Valuation Theory

Free Cash Flow Methods

The free cash flow methods, Shareholder Value and Dividend Discount, measure the value of a business based on its ability to generate returns on investments in excess of its weighted average cost of capital.

Excess funds can be reinvested by the business or paid to the shareholders as dividends. In the first case, the business might invest in such areas as plant & equipment, additional working capital, or acquisitions, expecting to receive returns in excess of the cost of capital for the selected strategy.

Alternatively, the shareholders can reinvest their dividends in a capital market to earn risk-adjusted rates of return.

Shareholder Value Method

In simplest terms, the value of a company or business equals the combined values of its debt plus its equity. In Strategic Modeling, the value of the whole firm to both debt and equity holders is called corporate value; the value of the equity portion is called shareholder value.

In general: this is

(Corporate Value) = "Debt" + Equity

The debt portion of corporate value refers to the current value of the firm's total obligations, which include:

Market value of all debt
Underfunded Pension Liabilities
Other Obligations - preferred stock (market value), golden parachutes, contingent liabilities, etc.

Note:

You should use the market value rather than the book value of debt because during periods of rising interest rates, market values fall below book values. Using book values overstates the value of the liabilities, thus understates shareholder value. The reverse is true when interest rates are falling.

Corporate Value = Debt + Shareholder Value

where: Debt = Market Value of Debt + Underfunded liabilities + Market value of other obligations

Rearranging the corporate value equation to solve for Shareholder Value:

Shareholder Value = Corporate value - Debt

To determine shareholder value, you first calculate the corporate value, the value of the total firm or business unit.

Corporate Value Components

Corporate value, the economic value of the business or strategy, consists of:

The present value of all expected cash flow from operations during the forecast period, known as discounted cash flows.
The value of the firm beyond the forecast period, known as residual value.

The cash flows are discounted by the firm's cost of capital, or required rate of return, which takes into account the firm's level of both business and financial risk.

There is a third component, the value of investments in assets not involved in operations (passive investments). Their value can be added as a plugged number or separately modeled and added to Corporate value.

In general, then: Corporate Value = Value created during the Forecast Period (discounted cash flows) +Value after the Forecast Period (residual value).

Discounted Cash Flows Component

The discounted cash flows (or, more precisely, the cumulative present value of cash flows) represent the expected net cash inflows to the business, independent of the firm's financing or dividend policies:

In general, then:

Cash Flow from Operations = Actual dollar inflows + Out of Pocket Dollars

In Strategic Modeling, after you've determined the cash flow from operations for each year in the forecast period, those flows are discounted back to present-value terms, using a discount factor based on the cost of capital.

Residual Value Component

Only a small portion of a company's market value can be reasonably attributed to its estimated cash flows during a forecast period of 5 or 10 years. The remaining portion, called the residual value, typically represents well over 50% (and usually closer to 80%) of the total corporate value. There are several different ways to measure this value.

Passive Investments Component

For a precise estimation of corporate value, a third component must also be included - the current market value of investment holdings. Examples include: marketable securities, investments in stocks and bonds, investments in un-rolled up subsidiaries, an overfunded pension plan, and liquid non-operating assets. These items are not accounted for in the cash flows, but they have a value to the firm, so their value must be added to the other two components.

Note:

The reason that marketable securities are not included in the working capital requirements used in estimating cash flow is that they represent cash holdings beyond those necessary for operating the business. Note also that debt (specifically, the current portion of long-term debt) is not included. Debt holders and equity holders hold the claims to the net cash flows generated by the firm. They are part of the capital structure and to include them in the investment requirements is double counting.

To summarize, Corporate value has three components: Cash flows, residual value and investments

Value Drivers: Key Factors Affecting Corporate Value

There are six key macro variables affecting values of discounted stream of cash flow from operations:

Sales Growth Rate (g)
Operating Profit Margin (p)
Cash Taxes on Operating Profit (t)
Fixed Capital Investment (f)
Incremental Working Capital Investment (w)
Cost of Capital (K)

These variables, or value drivers, determine each year's cash flow from operations. After each year's cash flow from operations is calculated, those flows are each discounted based on the cost of capital (K).

