MERGERS AND THE COST OF CAPITAL
MERGERS AND THE COST OF DEBT CAPITAL
The concept explored here, and by Brealey & Myers (B&M) on pages 936-937, is that, although merger (even if non-synergistic) is likely to reduce the promised interest rate on borrowing by one or both of the merging firms, shareholders do not necessarily benefit as a result. This is a very important, and counterintuitive, point (however, it will not appear on the Final Exam).
Promised versus Expected Interest
At the end of 2003, Advanced Micro Devices (AMD) December 1, 2007 bonds were priced to have a yield to maturity of 19.5%. The yield to maturity is the rate of return that someone now buying an AMD bond and holding the bond to maturity would earn if AMD were not to default. The coupon rate on the bonds is 4.5%, so the bonds sold at a deep discount from par.
The prevailing yield to maturity on a 3-year U.S. Government bond was about 2.6%, so 19.5% was clearly not the risk-free rate. The market believed that the AMD bonds that yielded 19.5% were not risk-free; there was a high-probability of default. Investors believed that there was a good chance that anyone buying an AMD bond would ultimately earn much less than 19.5%.
Suppose that you were comparing the AMD bonds with Merrill Lynch (MER) September 14, 2007 bonds, which had e a yield to maturity of approximately 3.6% and a coupon rate of 3.375%. An investor who made the mistake of simply looking at the yield to maturity would have rated the AMD bonds as screamingly better. In fact, such an investor would only have bought the junkiest of junk bonds; this is because the junkier, the higher the yield to maturity.
B&M (pages 683-686) explain the difference between the promised interest rate and the expected interest rate. The promised interest rate is the yield to maturity; it is the rate of return that will be earned on the bond if held to maturity and if there is no default. The expected interest rate (or expected rate of return) is the mean of the probability distribution of possible rates of return that will be provided by the bond taking into account that there may be default, in which case the bondholder will earn less than the promised interest rate on the bond.
For example, suppose that Sorry Corporation just issued a 1-year $1 million note in order to raise capital to sustain its operations. The interest and principal on the note are payable in one year (at time 1). Suppose that the promised interest rate (yield to maturity) on the note is 20%; so Sorry will owe $1.2 million in one year. This rate is far above the risk-free rate because the lender recognizes that Sorry may default. Exhibit 1 below shows the computation of the expected interest rate on the note. The expected interest rate (expected rate of return) on the note is 11%, significantly below the promised yield of 20%.
Exhibit 1. Expected Interest Rate on Loan
|Payment by Sorry at time 1 |Probability |Payoff weighted by probability [= (1) ( (2)] |
|(1) |(2) |(3) |
|$1.2 million |.90 |$1.08 million |
|$.5 million |.06 | .03 million |
|$0 |.04 |0 |
|Expected Payment | |$1.11 million |
|Expected interest rate = [$1.11/$1.0] ( $1.0 = 11% |
MERGER AND THE COST OF BORROWING
It is often argued that, even in perfect markets (no transaction costs, no financial distress costs, etc.), merger can benefit shareholders by reducing the promised interest paid on debt. B&M argue that no such benefit arises even if the promised interest rate on debt is lower with merger (B&M, pp. 937-937). We explain this point, and then qualify the B&M analysis.
IF FIRMS A AND B ARE SEPARATE COMPANIES: Now is time 0. Assume that each of all-equity firms A and B decide to borrow $100 million at time 0 on a one-year basis. Suppose that the lenders want to earn a five percent expected rate of return on their loans to A and B. The business risks of firms A and B assumed in Exhibits 2a and 2b imply that the promised interest rate on the firm A and firm B debt must be 10 percent. Let’s see why.
