## Implied Volatility

The only input on which there can be significant disagreement among investors is the variance. While the variance is often estimated by looking at historical data, the values for options that emerge from using the historical variance can be different from the market prices. For any option, there is some variance at which the estimated value will be equal to the market price. This variance is called an implied variance. Consider the Cisco option valued in the last illustration. With a standard...

## Comparative Analysis of Risk and Return Models

Figure 4.5 summarizes all the risk and return models in finance, noting their similarities in the first two steps and the differences in the way they define market risk. 4 A price multiple is obtained by dividing the market price by its earnings or its book value. Studies indicate that stocks that have low price to earnings multiples or low price to book value multiples earn higher returns than other stocks. 5 The book to price ratio is the ratio of the book value of equity to the market value...

## K 0 v j

From an intuitive standpoint, the adjustments have two effects. First, the value of the asset is discounted back to the present at the dividend yield to take into account the expected drop in asset value resulting from dividend payments. Second, the interest rate is offset by the dividend yield to reflect the lower carrying cost from holding the asset (in the replicating portfolio). The net effect will be a reduction in the value of calls estimated using this model. stopt.xls This spreadsheet...

## The H Model for valuing Growth

The H model is a two-stage model for growth, but unlike the classical two-stage model, the growth rate in the initial growth phase is not constant but declines linearly over time to reach the stable growth rate in steady stage. This model was presented in Fuller and Hsia (1984). The model is based upon the assumption that the earnings growth rate starts at a high initial rate (ga) and declines linearly over the extraordinary growth period (which is assumed to last 2H periods) to a stable growth...

## FCFFt [FCFFniWACC gn 1 WACCt1 WACCn

The final problem is that the use of a debt ratio in the cost of capital to incorporate the effect of leverage requires us to make implicit assumptions that might not be feasible or reasonable. For instance, assuming that the market value debt ratio is 30 will require a growing firm to issue large amounts of debt in future years to reach that ratio. In the process, the book debt ratio might reach stratospheric proportions and trigger covenants or other negative consequences. In fact, we count...

## Problems

In December 1995, Boise Cascade's stock had a beta of 0.95. The treasury bill rate at the time was 5.8 and the treasury bond rate was 6.4 . a. Estimate the expected return on the stock for a short term investor in the company. b. Estimate the expected return on the stock for a long term investor in the company. c. Estimate the cost of equity for the company. 2. (Continuing problem 1) Boise Cascade also had debt outstanding of 1.7 billion and a market value of equity of 1.5 billion the corporate...

## From Cost of Equity to Cost of Capital

While equity is undoubtedly an important and indispensable ingredient of the financing mix for every business, it is but one ingredient. Most businesses finance some or much of their operations using debt or some security that is a combination of equity and debt. The costs of these sources of financing are generally very different from the cost of equity and the cost of financing for a firm should reflect their costs as well, in proportion to their use in the financing mix. Intuitively, the...

## FCFE Valuation versus Dividend Discount Model Valuation

The discounted cash flow model that uses FCFE can be viewed as an alternative to the dividend discount model. Since the two approaches sometimes provide different estimates of value, it is worth examining when they provide similar estimates of value, when they provide different estimates of value and what the difference tells us about the firm. There are two conditions under which the value from using the FCFE in discounted cashflow valuation will be the same as the value obtained from using...

## Valuation and Portfolio Management

The role that valuation plays in portfolio management is determined in large part by the investment philosophy of the investor. Valuation plays a minimal role in portfolio management for a passive investor, whereas it plays a larger role for an active investor. Even among active investors, the nature and the role of valuation is different for different types of active investment. Market timers use valuation much less than investors who pick stocks, and the focus is on market valuation rather...

## APV and Financial Leverage

In the adjusted present value (APV) approach, we begin with the value of the firm without debt. As we add debt to the firm, we consider the net effect on value by considering both the benefits and the costs of borrowing. The value of the levered firm can Change in stock price - 0.23 per share then be estimated at different levels of the debt and the debt level that maximizes firm value is the optimal debt ratio. Steps in the Adjusted Present Value approach The unlevered firm value is not a...

