Foundations of Financial Management: An Analysis (part 43)

 “Success isn’t measured by money or power or social rank. Success is measured by your discipline and inner peace.” 

– Mike Ditka

Cost of Capital (part E)

By

Charles Lamson

The Marginal Cost of Capital

Nothing guarantees the Lamson Corporation that its cost of capital will stay constant for as much money as it wants to raise even if a given capital structure is maintained. If a large amount of financing is desired, the market may demand a higher cost of capital for each amount of funds desired. The point is analogous to the fact that you may be able to go to your relatives and best friends and raise funds for an investment at 10 percent. After you have exhausted the lending or investing power of those closest to you, you will have to look to other sources and the marginal cost of your capital will go up.

As a background for this discussion, the cost of capital table for the Lamson Corporation is reproduced again as follows:

You need to review the nature of the firm's capital structure to explain the concept of marginal cost of capital as it applies to the firm. Note the firm has 60 percent of the capital structure in the form of equity capital. The equity ownership capital is represented by retained earnings. It is assumed that 60 percent is the amount of equity capital the firm must maintain to keep a balance between fixed income securities and ownership interest. But equity capital in the form of retained earnings cannot grow indefinitely as the firm's capital needs expand. Retained earnings is limited to the amount of past and present earnings and can be deployed into the investment projects of the firm. Let's assume the Lamson Corporation has $23.40 million of retained earnings available for investment. Since retained earnings is to represent 60 percent of the capital structure, there is adequate retained earnings to support a capital structure of up to $39 million. More formally, we say: 

(where X represents the size of the capital structure that retained earnings will support.)

After the first $39 million of capital is raised, retained earnings will no longer be available to provide the 60 percent equity position in the capital structure. Nevertheless lenders and investors will still require that 60 percent of the capital structure be in the form of common equity (ownership) capital. Because of this, new common stock will replace retained earnings to provide the 60 percent common equity component for the firm. That is, after $39 million, common equity capital will be in the form of new common stock rather than retained earnings.

In the left-hand portion of Table 5, we see the original cost of capital that we have been discussing throughout the last several posts. This applies up to 39 million dollars. After 39 million dollars, the concept of marginal cost of capital becomes important. The cost of capital then goes up as shown on the right hand portion of the table.

Table 5 Cost of capital for different amounts of financing

The marginal cost of capital has increased after 39 million dollars because common equity is now in the form of new common stock rather than retained earnings. The after-tax (A/T) cost of new common stock is slightly more expensive than retained earnings because of flotation costs (F). The equation for the cost of new common stock was shown in part 41 of this analysis as Formula 7 and now we are using it:

Flotation cost (F) is $4 and the cost of new common stock is 12.60 percent. This is higher than the 12% cost of retained earnings that we have been using and causes the increase in the marginal cost of capital.

To carry the example of it further, we will assume the cost of debt of 7.05 percent applies to the first $15 million of debt the firm raises. After that the aftertax cost of debt will rise to 8.60 percent. Since debt represents 30 percent of the capital structure for the Lamson Corporation, the cheaper form of debt can be used to support the capital structure up to $50 million. We derive the $50 million by using Formula 9.

(Where Z represents the size of the capital structure in which lower-cost debt can be utilized.)

After the first $50 million of capital is raised, lower-cost debt will no longer be available to provide 30 percent of the capital structure. After 50 million dollars in total financing, the after-tax cost of debt will go up to the previously specified 8.60 percent. The marginal cost of capital for over $50 million in financing is shown in Table 6.

Table 6 Cost of capital for increasing amounts of financing

We could continue this process by next indicating a change in the cost of preferred stock, or by continually increasing the cost of debt for new common stock as more capital is used. For now it is sufficient that you merely observe the basic process. To summarize, we have said the Lamson Corporation has a basic weighted average cost of capital of 10.41%. This value was developed throughout the last several posts and was originally presented in Table 1 from part 39 of this analysis. However, as the firm began to substantially expand its capital structure, the weighted average cost of capital increased. This gave way to the term, marginal cost of capital. The first increase or break point was at $39 million in which the marginal cost of capital went up to 10.77% as a result of replacing retained earnings with new common stock. The second increase or break point was at $50 million in which the marginal cost of capital increased to 11.23 percent as a result of the utilization of more expensive debt. The changes are summarized below.

In previously presented Figure 3 from last post, we showed returns from investments A through H. In Figure 4 we reproduce the returns originally shown in figure 3 but include the concept of marginal cost of capital. Observe the increasing cost of capital (dotted lines) in relationship to the decreasing returns (straight lines).

In Figure 3 the Lamson Corporation was justified in choosing projects A through E for a capital expenditure of $50 million. This is no longer the case in Figure 4. Because of the increasing marginal cost of capital, the returns exceed the cost of capital only up to $39 million. And now only projects A through D are acceptable.

Although the concept of marginal cost of capital is very important, for most of our capital budgeting decisions in the next several posts, we will assume we are operating on the initial flat part of the marginal cost of capital curve in Figure 4, and most of our decisions can be made based on the initial weighted average cost of capital. 

*MAIN SOURCE: BLOCK & HIRT, 2005, FOUNDATIONS OF FINANCIAL MANAGEMENT, 11TH ED., PP. 326-330*

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