Week 3 Notes:

Financial Valuation
(rev 2/19/04)




I. Valuation of financial securities
The value of every financial security, debt or equity, is determined by finding the equivalent economic value today of all expected cash flows. This means discounting all future cash flows using the investor's opportunity cost, which is the return an investor could earn in the next best investment opportunity of equal risk. This is the investor's required return. The cash flows for a bond are easily determined because they are specified in the bond contract and the company has a legal obligation to pay them. Typically, the cash flows are an annual cash payment plus the face value of the bond at maturity. The opportunity cost is the market return on bonds of similar risk. You can review some notes on bond valuation.

The cash flows for a share of common stock are more difficult to estimate accurately. The company has no legal obligation to make any payment to stockholders. However, once a company pays a dividend, it usually tries to maintain it. Because the company has no obligation to buy back shares of stock, stock valuation models assume that the only cash an investor would receive are dividends. There are two forms of the dividend valuation model. The first assumes that the dividend remains constant in the future. The value of a share of stock equals the dividend divided by the investor's opportunity cost. This is a useful model for valuing preferred stock because preferred stock dividends rarely change over time. The other form of the dividend valuation model assumes that the dividend grows at a constant rate each year. This is a useful approximation because many companies do try to increase the dividend per share they pay each year. The value of a share of stock today is equal to the next year's dividend divided by the investor's opportunity cost minus the dividend growth rate. The investor's opportunity cost for common and preferred stock is difficult to estimate. For common stock the Capital Asset Pricing Model is often used to estimate investors' required return for a particular company's stock. Another method of estimating the opportunity cost is to use the yield on the company's bonds and several percentage points. For preferred stock, perhaps 2 to 3 percentage points might be added. For common stock, 4 to 6 points might be added. For example, if the yield (market return) on a company's bonds is 10%, the opportunity cost for its preferred stock might be 12% to 13% and 14% to 16% on its common stock. You can review these notes on stock valuation.

Cost of capital
Cost of capital is the rate of return a company must earn on the money it uses to finance the acquisition of new assets. The source of that money determines the return. This money can come from several sources: the sale of new bonds, the sale of new shares of common or preferred stock; or cash that the firm has on hand. The return that the firm and the new investment must earn is determined by the return demanded by the people whose money the firm is using. If the firm finances the investment with new debt, then the cost of capital must be the return demanded by these new bondholders. If money from the sale of new shares of common stock, the cost of this capital is the return that these new shareholders demand on their money. The same is true when new shares of preferred stock are issued. If the company uses money that is on hand, the cost of this money is the return that existing shareholders require. The cost of capital is the return required by those who provided the money used to acquire the new assets. In short, it is a required return.

The return that bondholders demand on their investment in a firm's bonds is their opportunity cost. It is the return that they could have earned in their next best investment opportunity of equal risk. The return that stockholders demand is also their opportunity cost, which is the return they could have earned in their next best investment opportunity of similar risk. This is true whether the stockholders own common or preferred stock. The cost of new debt is pretty straightforward. Because the risk of all debt is rated by one of several agencies, e.g., Standard & Poors and Moody's, the return demanded by investors on new debt is the return that is currently being provided by bonds in the same risk category. The cost of new shares of common stock is more difficult to determine precisely. However, it must be true that the return is based on the perceived risk of the stock. There are several ways to measure this risk-return relationship. The most popular come from portfolio theory, which assumes the stock market is generally in equilibrium at any point in time, which means that current prices reflect the required return that stockholders demand and that the market is filled with investors who have well diversified portfolios. One such model is the Capital Assert Pricing Model, which assumes that the only risk investors bear is the market risk that they cannot diversify away. It is based on the premise that all common stock is positively correlated, that is, the prices of all stock tend to move in the same direction in the long run. It is measured by beta. Another model assumes that the value of a share of stock, common or preferred, is determined by the dividends expected by investors. If these dividends are assumed constant or are expected to grow at a constant rate, a simple model can be developed to estimate the required return. This is the model used to estimate the required return on preferred stock. Because money that a firm has on hand and uses to finance new assets belongs to existing common stockholders, the process of calculating the required return is the same as it is for new shares of common stock.