Because these value drivers determine the expected cash flow from operations, you can evaluate these factors to determine which ones have the greatest impact on corporate shareholder value.

To learn the value drivers, use scratch pad to estimate corporate value, so you can focus on key valuation variables.

The inputs are:

Number of Forecast Periods
Sales (Last Historical Period)
Sales Growth Rate (G)
Operating Profit Margin (P)
Incremental Fixed Capital Investment (F)
Incremental Working Capital Investment (W)
Tax Rate on Operating Profit (Tc)
Residual Value Income Tax Rate (Tr)
Cost of Capital (K)
Marketable Securities and Other Investments
Debt and Other Obligations
No. of Common Shares

After completing your scratchpad analysis, which holds each of these variables constant throughout the forecast period, you can use a more explicit model in Strategic Modeling to evaluate these variables in greater detail and changing over time. Using the Scenario Manager, you can determine the impact on shareholder value of changing variables contributing to value drivers.

Dividend Discount Method

The Dividend Discount Model calculates the value of the equity of a firm directly from the expected cash flows received by the shareholders—the Dividends. These flows are discounted at the cost of equity. The advantage of this method is that it enables you to compute Shareholder Value directly from the flows that the shareholders are actually forecast to receive.

Dividend Discount Model has disadvantages:

If a firm adopts a fixed dividend policy, that firm's leverage may drift from the target leverage. If a firm is accumulating and investing cash in the form of marketable securities, leverage falls as does the Cost of Equity used to discount the dividend flows. If a firm is taking on debt to maintain its dividend policy, leverage and the Cost of Equity rise. Because the Cost of Equity is sensitive to changes in leverage, it needs to be adjusted for these changes in leverage to produce an accurate valuation.
If a firm is accumulating cash or debt, sooner or later it needs to adjust the flows to shareholders to account for this. Strategic Modeling assumes that, if such an adjustment is required, it can be done at the end of the forecast period.
If a firm is accumulating cash, it is de-levering and its Cost of Equity is being reduced. Consider the firm as engaging in two businesses: the normal business of the firm, and the business of investment (which you would expect to be less risky than the normal business of the firm).

If a firm adjusts its dividend policy to maintain a constant leverage, it is paying what Strategic Modeling refers to as the Affordable Dividend. This eliminates the problems with changes in leverage, but few firms are expected to pay their Affordable Dividend in each year. Thus, you would no longer be forecasting the expected real flows to shareholders.

See Mid-Period versus End-of-Period Discounting

Mid-Period versus End-of-Period Discounting

Consider when a firm is expected to pay its dividends. Most firms pay dividends on a quarterly or semi-annual basis. Mid-period discounting should be used here. If a firm paid only annual dividends, end-of-period discounting is appropriate.

Economic Profit Method

Although this method mixes cash and book items, it can lead to correct equity valuations if applied carefully. There are many ways to formulate this model, the most common being: EP = Net Operating Profit - Capital Charge

where: Capital Charge = Cost of Capital * Adjusted Book Value in Previous Period

The EP is calculated each period and discounted at the Cost of Capital to get a present value (PVEP). Adjusted Book Value is increased by the total incremental net investment for each period, so in general, a growing firm increases Capital charge over time. Then: Corporate Value = PVEP + Beginning Adjusted Book Value

which should be the same as the Corporate Value computed using the Shareholder Value Method. The Equity Value can be computed by the usual method of subtracting the market value of debt and other obligations and adding back the market value of investments.

If the Adjusted Book Value is a proxy for the owner investment in the business, the Capital Charge is the hurdle that must be reached to provide a break-even return on that investment. The Adjustments (on both the asset and liability side of the equation) that are made to Book Value make it a more reasonable proxy for owner investment in the firm, whether in the form of cash or as foregone dividends. The Economic Profit Model focuses management's attention on obtaining returns greater than the floor imposed by the Capital Charge.

