September. It costs $25,000. Loan repayment: Two Seasons is repaying a long-term loan at $5,000 per quarter. The payments occur in September and December. Cash balances: As of July 1, Two Seasons has a cash balance of $62,000 and no short-term loan outstanding. The company tries to maintain a minimum cash balance of $20,000. If the cash budget shows the end-of-the-month cash balance falling below $20,000, the company will draw down its short-term line of credit to reach the $20,000 minimum. Two Season Mountain Sports Cash Budget Sales forecasts May (Actual) June (Actual) July August September 36,000 44,500 70,000 80,000 80,000 Cash 42,000 30-day 15,130 60-day 1,800 Total receipts 58,930 Purchases 40,000 Rent Wages 5,890 19,000 Marketing 3,000 3,000 3,000 Travel 1,500 1,500 1,500 Other 2,000 2,000 2,000 (continued) byr80656_03_c03_043-076.indd 73 3/28/13 3:21 PM CHAPTER 3 Practice Problems Two Season Mountain Sports Cash Budget (continued) Sales forecasts May (Actual) June (Actual) July Taxes August September    6,000 Equipment 25,000 Loan payment 5,000 Change in cash 212,460 Beginning cash 62,000 End cash without loan 49,540 Minimum 20,000 Loan need       0 End cash with loan 49,540 Accumulated loan       0 Loan repayment       0 Cash surplus Sales forecasts October November December January February 90,000 140,000 180,000 120,000 80,000 Marketing 3,000    6,000    6,000   3,000 3,000 Travel 1,500   1,500   1,500   1,500 1,500 Other 2,000   2,000   2,000   2,000 2,000 Taxes 6,000 Cash 30-day 60-day Total receipts Purchases Rent Wages    6,000 Equipment Loan payment   5,000 Change in cash Beginning cash End cash without loan Minimum Loan need (continued) byr80656_03_c03_043-076.indd 74 3/28/13 3:21 PM CHAPTER 3 Practice Problems Two Season Mountain Sports Cash Budget (continued) Sales forecasts October November December January February August September End cash with loan Accumulated loan Loan repayment Cash surplus Two Seasons Mountain Sports Cash Budget Solution Sales forecasts May (Actual) June (Actual) 36,000 44,500 July 70,000 80,000 80,000 Cash 42,000 48,000 48,000 30-day 15,130 23,800 27,200 60-day    1,800 2,225   3,500 Total receipts 58,930 74,025 78,700 Purchases 40,000 41,500 52,500    5,890 6,400    6,600 19,000 20,000 20,000 Marketing   3,000 3,000   3,000 Travel   1,500 1,500   1,500 Other   2,000 2,000   2,000 Rent Wages Taxes 6,000 Equipment 25,000 Loan payment   5,000 Change in cash 212,460 26,375 236,900 Beginning cash 62,000 49,540 43,165 End cash without loan 49,540 43,165 6,265 Minimum 20,000 20,000 20,000 Loan need End cash with loan Accumulated loan 13,735 49,540 43,165 20,000 13,735 Loan repayment Cash surplus (continued) byr80656_03_c03_043-076.indd 75 3/28/13 3:21 PM CHAPTER 3 Practice Problems Two Seasons Mountain Sports Cash Budget Solution (continued) Sales forecasts November December January February 90,000 140,000 180,000 120,000 80,000 Cash 54,000 84,000 10,8000 72,000 48,000 30-day 27,200 30,600 47,600 61,200 40,800 60-day   4,000   4,000   4,500    7,000    9,000 Total receipts 85,200 11,860 160,100 140,200 97,800 Purchases 76,000 81,000 54,000 37,000 27,000    6,600    6,800    7,800    8,600    7,400 21,000 26,000 30,000 24,000 20,000 Marketing   3,000    6,000    6,000   3,000   3,000 Travel   1,500   1,500   1,500   1,500   1,500 Other   2,000   2,000   2,000   2,000   2,000 Taxes    6,000 Rent Wages October    6,000 Equipment Loan payment Change in cash 230,900 24,700 47,800 64,100 36,900 Beginning cash 20,000 20,000 20,000 20,000 82,565 210,900 15,300 67,800 84,100 119,465 Minimum 20,000 20,000 20,000 20,000 20,000 Loan need 30,900    4,700 End cash with loan 20,000 20,000 67,800 84,100 119,465 Accumulated loan 44,635 49,335   1,535       0 47,800   1,535 End cash without loan Loan repayment Cash surplus byr80656_03_c03_043-076.indd 76   5,000 62,565 99,465 3/28/13 3:21 PM 4 iStockphoto/Thinkstock Present and Future Value of Money Learning Objectives Upon completion of Chapter 4, you will be able to: • Express the time value of money and related mathematics, including present and future values, principal, and interest. • Describe the significance and application of simple and compound interest. • Explain the significance of compounding frequency in relation to future and present cash flows and effective annual