Usually companies finance new investments with money from several sources. The cost of capital is a weighted average of the required returns of the different sources of money in a firm's capital structure. A firm's capital structure is comprised of all long-term debt plus all equity. The cost of capital is calculated by multiplying the required return for each separate source of money by its proportion of the total investment and then summing the result across all sources. The use of the cost of capital in evaluating investment opportunities when their risk is commensurate with that of the entire company and when the investments are financed in the same proportion as the existing capital structure.

Investment decision making
In order to achieve its long-term objectives, an organization must have the appropriate resources in place. Often this requires a substantial investment in resources that offer benefits over a period of many years. There are typically many different ways in which resources can be used to achieve these objectives. The economic decision-making process is used to choose from among the different alternatives. Each alternative is evaluated on the basis of its expected benefits and costs. This type of analysis is also called simply cost-benefit analysis and is applicable in business and nonbusiness organizations alike.

The first step is to identify all the benefits and costs expected with each alternative. The next step requires that these benefits and costs be quantified using the same unit of measurement, dollars. Because the expected benefits and costs of an alternative are typically realized over a period of years, their dollar amounts cannot be added together because dollars either received or paid out at different points in time have different economic values. Adding dollars to be received in one year to dollars to be received in two years is like adding apples and oranges. It is necessary to find a common basis on which to add all the dollars. The usual method is to find the equivalent economic value for all dollars at the same point in time. The point in time most commonly used is the present, although any point in time may be used as long as all dollars are converted to that same point in time.

This process of finding equivalent economic values of dollars at different points in time is called the time value of money. The key element is the opportunity cost of the decision-maker. By identifying the appropriate opportunity cost, all future sums of money can be converted into equivalent present sums. Once each future sum has been given an equivalent present value, the benefits and costs can be summed up individually and directly compared. The alternative for which the present value of all the benefits is greater than the present value of all the costs is the preferred alternative.

Evaluating investment alternatives using cash values for the benefits and costs is called discounted cash flow (DCF) analysis. Net Present Value (NPV) and Internal Rate of Return (IRR) are the two major forms of DCF analysis. The NPV for an alternative is the present value of all expected benefits less the present value of all expected costs. The alternative with the highest NPV should be the one selected. The IRR for an alternative is the rate of return that makes the present value of all expected benefits equal to the present value of all expected costs. If the IRR is greater than the appropriate opportunity cost, the alternative is acceptable. However, the alternative with the highest IRR is not always the preferred alternative. The preferred alternative is always the one with the highest NPV, which is why NPV should be used to compare different alternatives.

You can view a "movie" that describes the investment decision making process.
 

II. Business Valuation

Introduction

Accounting analysis and financial analysis form the foundation for successful business valuation. While business valuation is useful in a number of contexts, its treatment in this lesson is focused on investment analysis and more particularly, acquisition and merger strategies. An organization that is considering an acquisition or merger is seeking to increase the firm’s value for its stockholders. It is useful to begin by briefly reviewing accounting and financial analysis.

Accounting and Financial Analysis

Four major financial statements provide an accounting overview of an organization’s financial position. Organizations use accepted accounting principles in the preparation of these financial statements. The Income Statement provides a summary of the revenues generated, expenses incurred and net income earned during a specified period of time. The Balance Sheet shows the organization’s assets, liabilities, and stockholders equity at a specific point in time. In essence, it shows how a firm’s assets are financed. The Statement of Retained Earnings gives the amount of net income or earnings that have been “retained” (not paid out in dividends) by the organization to acquire assets. The purpose of the Statement of Cash Flows is to show how the operations of an organization affect its cash flow over a specific period of time.

In analyzing accounting information, keep in mind that organizations have flexibility in preparing these reports and often seek to present them in the best light possible. Still, accounting analysis is useful in assessing the financial position of an organization. The analysis includes evaluating the degree to which the organization is likely to be adhering to well established accounting practices, primarily by looking at the incentives and disincentives to do so. Observe the overall goals and strategies of a firm and whether the accounting information reflects these goals and strategies. Review the accounting related goals and strategies of a firm and determine whether these are being met. Consider whether the information provided reflects observed reality in its business operations and is of good quality, including its completeness and accuracy. Analyze the reasons for any unexpected accounting data. Finally, analysis may require the recasting of “unbiased” accounting data.

