## Info

Sunshine Swimwear

Polar Winterwear

Market value of equity

\$20.394 million

\$6.992 million

Market value of debt

\$ 9.606 million

\$3.008 million

If you do check these, you may get slightly different answers if you use Table 24.3 (we used an options calculator).

After the merger, the combined firm's assets will simply be the sum of the premerger values, \$30 + \$10 = \$40, because no value was created or destroyed. Similarly, the total face value of the debt is now \$16 million. However, we will assume that the combined firm's asset return standard deviation is 40 percent. This is lower than for either of the two individual firms because of the diversification effect.

So, what is the impact of this merger? To find out, we compute the postmerger value of the equity. Based on our discussion, here is the relevant information:

 Combined Firm Market value of assets \$40 million Face value of pure discount debt \$16 million Debt maturity 3 years Asset return standard deviation 40 percent

Once again, we can calculate equity and debt values:

 Combined Firm Market value of equity \$26.602 million Market value of debt \$13.398 million

What we notice is that this merger is a terrible idea, at least for the stockholders! Before the merger, the stock in the two separate firms was worth a total of \$20.394 + 6.992 = \$27.386 million compared to only \$26.602 million postmerger, so the merger vaporized \$27.386 - 26.602 = \$.784 million, or almost \$1 million, in equity.

Where did \$1 million in equity go? It went to the bondholders. Their bonds were worth \$9.606 + 3.008 = \$12.614 million before the merger and \$13.398 million after, a gain of exactly \$.784 million. Thus, this merger neither created nor destroyed value, but it shifted it from the stockholders to the bondholders.

Our example shows that pure financial mergers are a bad idea, and it also shows why. The diversification works in the sense that it reduces the volatility of the firm's return on assets. This risk reduction benefits the bondholders by making default less likely. This is sometimes called the "co-insurance" effect. Essentially, by merging, the firms insure each other's bonds. The bonds are thus less risky, and they rise in value. If the bonds increase in value, and there is no net increase in asset values, then the equity must decrease in value. Thus, pure financial mergers are good for creditors, but not stockholders.

Another way to see this is that since the equity is a call option, a reduction in return variance on the underlying asset has to reduce its value. The reduction in value in the case of a purely financial merger has an interesting interpretation. The merger makes default (and, thus, bankruptcy) less likely to happen. That is obviously a good thing from a bondholder's perspective, but why is it a bad thing from a stockholder's perspective? The answer is simple: The right to go bankrupt is a valuable stockholder option. A purely financial merger reduces the value of that option.

© The McGraw-Hill Companies, 2002 Edition, Alternate Edition

CHAPTER 24 Option Valuation 831

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