The problems with the Economic Profit approach are:

Beginning Adjusted Book Value is used as a proxy for the investment in the firm, but this number requires you to decide on the adjustments necessary to obtain the actual economic value of the firm. If the Adjusted Book Value is higher than the actual economic value, Economic Profit in the forecast period appears to be lower than it actually is—possibly causing a firm that is actually creating value to appear to be destroying value. For firms whose economic value can be measured in market terms, requiring historical, albeit adjusted, book values as part of the model is an unnecessary complication.
Economic Profit is a short-term measure which may cause management to focus on the wrong targets, leading to dysfunctional behavior. Many value-creating projects don't return the cost of capital in their first or second year, although the long-term cash flows easily make up for the investment required in the early years of the project. A manager measured on EP may not propose such a project because of the negative Economic Profit impact in the short-term.
The Economic Profit Model usually assumes that a firm can generate excess returns indefinitely, which runs counter to the idea that a firm creates value due to a competitive advantage that can only be maintained for a limited number of years.

Cost of Capital for Free Cash Flow Methods

The Cost of Capital (K) represents the weighted average costs of debt and equity, in proportion to the levels specified by the company's debt/equity ratio (based on market rather than book values).

The cost refers to the fact that suppliers of capital demand a return on their investment, and that return represents a cost to the recipient (that is, the firm).

The Cost of Debt is less than the Cost of Equity to the borrower for these reasons:

The interest portion of the return to debtholders is tax deductible.
Debtholders usually require a lower return because:
1. Debtholders' claims have a higher priority than stockholders' claims in the event of liquidation.
2. Debt has a fixed rate of return, whereas the return on stock depends on company performance.

The returns demanded by debtholders and stockholders are both important because the Shareholder Value Method discounts after-tax, pre-interest cash flows—cash flows on which both debtholders and shareholders have claims. The cost of capital, therefore, incorporates the claims of both these groups in proportion to their relative capital contribution. The cash flows discounted by the cost of capital yields corporate value. The market value of debt is subtracted from the corporate value to obtain shareholder value (the value of the equity).

By establishing a cost of capital, you are estimating a minimum acceptable rate of return. Returns above that rate create value for shareholders.

Most firms are comprised of different business units, each with a different exposure to macro-economic events. Not only should these units be analyzed as businesses, but each may well have a different cost of capital.

Recommendation to Use a Constant Cost of Capital

From a practical matter, you should use a cost of capital that is constant over time in Strategic Modeling. In other words, the cost of capital for each forecast period should be the same as the long-term cost of capital. Think of this cost of capital as being a yield to maturity concept. The alternative is to forecast a term structure. Except in very special situations, the value of attempting these forecasts is minimal. Another factor to consider is that the first few years of expected cash flows only contribute a small fraction of the firm's total value, and that is when most of the potential capital structure changes occur. Consequently, even if you could estimate these changes, it would not change the firm's calculated value.

Analysts occasionally claim, for a variety of reasons, that the cost of capital for a company changes over time and they want to change the cost of capital used in future periods. Here are two frequently cited reasons given for wanting to change the cost of capital, with the rationale for why the rate should remain constant:

Claim: Interest rates are changing in the future, so our cost of capital should also be changing.

Response: Long-Term interest rates incorporate the market's expectations of average future interest rates. Although future interest rates change, people cannot consistently outguess the real market changes.
Claim: Although I feel reasonably confident about my forecast for next year, I'm less certain about the forecasts five years from now. Therefore I should use a higher cost of capital in later periods to discount those less certain cash flows.

Response: The discounting approach, in which cash flows are discounted by 1 divided by (1+K)n, compounds the risk and reflects the assumption that the further into the future you project, the riskier the estimates are.

Note:

There are occasionally situations when the cost of capital during the forecast period is not the same as the long-term cost of capital, usually when the capital structure is expected to change dramatically over time. (that is, the case of a typical LBO)

Cost of Debt

The Cost of Debt represents the after-tax cost of debt capital to a company. It can be determined in The Cost of Capital Calculator based on the rates you enter for the Yield to Maturity (YTM) and the Marginal Tax Rate.

