CAPITAL BUDGETING AND CORPORATE VALUATION

CHAPTER 7 CAPITAL BUDGETING AND CORPORATE VALUATION Capital Budgeting When your company invests in a new asset, the asset usually appears on the balance sheet rather than being immediately charged against income as an expense. The asset is then charged against income through depreciation expense over its estimated useful life. This expense is supposed to match the timing of the income generated by the asset. Because there are often differences between depreciation for tax and accounting purposes, it may be necessary to create a liability account for deferred taxes if the tax depreciation is greater than the financial-accounting depreciation. Although the income statement provides some indication of the profitability of the business, it provides little indication of the true return on invested capital or whether a particular capital investment is worthwhile. A project may provide a positive return but the return may be too small to justify the investment. The return on capital invested must be measured on a cash-flow basis and take time into account. That is the purpose of capital investment analysis, also called capital budgeting.  KEY POINT: Capital budgeting involves the analysis of project proposals and the ranking and selection of those projects suitable for investment. It is an integral part of a company’s strategic-planning proess. Capital budgeting is a process of analyzing expected cash flows and expected risks in a disciplined, quantitative way against a backdrop of overall corporate strategy. For a company of any size, an overriding concern of management is to increase the owners’ value. To do so requires investing in projects that return more than the cost of capital. That idea is the foundation for performance metrics such as economic value added, which was discussed in Chapter 1. Capital budgeting deals with the asset side of the balance sheet. It is concerned with what investments should be made, not how the projects Capital Budgeting and Corporate Valuation 143 are financed. Inevitably, those two decisions overlap in the minds of a company’s CFO and treasurer. A simple comparison of the next project to the next financing can be misleading, however, particularly if that financing includes debt with tax-deductible interest payments. You and the CFO should take a broad look at all of the company’s investment opportunities and all of its capital sources, including both debt and equity, when making capital-investment decisions. In theory,the company should increase your (and any other owners’) worth by investing in all projects earning more than the firm’s cost of capital, adjusted for project risk. In reality, however, you will usually limit the number of projects you are willing to oversee at a given time because your company will be stretched thin with too many projects. As the owner of a privately held company, you may be reluctant to seek outside financing for additional projects if such financing would dilute your ownership or control.  SMART FINANCIAL MANAGEMENT: Capital budgeting involves qualitative as well as quantitative analysis. You must consider how well each project fits into the company’s business strategy, how much management time it will absorb, whether forecasted returns justify assuming identified risks, and how that project might affect other projects under consideration. Capital budgeting requires assumptions about the future. To decide how a proposed project compares with other investment opportunities and to identify risks and pitfalls, you should ask for the insights of thoughtful individuals from different departments and different professional experience. In addition to sharing their views on whether a project should be a strategic priority, these individuals may review items in the project proposal, such as raw material costs, labor costs, the market for the product to be produced, when the product will become obsolete, price points, competition, and terminal value of the capital assets. From a quantitative perspective, the key concepts are: ➤ The time value of money ➤ Discounted cash flow analysis ➤ Four methods for evaluating projects: o o o o Financial Planning and Asset Management 144 Net present value Internal rate of return Payback Profitability index TIME VALUE OF MONEY The time value of money is based on a simple truism: a dollar received today is worth more than a dollar received a year from now because today’s dollar can be invested and will be worth more a year later. A dollar deposited in a 5-percent savings account will have a future value of $1.05 a year from now and $1.1025 two years from now. Conversely, the present value of $1.05 a year from now or $1.1025 two years from now is $1.00. In this case, 5 percent is variously called the reinvestment rate, the opportunity cost of funds, or the hurdle rate. A dollar is worth 5 percent a year to an investor who can either invest at that rate or retire existing capital costing that rate. As will be discussed later,the hurdle rate a company uses for capital budgeting is approximately equal to its cost of capital.  