The managers of State Bank have been approached by City Bank about a possible merger. State Bank is asking a price of $171.78 million to be purchased by City Bank. City Bank currently has total cash flows of $30 million that are growing at 2 percent annually. Managers of State Bank estimate that because of synergies the merged firm's cash flows will increase by an additional 6 percent for the first four years following the merger. After the first four years, managers of State Bank have estimated that incremental cash flows will grow at a rate of 3 percent. The WACC for the merged firms is 11 percent. Managers of City Bank agree that cash flows should grow at an additional 6 percent for the first four years, but are unsure of the long-term growth rate in incremental cash flows estimated by City Bank. Calculate the minimum growth rate needed after the first four years such that City Bank would see this merger as a positive NPV project.

Question

Quizplus · Accepted Answer

The correct answer is A.The minimum growth rate needed after the first four years such that City Bank would see this merger as a positive NPV project is 7.26%. This is because the WACC for the merged firms is 11%, and the incremental cash flows are expected to grow at 6% for the first four years and then at a rate of g after that. In order for the merger to be a positive NPV project, the present value of the incremental cash flows must be greater than the purchase price of $171.78 million. This implies that the following inequality must hold:$$\sum_{t=1}^4\frac{30	imes(1.06)^t}{(1.11)^t}+\sum_{t=5}^\infty\frac{30	imes(1.06)^4	imes(1+g)^{t-4}}{(1.11)^t}>171.78$$Solving for g, we get:$$g>7.26%$$

The Managers of State Bank Have Been Approached by City