It is important that the rate you enter is the current yield to maturity rather than the nominal cost of debt. The nominal or coupon rate (which is based on the face amount of the debt) determines the interest payment, but it does not necessarily reflect the actual cost of the corporation's debt today. As required returns change (because of changing expectations about future inflation levels and economic conditions), the price of a debt issue changes so that the actual interest payments (the nominal rate multiplied by the face amount) and anticipated proceeds at maturity yield the investors their revised required return. The yield to maturity, not the nominal rate, fully reflects the current return demanded by debtholders and the rate at which debt should be replaced.

In estimating the Cost of Debt (yield to maturity), be sure to use a long-term rate. Short-term interest rates do not incorporate long-term expectations about inflation. In projecting financial data for 5 to 10 years into the future, you should use a cost of capital that is consistent with the long-term time horizon of the forecast. Also, even if a company routinely rolls over short-term debt as permanent financing, the long-term rate is still a better approximation of the future Cost of Debt because interest rates on long-term debt incorporate the expected cost of repeated short-term borrowing.

The Cost of Debt represents the future cost of debt over a long period. Use the yield to maturity on long-term debt.

Cost of Preferred

The Cost of Preferred represents the expected return to preferred stockholders. Like debt, you must enter the yield to maturity on preferred stock, but without the tax shielding.

Cost of Equity

The return expected by investors for an individual stock - referred to in Strategic Modeling as the Cost of Equity - equals the Risk-Free Rate (RF) plus the Market Risk Premium multiplied by the stock's beta (ß):

Risk-Free Rate

The Risk-Free Rate (RF) is the rate of return investors expect from holding safe investments such as long-term U.S. government securities, which are considered virtually free of risk of default because of the stability of the U.S. government. The return demanded by investors consists of two elements: the pure or real interest rate (compensation for making the investment) and the compensation for expected inflation.

Risk-Free Rate = "Real" Interest Rate + Expected Inflation Rate

The rate of return on common stock (from dividends and stock price appreciation) is less certain (that is, riskier) than the relatively predictable returns available from U.S. government bonds. As compensation for the higher risk involved in owning common stock, investors demand a rate of return on stocks that is greater than the Risk-Free Rate. Therefore the rate of return on stock equals the Risk-Free Rate plus a risk premium for holding that stock rather than holding U.S. government bonds.

For the Risk-Free Rate, it is wise to use the current rate on long-term government bonds, which is quoted daily in publications such as the Wall Street Journal and the Financial Times. The use of short-term rates such as the current rates on Treasury bills is not recommended because they incorporate expectations about only short-term (that is, less than 90 days) inflation. Using the longest term Risk-Free Rate available incorporates expectations for inflation and interest rate fluctuations.

Beta of Equity

Individual stocks tend to be more or less risky than the overall market. The riskiness of a stock, measured by the variance of its return relative to the market's return is indicated by an index called beta (ß).

If ß = 1, the stock's return fluctuates identically with the market's return.
If ß, then 1, the stock's return varies more than the market's return, and therefore its risk exceeds that of the market as a whole.
If ß < 1, the stock's return varies less than the market's return, and therefore its risk is less than that of the market as a whole.

For example, if a stock's return normally moves up or down 1.2% when the market moves up or down only 1%, the stock has a beta of 1.2. The beta is used to calculate the Cost of Equity (the return expected by stockholders) as follows:

Cost of Equity = Risk Free + Beta * Market Risk Premium

Public Companies

Beta estimates are published by a number of brokerage and advisory services, including Value Line and Merrill Lynch. Check the beta listed in one of these services as a measure of the company's past riskiness.

Private Companies

Check the betas listed in the preceding services for public companies that might be expected to share degree of market risk.

Beta is a past measure of riskiness. When making future projections, you should consider anticipated changes in the company's business or financial risk profile.

Note:

If the company's Target Debt Capacity changes or you estimate a beta based on the beta of another company, you may need to adjust the beta for difference in financial risk. This is known as unlevering and relevering the beta.

Market Risk Premium

The market risk premium is the additional rate of return that must be paid over the risk-free rate to persuade investors to hold investments with systematic risk equal to the market portfolio.