IMPORTANT: A commonly used hurdle rate is 12 percent. This rate may be too low for smaller enterprises. It is certainly too low for startups, whose debt and equity are very expensive. It would be a rate appropriate for safe investments. Table 7-1 shows how present values and future values are related and calculated. On the first line, $1.00 is invested at Year 0, the beginning of Year 1, and reinvested each year at 12 percent. It compounds to $1.76 at the end of Year 5. On the second line, $1.00 is divided by the future value of $1.00 to calculate a present-value factor. The present value (today’s value) of $1.00 received at the end of Year 5, using a 12 percent discount rate, is the $1.00 times the present-value factor for the end of Year 5, or $0.57. In a capital budgeting analysis, as illustrated below, the presentvalue factor for each year is multiplied by a project’s net cash flows for that year. TABLE 7-1 Present and Future Value Calculation at 12 Percent YEAR Future value Present value = 1 ÷ Future value 0 $1.00 1.00 1 $1.12 0.893 2 3 4 5 $1.254 $1.405 $1.574 $1.762 0.797 0.712 0.635 0.567 Discounted Cash Flow Analysis Discounted cash flow analysis is the quantitative base used for capital budgeting. It is a method for identifying all of the cash outflows and inflows relevant to a project and adjusting them for both risk and the time value of money. Cash outflows include all of the cash necessary to fund the project, such as the cost of the property, plant, and equipment; legal fees; working capital needs; and taxes before the assets are put into use. Capital Budgeting and Corporate Valuation 145 Cash inflows include net income from the project; tax benefits from depreciation of project assets; tax benefits from amortization of project assets such as patents; and the terminal or residual value, the estimate of the project’s value at the end of the analysis period. NET PRESENT VALUE A project’s net present value (NPV) is the sum of the present values of all its projected cash outflows and inflows, including all investments made and returns realized. A positive NPV suggests a financially attractive proposal. To illustrate the technique, consider a manufacturing company with a 12-percent hurdle rate having an opportunity to invest $100,000. The machine being purchased is projected to produce estimated savings of $30,000 per year over the next four years. Management’s “base case” estimates the machine’s terminal value will be $20,000, its worth at the end of the five-year period. The $100,000 investment is shown as a negative number in the Exhibit 7-1 analysis because it is a cash outflow. The cash inflows and the residual value are positive figures. In Exhibit 7-1, first, the present values are calculated for each year’s flows. These annual figures are then added to determine the NPV of $2,469. EXHIBIT 7-1 Net Present Value Calculation for Cost-Saving Machinery Project at a 12 Percent Discount Rate YEAR 0 1 2 3 4 5 1.0000 0.8929 0.7972 0.7118 0.6355 0.5674 Cash flows ($100,000) $30,000 $30,000 $30,000 $30,000 $20,000 Present value ($100,000) $26,786 $23,916 $21,353 $19,066 $11,349 Presentvalue factor @ 12% BASE CASE Net present value $2,469 SENSITIVITY ANALYSIS: LESS FAVORABLE ASSUMPTIONS Financial Planning and Asset Management 146 Cash flows ($100,000) $25,000 $25,000 $25,000 $25,000 $10,000 Present value ($100,000) $22,321 $19,930 $17,795 $15,888 $ 5,674 Net present value ($18,392) The NPV of $2,469 for the base case is an estimate of how much the project will add to the net worth of the business in today’s dollars. (The actual increase over time would be the sum of the undiscounted flows, but there would be no year-to-year correlation with the annual figures shown in Exhibit 7-1.) Because the NPV is positive, the project clears the 12-percent hurdle rate. SENSITIVITY ANALYSIS The base case,of course,is only a forecast. Actual results likely will be different. One way of testing the effects of alternate results is to vary assumptions within the likely ranges. For example, in a more difficult economic environment, the annual savings for Years 1 through 4 might be only $25,000 and the residual value only $10,000. Under these assumptions, the NPV at a 12 percent discount rate is a decidedly negative $18,392, as also shown in Exhibit 7-1.  