Yin Corp and Yang Inc are considering a merger. Yin expects $75 million in free

Question

Yin Corp and Yang Inc are considering a merger. Yin expects $75 million in free cash flow next year, which is forecast to grow at 1% forever. Yang expects $25 million in free cash flow next year, which is forecast to grow at 3% forever. Because their cash flows are quite volatile, neither firm has any leverage right now. By merging, Yin and Yang expect to generate more stable cash flows that would allow the combined firm to have 20% leverage without risking default. Suppose the tax rate is 40%, the risk-free rate is 2%, current equity betas for both companies is 1, and the market risk premium is 5%. If the cost of debt issued by the combined firm would be 3%, how much value could the two companies create by merging together?

Explanation / Answer

Using CAPM, Cost of equity, r = rf + beta x mrp = 2% + 1 x 5% = 7%

Value of Yin, P1 = FCF / (r - g) = 75 / (7% - 1%) = $1,250 million

Value of Yang, P2 = FCF (r - g) = 25 / (7% - 3%) = $625 million

Without merger, their total value = $1,250 + $625 = $1,875 million

Using MM hypothesis, Value of levered firm (Vl) = Value of unlevered firm (Vu) + Tax rate x Debt

Here, Vu = 1,875, Debt = 1,875 x 20% = 375 million, Tax rate = 40%

=> Vl = 1,875 + 375 x 40% = $2,025 million

=> Increase in value = 2,025 - 1,875 = $150 million

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