The managers of BSW Inc. have been approached by EAG Corp. for a possible merger. EAG Corp. is asking a price of $50 million to be purchased by BSW Inc. The two firms currently have cumulative total cash flows of $2.5 million that are growing at 2 percent annually. Managers of EAG estimate that because of synergies the merged firm's cash flows will increase by an additional 5 percent for the first three years following the merger. After the first three years, managers of EAG have estimated that cash flows will grow at a rate of 2 percent. The WACC for the merged firms is 12 percent. Managers of BSW Inc. agree that cash flows should grow at an additional 5 percent for the first three years, but are unsure of the long-term growth rate in cash flows estimated by EAG. Calculate the minimum growth rate needed after the first three years such that BSW Inc. would see this merger as a positive NPV project.

Question

Quizplus · Accepted Answer

To calculate the NPV of the merger, we need to find the present value (PV) of both the current cash flows and the expected future cash flows.

PV of current cash flows = $2.5 million / (0.12 - 0.02) = $25 million

PV of future cash flows = ($2.5 million * 1.05^3) / (0.12 - 0.05) + ($2.5 million * 1.05^3 * x) / (0.12 - x)

where x is the unknown long-term growth rate in cash flows.

Setting the NPV of the merger equal to zero and solving for x, we get:

$50 million - $25 million - (($2.5 million * 1.05^3) / (0.12 - 0.05)) - (($2.5 million * 1.05^3 * x) / (0.12 - x)) = 0

Solving for x, we get x = 6.925 percent. Therefore, the minimum growth rate needed after the first three years such that BSW Inc. would see this merger as a positive NPV project is 6.925 percent.

The Managers of BSW Inc