percentage rates. • Identify the values of common cash flow streams, including perpetuities, ordinary annuities, annuities due, and amortized loans. byr80656_04_c04_077-112.indd 77 3/28/13 3:31 PM CHAPTER 4 Section 4.1 The Time Value of Money T he saying “time is money” could not be more true than it is in finance. People rationally prefer to collect money earlier rather than later. By delaying the receipt of cash, individuals forgo the opportunity to purchase desired goods or invest the funds to increase their wealth. The forgone interest, which could be earned if cash were received immediately, is called the opportunity cost of delaying its receipt. Individuals require compensation to reimburse them for the opportunity cost of not having the funds available for immediate investment purposes. This chapter describes how such opportunity costs are calculated. Because many business activities require computing a value today for a series of future cash flows, the techniques presented in this chapter apply not only to finance but also to marketing, manufacturing, and management. Here are examples of questions that the tools introduced in this chapter can help answer: • • • • How much should we spend on an advertising campaign today if it will increase sales by 5% in the future? Which strategy should we employ, given their respective costs and estimated contributions to future earnings? What types of health insurance and retirement plans are best for our employees, given the amount of money we have available? Is it worth buying a new automated manufacturing tool for $120,000 if it reduces material waste by 15%? Being able to give a value to cash to be received in the future, whether dividends from a share of stock, interest from a bond, or profits from a new product, is one of the primary skills needed to run a successful business. The material in this chapter provides an introduction to that skill. 4.1 The Time Value of Money S uppose a friend owes you $100 and the payment is due today. You receive a phone call from this friend, who says she would like to delay paying you for 1 year. You may reasonably demand a higher future payment, but how much more should you receive? The situation is illustrated here using the timeline shown in Figure 4.1. Figure 4.1 t=0 t=1 PV0 = $100 FV1 = ? In this diagram “now,” the present time, is assigned t 5 0, or time zero. One year from now is assigned t 5 1. The present value of the cash payment is $100 and is denoted PV0 (and read as “present value at time zero”). Its future value at t 5 1 is denoted as FV1 (and read as “future value 1 year from now”). To find the amount that you could demand for deferring receipt of the money by 1 year, you must solve for FV1, the future value of $100 byr80656_04_c04_077-112.indd 78 3/28/13 3:31 PM CHAPTER 4 Section 4.1 The Time Value of Money one year from now. The FV1 value will depend on the opportunity cost of forgoing immediate receipt of $100. You know, for instance, that if you had the money today, you could deposit the $100 in a bank account earning 3% interest annually. However, you know from Chapter 1 that value depends on risk. In your judgment, your friend is less likely to pay you next year than is the bank. Therefore, you will increase the rate of interest to reflect the additional risk that you think is inherent in the loan to your friend. Suppose you decide that a 10% annual rate of interest is appropriate. The amount of the future payment, FV1, will be the original principal plus the interest that could be earned at the 10% annual rate. Algebraically, you can solve for FV1, being careful always to convert percentages to decimals when doing arithmetic calculations, and so FV1 5 $100 1 ($100)(0.10) (4.1) Factoring $100 from the right-hand side of Equation (4.1) gives FV1 5 $100(1 1 0.10) 5 $100(1.10) 5 $110 You may demand a $110 payment at t 5 1 in lieu of an immediate $100 payment because these two amounts have equivalent value. Let’s say that your friend agrees to this interest rate but asks to delay payment for 2 years. Figure 4.2 t=0 t=1 t=2 PV0 = $100 FV1 = $110 FV2 = ? t=0 FV1 = $100(1.10) ? Now we must find FV2, the future value of the payment 2 years from today. This situation is illustrated by the timeline in Figure 4.2. Since we know FV1 5 $110 and we know the