In financial analysis, accounting data is often used to assess the financial position of an organization — past, present, and future. Ratio analysis is a primary tool in this analysis. From an investment standpoint, accurate valuation is the objective.  Ratio analysis depicts relationships both within and among firms. Ratios fall primarily into four major categories — liquidity, asset management, debt management and profitability ratios. Liquidity ratios measure relationships of current assets and current liabilities. Asset management ratios and debt management ratios measure how effectively an organization manages its assets and debts, respectively. Profitability ratios measure how a firm’s actions affect operating results. While ratios are beneficial, the limitations of their use are important as well. The analysis of a firm’s cash position is another key tool in financial analysis. While a firm may show a positive net income, analysis of its cash flows may show that from this view, a firm’s financial position may be relatively weak.

Valuation techniques are used to determine the value of an organization or some part of it. There are a number of approaches to valuation of an organization, such as discounted dividends, abnormal return on equity, and discounted cash flow analysis. The discounted dividends method calculates the value of equity as the present value of expected future dividends. The abnormal return on equity method finds the value of equity by combining the firm's current book value with the present value of expected abnormal earnings. The discounted cash flow analysis uses forecasts of estimated future cash flow to find the value of a firm’s stock value. In practice, it is best to utilize as many techniques as possible in estimating the value of a firm's equity.

Business Valuation

In terms of acquisition and merger strategies, a number of factors must be considered when valuing a potential acquisition or merger. It is not enough to do simple projections of future expected earnings or rely on managerial “instinct” to determine this value. An analysis must first begin with defining the acquiring organization’s investment strategy and determining whether the acquisition under consideration is consistent with this strategy.

The next step is to find the value of the acquisition or merger target. There are a variety of ways to value an acquisition. The most common valuation techniques can be categorized as discounted cash flow analysis. Discounted cash flow analysis estimates the annual expected cash flows to be generated by a firm over a period of time and then calculates the present value of those cash flows using the firm's weighted average cost of capital. The difference among the various methods of discounted cash flow analysis is centered on the way in which the annual expected cash flows are estimated. One approach to valuing  a firm uses the present value of future free cash flows expected to be generated over a forecast period and adds the present value of the continuing or residual value of the firm. A second approach estimates the expected future cash flows using either abnormal earnings or abnormal net operating income after taxes. The present value is found by discounting the expected cash flows using the pre-acquisition cost of equity for the target firm. Alternatively, the expected cash flows can be discounted using the pre-acquisition weighted average cost of capital and then subtracting the value of the target firm's debt.

Another approach to firm valuation calculates the stand-alone value of a firm to be acquired and adds to it the synergy value associated with the merger. The intrinsic value of the target firm can be calculated by finding the net present value of future free cash flows expected to be generated by the firm to be acquired over a specific period. The synergy value is then calculated. The synergy value is the present value of the expected incremental cash flows resulting from the assets of the target firm being combined with the assets of buying firm. While it is often difficult to calculate the synergy value, care must be taken not to overestimate it. Most companies today pay a premium above the fair market value, or intrinsic value, of the assets of the target firm. In theory, the premium should be exactly equal to the value of the synergy to be realized in the acquisition or merger. In order for the value of the equity of the shareholders of the acquiring firm to increase in value, the value of the synergy must be greater than the premium paid. This valuation framework can be summarized in the following series of equations:

Value Created By Acquisition = Value of Combined Firm – (Stand-alone Value of Buyer + Stand-alone Value of Seller)

