Company Cross-Holdings and Investment Analysis

CFA Institute

Company Cross-Holdings and Investment AnalysisAuthor(s): Ranjan SinhaSource: Financial Analysts Journal, Vol. 54, No. 5 (Sep. - Oct., 1998), pp. 83-89Published by: CFA InstituteStable URL: http://www.jstor.org/stable/4480112 .

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Company Cross-Holdings and

Investment Analysis

Ranjan Sinha

Some analysts have suggested that the prevalence of cross-holdings leads to a significant distortion in aggregate market capitalizations. Moreover, equity investors and creditors are advised to undo the effects of these distortions when analyzing companies in markets where cross-holdings are common. The analysis here shows thatfor most equity investment decisions, undoing the effects of cross-holdings is inappropriate. Furthermore, cross- holdings do increase the debt-bearing capacity offirms and should not be entirely eliminated during credit analysis. Finally, empire building is unlikely to be the primary reason for cross-holdings.

T he investment implications of the cross- ownership of shares that is prevalent in some countries, notably Japan and South Korea, has not been fully investigated.

Ferguson and Hitzig showed the ease with which corporate managers can manipulate the size of their companies through cross-ownerships and consid- ered some of the implications of cross-ownership for aggregate market capitalizations and investor anal- yses.1 This article takes another look at the issue of cross-holdings and reports interesting results that are sometimes counterintuitive. The questions addressed here are the extent to which cross- holdings create difficulties for investment decision making, whether those difficulties affect debt analysis and equity analysis in the same way, and whether company cross-holdings distort the aggregate market capitalization in markets where cross- holdings are prevalent.

The Basic Issue In a 1993 article, Ferguson and Hitzig analyzed some implications of cross-ownership of shares. Their example provides the point of departure for the analysis presented here. Ferguson and Hitzig discussed the strategy used by two friends, owners of separate businesses and both well versed in financial legerdemain, to get rich quick even though their businesses weren't growing. The company each man owned invested in shares of the other man's company. The result was that, without violating

generally accepted accounting principles (GAAP), the friends were able to create a manifold increase in the market values of both companies-and both individuals became rich and famous. This strategy may resemble a pyramid scheme, but it is perfectly legal.

Consider this generalization of the example: Two identical companies come into existence by issuing 200 shares of stock at $1 a share. Each company invests $100 in real assets but retains $100 in cash to invest in the other. Under the assumption that the investments in real assets are made in projects of zero net present value, the market value of each company's investment in real assets equals $100.2 Table 1 contains each company's balance sheet. The market value of the 200 outstanding shares of each company exactly equals the book value of equity, $200.

Now, suppose Company A purchases 100 newly issued shares of Company B. The appropriate price at which Company A buys the newly issued shares is $1 a share. Table 2 shows the balance sheets of each company after this transaction. Note that the aggregate book value of the two companies together, as well as total market capitalization, has increased from $400 to $500. Subse- quent to the transaction, the price per share of each company's common stock remains at $1.

Next, Company B buys 100 newly issued shares of Company A for $1 a share. Table 3 shows the balance sheets of the two companies after the first round of investments. Each company's book value of equity and market capitalization is now $300; that is, each company is $100 larger now than it was before the stock buys. The aggregate book

Ranjan Sinha is an assistant professor at the Leavey School of Business and Administration, Santa Clara University.

September/October 1998 83



Financial Analysts Journal

Table 1. Original Balance Sheets Item Company A Company B

Assets Cash $100 $100 Real assets 100 100

Total assets $200 $200

Liabilities and equity Equity $200 $200

Shares outstanding (number) 200 200

Table 2. Balance Sheets after Company A Buys 100 Shares of Company B Stock

Item Company A Company B

Assets Cash $ 0 $200 Real assets 100 100 Investments 100 0

Total $200 $300


Shares outstanding (number) Original owners 200 200 Held by other company 0 100

Total 200 300

Table 3. Balance Sheets after One Round of Mutual Investment


Assets Cash $100 $100 Real assets 100 100 Investments 100 100

Total $300 $300

Liabilities and equiity Equity $300 $300


Total 300 300

value of equity and market capitalization has increased from $400 to $600, even though the pair of transactions appears to lack any economic content.