## Gross Debt versus Net Debt

Gross debt refers to all debt outstanding in a firm. Net debt is the difference between gross debt and the cash balance of the firm. For instance, a firm with 1.25 billion in interest bearing debt outstanding and a cash balance of 1 billion has a net debt balance of 250 million. The practice of netting cash against debt is common in both Latin America and Europe and the debt ratios are usually estimated using net debt. It is generally safer to value a firm based upon gross debt outstanding and...

## Ke gn

P0 Value of equity per share today DPS1 Expected dividends per share next year gn Growth rate in dividends (forever) Substituting in for DPS1 (EPS1)(Payout ratio), the value of the equity can be written as Defining the return on equity (ROE) _EPS'_, the value of equity can be Rewriting in terms of the PBV ratio, If we define return on equity using contemporaneous earnings, ROE _EPS _, the price to book ratio can be written as The PBV ratio is an increasing function of the return on equity, the...

## Net Debt versus Gross Debt

In valuing Embrarer, we used net debt where cash was netted out against debt. In all of the earlier valuations, we used gross debt. What is the difference between the two approaches and will the valuations from the two approaches agree A comparison of the Embraer and the earlier valuations reveals the differences in the way we approach the calculation of key inputs to the valuation. We summarize these. Unlevered beta is levered using gross debt to market equity ratio. Unlevered beta is levered...

## Leverage FCFE and Equity Value

Embedded in the FCFE computation seems to be the makings of a free lunch. Increasing the debt ratio increases free cash flow to equity because more of a firm's reinvestment needs will come from borrowing and less is needed from equity investors. The released cash can be paid out as additional dividends or used for stock buybacks. In the case for Singapore Airlines, for instance, the free cash flow to equity is shown as a function of the debt to capital ratio in Figure 14.3 Figure 14.3 FCFE and...

## Extensions of Option Pricing

All the option pricing models we have described so far - the Binomial, the Black-Scholes and the jump process models - are designed to value options, with clearly defined exercise prices and maturities, on underlying assets that are traded. The options we encounter in investment analysis or valuation are often on real assets rather than financial assets, thus leading to them to be categorized as real options, can take much more complicated forms. In this section, we will consider some of these...

## Ignoring Acquisitions in Valuation A Possibility

Incorporating acquisitions into net capital expenditures and value can be difficult and especially so for firms that do large acquisitions infrequently. Predicting whether there will be acquisitions, how much they will cost and what they will deliver in terms of higher growth can be close to impossible. There is one way in which you can ignore acquisitions, but it does come with a cost. If you assume that firms pay a fair price on acquisitions, i.e. a price that reflects the fair value of the...

## Market Anomalies

Webster's Dictionary defines an anomaly as a deviation from the common rule . Studies of market efficiency have uncovered numerous examples of market behavior that are inconsistent with existing models of risk and return and often defy rational explanation. The persistence of some of these patterns of behavior suggests that the problem, in at least some of these anomalies, lies in the models being used for risk and return rather than in the behavior of financial markets. The following section...

## Conclusion

The question of whether markets are efficient will always be a provocative one, given the implications that efficient markets have for investment management and research. If an efficient market is defined as one where the market price is an unbiased estimate of the true value, it is quite clear that some markets will always be more efficient than others and that markets will always be more efficient to some investors than to others. The capacity of a market to correct inefficiencies quickly...

## Why is the marginal investor assumed to be diversified

The argument that diversification reduces an investor's exposure to risk is clear both intuitively and statistically, but risk and return models in finance go further. The models look at risk through the eyes of the investor most likely to be trading on the investment at any point in time, i.e. the marginal investor. They argue that this investor, who sets prices for investments, is well diversified thus, the only risk that he or she cares about is the risk added on to a diversified portfolio...