🔎 Tax savings and Diversification as reasons for merging

Tax Savings

Problem:

• Consider two firms, Yin Corporation and Yang Corporation.
• Both corporations will either make $50 million or lose $20 million every year with equal probability.
• The only difference is that the firms’ profits are perfectly negatively correlated.
• That is, any year Yang Corporation earns $50 million, Yin Corporation loses $20 million, and vice versa. Assume that the corporate tax rate is 34%.
• What are the total expected after-tax profits of both firms when they are two separate firms?
• What are the expected after-tax profits if the two firms are combined into one corporation called Yin-Yang Corporation, but are run as two independent divisions? (Assume it is not possible to carry back or carry forward any losses.)

Solution:

Plan:

• We need to calculate the after-tax profits of each firm in both the profitable and unprofitable states by multiplying profits by (1 - tax rate).
• We can then compute expected after-tax profits as the weighted average of the after-tax profits in the profitable and unprofitable states.
• If the firms are combined, their total profits in any year would always be $\$50 \text{ million} - \$20 \text{ million} = \$30 \text{ million}$, so the after-tax profit will always be $\$30 \times (1 - \text{ tax rate})$.

Execute:

• Let’s start with Yin Corporation. In the profitable state, the firm must pay corporate taxes, so after-tax profits are $\$50 \times (1 - 0.34) = \$33 \text{ million}$.
• No taxes are owed when the firm reports losses, so the after-tax profits in the unprofitable state are -$20 million.
• Thus, the expected after-tax profits of Ying Corporation are $33(0.5) + (-20)(0.5) = \$6.5 \text{ million}$.
• Because Yang Corporation has identical expected profits, its expected profits are also $6.5 million. Thus, the total expected profit of both companies operated separately is $13 million.
• The merged corporation, Yin-Yang Corporation, would have after-tax profits of $\$30 \times (1 - 0.34) = \$19.8 \text{ million}$.

Evaluate:

• Yin-Yang Corporation has significantly higher after-tax profits than the total stand-alone after-tax profits of Yin Corporation and Yang Corporation.
• This is because the losses on one division reduce the taxes on the other division’s profits.

🗝 The key point here is that the tax shield from the -$20 loss that Yin has can’t be used by Yin because it has no profits to shelter.

When Yin is profitable, it has a tax bill of $\$50 \times 34\% = \$17\text{M}$. This caused our profits to decrease from $50M to +$33M in the good state.

When it is unprofitable, it has a potential tax shield from this loss of $\$20 \times 34\% = \$6.8$. However, because it made a loss this year, it doesn’t have any profits to shield, and it’s loss is still -$20M

However, because it can’t carry forward this loss, that tax shield is completely lost, at the shareholder’s expense and much to the glee of the IRS and the other taxpayers.

In contrast, if they were merged, the loss from Yin division could be used to shield the income from Yang division.

Note that for simplicity, when the firms are separate, we are assuming that Yin can’t carry forward the loss. In reality, there may be limits on the ability to carry forward the loss. Therefore, the loss can’t be used to shield any profits.

Diversification

We can also use the Yin and Yang example to understand the diversification benefits of merging.

Suppose that the tax law is changed and Yin and Yang can carry forward any tax shields they get from negative net income. There still would be a large diversification benefit to the merger.

Investors far prefer steadily growing earnings. When earnings fluctuate, it makes them concerned about risk.

Reasons to Acquire

• Diversification
• Risk Reduction
• Debt Capacity and Borrowing Costs
• Liquidity

Applying this to Yin and Yang, investors may shy away from firms like Yin and Yang that will make $50M one year and then lose $20M the following year. That will strike them as a very risky, very scary path for earnings.

Because Yin and Yang are perfectly negatively correlated, the earnings of the combined company will always be $\$50 - \$20 = \$30$, because one division will be profitable and the other unprofitable.

The net result is that the combined company has extraordinarily smooth earnings.

Let’s put some numbers on this. Suppose that the market cap of Yin and Yang are both $250M. If you combined them without synergies, then the value of the combined company would be $\$250 + \$250 = \$500\text{M}$. However, because of the far steadier earnings in the combined company, the markets may value it at $600M. Thus, the diversification benefits of the merger have resulted in a synergy worth $\text{S}=\$100\text{M}$. (See Synergies).