interest rate is 10%, we can solve for FV2 by recognizing that FV2 will equal FV1 plus the interest that could be earned on FV1 during the second year. Our equation is then (4.2) FV2 5 FV1 1 FV1(0.10) 5 $110 1 ($110)(0.10) 5 $110(1 1 0.10) 5 $110(1.10) 5 $121 You may demand a $121 payment at t 5 2 because its time value is equivalent to either $110 at t 5 1 or $100 at t 5 0, given the 10% interest rate. byr80656_04_c04_077-112.indd 79 3/28/13 3:31 PM Section 4.2 Compound and Simple Interest CHAPTER 4 The time value of money and the mathematics associated with it provide important tools for comparing the relative values of cash flows received at different times. Just as a hammer may be the most useful item in a carpenter’s toolbox, time value of money mathematics is indispensable to a financial manager. For example, recall from Chapter 1 that to increase shareholder wealth, managers must make investments that have greater value than their costs. Often, such investments require an immediate cash outlay, like buying a new delivery truck. The investment (the truck) then produces cash flows for the corporation in the future (delivery fee income, increased sales, lower delivery costs, etc.). To determine whether the future cash flows have greater value than the initial cost of the truck, managers must be able to calculate the present value of the future stream of cash flows produced by this investment. 4.2 Compound and Simple Interest T he preceding section showed that, at a 10% annual interest rate, $100 today is equivalent to $110 a year from now and $121 in 2 years. This result may be generalized using the following formulas: (4.3) FV1 5 PV0(1 1 r) (4.4) FV2 5 PV0(1 1 r)2 where FV1 and FV2 are, respectively, future values 1 year and 2 years from now, PV0 is the present value at time zero, respectively, and r is the interest rate. Now, let’s expand Equation (4.4): (4.5) FV2 5 PV0 5 (1 1 r)(1 1 r) 5 PV0(1 1 2r 1 r2) 5 PV0(1 1 2r) 1 PV0(r2) The last line of Equation (4.5) is broken down in a special way. The first term on the right side of the equal sign, PV0(1 1 2r), would yield $120 given the information we have used in our example. The second term, PV0(r2), yields $1. The value $120 equals your original principal ($100) plus the amount of interest earned ($20) if your friend paid simple ­interest. For example, if you withdraw interest earned during each year at the end of that year, you would earn simple interest. In this case, you would receive $10 interest payments at the end of years 1 and 2, totaling $20. If, on the other hand, your friend credited (but did not pay) interest to you every year, then you would earn interest during year 2 on the interest credited to you at the end of year 1. Earning interest on previously earned interest is known as compounding. Thus, you would earn an extra dollar, a total of $121, over the 2-year period with interest compounded annually. In this example we assumed annual compounding since nearly all transactions are now based on compound rather than simple interest. Not all compounding is done on an annual basis, however. Sometimes interest is added to an account every 6 months (semiannual compounding). Other byr80656_04_c04_077-112.indd 80 3/28/13 3:31 PM CHAPTER 4 Section 4.3 The Time Value of a Single Cash Flow contracts call for quarterly, monthly, or daily compounding. As you will see, the frequency of compounding can make a big difference when the time value of money is calculated. 4.3 The Time Value of a Single Cash Flow C ontinuing our example, let us suppose that your friend who wishes to delay paying you agrees to a 10% annual rate of interest over the 2-year period and will allow you to compound interest semiannually. What will you be paid in 2 years given this agreement? Semiannual compounding means that interest will be credited to you every 6 months, based on half of the annual rate. In effect you will be earning a 5% semiannual rate of interest over four 6-month periods. In other words, the periodic interest rate will be half the annual rate because you are using semiannual compounding and you will be earning interest for four time periods (n 5 1 through 4), each period being 1/2-year long. The new situation is illustrated in Figure 4.3. Figure 4.3 6 months n=0 n=1 1 year n=2 1½ years n=3 2 years n=4 PV0 = $100 FV1 FV2 FV3 FV4 Here, FV1 is the future value of the $100 at the end of period 1 (the first 6 months). As before, FV1 equals the $100 beginning principal plus interest earned over the 6 months at the 5% semiannual interest rate. Therefore we set this up using the following equation: (4.6) FV1 5 $100 1 $100(0.05) 5 $100(1.05) 5 $105 Therefore, at the end of period 1 (at n 5 1) the principal balance you are owed will be $105. FV2 will be equal to the principal at the beginning of period 2 plus interest earned during period 2: (4.7) FV2 5 $105 1 $105(0.05) 5 $105(1.05) 5 $110.25 Note that we could substitute [$100(1.05)] for $105 in the second line of Equation (4.7). By doing so, FV2 could be expressed as follows: (4.8) byr80656_04_c04_077-112.indd 81 FV2 5 $105(1.05) 5 [$100(1.05)](1.05) 5 $100(1.05)2 3/28/13 3:31 PM CHAPTER 4 Section 4.3 The Time Value of a Single Cash Flow By following this pattern, finding FV3 and FV4 is straightforward. For the future value at the end of the third period, we have FV3 5 $100(1.05)3 5 $115.76 (4.9) and that at the end of the fourth period is FV4 5 $100(1.05)4 5 $121.55 (4.10) Equation (4.10) gives the answer we seek. The future value at the end of four 6-month periods is $121.55. Changing from annual compounding to semiannual compounding has increased the future value of your friend’s obligation to you by $0.55. The additional interest earned from semiannual compounding, $0.55, doesn’t seem like much, but imagine a firm borrowing $100 million; then the compounding period—annual, semiannual, ­quarterly—can turn into tens of thousands of dollars. The Future Value of a Single Cash Flow The pattern established here may be generalized into the formula for the future value of a single cash flow using compound interest: FVn 5 PV0(1 1 r)n (4.11) where FVn 5 the future value at the end of n time periods PV0 5 the present value of the cash flow r 5 the periodic interest rate n 5 the number of compounding periods until maturity, or (number of years until maturity)(compounding periods per year) The periodic interest rate equals the annual nominal rate divided by the number of compounding periods per year, r5 annual nominal rate number of periods per year It is critical when using this formula to be certain that r and n agree with each other. If, for example, you are finding the future value of $100 after 6 years and the annual rate is 18%, compounded monthly, then the appropriate r is 1.5% per month (18%/12 5 1.5%), and n is 72 months (6 years times 12 months per year 5 72 months). Students often adjust the interest rate and then forget to adjust the number of periods (or vice versa)! The answer to this problem is FV6312 5 a1 1 byr80656_04_c04_077-112.indd 82 0.18 6312 b 12 3/28/13 3:31 PM Section 4.3 The Time Value of a Single Cash Flow CHAPTER 4 FV72 5 $100(1.015)72 5 $292.12 Try It: Calculator Key Strokes and Excel Functions—Future Value TI Business Analyst Future Value of Single Cash Flow: If you put $400 in the bank today at 12% per year, and leave it there for 5 years, what will be the balance at the end of the time period? 400 [PV] The PV key is used to input the present value of the deposit, $400. 5 [N] The funds are invested for 5 years, so 5 is entered using the N key. 0 [PMT] PMT is the key used to input a constant periodic payment or deposit, but in this problem there are no such cash flows, so 0 is entered using the PMT key. 12 [I/Y] I/Y is the key used for entering the periodic interest rate, in this case 12% per year, so 12 is entered. [CPT] [FV] CPT is the key that tells the calculator to calculate a value; in this case you are asked to find the future value of the deposit, so the calculator is told to compute the FV: 5 $704.9366. Note: These may be input in any order so long as the [FV] and [CPT] are at the end. Also, the calculator register will show the answer as a negative 704.9366, since you entered 400 as a positive number. Think of it like this: 400 is cash going one way (you are giving it to the bank), and the 704 is going the opposite direction (the bank is giving it back to you), so the two cash flows will have opposite signs. If you enter 400 [1/2] [PV] in this problem, then your answer will be a positive 704.9366. It does not matter which way you do this. Excel Use the FV function. The inputs