Math Problem Statement

Natsam Corporation has

$ 212$212

million of excess cash. The firm has no debt and

530530

million shares outstanding with a current market price of

$ 17.60$17.60

per share. Suppose the board decided to do a​ one-time share​ repurchase, but​ you, as an​ investor, would have preferred to receive a dividend payment. How can you leave yourself in the same position as if the board had elected to make the dividend payment​ instead?

Question content area bottom

Part 1

Which of the following is true regarding the effect of a​ one-time share repurchase on the stock price in a perfect​ market?  ​(Select the best choice​ below.)

A.

An​ open-market share repurchase has no effect on the stock price.

B.

An​ open-market share repurchase decreases the share price because the​ firm's assets decline by purchases of the shares.

C.

An​ open-market share repurchase increases the stock price due to the decrease in shares in the marketplace.

D.

An​ open-market share repurchase has no effect on the stock​ price, but the stock price is not the same as the​ cum-dividend price if a dividend were paid instead.

Solution

Let's analyze the question step-by-step, including the effect of a one-time share repurchase on stock price in a perfect market.

Part 1: The Share Repurchase Effect

A one-time share repurchase involves the company using its excess cash to buy back shares from investors. In a perfect market (without taxes, transaction costs, or other frictions), the following insights can be drawn:

  1. The market price per share after the repurchase is influenced by the fact that the firm's total assets decrease by the amount spent on repurchasing shares.
  2. The number of outstanding shares is reduced, which increases the earnings per share (EPS) and potentially the intrinsic value of the remaining shares.
  3. The cash holdings of the firm are reduced, but the overall equity value of the firm decreases by the same amount of cash used for the buyback. As a result, the stock price after the repurchase may adjust based on the decrease in assets.

Answer to Part 1:

  • Option A ("An open-market share repurchase has no effect on the stock price") is incorrect because repurchasing shares reduces the firm's assets (cash) and thus changes its overall value.

  • Option B ("An open-market share repurchase decreases the share price because the firm's assets decline") is also not completely accurate. Although the firm’s assets do decrease, the reduction in shares offsets this, so the price per share doesn't necessarily fall.

  • Option C ("An open-market share repurchase increases the stock price due to the decrease in shares in the marketplace") is not always correct. While the reduction in outstanding shares does improve metrics like earnings per share, it doesn't mean the stock price will directly rise after a repurchase.

  • Option D ("An open-market share repurchase has no effect on the stock price, but the stock price is not the same as the cum-dividend price if a dividend were paid instead") is the most accurate. In a perfect market, a share repurchase should not affect the stock price directly, but the stock price after the repurchase will not match the cum-dividend price (the price before a dividend is distributed).

Conclusion: Option D is the best choice. It reflects that while the stock price may not change directly after the repurchase, the result is different from paying a dividend.


How You Can Simulate the Dividend

As an investor who preferred a dividend, you can sell enough shares in the open market to replicate the cash inflow that you would have received from a dividend. This way, you leave yourself with the same value you would have had if a dividend were paid.

Would you like more details on share repurchases or how to calculate the exact value you should sell to replicate a dividend?


Further Questions to Explore:

  1. How does a share repurchase affect a company's earnings per share (EPS)?
  2. What are the tax implications of dividends versus share repurchases for investors?
  3. How does the stock price behave in an imperfect market after a repurchase?
  4. What is the difference between an open-market repurchase and a tender offer?
  5. How can an investor decide between selling shares or keeping them after a repurchase?

Tip: Repurchasing shares can be seen as a signal that the company believes its stock is undervalued, which may have positive effects on the market's perception.

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Math Problem Analysis

Mathematical Concepts

Corporate Finance
Market Efficiency
Stock Repurchase

Formulas

Price per share = (Firm value - Cash used for repurchase) / Remaining shares

Theorems

Efficient Market Hypothesis (EMH)

Suitable Grade Level

College-level Corporate Finance