If assets = liabilities + equity, what do we mean by overcapitalization? Overcapitalization doesn't seem to have a clear-cut definition.

For some it seems to deal with the ratio of current output (Y) over optimal output (Y*). A company would then be overcapitalized if Y &lt; Y*, meaning it could raise its output without having to recapitalize.

Others define it as Equity + Debt > "True Value of assets"

I like the second definition but it is subjective.

I am trying to understand the concept of overcapitalization in the context of a firm's valuation.
A firm's Output $Y$ (in value-added terms, i.e. over and above the value of purchases of third-party services and materials) is distributed as reward to the factors of production. Denote $K$ the book value of the company's assets.  Use the standard notation $L$ for payments to the labor/human capital input to production. Denote $r$  the capital rate of return as measured with respect to the book value of firm's capital and denote $w$ the average remuneration of human capital services. Then we have

$$Y = rK + wL$$

Depending on the market, the industry, and a few other things, we can estimate  $r^*$, the rate of return that the firm "should" have on average, if it should be judged as an efficient user of capital allocated to it, for given output and human capital costs. $r^*$ is usually estimated by what are the returns on the market and the industry (we do not go outside the industry since we recognize the existence of "asset specificity"). Associated with $r^*$ goes the efficient level of capital, $K^*$. So we also have

$$Y = r^*K^* + wL$$

leading to 

$$rK = r^*K^*  \implies r = r^*\frac {K^*}{K}$$

If we have that 

$$r &lt; r^* \implies r^*\frac {K^*}{K} &lt; r^* \implies K^* &lt; K$$

and we can say with some certainty that the inequality does not show a tendency to change in the near future, then we can argue that the company does not make efficient use of the current amount of capital it appears to have, either due to "functional inefficiency" (how things are organized and work inside the company and in the delivery of of its business, a qualitative aspect), or due to plain under-utilization of the existing capital (a quantitative aspect).  

The "over-capitalization" story essentially assumes "functional efficiency" but it sees under-utilization of capital, and so it advocates the reduction of the capital/assets currently under the control of the company.

To measure it we have the relation ($K_E=$ Excess Capital)

$$ K_E = K - K^* = K- \frac {r}{r^*}K = \left (1-\frac {r}{r^*}\right)K$$

$r$ and $K$ is measured from the firms financial statement, while $r^*$ from Industry weighted averages.