This process can be continued without end. After 17 more cycles, the balance sheets of the two companies will be as shown in Table 4. Each company is now 10 times its original size, and the aggregate book value of equity and market capitalization has grown to $4,000.

The appropriate application of GAAP to the financial statement presentations of both companies would require consolidation and a consequent elimination of the cross-ownership effect. But as Ferguson and Hitzig pointed out, this problem can

Table 4. Balance Sheets after 18 Rounds of Mutual Investment


Assets Cash $ 100 $ 100 Real assets 100 100 Investments 1,800 1,800

Total $2,000 $2,000

Liabilities and equity Equity $2,000 $2,000

Shares outstanding (number) Original owners 200 200 Held by other company 1,800 1,800

Total 2,000 2,000

be overcome by increasing the number of companies that participate in the game. For example, with a total of 19 companies, each company can invest $100 in each of the other 18 and achieve an effect similar to that shown in Table 4 but each company will own only 5 percent of any other company; thus, all avoid the need to present consolidated financial statements. Furthermore, if the number of participating companies is large, so each company's per- centage ownership is small, then the very existence of the scheme may go unnoticed.

Analyzing Prior Conclusions There is nothing illegal about these transactions, and with a sufficiently large number of companies participating, the public presentation of the inflated balance sheets is even consistent with GAAP. The set of transactions, however, has all the appearances of a pyramid scheme. Should such schemes be cause for concern?

Ferguson and Hitzig showed that the market value of each participating company can increase manifold and that each can become an arbitrarily large portion of capitalization-weighted stock indexes. For example, with a total of 100 companies, if each company bought 1 percent of each of the other 99 through a series of transactions as described here, at the individual-company level and at the aggregate level, both market capitalization and reported earnings would be distorted by 10,000 percent. That is, market capitalization and reported earnings would be 100 times as large as, respectively, the market value of business assets and business earnings. As a result, each company would be viewed as offering better collateral to lenders than it would without the cross-investing and would be able to increase its borrowing capacity. The owners (original investors/managers) would profit personally and become rich and influ- ential.

84 ?Association for Investment Management and Research



Company Cross-Holdings and Investment Analysis

The conclusions of Ferguson and Hitzig sug- gest that investors and lenders must be particularly wary when participating in markets where the practice of cross-holding is common, such as Japan and Korea. Even if the intention behind the creation of cross-holdings is not fraudulent but is based on a particular philosophy of industrial organization, unwitting investors and lenders may be led to make poor business decisions unless they undo the effects on financial reports of these cross-holdings.

Ferguson and Hitzig's analysis raises another issue: If this procedure for creating wealth and influence is both effortless and painless, why is it confined to a few countries where it has historical roots? Why aren't more individuals and businesses getting into the act?

A possible answer is that the pursuit of wealth and influence is not a significant motivation for the existence of cross-holdings in certain economies. Consider again the change that occurs in going from Table 1 to Table 3. First, the original owners of the firms are clearly not attempting to directly increase the productive assets they control. If they needed to increase investment in productive assets in order to, for example, implement new business ideas, they would need to borrow or raise the required capital by issuing new shares to outside investors. Those new shares would result in a very real increase in the value of each company.

What might the original owners be attempting? Neither company is simply acquiring an interest in the other company; they could easily acquire such an interest by purchasing shares from the original investors in the open market. Buying shares in the secondary market would not increase the total market value of either company or of the market as a whole, but it would use up cash, something the acquiring company might not want to do.

Possibly, cross-holdings are simply a means of expressing a commonality of interests with other companies in a binding manner. If the companies wish to express, publicly and forcefully, their commonality of interests, they can do so in the manner described in the example without a drain of cash from the system. Cross-ownership can also achieve stability in the relationship between companies that mitigates the ill effects of uncertainty. There- fore, the prevalence of cross-holdings in certain markets may have nothing to do with investors trying to obtain something from nothing.

Equity Valuation Should investors undo the effects of cross-holdings when valuing equities? Consider the case of an investor who currently does not own any stock in

either Company A or Company B and desires to purchase all of Company A. Prior to the creation of any cross-holding (when Company A appears as depicted in Table 1), in the absence of a takeover premium, the new investor will pay exactly $200 to buy all of Company A. After the first round of mutual investment described previously (when Company A appears as shown in Table 3), how much should the new investor pay to acquire all outstanding shares of Company A?

