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 to 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.
A) 5.00 percent
B) 6.925 percent
C) 1.728 percent
D) 12.00 percent

Question

Quizplus · Accepted Answer

To determine the minimum growth rate needed after the first three years for the merger to have a positive NPV, we first calculate the present value (PV) of the cash flows for the first three years using the given growth rate of 5% and then find the growth rate needed for the cash flows after the first three years to justify the $50 million purchase price.1. Calculate the cash flows for the first three years with a 5% growth rate:- Year 1: $2.5M * (1 + 5%) = $2.625M- Year 2: $2.625M * (1 + 5%) = $2.75625M- Year 3: $2.75625M * (1 + 5%) = $2.8940625M2. Calculate the present value of these cash flows using the WACC of 12%:- PV Year 1: $2.625M / (1 + 12%)^1 = $2.34375M- PV Year 2: $2.75625M / (1 + 12%)^2 = $2.19777M- PV Year 3: $2.8940625M / (1 + 12%)^3 = $2.05986M3. Calculate the terminal value at the end of Year 3, assuming a constant growth rate g after Year 3. The terminal value formula is: TV = (Cash Flow Year 3 * (1 + g)) / (WACC - g). We set this equal to the remaining value needed to justify the $50M purchase price minus the PV of the cash flows from the first three years.4. Solve for g, the growth rate after Year 3, that makes the NPV of the project equal to zero (or makes the total PV of cash flows and terminal value equal to $50M). This involves setting up the equation based on the NPV formula and solving for g, which requires iterative calculation or financial calculator/software.Given the complexity of the calculation and the need for iterative solving, the correct answer is B) 6.925 percent, which is the growth rate that would make the present value of future cash flows from the merger (including the increased growth rate in the first three years and the minimum required growth rate afterward) equal or exceed the $50 million purchase price, thus resulting in a positive NPV for BSW Inc.

The Managers of BSW Inc