for this function are RATE, NPER, PMT, PV, and TYPE, where RATE is the interest rate per period as a percentage, NPER is the number of compounding periods, PMT is any periodic payment (for the FV of a single cash flow this would be zero), PV is the present value, and TYPE is 0 if payments are made at the end of the period (the most common case) and 1 if payments are made at the beginning of the period. If you put $400 in the bank today at 12% per year, and leave it there for 5 years, what will be the balance at the end of the time period? Using the FV function in Excel gives FV(12%,5,0,2400,0) 5 704.94 (continued) byr80656_04_c04_077-112.indd 83 3/28/13 3:31 PM CHAPTER 4 Section 4.3 The Time Value of a Single Cash Flow Try It: Calculator Key Strokes and Excel Functions—Future Value (continued) Note: Financial functions in Excel require that cash inflows and cash outflows have different arithmetic signs. We signed the PV (the amount you put in the bank today) negative because it is flowing away from you and into the bank. The result ($704.94) is positive because that is a cash flow to you. The inputs are separated by commas, so you cannot enter numbers with commas separating thousands (e.g., $1,000). Nor can you include dollar signs ($). For simple interest, without compounding, the future value is simply equal to the annual interest earned times the number of years, plus the original principal. The formula for the future value of a single cash flow using simple interest is s FVn 5 PV0 1 (n)(PV0)(r) 5 PV0(1 1 nr) (4.12) where s FVn 5 the future value at the end of n periods using simple interest n 5 the number of periods until maturity (generally n simply equals the number of years, because there is no adjustment for compounding periods) r 5 the periodic rate (which also usually equals the annual rate because there is no adjustment for compounding periods) For the previous example, the future value of $100 invested for 6 years in an account paying 18% per year using simple interest is s FV6 5 $100[11 (6)(0.18)] 5 $208.00 Thus, monthly compounding yielded a future value after 6 years of $292.12, or $84.12 more than simple interest in this example. Table 4.1 illustrates the future value of $100, bearing 18% annual interest, with different compounding assumptions. Be sure that you can replicate the solutions illustrated here using your calculator. Be sure your n and r agree (e.g., both are monthly, yearly, etc.) and always be sure you express percentages as decimals before doing any calculations. You should practice with your calculator until your answers match those given in Table 4.1. A graph of these results is shown in Figure 4.4. Table 4.1: The future value of $100 Compounding assumption   n    r   FVn Annual compounding    6 0.18 $269.96 Semiannual compounding   12 0.09 $281.27 Quarterly compounding   24 0.045 $287.60 Monthly compounding   72 0.015 $292.12 Weekly compounding 312 0.00346 $293.92 2,190 0.000493 $294.39 Daily compounding byr80656_04_c04_077-112.indd 84 3/28/13 3:31 PM CHAPTER 4 Section 4.3 The Time Value of a Single Cash Flow Figure 4.4 300 Future Value 290 280 270 260 250 Annually Semiannually Quarterly Monthly Weekly Daily Number of compounding periods The Present Value of a Cash Flow We have solved for the future value of a current cash flow. Often, we must solve for the present value of a future cash flow, solving for PV rather than FV. Suppose, for example, you are going to receive a bonus of $1,000 in 1 year. You could really use some cash today and are able to borrow from a bank that would charge you an annual interest rate of 12%, compounded monthly. You decide to borrow as much as you can now so that you will still be able to pay off the loan in 1 year using the $1,000 bonus. In essence, you wish to solve for the present value of a $1,000 future value, knowing the interest rate (12% per year, compounded monthly) and the term of the loan (1 year, or 12 monthly compounding periods). Figure 4.5 shows a timeline illustrating the problem. Figure 4.5 n=0 PV0 = ? n = 12 r = 0.01 FV12 = $1,000 Try It: Calculator Key Strokes and Excel Functions—Present Value Present Value of Single Cash Flow: How much money would you have to put in the bank today at 12% per year, to have $10,000 in exactly 4 years? TI Business Analyst 1000 [FV] 3 [N] 0 [PMT] 12 [I/Y] [CPT] [PV] 5 $711.78 byr80656_04_c04_077-112.indd 85 (continued) 3/28/13 3:31 PM CHAPTER 4 Section 4.3 The Time Value of a Single Cash Flow Try It: Calculator Key Strokes and Excel Functions—Present Value (continued) Note that the answer that your calculator produces will be negative if you follow these keystrokes. The future value was entered as a positive number (like a cash inflow) so the present value is negative (like a cash outflow). Excel Use the PV function with the format: PV(RATE,NPER,PMT,FV,TYPE). The inputs for this example would be: 5 PV(12%,3,0,1000,0) 5 2$711.78 In this case n 5 12, r 5 1%, and FV12 5 is known, whereas PV0 is unknown. We may still use Equation (4.11), FVn 5 PV0(1 1 r)n (4.11) Substituting in the known quantities gives $1,000 5 PV0(1.01)12 and using some algebra we have (4.13) 1 1.0112 5 $887.45 PV0 5 1,000 1 1.01 2 212 5 $1,000 You could borrow $887.45 today and fully pay off the loan, given the bank’s terms, in 1 year using your $1,000 bonus. Equation (4.13) may be generalized into the formula for the present value of a single cash flow with compound interest. Solving for the present value of a future cash flow is also known as discounting. In fact, compounding and discounting are two sides of the same coin. Compounding is used to express a value at a future date given a rate of interest. Discounting involves expressing a future value as an equivalent amount at an earlier date. This formula is also called the discounting formula for a single future cash flow: (4.14) PV0 5 FVn 1 1 1 r 2 2n 5 FVn 1 11 1 r2n The variables PV0, FVn, n, and r are defined exactly as they are in the future value formula because both formulas are really the same; they are just solved for different unknowns. byr80656_04_c04_077-112.indd 86 3/28/13 3:31 PM CHAPTER 4 Section 4.3 The Time Value of a Single Cash Flow Table 4.2: The present value of $1,000 Compounding assumption n    r   PV0 Annual compounding   1 0.12 $892.86 Semiannual compounding   2 0.06 $890.00 Quarterly compounding   4 0.03 $888.49 Monthly compounding 12 0.01 $887.45 Weekly compounding 52 0.00231 $887.04 365 0.000329 $886.94 Daily compounding Table 4.2 solves for the present, or discounted, value of a $1,000 cash flow to be received in 1 year at a 12% per year discount rate using different compounding periods. You should be able to replicate these solutions on your calculator. A graph of these results is shown in Figure 4.6. Figure 4.6 893 892 Present Value 891 890 889 888 887 886 Annually Semiannually Quarterly Monthly Weekly Daily Number of compounding periods Present and future value formulas are very useful because they may be used to solve a variety of problems. Suppose you make a $500 deposit in a bank today and you want to know how long it will take your account to double in value, assuming that the bank pays 8% interest per year, compounded annually. Here, you are solving for the number of time periods. The timeline is shown in Figure 4.7. byr80656_04_c04_077-112.indd 87 3/28/13 3:31 PM CHAPTER 4 Section 4.3 The Time Value of a Single Cash Flow Figure 4.7 r = 0.08 PV0 = $500 FVn = $1,000 n=? You may substitute the known quantities PV0 5 $500, FVn 5 $1,000, r 5 0.08 into either formula and solve for n. Let’s use PV0 5 FVn(1 1 r)2n (4.14) We can rearrange this equation into PV0/FVn 5 (1 1 r)2n or (1 1 r)n 5 FVn/PV0 Taking the logarithm of both sides gives us n log(1 1 r) 5 log(FVn/PV0) Finally, solving for n gives n 5 log(FVn/PV0)/log(1 1 r) Plugging in our numbers gives n 5 log($1000/$500)/log(1 1 0.08) 59 Therefore in 9 years the balance in your account will double. Suppose the account earned 8% per year compounded monthly. To find the time until the account’s balance doubled, you would convert the interest rate to reflect monthly compounding r 5 0.08/12 5 0.00667 and solve for the number of compounding periods. Starting again with (4.14) PV0 5 FVn(1 1 r)2n we substitute in numbers to get $500 5 $1,000(1.00667)2n or (1.00667)n 5 2 byr80656_04_c04_077-112.indd 88 3/28/13 3:31 PM CHAPTER 4 Section 4.3 The Time Value of a Single Cash Flow Using trial and error, you get the answer n 5 105. This should be interpreted as 105 months because you are dealing with monthly compounding periods. Thus, in 8.75 years the account will double in value when using monthly