Question 9.2: Chang plc has 1 million shares in issue and surplus cash of ...
Chang plc has 1 million shares in issue and surplus cash of £2 million, which is to be distributed to shareholders. Following this distribution, earnings are expected to be £1 million per year and the price/earnings ratio is expected to be 8 times. The distribution will be made by either:
(i) a dividend of £2.00 per share, or
(ii) a tender offer of 200,000 shares at £10 per share.
The risk and growth prospects of the business will be unaffected by the choice of distribution method and so the total market value (TMV) of the shares following distribution will be unaffected. The TMV (whichever distribution method is used) will therefore be:
TMV = Earnings × P/E ratio = £1 million × 8 =\underline{£8 million.^{*}}
Under the dividend option, however, there will be 1 million shares in issue and under the buyback option there will be 800,000 shares in issue. This means that the value per share will be £8 (£8m/1m) under the dividend option and £10 (£8m/800,000) under the buyback option.
Let us now consider the situation of a shareholder with 10,000 shares under both the dividend option and the buyback option – where there is a choice of either holding or selling the shares.
| Dividend option | Buyback option | ||
| Hold | Sell | ||
| £ | £ | £ | |
| 10,000 shares held at £8 per share | 80,000 | ||
| 10,000 shares held at £10 per share | 100,000 | ||
| 10,000 shares sold at £10 per share | 100,000 | ||
| Dividend received (10,000 × £2) | \underline{20,000} | _______ | _______ |
| \underline{100,000} | \underline{100,000} | \underline{100,000} | |
We can see that total wealth is the same under each option and so the shareholder should be indifferent between them.
* We know from Chapter 3 that the price/earnings (P/E) ratio is MV/EPS. This can be rearranged so that MV = EPS × PE ratio (where MV = market value per share and EPS = earnings per share).
To find the TMV of the shares, rather than the value of a single share, it is therefore:
TMV = (Total) Earnings × P/E ratio