The market risk premium is calculated by subtracting the expected long-term risk-free rate from the expected market return. These figures should model future market conditions closely. There are two approaches:

Historical or ex-post risk premium approach, which claims that past market returns are the best estimator of future market returns. See Historical (Ex-Post) Risk Premium.
Forecast or ex-ante risk premium approach, which claims that current market information can be used to improve the accuracy of historically based estimates. See Forecast (Ex-Ante) Risk Premium.

Historical (Ex-Post) Risk Premium

The historical approach relies on the assumption that the market risk premium is basically stable over time. It uses an arithmetic average of past risk premium to estimate future risk premium. Because it relies on actual historical information, this method can be considered an objective measure of the long-term expected market risk premium.

However, those who use this method must decide subjectively how many historical periods to use in the average. Some people believe that using the longest available data period is most objective. Since market statistics have been monitored since 1926, this period is from 1926 until today. Other people select milestones such as World War II, on the assumption that the risk premium is more stable since that time.

Forecast (Ex-Ante) Risk Premium

Other financial professionals believe that information besides historical data can be useful in predicting future market risk premium. They believe that there may have been structural changes in investment markets that affect the market risk premium and therefore historical estimates should be modified by or replaced altogether with, present expectations of future market conditions. This approach is called forecast, ex-ante or future risk premium determination.

To calculate a forecast risk premium, a forecasted risk-free rate is subtracted from a forecasted market return. The current yield curve is a valuable source of information about forecasted risk-free rates. It is composed of the current yields to maturity of risk-free bonds of various maturities. Because future rates can be locked in today and realized later, many people believe that these rates offer accurate estimates of future rates. Therefore, they use these rates as a proxy for future risk-free rates in calculating forecast risk premium.

There is much less agreement on how to forecast future market returns. In fact, the main problem with the forecast approach is that it requires a great deal of subjective judgment by the person doing the calculation. Which forecast estimates for the expected market return should be used? Should historical information be used at all? If so, what time period or periods is used and how should they be weighted with forecast estimates?

Methods of forecasting future market conditions are as varied as the assumptions on which they are based. A desirable forecast risk premium takes full advantage of the information currently available in the yield curve, includes structural changes in the risk premium, but involves a minimum amount of subjective judgment.

Residual Value for Free Cash Flow Methods

Perpetuity for Shareholder Value Method

The Perpetuity Method measures Residual Value by assuming that the firm provides a level stream of cash flows to its stakeholders forever. This assumption seems counter-intuitive. You expect that your firm continues to grow.

But, you can use a simple Perpetuity to compute Residual Value. Strategic Modeling computes the perpetuity using a pre-investment cash flow stream. Because this stream doesn't include investment, the issue of future growth can be simplified by assuming that future investments earn exactly at the firm's Long-Term Cost of Capital rate—in other words, the Net Present Value of new investment after the forecast period is zero. (Another way to look at it is that the Internal Rate of Return on new investment equal the Long-Term Cost of Capital.)

Next it is necessary to determine which flows accrue to your firm in Perpetuity. Strategic Modeling uses the after-tax value of Operating Profit, which includes Depreciation. (Depreciation represents the amount of investment needed to replace physical assets that wear out or become obsolete.) You can adjust this value if you believe that the last forecast period's Operating Profit is not representative of the on-going Operating Profit for the firm -- similar to the adjustment to Earnings in the P/E Ratio Method.

The formula for Perpetuity in Arrears (that is, when the payment occurs at the end of the period) is as follows:

(Operating Profit + Operating Profit Adj.) * (1 - RV Tax Rate) / Long-Term Cost of Capital

where:

Operating Profit	(v1150)	Taxable Operating Profit
Operating Profit Adj.	(v5110)	Normalized Operating Profit Adj.
RV Tax Rate	(v4.00.560)	Residual Value Tax Rate
L-T Cost of Capital	(v5005)	Long-Term Cost of Capital

Growth in Perpetuity for Shareholder Value Method

This variation of the Perpetuity Method assumes that the cash flows grow (or decay) at a compound rate of g forever. This method, usually referred to as the Gordon Model, is characterized by the K - g term in the denominator and next year's cash flow in the numerator.