SMART FINANCIAL MANAGEMENT: Having prepared two calculations of this type (or as many as necessary to provide a clear representa- tion), you must then think about the probability of each alternative outcome. If you think the base case is highly likely, you may want to go on with the project. On the other hand, if you assign a 50 percent probability to each of the two alternatives, the resulting probability-adjusted NPV is negative, as shown below in Table 7-2. You should not go ahead unless there are compelling nonfinancial reasons for the investment. It is not unusual for a corporation to calculate half a dozen alternative situations in this way, assigning them probability factors that add up to 1. These NPV calculations are important but not the only part of the decision process. Equally important is your consideration of the relative probability of each alternative and all the strategic and other nonfinancial reasons for considering the investment. TABLE 7-2 Adjusting Alternate Outcomes for Their Probability NET PROBABILITY PROBABILITY- FACTOR ADJUSTED NPV $ 2,469 .50 $1,234.50 (18,392) .50 ( 9,196.00) PRESENT VALUE ($7,961.50) Capital Budgeting and Corporate Valuation 147 Comparing Different Investment Opportunities NPV is a particularly useful calculation for comparing investment opportunities that have different schedules of investments (cash outflows) and returns (cash inflows). This type of analysis is useful in ranking investment opportunities.  KEY POINT: Of course, ranking capital investments is never done on purely quantitative grounds; there are always strategic, marketing, competitive, risk, legal, regulatory, human resources, environmental, and other qualitative factors to consider for each proposed investment. Exhibit 7-2 compares three different investment opportunities. The first alternative is the base-case cost-saving machinery project from Exhibit 7-1. Exhibit 7-2 includes an analysis of two other projects—an efficiency-improvement project and a plant-expansion project. The efficiency-improvement project is a two-stage investment, $50,000 now, in Year 0, and another $50,000 at the end of Year 1. The NPV of $274 just clears the 12-percent hurdle rate. The plant-expansion project requires cash outflows of $150,000 in Years 0 and 1 and $50,000 in Year 2. The increased cash flow estimated to result from this project begins with $100,000 in Year 2, followed by $120,000, $140,000, and $170,000 in the three succeeding years. In Year 2, therefore, there is both a cash outflow of $50,000 and an estimated cash inflow of $100,000. In a spreadsheet format, it is convenient first to list estimated cash flows individually. Then, net out multiple cash flows in a single year when necessary. Finally, multiply the net cash flow for each year by the present-value factor. The plant-expansion project appears very attractive, with a positive NPV of $26,780. It may be significantly more risky than the other two projects, however, which must be considered in selecting the final portfolio of investments. INTERNAL RATE OF RETURN Financial Planning and Asset Management 148 A calculation related to NPV is the internal rate of return (IRR). This is the reinvestment or hurdle rate at which the NPV is zero. You can calculate IRR on an iterative, trial-and-error basis, by testing the effect of different discount rates until the one is found that results in a zero NPV. One way to reduce the calculations needed is to compute the NPV at two rates, chart the results on a graph, and extend the line connecting the two points until it crosses the zero point on the vertical axis. Most spreadsheet programs, however, have functions that will calculate the NPV of a series of numbers and also calculate the IRR. (Internal rates of return for the effi- EXHIBIT 7-2 Analysis of Alternative Investment Opportunities Discounted at a 12 Percent Rate YEAR Presentvalue factor @ 12% 0 1 2 3 4 5 1.0000 0.8929 0.7972 0.7118 0.6355 0.5674 COST-SAVING MACHINERY PROJECT Cash flows ($100,000) $30,000 $30,000 $30,000 $30,000 $20,000 