The answer is that the investor should be willing to pay $300. The reason is that the investor can no longer purchase Company A alone. When the investor buys the Company A of Table 3, she or he will also be buying a one-third share in Company B. The one-third share in Company B is worth exactly $100. Of the 300 outstanding shares of Com- pany A that the new investor must buy, Company B owns 100 shares. The act of purchasing all 300 outstanding shares of Company A requires the investor to buy the 100 shares from Company B, which injects $100 into Company B. So, Company B will now have $100 in real assets and $200 in cash for a total asset value of $300. This situation is illustrated in Table 5. That is, the fair market value of Company A subsequent to its purchase is $300, which is the same as the $300 market value prior to the purchase.

Table 5. Balance Sheets after One Round of Mutual Investment and Investor Pur- chase of Company A


Assets Cash $100 $200 Real assets 100 100 Investmenits 100 0

Total $300 $300

Liabilities anid equity Equity $300 $300

Shares outstanding (number) Original owners 0 200 New investor 300 0 Held by other company 0 100

Total 300 300

This same result holds when the level of cross- holdings increases. Table 6 shows the balance sheets of the two companies after two rounds of mutual investment but prior to the new investor's purchase of the shares of Company A. An investor who wishes to purchase all outstanding stock of Company A at this point should be willing to pay $400. Of this $400, $200 will go to the original





Table 6. Balance Sheets after Two Rounds of Mutual Investment



Total $400 $400



Total 400 400

owners of Company A and $200 to Company B. After this injection of $200 in cash, Company B will have $300 in cash and $100 in real assets for a total value of $400. Because Company B's original owners and Company A will each own exactly 50 percent of these assets, Company A's investment in Company B will be worth exactly $200, and the value of Company A will be exactly $400.

Therefore, irrespective of the level of cross- holdings, equity investors have no need to eliminate the effect of cross-ownership when determin- ing the market value of a company. Investors need not focus exclusively on business assets; all assets, including investments in financial assets, are equally valuable.

How the existence of cross-holdings in any way unduly enriches the original owners or the managers of the concerned companies is not obvi- ous. Each firm appears bigger because, in one sense, it actually is bigger: Primary share issues create the cross-holdings. The firm can achieve the same increase in size by issuing primary shares to outside investors-in which case, the firm will not only appear bigger but will actually be bigger. The fact that these companies are not issuing shares to the public indicates a reluctance to do so, maybe because they fear a loss of control. As long as the original investors do not issue new shares to outside investors, the fact that they appear to own a larger firm does not benefit them in any way. They do not control a greater amount of productive assets. As the analysis here shows, the benefit of controlling a larger asset base is realized only when the shares are finally sold to outside investors, at which time the firm becomes exactly as large as it appears to be. The outcome for the original owner, however, is that the feared loss of control necessar- ily accompanies the increase in value-which explains why cross-holdings are not more common. Cross-holdings are not a free lunch: They

cannot be used directly by investors as a means of self-aggrandizement.

Debt-Bearing Capacity Cross-holdings do not distort equity values from the point of view of equity investors, but what about the perspective of a creditor? Do cross- holdings inappropriately distort the debt-bearing capacity of the company? This question can be addressed by comparing the respective debt- bearing capacities of Company A as it appears in Tables 1 and 3-that is, before and after the estab- lishment of cross-holdings. If the fact of cross- holdings is devoid of economic content, then the true debt-bearing capacity of the Company A of Table 3 should be no different from the capacity of the Company A of Table 1. Table 7 presents the balance sheets for Company A with and without the cross-holding after Company A has obtained a loan for $100. The proceeds of the loan are included in cash.

Table 7. Balance Sheets without and with Cross-Holdings and after $100 Loan

Company A Company A after One Round

Prior to Cross- of Cross- Item Holdings Holdings


Total $300 $400

Liabilities and equity Liabilities $100 $100 Equity 200 300

Total $300 $400


Total 200 300

The two situations are clearly not the same. Without the cross-holding, the company has assets worth $300 to cover the loan; with the cross- holding, the assets are worth $400. The reason for this difference is that the $100 investment made by Company A in the common stock of Company B clearly offers real collateral to the creditors of Com- pany A, and the worth of this investment as collateral to the creditor is the appropriate measure of the increase in debt-bearing capacity created by cross- holdings.