Maximum Acceptable Purchase Price = Stand-alone Value of Seller + Synergy Value

Value Created for Buyer = Maximum Acceptable Purchase Price – Price Paid

Premium Price = Purchase Price – Stand-alone value of Seller

Synergy value is often based on four factors — cost savings, revenue increases, changes in financial structure, and tax benefits. First, cost savings is the most common because it is the easiest to estimate. In an acquisition or merger, there are usually going to be some duplicate activities being performed in both companies as well as excess property, plant and equipment. Economies of scale and process improvements also lead to cost savings. Second, increases in revenue from the combined firms are more difficult to estimate because the sale increases for specific products may or may not materialize. Third, sometimes consolidation may lead to beneficial changes in financial structure. There can be substantial reductions in amount of working capital as well as reductions in the cost of equity and debt financing for the combined firm. Fourth, tax benefits may also result but are often the most difficult to estimate. The strategic value of an acquisition should not be based on tax implications. This is strictly an ancillary benefit of an acquisition or merger.

The earnings multiple technique is yet another method for valuing a target firm. The earnings multiple technique entails estimating future earnings for the target firm and then applying an earnings multiple to determine the value of the firm's equity. Future earnings are often based on the next period’s pro forma income statement that estimates the net income of the target firm in the absence of the acquisition. To calculate the value of the target firm independently, the current price-earnings multiple can be applied. To calculate the value of the target firm, the synergies to be expected from the acquisition or merger should be incorporated into the target firm's pro forma statement. A price-earnings multiple is again applied. This multiple should not automatically be the target firm's current one, if available. Although it is often difficult to estimate such a multiple, the best approach is often to use the price-earnings multiple of a firm that possesses the same characteristics as the target firm will exhibit after the acquisition or merger.

No matter which valuation technique is used, it is strongly recommended that a sensitivity analysis be performed to determine how significantly the value of the target firm changes when any of the key assumptions are altered. It is important to determine not only the most likely outcome, but also the worst and best possible outcomes as well. The method of financing the acquisition is an important part of the risk analysis. The cost of equity and the cost of debt for the combined firm will likely be different from what they were for the acquiring firm before the acquisition or merger. If the combined firm is viewed in the financial markets as being more risky than the firms were separately, the cost of issuing new shares of common stock and new bonds will increase. The result is that the combined firm will end up paying higher financing costs.

It can very useful to observe changes in the prices of the common stock for both the acquiring firm and the target firm during the acquisition process. When a firm announces its intent to acquire or merge with another company, the price of the common stock of both firms is likely to change. The direction of the change depends on how the market views the potential acquisition. If the market believes the acquisition makes economic sense, the price of the acquiring firm's stock and the target firm's stock will both increase. If the market does not believe the acquisition makes economic sense, the price of the acquiring firm's stock will fall while the price of the target firm's stock could rise.

Model

The value of a firm (Vf) equals the present value of the operating cash flows over the forecast period plus the present value of a residual value beyond the forecast period plus the value of the firm's marketable securities.

1. The first step is to calculate the expected free cash flows over the forecast period (i.e., competitive advantage period). To calculate each year's expected free cash flow take the sales for the most recent year and by multiply it by the (1 plus the sales growth rate). This estimate of sales for the next period is multiplied by the operating profit margin to get an estimate of operating income. This estimate of operating income is multiplied by the income tax rate to get an estimate of after-tax operating income (often referred to as NOPLAT). The next step is to add the company's depreciation expense back into the after-tax operating income to get an estimate of gross cash flow. Depreciation is added back because it is not a cash expense. To get the expected free cash flow, subtract the increase in new capital investment and the increase working capital needed to support the increased sales each year over the forecast period from the gross cash flow. The expected cash flows are calculated for each year of the forecast period (i.e., competitive advantage period). The present value of each year's cash flow is found by discounting the cash flow by the firm's cost of capital.

2. The residual or continuing value of the firm after the forecast period (i.e., competitive advantage period has expired and the rate of the firm's sales and earnings decline) equals the present value of all cash flows after the forecast period.  It is assumed that after a period of time, competitors will cut into a firm's competitive advantage dissipating its growth in sales and profit margin. At this point no incremental capital investments or additional investments in working capital are required and the firm's net cash flows become a perpetuity. The present value of this perpetuity at the end of the competitive advantage period is equal to the expected cash flow for the last year of the forecast period multiplied by the revised rate of growth in sales (if any) divided by the discount rate (i.e., cost of capital) minus the revised growth rate (if any).