Present value ($100,000) $26,786 $23,916 $21,353 $19,066 $11,349 Net present value $2,469 EFFICIENCY-IMPROVEMENT PROJECT Cash flows ($50,000) ($50,000) $35,000 $35,000 $35,000 $35,000 Present value ($50,000) ($44,643) $27,902 $24,912 $22,243 $19,860 Net present value $274 PLANT-EXPANSION PROJECT Cash flows ($150,000) ($150,000) ($50,000) — — — Cash flows — — 100,000 $120,000 $140,000 $170,000 Net cash flows ($150,000) ($150,000) $50,000 $120,000 $140,000 $170,000 Present value ($150,000) ($133,929) $39,860 $85,414 $88,973 $96,463 Net present value $26,780 ciency and the expansion project are shown in Exhibit 7-3.) Several pocket calculators, such as the Hewlett-Packard HP-12C, also have programs that will calculate these measures.  KEY POINT: One important distinction between NPV and IRR is the different implicit reinvestment-rate assumption each has for the reinvest- ment rate applied to the cash flow generated each year by the project. The NPV calculation assumes that a dollar can be reinvested at the hurdle rate, the rate used for discounting the cash flows. The IRR, on the other hand, assumes that a dollar can be reinvested at the IRR. For a project Capital Budgeting and Corporate Valuation 149 EXHIBIT 7-3 Trial-and-Error Calculation of Internal Rate of Return YEAR 0 1 2 3 4 5 EFFICIENCY-IMPROVEMENT PROJECT Cash flows ($50,000) ($50,000) $35,000 $35,000 $35,000 $35,000 Presentvalue factor @ 12% 1.000 0.8929 0.7972 0.7118 0.6355 0.5674 Present value ($50,000) ($44,643) $27,902 $24,912 $22,243 $19,860 Net present value $274 Present value factor @ 13% 1.000 0.8850 0.7831 0.6931 0.6133 0.5428 Present value ($50,000) ($44,248) $27,410 $24,257 $21,466 $18,997 Net present value ($2,118) Estimated by interpolation: 12.1% = (1% × 274/[274 + 2,118]) + 12% PLANT-EXPANSION PROJECT Cash flows ($150,000) ($150,000) ($50,000) – – – Cash flows – – 100,000 $120,000 140,000 $170,000 Net cash flows ($150,000) ($150,000) $50,000 $120,000 140,000 $170,000 Presentvalue factor @ 15% 1.000 0.8696 0.7561 0.6575 0.5718 0.4972 Present value ($150,000) ($130,435) $37,807 $78,902 $80,045 $84,520 Net present value $840 Presentvalue factor @ 16% 1.000 0.8621 0.7432 0.6407 0.5523 0.4761 Present value ($150,000) ($129,310) $37,158 $76,879 $77,321 $80,939 Net present value ($7,013) Financial Planning and Asset Management 150 Estimated by interpolation: 15.1% with an IRR significantly above the company’s normal hurdle rate, that assumption might not be realistic. PAYBACK A simple capital budgeting measure, sometimes used alone but often used with NPV or IRR, is the payback. This measure is simply the number of years required for the project’s cash inflows to repay the capital investment. If two projects have about equal NPVs and IRRs, the one with the shorter payback probably has lower risk. To illustrate how payback is calculated, a project with an initial cash outlay of $300,000 and a positive cash inflow of $100,000 per year for five years will have a payback of three years. A similar project with a threeyear life also has a three-year payback although it is clearly an unattractive investment.  SMART FINANCIAL MANAGEMENT: Payback is thus a useful comparison measure for longer-lived projects and for projects with lives of similar lives. PROFITABILITY INDEX The profitability index is another measure used to compare projects. This measure is a ratio of the present value of cash inflows divided by the present value of cash outflows. A profitability index greater than 1.0 indicates the project’s IRR is greater than the discount rate and it has a positive NPV. The profitability indexes for the cost-saving machinery project, the efficiency-improvement project, and the plant-expansion project are illustrated in Exhibit 7-4. This analysis suggests that a present-value dollar invested in the expansion project is the most productive. For every presentvalue dollar invested, the project returns $1.08 present-value dollars. Calculating a Hurdle Rate The hurdle rate a company uses in its capital budgeting analysis is usually close to its weighted average cost of capital (WACC). Although there are other considerations, theoretically you should be receptive to projects that return more than the WACC and turn down those that return less. A company’s WACC is the weighted average of its long-term debt and its equity costs. An example of how a company’s WACC is calculated is shown in Table 7-3. The equity component is the most complicated part of this calculation. The cost