To assess the worth of the collateral, assume a





situation where, through actions taken after obtain- ing the loan, Company A completely fritters away all of its cash and real assets. Company A will be in default of its repayment obligations, and the creditors will own the asset that remains, namely, the investment in Company B. This investment repre- sents claims to one-third of the assets of Company B. The actions of Company A's management will also have eroded some of the value of this investment because a part of the value of Company B derives from its reciprocal investment in Company A. The erosion in value occurs because all of Com- pany A's assets now belong to its creditors, so Company B's equity investment in Company A is now worth nothing. If the value of Company B's cash and real assets remains unchanged at $200, then the creditors of Company A will have a claim that is worth one-third of this value, or $66.67. The expected value of this claim will be less than $66.67 only if mismanagement or adverse circumstances at Company A also led to mismanagement or adverse circumstances at Company B. Such mismanagement could have occurred if the two companies had interlocking management structures or if their businesses were subject to similar economic uncertainties, or so forth. In the absence of perfect positive correlation in the fortunes of the two companies, however, cross-holdings do offer value as collateral. The value of the collateral is less than the full value of the investments because of the reci- procity in the investments.

To more fully understand the effect on credit capacity of cross-holdings, consider the collateral value offered by the investment portfolio that arises from two complete rounds of mutual investment. The balance sheet prior to the loan is shown in Table 6. Once again, assume that Company A fritters away the proceeds of the loan and the value of all productive assets under its control. Creditors of Company A again have recourse only to Com- pany A's investment in Company B, which now gives them a 50 percent ownership stake in Com- pany B. Company B's investment in Company A is worthless after Company A's loan default; therefore, Company B is now worth $200. The collateral is worth 50 percent of this value, or $100.

In other words, two rounds of mutual investment offer greater security for a loan than one round of mutual investment, which in turn, offers more collateral for a loan than zero mutual investment. Although the value of the collateral increases with increased investment, the rate of increase diminishes as the investment increases.

Going farther than this observation by propos- ing a general rule that relates the rate of growth in collateral value to the number of cycles of mutual

investment would not be very useful because these circumstances are unlikely to be met in practice. The value of financial investments as loan collateral can be more usefully expressed by the following rule: The collateral value of financial investments made by Company A arises from the fact that the value of these investments is insulated from the actions of Company A's management. Therefore, the collateral value of Company A's investment portfolio is equal to the sum of the market values of all investments held by Company A less any part of this value that depends on the value of Company A's own equity. This rule is quite general and applies to all investments in financial assets, not cross-holdings alone. What is special about cross- holdings is that a significant proportion of the value of investments that represent cross-holdings will, in fact, depend on the value of the borrowing firm's own equity. As a consequence, only a portion of the total cross-holdings offers any real collateral. Cred- itors would be well advised to take this limitation into account.

The original investors can use the increased debt-bearing capacity resulting from cross-holdings to build an empire only if creditors mistakenly consider that the entire value of the investment account offers collateral. Moreover, any misuse of the increased debt-bearing capacity for empire building might be costly because default by Company A would result in the ownership of its investments in Company B passing into the hands of a third party, the lending institution, with no guarantees as to how this investment would be liquidated. If Com- pany B did not have the resources to buy back those shares, ownership of the shares could pass into the hands of a hostile group of investors. This possibil- ity should serve as a deterrent to any empire- building tendencies that might arise from creditors overestimating the increase in debt-bearing capacity resulting from cross-holdings.

Valuing Markets The previous analysis suggests that cross-holdings do have economic significance from the point of view of equity investors and creditors; therefore, neither group should simply undo its effects on the equity value of any company they are analyzing. The question now is whether cross-holdings distort the size of markets or entire economies. That is, if an analyst is comparing the size of two markets, should the analyst eliminate the effect of cross- holdings?

The answer to this question depends on the purpose for which the total market capitalization is being computed. If the analyst is interested in com-





paring the productive capacities of two economies, then elimination of all investments in financial assets is the most appropriate course. The role of cross- holdings in such an analysis is no different from that of any other investment in nonproductive assets. Most analysts would not actually compute the market value of productive assets, of course, because the computation is time consuming and subject to errors.3 For the value of a market's productive capacity, a measure such as GDP is easily available and may be more appropriate than the analyst's computation.