In one year (at time 1), each firm will owe $110 million (principal plus 10 percent interest). From Exhibits 2a and 2b, the time 1 values of firms A and B ([pic] and [pic]) are first paid to the firm’s lenders; what remains goes to shareholders. There are two states of the world at time 1 (e.g., boom and recession), each with a probability of .5. At time 0, lenders know that each firm’s debt is risky and they charge a promised interest rate of 10 percent. The 10 percent promised interest rate produces a 5 percent expected interest rate (due to default risk).
Exhibit 2a. Firm A: Time 0 Loan = $100; Promised Time 1 Payment = $110 (in $million)
|Time 1 state |[pic] |Owed to lenders of firm|Paid to lenders of firm A |Residual to shareholders of firm A |
| | |A | | |
|X (Prob. = 1/2) |$250 |$110 |$110 |$140 |
|Y (Prob. = 1/2) |$100 |$110 |$100 |0 |
|Expected Amt. |$175 |$110 |$105 |$70 |
|Expected rate of return for firm A lenders = [$105 ( $100]/$100 = 5% |
Exhibit 2b. Firm B: Time 0 Loan = $100; Promised Time 1 Payment = $110 (in $million)
|Time 1 state |[pic] |Owed to lenders of firm|Paid to lenders of firm B |Residual to shareholders of firm B |
| | |B | | |
|X (Prob. = 1/2) |$100 |$110 |$100 |$0 |
|Y (Prob. = 1/2) |$350 |$110 |$110 |$240 |
|Expected Amt. |$225 |$110 |$105 |$120 |
|Expected rate of return for firm B lenders = [$105 ( $100]/$100 = 5% |
Exhibit 3 sums up the quantities in Exhibits 2a and 2b.
Exhibit 3. Sum of Firm A and Firm B Outcomes
|Time 1 state |[pic]+ [pic] |Total owed to lenders of |Total paid to lenders of |Residual to shareholders of firms |
| | |firms A and B |firms A and B |A and B |
|X (Prob. = 1/2) |$350 |$220 |$210 |$140 |
|Y (Prob. = 1/2) |$450 |$220 |$210 |$240 |
|Expected Amt. |$400 |$220 |$210 |$190 |
|Expected rate of return for firm A and firm B lenders combined = [$210( $200]/$200 = 5% |
Notice that total paid to lenders is $210 in both states X and Y. So, if you lent firm A, say, $20 and firm B $20 (one-fifth of the $200 lent to the two firms), you would receive $42 with certainty at time 1 and earn a risk-free return of 5 percent (the riskless rate). Thus:
• If firms A and B are separate, and they borrow at a promised rate of 10 percent, the lenders will only earn an expected return of only 5 percent.
• If firms A and B are separate, risk-averse lenders will diversify by lending equal amounts to A and B because, in doing so, they earn the 5 percent with certainty.
IF A AND B ARE MERGED INTO FIRM AB: Suppose now that all-equity firms A and B merge into one all-equity firm, firm AB, and that the merger is non-synergistic (this is not necessary but simplifies the example). Thus, [pic] = [pic] + [pic] (by the Value Additivity Principle). At time 0, firm AB borrows $200 million for one year. As before, lenders want to earn an expected return of 5 percent. Exhibit 4 shows that, to achieve this, the promised interest rate will be 5 percent (not the 10 percent if the companies were unmerged). At time 1, firm AB will owe, and will pay, $210 million ($200 principal + $10 million interest).
Exhibit 4. Firm AB: Loan = $200; Promised Time 1 Payment = $210 (in $million)
|Time 1 state |[pic] |Owed to lenders of firm AB |Paid to lenders of firm |Residual to shareholders of firm AB |
| | | |AB | |
|X (Prob. = 1/2) |$350 |$210 |$210 |$140 |
|Y (Prob. = 1/2) |$450 |$210 |$210 |$240 |
|Expected Amt. |$400 |$210 |$210 |$190 |
|Expected rate of return for firm AB lenders = [$210( $200]/$200 = 5% |
In both Exhibit 4 (merger) and Exhibit 2a, 2b and 3 (no merger) total debt is $200 million and lenders in total are paid $210 million at time 1 (5 percent rate of return). Without merger, a 10 percent promised interest rate is needed to produce a 5 percent expected interest (because A defaults in state Y, and B defaults in state X). With merger, A and B are combined into firm AB and there is no default at time 1; [pic]is sufficient to cover the $210 million (the 5 percent promised rate) in either state X or state Y. Firm AB debt of $200 million is riskless, so a promised interest rate of 5 percent results in a realized interest rate of 5 percent.