of equity is often calculated using the Capital Asset Pricing Model (CAPM). Capital Budgeting and Corporate Valuation 151 EXHIBIT 7-4 Profitability Index Calculation at a 12 Percent Discount Rate YEAR Presentvalue factor @ 12% 0 1 2 3 4 5 1.0000 0.8929 0.7972 0.7118 0.6355 0.5674 COST-SAVING MACHINERY PROJECT Cash outflows ($100,000) — — — — — Present value, cash outflows ($100,000) — — — — — Cash inflows — $30,000 $30,000 $30,000 $30,000 $20,000 Present value cash inflows — $26,786 $23,916 $21,353 $19,066 $11,349 Cash inflows $102,469 Cash outflows $100,000 Profitability index 1.02 EFFICIENCY-IMPROVEMENT PROJECT Cash outflows ($50,000) ($50,000) — — — — Present value, cash outflows ($50,000) ($44,643) — — — — Total present value, cash outflows ($94,643) Cash inflows — — $35,000 $35,000 $35,000 $35,000 Present value, cash inflows — — $27,902 $24,912 $22,243 $19,860 Total present value, cash inflows $94,917 Financial Planning and Asset Management 152 Cash inflows $94,917 Cash outflows $94,643 Profitability index 1.0029 YEAR 0 1 2 3 4 5 PLANT-EXPANSION PROJECT Cash outflows ($150,000) ($150,000) ($50,000) — — — Present value, cash outflows ($150,000) ($133,929) ($39,860) — — — Total present value, cash outflows ($323,788) Cash inflows — — $100,000 $120,000 $140,000 $170,000 Present value, cash inflows — — $79,719 $85,414 $88,973 $96,463 Total present value, cash inflows $350,568 Cash inflows $350,568 Cash outflows $323,788 Profitability Index 1.08 TABLE 7-3 Weighted Average Cost of Capital (WACC) Calculation PREMARKET COMPONENT Debt Equity Total VALUE WEIGHT $3,000,000 37.5% 5,000,000 62.5 AFTER- TAX TAX WEIGHTED COST COST COST 5.6% 2.10% 8% 15 15.0 $8,000,000 9.38 11.48% CAPITAL ASSET PRICING MODEL The Capital Asset Pricing Model is a technique for calculating the cost of equity capital. The formula is: Cost of equity = Current risk-free rate + (beta × market risk premium for common stocks) The risk-free rate, as its name implies, is the return available from an investment that carries no risk. In practice,U.S. Treasury bill rates often are Capital Budgeting and Corporate Valuation 153 used as a proxy for the risk-free rate. Some companies, however, consider a longer-term Treasury bond rate to be a more appropriate risk-free rate to use in developing the cost of equity. Beta is a measure of the risk of a particular stock compared to the entire stock market. It is the covariance of the stock with the market. It is derived by running a regression analysis between the returns on a specific stock and those of a broad index of stocks such as the S&P 500. A stock with a beta of more than one has greater volatility than the underlying market, and vice versa. The CAPM states the expected risk premium for a given stock is proportional to its beta. Although CAPM is widely used,the accuracy of betas for particular company stocks has been questioned in recent years.  WATCH THIS: A more difficult problem for you and other owners of private companies is that a beta for such companies cannot be calcu- lated. There is no way to compare the performance of your company’s value to the stock market as a whole. One approach to estimating a beta in this situation is simply to make a managerial judgment about how well the company’s performance tracks the overall market. Another way to estimate a beta is to look for the betas of comparable companies that are traded. Calculations of betas are available from several sources, such as Value Line. The market-risk premium is the incremental rate of return required by investors to hold a well-diversified portfolio of stocks rather than risk-free securities. The historical difference between the stock-market return and the risk-free rate, used in the formula above, is available in the frequently used yearbook, Stocks, Bonds, Bills and Inflation, published by Ibbotson Associates of Chicago. According to the 2002 Yearbook, the compound annual return for United States Treasury Bills between the end of 1925 and the end of 1998 was 3.8 percent. Over the same period, the compound annual return for large company stocks was 10.2 percent and for small company stocks 12.1 percent. Therefore, the market risk premium for large company stocks was 6.4 percent (10.2 minus 3.8 percent) and for small companies 8.3 percent (12.1 minus 3.8 percent). The CAPM cost-of-equity calculation for a small company with a beta of 1.2 is calculated as: 3.8% + (1.2 × 8.3%) = 13.96%. Financial Planning and Asset Management 154 ADJUSTMENT FOR