Simple interest
2.2
where
Compound interest
2.3
where
Personal preference determines which method is used. Simple interest is useful if the returns are compared to money market yields that are also computed with the simple interest method, such as the London Interbank Offered Rate (LIBOR) or Treasury bills (T-bills). Compound interest is preferable if the result is used in further quantitative studies. If the returns are compared to bond yields, they should be adjusted for semiannual compounding used in bonds. It is an error encountered frequently, even in research by otherwise experienced analysts and academics, that yields calculated on different bases are compared with one another.
A projected annualized return of 6.74 percent is sufficient to make this investment highly desirable at a time when overnight LIBOR rates in Sterling were around 0.58 percent and the 10-year benchmark Gilt yielded around 2.6 percent.
It is helpful to look at the actual outcome of this merger arbitrage. The Autonomy acquisition closed earlier than an arbitrageur would have assumed: November 14, 2011. With this shorter 88-day time frame to closing, the realized annualized return was 9.65 percent and 10.01 percent for the simple and compound interest methods, respectively. Over the same period, the FTSE returned 10 percent, or an annualized 48.5 percent. However, this better short-term performance came at a price of a volatility that was also significantly higher: Autonomy's daily volatility was 3.4 percent, whereas that of the FTSE was 25 percent.
Autonomy was a non–dividend-paying company. In case a company does pay dividends, there is another source of income that the arbitrageur must factor into the return calculation. For an example, consider Australian bulk grain exporter GrainCorp Limited, which was acquired by Archer-Daniels-Midland Co. for A$2.8 billion. The per-share acquisition price was only A$12.20, but an additional A$1 was to be paid in dividends. Due to the large dividends to be received by shareholders, the stock traded above the A$12.20 level following the announcement of the merger. On April 30, 2013, four days after the announcement, an arbitrageur could have acquired GrainCorp for a volume weighted average price of $12.8239, with an expectation that the transaction would close by September 30, 2013, or within 157 days. A back-of-the-envelope calculation for the net return with dividends is to add the dividend to the merger consideration received. This gives an annualized return of 6.95 percent if the compound interest method is used:
2.4
where
A more accurate method is the calculation of the internal rate of return (IRR). Spreadsheets have built-in functions to calculate IRRs that require the user to enter each payment with the associated date, as shown in Figure 2.3. It is important to note that the dividends were spread over different payment dates. A first net dividend payment of A$0.25, consisting of a $0.20 interim dividend and a $0.05 special dividend, was to be paid on July 19. The dates of any future dividends were not yet known, Since Australian companies pay semiannual dividends, it is safe to assume that no dividend will be received during the 10-week period between July 19 and the closing on September 30. The prior final dividend was paid on December 17, 2012, so that the final dividend would probably also be paid in the middle of December should the merger not be completed by then. Since the arbitrageur is working for now with a closing date of September 30, it is assumed that the final dividend payment will be made simultaneously with the payment of the merger consideration on September 30.
Figure 2.3 IRR Calculation of Annualized Return in Excel
The resulting projected return is an annualized return of 7.21 percent, slightly higher than in the simplified calculation. The reason for the difference lies in the earlier receipt of the dividend cash flow in the IRR calculation.
The actual date of the dividend payment and its amount are not always known at the time of the announcement of a merger. In this case, the arbitrageur will make an educated guess for the next payment date based on the company's payment frequency and past dividend amounts. Care must be taken when foreign companies are listed in another country. For example, U.S. companies pay dividends with a quarterly frequency. However, U.K. companies listed in the United States and their ADRs pay semiannual dividends to all of their shareholders, even those who purchased the shares in the U.S. market. Similarly, Swiss companies pay only one dividend per year even when listed in the United States. Whenever the dividend information becomes known, such as the announcement of the dividend date or the exact amount, arbs must update their spreadsheets promptly.
Arbitrageurs must be aware of a few limitations of this approach:
• The returns calculated are projections that are highly dependent on the date of the closing of the merger. A delay can quickly lower the return on the investment.
• The projections say nothing about the path that the investment takes on its way to closing. Sometimes, following an initial spike after the merger announcement, a target company's stock weakens. An arbitrageur will then have to book a temporary loss on the investment. Of course, this marked-to-market loss will be reversed eventually when the merger closes. However, the projection cannot make a prediction on the trading dynamics of the stock between purchase and merger closing.
Stock-for-Stock Mergers
Stock-for-stock mergers are more complicated than cash mergers. In stock-for-stock mergers, a buyer proposes to acquire a target by paying in shares rather than cash. Sometimes the consideration paid can be a combination of stock and cash. That case is addressed later.
A good example of a stock-for-stock merger announcement is shown in Exhibit 2.2. It is the $4 billion acquisition of Australian gold miner CGI Mining Ltd by Canada's B2Gold Corp, announced in September 2012.
VANCOUVER, BRITISH COLUMBIA–(Marketwire – Sept. 19, 2012) – B2Gold Corp. (TSX: BTO)(OTCQX: BGLPF)(PINKSHEETS: BGLPF)(NAMIBIAN:B2G) (“B2Gold”) and CGA Mining Limited (TSX: CGA)(ASX: CGX) (“CGA”) are pleased to announce that they have entered into a definitive Merger Implementation Agreement (“Merger Agreement”) to combine the two companies at the agreed exchange ratio of 0.74 B2Gold common shares for each CGA share held, which represents a purchase price of approximately C$3.18 per CGA share and a premium of 22 % using the 20 day volume weighted average share price of each respective company, and a 26 % premium over the CGA closing share price on September 17, 2012 based on the closing price for the B2Gold shares as of such date. The transaction is valued at approximately C$1.1 billion.
The merger will be implemented by way of a Scheme of Arrangement under the Australian Corporations Act 2001 (“Scheme”). Upon completion of the Scheme, existing B2Gold shareholders and CGA shareholders will own approximately 62 % and 38 %, respectively, of the issued common shares of the combined company.
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Transaction Structure and Terms
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The merger is subject to regulatory, Australian Court, shareholder, and third party approvals, together with other