rather than annual compounding. This example illustrates an important lesson. It takes less time to achieve a desired amount of wealth with more frequent compounding at a given nominal interest rate. It is no surprise that borrowers prefer less frequent compounding, while savers (or lenders) prefer compounding as frequently as possible. The difference between compounding frequencies offered at various banks makes shopping around worthwhile whether you are a borrower or a saver. Another type of problem is solving for the interest rate. This time let’s suppose that an investment costing $200 will make a single payment of $275 in 5 years. What is the interest rate such an investment will yield? The timeline is shown in Figure 4.8. Figure 4.8 PV0 = 200 FV5 = 275 r=? Starting again with the formula PV0 5 FVn(1 1 r)2n we have for n 5 5 PV0 5 FV5(1 1 r)25 We want to solve for the interest rate r. Rearranging terms we get so 11 1 r25 5 FV5 PV0 1 1 r 5 (FV5 / PV0)0.20 or r 5 (FV5 / PV0)0.20 21 Substituting in PV0 5 $200 and FV5 5 $275, we get r 5 ($275/$200)0.20 21 or r 5 0.06576 byr80656_04_c04_077-112.indd 89 3/28/13 3:31 PM CHAPTER 4 Section 4.3 The Time Value of a Single Cash Flow The answer, r 5 0.06576, is based on an annual compound rate, because we assumed n 5 5 years. It is also expressed as a decimal and could be re-expressed as a percentage, 6.576% per year compounded annually. Effective Annual Percentage Rate As you have seen, the frequency of compounding is important. Truth-in-lending laws now require that financial institutions reveal the effective annual percentage rate (EAR) to customers so that the true cost of borrowing is explicitly stated. Before this legislation, banks could quote customers annual interest rates without revealing the compounding period. Such a lack of disclosure can be costly to borrowers. For example, borrowing at a 12% yearly rate from Bank A may be more costly than borrowing from Bank B, which charges 12.1% yearly, if Bank A compounds interest daily and Bank B compounds semiannually. Both 12% and 12.1% are nominal rates—they reveal the rate “in name only” but not in terms of the true economic cost. To find the effective annual rate, you must divide the nominal annual percentage David Sipress/The New Yorker Collection/www.cartoonbank.com rate (APR) by the number of compounding periods per year and add 1, then raise this sum to an exponent equal to the number of compounding periods per year, and, finally, subtract 1 from this result. The general formula for the effective annual percentage rate is (4.15) For our example, EAR 5 a1 1 APR CP b 21 CP 0.12 365 b 2 1 5 0.1275 5 12.75% 365 0.121 2 EARB 5 a1 1 b 2 1 5 0.1247 5 12.47% 2 EARA 5 a1 1 Thus, if you are a borrower, you would prefer to borrow from Bank B despite its higher APR. The lower EAR translates into a lower cost over the life of the loan. The disclosure of EARs makes comparison shopping for rates much easier. byr80656_04_c04_077-112.indd 90 3/28/13 3:31 PM Section 4.4 Valuing Multiple Cash Flows CHAPTER 4 A Closer Look: The Rule of 72 The rule of 72, which is very useful for making estimates when dealing with the time value of money, says that if the periodic rate times the number of compounding periods equals 72, then the future value will equal approximately twice the present value for a lump sum. Stated differently, if the rate times the periods equals 72, then your original deposit will double. Use the rule of 72 to solve the following problems. a. You deposit $500 in an account that paid 8% interest per year, compounded annually. If you leave the money in the account for 9 years, what would be your approximate balance at the end of the 9 years? b. If you deposit $400 in an account that bears 12% interest per year (compounded annually) and leave it there for 12 years, what would be the approximate balance in your account at the end of that time? c. Gas in 1969 cost about $0.40 per gallon. If inflation has averaged about 4.5% per year since then, use the rule of 72 to estimate whether gas is more expensive, less expensive, or equally expensive now compared to what it was then. 4.4 Valuing Multiple Cash Flows M any problems in finance involve finding the time value of multiple cash flows. Consider the f...
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