HIGHER RISK OR UNCERTAINTY For projects with higher than normal business risk,some adjustment to the hurdle rate is advisable. Some companies raise the discount rate by one or two percentage points for riskier projects. Others apply a probability adjustment,cutting projected future cash inflows by 5 or 10 percent. Based on a 1996 survey,1 practice is evenly divided. Corporate Valuation Corporate valuation is central to all corporate financial activities. Management’s most important objective is to create value for the owners by increasing the value of the firm. Nearly all business decisions are made with this duty in mind. There is no single, correct method to value a company. Various parties, such as potential or actual investors, potential acquirers of controlling interests, CFOs and other managers, lenders, and vendors, use different methods depending on their reasons for valuing the company. Most will use several methods to validate assumptions and judgments. Some techniques base valuation on past performance, others on expected performance. Value may be based on assets, profits, or expected cash flow. There are at least five commonly used methods to value a company: 1. 2. 3. 4. 5. Book value Market value Liquidation value Replacement value Discounted cash flow BOOK VALUE Book value is simply the value of total equity on the balance sheet, total assets minus total liabilities. Equity is created and increased by the sale of stock, and it is increased or decreased by additions or subtractions to retained earnings. Book value is backward looking. It is based on a company’s historical performance, governed by the conventions of doubleentry bookkeeping and generally accepted accounting principles (GAAP). Therefore,it does not reflect the changing worth of balance-sheet assets and liabilities or the company’s future earnings potential as a going concern. Book value is most used in regulated industries. For example,a bank’s required ratio of capital to total assets is based on book value. The rates a public utility is permitted to charge are based on the book value of its assets and an allowable rate of return. Book value has greater importance for financial institutions than many other industries because of the predominance of financial assets on the balance sheet. The presumption is that financial assets are more likely worth their book value than machinery and intangibles.  SMART FINANCIAL MANAGEMENT: Book value is used also, however, for bank-loan covenants such as debt-equity ratios because lenders 1. Henry A. Davis, Cash Flow and Performance Measurement: Managing for Value (Morristown, NJ: Financial Executives Research Foundation, 1996). Capital Budgeting and Corporate Valuation 155 are concerned about worst-case problems requiring liquidation. Basing a loan on a percentage of book value typically results in a lower figure than the same percentage of current market value. MARKET VALUE Market value is the price of a company’s stock multiplied by the number of outstanding shares. The market values of different companies may be compared with two ratios: market to book value and price-earnings ratio. Market to book value is often used to compare the values of banks and other financial institutions. The stock of a bank with flat earnings growth and a high percentage of nonperforming loans might sell for only two-thirds of book value. The stock of a bank with good earnings growth, a high-quality loan portfolio, and significant non-credit service income might sell for two or even three times book value. The price-earnings ratio (P-E ratio) is the ratio of a company’s total value to its annual net income. This is often calculated as the ratio of its stock price to annual earnings per share. P-E ratios are easy to understand, easy to calculate,and widely used. Even for experienced securities analysts, they can be a convenient shorthand for more complicated valuation methods. A P-E ratio,however,is based on just one period’s earnings, either recent past or forecasted.  