## Table 1611

New Issues and Dilution: The Case of Upper States Manufacturing

Ross et al.: Fundamentals I VI. Cost of Capital and I 16. Raising Capital I I © The McGraw-Hill of Corporate Finance, Sixth Long-Term Financial Companies, 2002

Edition, Alternate Edition Policy

556 PART SIX Cost of Capital and Long-Term Financial Policy

USM has experienced a variety of difficulties in the past, including cost overruns, regulatory delays in building a nuclear-powered electricity-generating plant, and below-normal profits. These difficulties are reflected in the fact that USM's market-to-book ratio is \$5/10 = .50 (successful firms rarely have market prices below book values).

Net income for USM is currently \$1 million. With one million shares, earnings per share are \$1, and the return on equity is \$1/10 = 10%.10 USM thus sells for five times earnings (the price-earnings ratio is 5). USM has 200 shareholders, each of whom holds 5,000 shares. The new plant will cost \$2 million, so USM will have to issue 400,000 new shares (\$5 X 400,000 = \$2 million). There will thus be 1.4 million shares outstanding after the issue.

The ROE on the new plant is expected to be the same as for the company as a whole. In other words, net income is expected to go up by .10 X \$2 million = \$200,000. Total net income will thus be \$1.2 million. The following will result if the plant is built:

1. With 1.4 million shares outstanding, EPS will be \$1.2/1.4 = \$.857, down from \$1.

2. The proportionate ownership of each old shareholder will drop to 5,000/1.4 million = .36 percent from .50 percent.

3. If the stock continues to sell for five times earnings, then the value will drop to 5 X \$.857 = \$4.29, representing a loss of \$.71 per share.

4. The total book value will be the old \$10 million plus the new \$2 million, for a total of \$12 million. Book value per share will fall to \$12 million/1.4 million = \$8.57.

If we take this example at face value, then dilution of proportionate ownership, accounting dilution, and market value dilution all occur. USM's stockholders appear to suffer significant losses.

A Misconception Our example appears to show that selling stock when the market-to-book ratio is less than 1 is detrimental to the stockholders. Some managers claim that the resulting dilution occurs because EPS will go down whenever shares are issued when the market value is less than the book value.

When the market-to-book ratio is less than 1, increasing the number of shares does cause EPS to go down. Such a decline in EPS is accounting dilution, and accounting dilution will always occur under these circumstances.

Is it furthermore true that market value dilution will necessarily occur? The answer is no. There is nothing incorrect about our example, but why the market value has decreased is not obvious. We discuss this next.

The Correct Arguments In this example, the market price falls from \$5 per share to \$4.29. This is true dilution, but why does it occur? The answer has to do with the new project. USM is going to spend \$2 million on the new plant. However, as shown in Table 16.11, the total market value of the company is going to rise from \$5 million to \$6 million, an increase of only \$1 million. This simply means that the NPV of the new project is —\$1 million. With 1.4 million shares, the loss per share is \$1/1.4 = \$.71, as we calculated before.

So, true dilution takes place for the shareholders of USM because the NPV of the project is negative, not because the market-to-book ratio is less than 1. This negative NPV causes the market price to drop, and the accounting dilution has nothing to do with it.

10Return on equity, or ROE, is equal to earnings per share divided by book value per share, or, equivalently, net income divided by common equity. We discuss this and other financial ratios in some detail in Chapter 3.

Ross et al.: Fundamentals I VI. Cost of Capital and I 16. Raising Capital I I © The McGraw-Hill of Corporate Finance, Sixth Long-Term Financial Companies, 2002

Edition, Alternate Edition Policy

### CHAPTER 16 Raising Capital 557

Suppose the new project has a positive NPV of \$1 million. The total market value rises by \$2 million + 1 million = \$3 million. As shown in Table 16.11 (third column), the price per share rises to \$5.71. Notice that accounting dilution still takes place because the book value per share still falls, but there is no economic consequence of that fact. The market value of the stock rises.

The \$.71 increase in share value comes about because of the \$1 million NPV, which amounts to an increase in value of about \$.71 per share. Also, as shown, if the ratio of price to EPS remains at 5, then EPS must rise to \$5.71/5 = \$1.14. Total earnings (net income) rises to \$1.14 per share X 1.4 million shares = \$1.6 million. Finally, ROE will rise to \$1.6 million/12 million = 13.33%.

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