Consider a firm that has decided to make, but has
not yet announced, a large “bonus” cash dividend amounting in the aggregate to $5 million.
The firm has 1 million shares outstanding that sell for $20 each. The firm has no debt;
there are no taxes; and all transactions take place in a perfect capital market. Using calculations
like those in the illustration of dividend irrelevance in a perfect capital market, show that shareholders will be indifferent between whether the firm pays out the “bonus” as a
dividend or uses the money to buy back $5 million of its shares.
To analyze whether shareholders will be indifferent between the firm paying out a cash dividend or buying back its shares, we need to consider the effects of both scenarios on the value of the firm and the value of the shareholders' holdings.
1. Paying out the bonus as a cash dividend:
If the firm pays out a $5 million cash dividend, the total value of the firm will decrease by $5 million. The number of shares outstanding remains the same, so the price of each share will decrease. Let's calculate the new share price.
Total value of the firm before the dividend = 1 million shares * $20 per share = $20 million.
Total value of the firm after the dividend = $20 million - $5 million = $15 million.
New share price = Total value of the firm after the dividend / Number of shares outstanding
= $15 million / 1 million shares
= $15 per share.
So, if the firm pays out the bonus as a cash dividend, the share price will decrease to $15 per share.
2. Using the money to buy back $5 million of its shares:
If the firm uses the $5 million to buy back its shares, the total value of the firm will remain the same, but the number of shares outstanding will decrease. Let's calculate the new share price.
Total value of the firm before the buyback = 1 million shares * $20 per share = $20 million.
Total value of the firm after the buyback = $20 million - $5 million = $15 million.
Number of shares after the buyback = Number of shares outstanding - Number of shares bought back
= 1 million shares - ($5 million / $20 per share)
= 1 million - 250,000 shares
= 750,000 shares.
New share price = Total value of the firm after the buyback / Number of shares outstanding
= $15 million / 750,000 shares
= $20 per share.
So, if the firm uses the money to buy back $5 million of its shares, the share price will remain at $20 per share.
Based on the calculations, we can see that the share price will be the same whether the firm pays out the bonus as a cash dividend or uses the money to buy back its shares. Therefore, shareholders will be indifferent between these two scenarios.