It is likely that warrants will be used increasingly in the future by corporations both as means of sweetening other securities such as preferred stocks and bonds, and as securities in their own right. Many authors have analyzed the characteristics of warrants from the point of view of investors but attempts to develop a procedure for determining the cost to a corporation of issuing warrants have been lacking. We will find it convenient to measure the yield to a corporation of issuing warrants instead of common stock, rather than determining the percentage cost of warrants analogous to the cost of common stock equity, preferred stock, and interest-bearing debt.

This paper investigates how the addition of debt to the capital structure of a corporation affects the risk of the stockholders. In the first instance, we will hold the size of the firm constant and substitute debt for common stock. In the second situation, we will allow firm size to change, and will accomplish the increase in size by issuing debt. For both situations, we will first observe the effect of debt on the earnings per dollar of common stock investment. The analysis could also be made using the number of shares of common stock. Since the number of shares of common stock may be changed quite arbitrarily (as, for example, by stock dividends), we want to make the measure invariant to the number of shares outstanding. We will do this by using value of common stock and value of debt. We are then computing the variance of return on common stock investment when we compute variance of earnings per dollar of common stock investment. After considering how debt affects earnings per dollar of stockholders' investment, we will investigate the effect of debt on the total earnings of the stockholders, and on the probability of a deficit.

It is well known that different combinations of investments involve different risks. In recent years the analysis of risk has tended to focus on two moments of the probability distribution of returns, the mean and variance. This paper considers the effect on the variance of an investment fund of adding dependent investments.

There is little question that stock options have value, but there is considerable question as to how stock options should be valued. Persons studying the valuation question and writing in business periodicals have tied the value of the stock option to the expected or the actual appreciation in the value of the stock.

The highly quantitative bond issue size decision is generally made in a somewhat qualitative manner. The subjective opinions of brokers and intuitive rules of thumb of financial officers are rarely, if ever, compared to the optimum issue size resulting from calculations incorporating the costs of issuing bonds, and the costs of carrying extra cash. Unfortunately performance measurement in this area is very difficult, thus both good and bad decision processes tend to go unnoticed. It is possible to look at a financial decision which has been made, and, with the aid of hindsight, conclude it was a bad decision, but this proves very little. Some financial officers have done very well administering the Financial affairs of their corporations, but this does not indicate that the decision process cannot be improved. In a previous article the author of this paper investigated the question of the optimum size of bond issue.

All the stock price models discussed in this paper are based on the assumption that the present value of a share of common stock is equal to the discounted value of all future expected dividends accruing to the stockholder:where Po : current value of a share of common stock, Dt: dividend expected to be received at end of period t, k : investor's discount or time-value rate, andt : time.

There is broad consensus that three types of risk confront the potential bond purchaser: the risk of default (possible interest and/or principal loss), the risk of interest rate changes (possible principal loss or gain if the bonds are sold before maturity), and price level risk (loss of purchasing power). The analysis in this paper is directed toward the first of these risks, the risk of default. By assuming that investors require interest rate adjustments on debt subject to default sufficient to give them an expected present value equal to the present value associated with the investment of their funds in default-free securities, we examine the process that determines the risk-adjusted equilibrium interest rate and the factors affecting that rate. We also examine the implications of the model for the cost of debt and a firm's debt capacity.

The current literature or business finance states that debt is a cheaper source of capital than stock (tending to reduce the firm's cost of capital), because interest is deductible for income tax purposes while the return to common stockholders is subject to tax. It is even possible to issue debt without increasing the risk to the owners (the debt is issued to stockholders in proportion to the ownership of stock, or equivalently investors buy a mixture of stocks and bonds on the market). However, it is argued in this paper that if we assume that the present stockholders have no further resources available for investment in the firm, but the enterprise needs additional resources, then the present stockholders have to make a basic decision about whether to issue stock or debt to raise the additional needed capital. The issuance of debt in this situation increases risk, and the issuance of stock dilutes ownership. Even when bondholders require a much lower contractual return than the expected annual return of stockholders, the issuance of more stock may be preferred to the issuance of debt.

In a previous paper we reviewed the literature on normative stock price models. These models specified the present value of a share of common stock to be equal to the discounted value of dividends accruing to the holder. Using continuous discounting, the present value of a share is (1) where Dt is the dividend rate at time t and k is the cost of equity capital. Presumably k is a function of both the stockholders' time value of money and the perceived risk or uncertainty associated with the future dividend stream.