3. A firm's marketable securities represent those debt and equity securities that the company is planning to sell within the next year. The value of the marketable securities on a firm's balance sheet represents the amount of cash the firm would receive if the securities were sold now (minus, of course the transaction costs associated with selling the securities). Therefore, the value of the marketable securities on a balance sheet is a present value and does not need to be discounted. Because marketable securities are not part of a firm's income generating assets, their value is measured by the cash the firm would receive upon their sale. This cash value is added to the present values of the annual cash flows and the residual value to get the total value of a firm.

To derive the "fair value" of equity, simply subtract the market value of the firm's debt from Vf (Equity value = Vf - Debt). The fair value value can be compared against the market value equity to determine whether the firm is under-valued or over-valued. The market value of equity is found by multiplying the number of shares of common stock outstanding by the current price per share.

Example

Assume that Firm A is considering the acquisition of Firm B. The common stock of both companies is publicly traded. The cost of capital for Firm B is 12% before and after the acquisition. For Firm B, sales for the latest year were $100 million. The sales growth rate is estimated to be 10%, and the operating profit margin is 5%. The company's depreciation expense for the latest year is $5 million and will grow at 3% each year. Both are assumed to hold for ten years. After the forecast period the growth rate in the after-tax operating income (NOPLAT) will be 5% and the return on invested capital (ROIC) is expected to be 20%. The income tax rate is 35 percent. The incremental capital investment rate is 2% and the incremental working capital rate is 1% over the ten-year forecast period. Market value of debt is $15 million. Firm B has 2 million shares of the common stock outstanding, and its current stock price is $55. Firm B has no marketable securities.

Calculate the acquisition value of Firm B

Present value of expected free cash flows

Expected free cash flow (year 1) = ($100 million)(1+.10)(.05)(.65) + ($5 million)(1+.03) + ($100 million)(1+.10)(.01) +  ($100 million)(1+.10)(.02)
 
Year
Sales
 After-tax operating income 
(NOPLAT)
Depreciation
expense
Increase in working capital
Increase in investment
 Expected free cash flow
2001 $121 3.575 5.15 1.21 2.42 $5.095
2002 $133.1 3.933 5.305 1.331 2.662 $5.245
2003 $146.41 4.758 5.464 1.464 2.928 $5.83
2004 $161.05 5.234 5.628 1.611 3.221 $6.03
2005 $177.16 5.758 5.797 1.772 3.543 $6.24
2006 $194.88 6.334 5.971 1.949 3.898 $6.458
2007 $214.37 6.967 6.15 2.144 4.287 $6.686
2008 $235.81 7.664 6.335 2.358 4.716 $6.925
2009 $259.39 8.43 6.525 2.594 5.188 $7.173
2010 $285.33 9.273 6.721 2.853 5.707 $7.434

Present Value of expected free cash flows = $5.095/(1.12) + $5.245/(1.12)^2 +  $5.83/(1.12)^3 +  $6.03/(1.12)^4 + $6.24/(1.12)^5 +  $6.458/(1.12)^6 + $6.686/(1.12)^7 + $6.925/(1.12)^8 + $7.173/(1.12)^9 +  $7.434/(1.12)^10
Present value of expected free cash flows = 4.549 + 4.181 + 4.15 + 3.832 + 3.541 + 3.172 + 3.024 + 2.797 + 2.587 + 2.394 = $34.327 million
 

Present value of the continuing or residual value
Continuing Value = [(last year's NOPLAT)(1 - NOPLAT growth rate/ROIC)]/(WACC - NOPLAT growth rate)
Continuing Value = ($9.273 - .05/.20)/(.12-.05) = $128.9 million
 

Total value of the firm
Total value of the firm = Present value of expected free cash flows + Present value of the continuing or residual value
Total value of the firm = $34.327 + $128.9 = $163.227 million
 

Total shareholder value
Total shareholder value = Total value of the firm - Market value of debt
Total shareholder value = $163.227 - $15 = $148.227 million
 

Premium
Premium = Total shareholder value - Market price of common stock
Premium = $148.227 - $110 = $38.227 million