WATCH THIS: The use of an average or representative industry’s P-E ratio to value a particular company, say at 15 times earnings, is judg- mental at best. Despite these limitations, industry P-E ratios are often used in valuing private companies in the absence of a comparable transaction. Business brokers will usually know the P-E ratios at which local transac- tions are taking place. LIQUIDATION VALUE Liquidation value is the expected net proceeds, after all expenses and taxes, of selling the company’s assets in an orderly liquidation. The more rapidly the liquidation must be accomplished, the smaller the proceeds are likely to be. Financial Planning and Asset Management 156  KEY POINT: Liquidation value is often the absolute minimum value for a business. It is relevant for poorly performing companies; for lenders who are concerned with the liquidity of inventory, receivables, and other assets pledged to them as collateral; and for creditors when bankruptcy becomes a possibility. REPLACEMENT VALUE Replacement value is the amount a potential purchaser would have to pay to duplicate the company’s assets at current market prices. As with liquidation value, replacement value is based strictly on a company’s assets and does not consider its earnings or its potential as an operating business. In some circumstances, this value will set a maximum on a company’s worth. A prospective buyer will start a new business if the price of an existing one is much more than its replacement value. DISCOUNTED CASH FLOW  SMART FINANCIAL MANAGEMENT: A discounted cash flow (DCF) valuation is based on a company’s forecasted future free cash flow dis- counted at a realistic reinvestment rate, such as its WACC. It is the most rigorous and conceptually sound method to value a company. DCF valuation is not as widely understood as are P-E ratios, however. It requires many assumptions and judgments about a company’s future performance, assumptions whose validity may be difficult to assess with agreement by all parties. The methodology for a DCF valuation of a company is similar to the present-value methodology described above for capital projects but is applied to the whole company rather than to an individual project. As with capital investment projects, a corporate valuation often recognizes the inherent difficulty in forecasting. It therefore considers several different alternative situations based on more and less favorable assumptions. Those alternatives can be probability weighted to create a risk-adjusted value. The following basic financial relationships are central to applying the DCF methodology to valuing a company: ➤ Corporate value = market value of debt plus market value of share- holders’ equity. ➤ Corporate value = net present value of future free cash flow. ➤ Shareholders’ equity = corporate value minus market value of debt. ➤ Shareholders’ equity = present value of future free cash flow minus market value of debt. Free Cash Flow Free cash flow represents all cash left from operating income after taxes and reinvestments necessary to continue growing the business—capital expenditures and additions to working capital—but before the payment of interest and dividends. Capital Budgeting and Corporate Valuation 157 Free cash flow = Net income + depreciation and other non-cash deductions + after-tax interest − increase in working capital − capital expenditures Alternatively: Free cash flow = Earnings before interest and taxes (EBIT) − taxes (on EBIT) + depreciation and other noncash deductions − increase in working capital − capital expenditures Example of Discounted Cash Flow Valuation The DCF method of valuation is best explained through an example. The most recent annual income statement of the Stalwart Manufacturing Company is shown in Exhibit 7-5. The company has long-term debt of $2 million,and its WACC is 12 percent. For the purpose of preparing a discounted cash flow valuation,Stalwart’s CFO makes the following forecast: ➤ Sales will increase by 15 percent per year. ➤ The gross profit margin will remain at 40 percent. ➤ SG&A will increase at 12 percent per year. ➤ Depreciation will increase at 10 percent per year. ➤ Interest expense will increase at 15 percent per year. ➤ Taxes will remain at 30 percent. ➤ Incremental working capital will be 10 percent of incremental sales. ➤ Capital expenditures will be 12 percent of incremental sales. Cash flow projections incorporating the CFO’s forecast are shown in Exhibit 7-6. What happens after the end of the five-year forecast period? Rather than extending the cash flow forecast beyond the number of years for which reasonable forecasts may be made, most analysts use either a perpetuity or a growing perpetuity to reflect the residual value, the value of cash flows beyond the forecast period. An alternative is to estimate what the company might be sold for at the end of the period using a P-E ratio. The perpetuity method is based on the assumption that,after some