If the measure of total market capitalization that is being sought by the analyst is meant to represent exactly how much must be spent to purchase the entire market, then surprisingly, the elimination of cross-holdings is once again inappropriate. That is, the conclusions here about what is true for each individual company also apply to the market as a whole.

Assume that the two companies in Table 6 constitute the entire capital market. Without the elimination of cross-holdings, the sum of the market values of the two companies is $800. The investor who desires to buy the entire market in Table 6 should be willing to pay $800. Because the two companies are identical, the analysis can begin by assuming that the investor buys any one of the companies first and then buys the other one. The investor who is interested in buying only Company A will be willing to pay $400 for the 400 outstanding shares of Company A. With this purchase, the investor will own all of Company A, which is com- posed of $100 cash, $100 in real assets, and 200 shares of Company B. This purchase will eliminate the ownership of Company B in Company A and inject $200 cash into Company B. The end result is shown in Table 8.

Table 8. Balance Sheets after Two Rounds of Mutual Investment and Investor Pur- chase of Company A



Total $400 $400


Shares outstanding (number) Original owners 0 200 New investor 400 0 Held by other company 0 200

Total 400 400

Having bought Company A, the investor must now buy Company B to complete the purchase of the entire market. As can be seen from Table 8, Company B has total assets of $400, so the investor will need $400 to buy the 400 outstanding shares of Company B. The investor buys 200 shares from the original investors and 200 shares from Company A, which eliminates the investment account of Com- pany A and replaces it with $200 in cash. The balance sheets of the two companies after comple- tion of the market takeover are shown in Table 9.

Table 9. Balance Sheets after Two Rounds of Mutual Investment and Investor Pur- chase of Company A and Company B


Assets Cash $300 $300 Real assets 100 100

Total $400 $400


Shares outstanding (number) New investor 400 400

The investor spent a total of $800, the aggregate market value of the equity prior to the takeover, to buy both companies. Furthermore, the takeover activity eliminated the cross-holdings completely, but the result was not a decrease in the market value of any individual firm or of the aggregate market.4 This result for two companies generalizes to the case of many companies and to an indefinite number of rounds of mutual investment.

Conclusion Company cross-holdings savor of get-rich-quick pyramid schemes, but the analysis presented here shows that for many practical investment decisions, the analyst is better off not eliminating the value of cross-holdings from the market value of equity. Cross-holdings have economic significance and must be taken into account in both equity investment and lending situations.

The analysis also suggests that cross-holdings are unlikely to be a significant source of self- aggrandizement for original investors or managers, which is probably why cross-holding has not become prevalent in countries where it does not have historical roots.

Cross-holdings in Japan and Korea are probably more significant for their contribution to the efficacy of decision making than to any distortion





they might cause of aggregate market values of equity. For example, cross-holdings, and the stability of relationships that result, probably allow Jap- anese and Korean companies to adopt a longer- term perspective in their decision making than is possible in the United States. On the other hand, as

is evident from the recent turmoil in the Asian markets, cross-holdings may create greater toler- ance for inefficiencies and mistakes. These effects, difficult as they are to quantify, are the ones investors must consider when assessing an investment situation involving cross-holdings.

Notes 1. Robert Ferguson and Neal B. Hitzig, "How to Get Rich

Quick Using GAAP," Financial Analysts Journal, vol. 49, no. 3 (May/Junel993):30-34.

2. Throughout this article, the assumption is that all investments in real assets are made in projects of zero net present value. This approach simplifies the examples considerably because, under it, the present values of investments (their market values) equal their book values.

3. Computing the market value of productive assets involves, first, adding to the market value of equity, which is observable, the market value of debt, which is not observable. The market value of debt equals the book value of debt only at the time of inception of a loan. At other times, there is no guarantee that the two will be even close to one another. Next, the analyst must subtract from the total market value

the market value of investments in financial assets, which is also often not observable. Under U.S. GAAP, for example, equity securities held by corporations are reported either at cost or at the lower of cost or market value as long as the ownership confers neither control nor significant influence. Investments that result in significant influence or in out- right control are accounted for, respectively, by the equity method or by consolidation of financial statements. In neither case does the book value of the investment purport to represent its market value.

4. Of course, once the investor acquires a controlling interest, he or she can pay out all "excess" cash as dividends, simul- taneously shrinking the size of the company and of the entire market.




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Company Cross-Holdings and Investment Analysis