Also notice from the last columns of Exhibit 3 and 4 that the total shareholder payoff without merger (and a 10 percent promised interest rate) equals the shareholder payoff with merger (and a promised interest rate of 5 percent). Shareholders are no better off promising 5 percent interest with merger than they are promising 10 percent interest with merger.
In summary, we can conclude the following:
• Unmerged, the firms promise interest of 10 percent but pay only 5 percent because each firm defaults in one state (i.e., shareholders are left out in the cold in one of the states).
• Merged, the firms promise 5 percent and pay 5 percent (because there is no default)
• Shareholders are equally well of with the unmerged firms borrowing at a promised interest rate of 10 percent and the merged firm (AB) borrowing at a promised interest rate of 5 percent.
QUALIFICATION OF THE BREALEY & MYERS ANALYSIS
Investment bankers, bond rating agencies, and lenders rarely compute the probability of default using a computer model. Rather, they judgmentally take into account their estimate of the probability and consequences (recovery rate) of default when rating, buying or selling a bond, or extending credit in any other way. The above principles describe the formal translation of what happens in credit markets.
The above analysis focused on one aspect of bond pricing and interest rates, and was not meant to imply that there can be no cost of capital benefits from merger. For example, merger can reduce the probability of default and thereby reduce expected financial distress costs. Financial distress costs are firm value reductions due to the expectation or occurrence of default. Examples of financial distress costs are financial distress induced legal costs due to litigation between the firm and its lenders, loss of customers, worsened terms from vendors, loss of key employees, and an inability to raise capital to finance positive NPV investments. In the examples in Exhibits 2a, 2b, 3 and 4, there is financial distress for unmerged firms A and B (for firm A there is financial distress in state Y, and for firm B there is financial distress in state X), but there is no financial default or distress if the two firms are merged. To see that the above example ignored financial distress costs, notice in Exhibit 4 that the time 1 value of the merged firm ([pic]) is $350 in both states X and Y; and in Exhibit 3, the time 1 value of firm A plus the time 1 value of firm B ([pic]+ [pic]) is also $350 in state X and in state Y. If financial distress costs were present, the sum of the time 1 values of unmerged firms A and B in Exhibit 3 would be less than the value of the merged firm in Exhibit 4 (because, in Exhibit 3, financial distress would have negatively impacted firm value). Therefore, there would be a benefit from merger equal to the financial distress costs avoided as a consequence of the merger.
A second merger-induced debt financing benefit is economies of scale in raising capital. The transaction costs (legal fees, accounting fees, management time, etc.) of raising capital are lower per dollar raised as the amount raised increases. There are economies of scale in raising funds. Thus, it is cheaper for one large company to borrow $200 million than for two smaller companies each to borrow $100 million. These scale economies also apply to equity financing.
In fairness to B&M, those who contend that merger will create benefits by lowering the cost of debt financing do so by simply stating that, for any given total amount of debt, the promised interest rate on debt is lower with merger than without and therefore there is a benefit. We found that B&M are correct in asserting that a lower promised rate does not imply a lower expected cost of debt taking into account default risk. Simply lowering the promised interest rate does not imply benefits from merger. The expected interest rate must be considered. Merger-created debt financing benefits require some factor other than simply a lower promised debt interest rate (such as financial distress costs, tax benefits, or economy of scale effects). So, the B&M point is well taken and helpful because it allows us to focus on what really produces financing benefits from merger.
10/24/2004
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