point,the business no longer will generate investment opportunities that return more than its cost of capital. Therefore, it no longer will produce real growth in value. Further investment still will create income,but the present value of that income will be equal to the pres- PERPETUITY METHOD Financial Planning and Asset Management 158 EXHIBIT 7-5 Income Statement, Stalwart Manufacturing Company (thousands of dollars) YEAR 0 1 $10,000 $11,500 Cost of goods sold 6,000 Gross profit Net sales 3 4 $13,225 $15,209 $17,490 $20,114 6,900 7,935 9,125 10,494 12,069 $ 4,000 $ 4,600 $ 5,290 $ 6,084 $ 6,996 $ 8,045 2,000 2,240 2,509 2,810 3,147 3,525 500 550 605 666 732 805 $ 1,500 $ 1,810 $ 2,176 $ 2,608 $ 3,117 $ 3,715 200 230 264 304 350 402 $ 1,300 $ 1,580 $ 1,912 $ 2,304 $ 2,767 $ 3,313 390 474 574 691 830 994 910 $ 1,106 $ 1,338 $ 1,613 $ 1,937 $ 2,319 Selling, general, & Admin. exp. Depreciation Operating profit Interest Pre-tax income Income taxes (30%) Net income $ 2 5 ent value of the investment. Because further investment is unwarranted, all the cash flow generated can be capitalized at the appropriate discount rate. For example, an investor who requires a rate of return of 10 percent should be willing to pay $1,000 for an annuity of $100 per year. The present value of the residual can be calculated with the following formula: Present value of residual = Yearly free cash flow × Present-value factor Discount rate The growing perpetuity is another frequently used method for calculating residual value. It assumes that free cash flow will grow at a given rate in perpetuity. The present value of the residual can be calculated with the following formula: GROWING PERPETUITY METHOD Present value of residual = Final year’s free cash flow × (1 + growth rate) × Discount rate − growth rate Present-value factor Capital Budgeting and Corporate Valuation 159 EXHIBIT 7-6 Free Cash Flow, Stalwart Manufacturing Company (thousands of dollars) YEAR Sales 1 2 3 4 5 $11,500 $13,225 $15,209 $17,490 $20,114 1,810 2,176 2,608 3,117 3,715 Taxes 543 653 782 935 1,115 Working capital increases 150 173 198 228 262 Capital expenditures 180 207 238 274 315 550 605 666 732 805 $ 1,487 $ 1,749 $ 2,055 $ 2,412 $ 2,829 Operating profit Less: Plus: Depreciation Free cash flow EXHIBIT 7-7 Discounted Cash Flow Valuation of Stalwart Manufacturing Company (thousands of dollars) YEAR Free cash flow Present-value factor @ 12% Present value of free cash flow Total discounted five-year cash flow 1 2 3 4 5 $1,487 $1,749 $2,055 $2,412 $2,829 0.893 0.797 0.712 0.636 0.567 $1,328 $1,394 $1,463 $1,533 $1,605 $7,322 Growing perpetuity, end of fifth year: ($2,829 × 1.04) ÷ (12% − 4%) = $36,776 Discounted to year zero: $36,776 × 0.567 = $20,868 Financial Planning and Asset Management 160 Summary Five-year discounted cash flow Plus Growing perpetuity Equals Enterprise value Less Outstanding long-term debt Equals Shareholder’s equity $ 7,322 20,868 $28,190 2,000 $26,190 This formula will not work if the growth rate is greater than the discount rate used to value the cash flows. Exhibit 7-7 illustrates the calculation of discounted free cash flow from Stalwart’s five-year forecast. It uses a growing-perpetuity analysis, assuming a 4 percent growth rate. The illustration also shows how the shareholders’ equity is calculated by subtracting existing debt from corporate value. Numerical Analysis Capital investments are seldom wisely made solely because of the numerical analysis. You must consider how the capital investment fits with the corporate strategy, the company’s financial planning, the risks associated with the investment, and your own (and the other owners’) wishes and objectives.  SMART FINANCIAL MANAGEMENT: Careful numerical analysis, however, can help prevent unwise investment whose superficial appeal can result in excessive enthusiasm. It also can help you put the opportunities in perspective so you can rank them effectively when available funds are insufficient to finance them all. The same techniques are useful when you must value an entire business either to buy or to sell it. Finally, intangible assets and intellectual property create significant value for many companies. Although the cash expenditures to develop these assets are written off as current-period expenses rather than capitalized, the same analytic procedures apply to the analysis of these investments that apply to traditional investments in plant and equipment. Capital Budgeting and Corporate Valuation 161