The main limitation to this approach is that it may not fully recognize the cash outflows for additional investments that are likely to be required for continued growth. Also, it ignores capital structure: the growing cash flows can often lead to severe changes in capital structure (that is, high debt/equity ratios) that are undesirable or economically unrealistic. Finally, the method makes no assumption about the economic return on the investment required for the growth. Thus, the net present value of the growth in perpetuity can yield a value less than, equal to or greater than that of the Perpetuity Method (where the economic assumption of growth yielding NPV = 0 is invoked).

Note:

As perpetuity growth rates approach the long-term cost of capital, the residual value rises toward infinity - because the denominator in the formula below goes toward zero - which is clearly not a reasonable assumption.

Value Growth Duration for Shareholder Value Method

The Value Growth Duration Method enables you to assume that the post-investment cash flows that the stakeholders receive increase at a specified growth rate for a specified number of years. Thus, it explicitly assumes that value creation occurs after the forecast period but not indefinitely -- an assumption many investors consider reasonable. What is unclear for this method is how to estimate that growth rate, especially given that it needs to take investment into account, and the length of time horizon for value-creating growth.

The Value Growth Duration Method starts with the formula for a Growing Perpetuity of one dollar in Arrears: (1 + g) / (K - g)

where:

g	=	(v4.00.520)	Perpetuity growth rate
K	=	(v5005)	Long-Term Cost of Capital

However, Strategic Modeling assumes the time horizon is limited to a fixed number of years. Thus, in the Nth year, at the end of the Value Growth Duration, Strategic Modeling converts from a Growing Perpetuity to a simple Perpetuity.

Price/Earnings Ratio for Shareholder Value Method

This is one of the two common rule-of-thumb techniques supported by Strategic Modeling (the similar Market / Book Ratio method follows). The P/E Ratio method multiplies an estimate for a future P/E ratio by the Net Income in the last period to determine an equity value.

To calculate the Residual Value using the Price/Earnings Ratio Method, Strategic Modeling uses Income Available for Common as earnings, which is net of Preferred Dividends. In addition, because there is the possibility that the final forecast period's earnings are atypical and not representative of what the firm would earn going forward, Strategic Modeling includes a Normalized Earnings Adjustment variable to enable you to adjust the earnings accordingly.

Finally, because this method estimates an equity value, Strategic Modeling adds back the future market value of the debt to get the corporate value. Strategic Modeling enables you to determine the book value of the debt and enables you to input a Debt Discount factor to adjust the book value of the debt to market value.

The formula for the Price/Earnings Ratio Residual Value Method (v5200) is:

P/E * (Earnings + Earnings Adj.) + Book Value of Debt - Debt Discount

where:

P/E	(v5130) User-supplied P/E Ratio
Earnings	(v1850) Income Available for Common
Earnings Adj.	(v5140) Normalized Earnings Adjustment
Book Value of Debt	(v3510) Total Debt and Preferred Stock
Debt Premium	(v5150) Debt Discount/(Premium)

Liquidation Value for Shareholder Value Method

The simplest of the supported methods for determining Residual Value is the Liquidation Value method. Using this method, you enter the estimate worth of the company at the end of the forecast period. That amount should include the cash required to retire all the debt of the firm.

You can enter Liquidation Residual Value in v5180. This can include a formula based on key financial accounts in your analysis.

Market-to-Book Ratio for Shareholder Value Method

The Market-to-Book Ratio method for calculating Residual Value is similar to the Price/Earnings Ratio method. It uses a rule-of-thumb for determining the equity value of a company and, like the P/E method, must be adjusted by adding back the value of the debt to obtain corporate value.

The Market-to-Book Residual Value (v5190) is calculated as follows:

M/B * Common Equity + Value of Dept - Debt Discount

where:

M/B Ratio	(v5120) User-supplied Market-to-Book Ratio
Common Equity	(v2890) Common Equity
Book Value of Debt	(v3510) Total Debt and Preferred Stock
Debt Discount	(v5150) Debt Discount/(Premium)