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Modigliani-Miller Meets BCG

Summary

M-M theorem does not consider time as a variable.

Optimal capital structures change over time.

The Boston Consulting Group matrix is descriptive of asset life cycles.

The Modigliani-Miller theorem states that a company’s value is not influenced by how it is financed if taxes and bankruptcy costs are ignored. The concept has been a tenet of the leveraged buyout industry as debt for equity substitution in a taxable world increases the firm’s value as the interest payments are tax deductible and thus lower the weighted cost of capital. The theorem does suggest that investors must be rewarded with a higher return on equity in a levered investment, yet it acts as if the equation is a continuous equation and will produce results that suggest the optimal capital structure is 100% debt. We will assume that a healthy business or acquisition can support an optimal capital structure of 100% debt. We suggest that the optimal capital structure for today may not be the optimal capital structure tomorrow. Changing business prospects from secular and cyclical forces cannot be ignored in the capital structure.

While readers may provide pushback on the prospects of a publicly traded company utilizing 100% debt and thus having no public equity, we will remind the reader that acquisitions are often made with nearly 100% debt for smaller transactions and are overweight debt in transformative transactions. Many times, a management team will utilize a healthy amount of debt in a large transaction in order to put some leverage on the transformed entity. It is at that point in time that the buyer is paying a full price for assets so the risk of being wrong is at the highest.

M-M theorem suggests that firms are not penalized for using debt rather than equity for capitalization. Management teams often base their capital structure based on peers, credit ratings and investor acceptance. Therefor the use of the M-M theorem is constrained in practice by stock market acceptance. Implied in the constraints placed on the optimal capital structure is the fact that business prospects change over time. We will use the Boston Consulting Group matrix as a tool to demonstrate the life cycle of a business.

The life cycle is four phases named question mark, star, cash cow and dog. The amount of debt that the marketplace will allow to be placed on a company is based on the perception of what box represents the company. The asset classes used by institutions also follow the BCG matrix and represent appetites for leverage. The boxes could also be named venture capital, public equity, venture capital and vulture capital.

Our theory is that when debt is mismatched with the life cycle the optimal capital structure no longer is optimal because the debt is based on historical results (t-1) and the cash flows are forward (t+1). We suggest that a M-M optimal capital structure formula suggests that the time frame is held constant. Stable M-M looks like this:

https://upload.wikimedia.org/wikipedia/commons/7/74/MM2.png

According to the theorem the weighted average cost of capital (KO) remains constant.

Now place time as the third axis:

See the source image

Now let’s look at the impact of time.

https://de.mathworks.com/help/examples/graphics/win64/QueryPlotBoxAspectRatioExample_01.png

Imagine that the plane is flat and creates a square with 0 being the Ko from the first graph. That is the baseline solution for the M-M equation and suggests the company is at the optimal capital structure of 100% debt. The 0 (a relative number) represents the optimal weighted average cost of capital at the beginning of the time period. The humps are then introduced. Now start on the other side of the hump (right side) and start tracing left over the hump and into the valley. That is the BCG life cycle over time. When the business is in the star category the impact on value of the debt/equity structure is creating equity value that then begins to go downhill in the cash cow era and then goes substantially negative in the dog phase.

The BCG life cycle is even more important when management does an acquisition. The buyer must determine where the acquisition is in the life cycle and how long the business will stay there. Corporate debt usually is described by the axiom that debt is not paid off but rolled over by creditworthy parties until they are not. The distractions of corporate management to resist paying down debt in order to maintain a growth story are real. Paying down debt relegates the stock to a “value story” and is not a “growth story” like an acquiror. This makes the right capital structure extremely important to investors because it is so hard to adjust or fix.

An optimal capital structure should not be an optimist’s capital structure.