Valuation of a Merger 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 present value of the cash flows, we need to use the WACC of 12% and discount the cash flows back to present value. The initial purchase price of $50 million is the outflow, which needs to be subtracted from the present value of cash inflows.

PV(Cash Flows) = -$50 million + PV(cumulative total cash flows) + PV(synergies)

PV(cumulative total cash flows) = $2.5 million / (12% - 2%) = $25 million
PV(synergies) = (1.05^1.05^2.05^3)(($25 million x 1.05) + ($25 million x 1.05^2) + ($25 million x 1.05^3)) / (1.12^3) = $34.22 million

PV(Cash Flows) = -$50 million + $25 million + $34.22 million = $9.22 million

To find the minimum growth rate needed after the first three years, we need to solve for the NPV being zero:

0 = -$50 million + $25 million + ($34.22 million / (1 + 0.12)^3) + (X / (0.12 - X)) * (34.22 million / (1 + 0.12)^3) * (1 + X + X^2 + ...)

Solving for X gives us a minimum growth rate of 6.925 percent, which is option B.

Valuation of a Merger the Managers of BSW Inc