# The concept of valuation

### Overview

Several of the theories reviewed in the taxonomy referred to the "Net Present Value" effect or "Discounted Cash Flows". Such models use the concept of the time value of money for evaluation purposes. The purpose of this lecture is two-fold: first, to describe a popular evaluation process for determining the adoption of a project using net present value. Second, to demonstrate the effect that the change in the debt/equity ratio on the optimum stock price of a firm.

As mentioned in the introductory material to week 4, the value of any financial asset, i.e., stocks or bonds, is simply the present value of future cash flows generated by their assets. Examples the use of present value in financial decision-making include such areas as: when to lease or purchase an asset, when considering mergers, or when deciding whether to adopt a certain project or not.

So, let's go "back to the basics" of present value by demonstrating how present value is used in several different types of financial decisions.

### Basics

The concept of present value is valuable to financial managers because it provides them with a uniform method of evaluation. For example, it can be used to decide among a number of proposed projects or investments.

Present value is defined as the cash value of future returns, or income, once a discount rate has been applied to it. The discount rate is also called the "capitalization rate". It is the interest rate, or desired rate or return applied to a future series of payments, income or returns. Essentially, the discount rate is a method of adjusting for risk and the uncertainty of time.

So, an investment that is associated with less risk or over a shorter period of time would be assigned a lower discount rate. You may be aware, for example, that bonds rated as "junk bonds carry a higher discount rate than high quality corporate bonds. Also, a 15 year fixed rate mortgage will carry a lower interest rate than a 30 year fixed rate mortgage. If you are a venture capitalist, you would require a higher rate of return for funds loaned to, say, a new start-up versus funds loaned to an established company with a solid track record.

Broadly speaking, risk is a measure of the volatility, or uncertainty of returns. Returns are the expected receipts or cash flows anticipated from an investment. Measuring risk and return are subjects unto themselves and are the subjects of much financial research.

One of the more popular theories in risk assessment is the Capital Asset Pricing Model (CAPM), which is included in our taxonomy database. CAPM is used extensively for security analysis, as well as for the assessment of risk/reward merits of investments and assets at the corporate level. In subsequent sections of this lecture, I will demonstrate how CAPM is used in security analysis.

### Using present value to justify a project

In this first example, I'll demonstrate the use of present value to evaluate a project.

The ABC company is considering an investment that will provide annual after-tax cash flows of $6000, 4000, 3000, and 2000, respectively, for four years. The discount rate for the project is 10% and the initial investment is $9000. Should the project be adopted?

In this type of problem, the annual cash flows are multiplied by the present value interest factor (10%) for each individual year. The present value interest factor is obtained from a Present Value Interest Factor table. These tables are available for a number of time periods and discount rates.

Following is the present value interest stream:

Year Cash Flow PVIF (10%) PV for each year (col. 2 x col. 3)

- 6000 .909 5454
- 4000 .826 3304
- 3000 .751 2253
- 2000 .683 1366

PV of total cash flows $12,377

The initial outlay of $9000 is subtracted from the PV of total cash flows ($12,377). The "net" present value of this project, therefore, is +$3,377. Since the present value is positive, the project is recommended.

Note that the PVIF decreases over time at the same rate. In this case, .909 in year one, versus .826 in year two. This demonstrates the effect of time on value.

### Debt/Equity analysis

In this second example, we will look at the effect of leverage, i.e., the debt/equity ratio on the value of the firm . Is there an optimum debt/equity ratio the results in an optimum price of the firm's stock?

As you may recall, Modigliani and Miller's theory on capital structure first indicated that the amount of leverage didn't matter. However, in a subsequent revision to their original theory, they argued that the amount of leverage did matter. Essentially, the revised theory argues that increased leverage will add tax benefits to a firm, but only up to a certain point. Beyond that point, however, too much debt has an adverse effect on both cost of capital and value of the firm.

Let's see how that works:

The benefits from financial leverage are reflected in a favorable attitude by investors towards a firm's stock. Investor's recognize that, up to a certain point, an increasing D/E ration will increase earnings per share, which will, in turn, compensate them for the higher financial leverage. The key is, up to a certain point!

If, for example, the firm should go to the unreasonable extreme of financing with a D/E ratio of 80%, the interest rate would be very high (certainly in the junk bond category) and the risk would increase. When the risk becomes unacceptable, the price of the stock will decline. Table 1, below, provides a possible scenario:

In this example, the optimum capital structure is at the debt level of 40%, where the price of the stock is estimated at $41.67. The mathematics for arriving at the estimated stock price is beyond the scope of this discussion, but will be discussed in detail in the Valuation lecture. The main point is that, under this theory, the estimated price of the stock falls, and continues to fall, beyond a d/e ratio of 40%. This is an indication that the investors become apprehensive about the ability of the firm to meet its financial obligations. Is this possible? What happened recently to K-Mart. Who would have thought!

There are a number of factors that can cause this situation to happen. Among the most prevalent include:

- An increase in the probability of bankruptcy
- An increase in agency costs because managers are forced to spend an inordinate amount of time to search for ways to protect creditors in case of insolvency.
- The tax benefits dissipate because the higher earnings, generated by financial leverage, are subject to a greater degree of risk. Hence, risk-adjusted earnings tend to decline. Groppelli, A.A., and Nikbakht, Ehsan, 1990).

With the result of the above events, investors will demand higher returns, followed by an increased cost of debt.

### Summary

In the first section, I demonstrated how the net present value analysis tool can empirically determine whether or not particular project should be adopted or not. If the net present value of the cash flows is positive, the project is a candidate for adoption. Further, several project with positive net cash flows can be compared to determine which has the most potential.

Financial managers are constantly faced with determining the firm's optimum capital structure. We know now that some of the initial findings of the M & M capital structure are invalid and there is such a thing as an optimum capital structure. The problem managers face, however, is that there is not a cookie-cutter approach or a magic formula for achieve the optimum ratio. Much depends on the relative health of the firm and how investors view the financial soundness of the firm. This will change from firm-to-firm and is based on a number of financial, as well as non-financial variables.

In the second section of this lecture a debt/equity analysis was conducted to determine that the optimum stock price was achieved at a debt/equity ratio of 40%.

### References

- Chew, H. Donald, Jr, Corporate Finance: Where Theory Meets Practice, 2002, McGraw-Hill Irwin: Boston.
- Groppelli, A.A., and Nikbakht, Ehsan, Finance: Second Edition, 1990, Barron's Educational Series, Inc: New York.