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 minimum growth rate needed after the first three years such that BSW Inc. would see this merger as a positive NPV project, we need to determine the present value of the cash flows for the merged firm and compare it to the purchase price of $50 million asked by EAG Corp.

First, we need to calculate the cash flows for the first three years:
CF1 = $2.5 million x (1 + 0.02 + 0.05) = $2,762,500
CF2 = $2.5 million x (1 + 0.02 + 0.05)^2 = $3,036,563
CF3 = $2.5 million x (1 + 0.02 + 0.05)^3 = $3,334,699

Next, we need to calculate the cash flows for the long-term period:
CF4 = $3,334,699 x (1 + g)
CF5 = $3,334,699 x (1 + g)^2
CF6 = $3,334,699 x (1 + g)^3
...
where g is the growth rate in cash flows beyond the first three years.

The present value of the cash flows at the end of year 3 is:
PV3 = CF3 / (WACC - 0.05) = $3,334,699 / (0.12 - 0.05) = $48,677,839.11

The present value of the long-term cash flows is:
PV4 = CF4 / (WACC - g)
PV5 = CF5 / (WACC - g)
PV6 = CF6 / (WACC - g)
...
PV_longterm = PV4 + PV5 + PV6 + ... = CF4 / (WACC - g) x [1 / (1 + WACC - g) + 1 / (1 + WACC - g)^2 + 1 / (1 + WACC - g)^3 + ...]
PV_longterm = $3,334,699 x (1 + g) / (WACC - g) x [1 / (1 + WACC - g) + 1 / (1 + WACC - g)^2 + 1 / (1 + WACC - g)^3 + ...]

To find the minimum growth rate that makes the NPV of the project zero, we need to solve for g in the following equation:
$50,000,000 = PV3 + PV_longterm

Substituting the values we get:

$50,000,000 = $48,677,839.11 + $3,334,699 x (1 + g) / (WACC - g) x [1 / (1 + WACC - g) + 1 / (1 + WACC - g)^2 + 1 / (1 + WACC - g)^3 + ...]

Simplifying the equation we get:

326,160.89 = 3,334,699 x (1 + g) / (WACC - g) x [1 / (WACC - g)]
326,160.89 = 3,334,699 / (WACC - g)^2 x (1 + g)

Solving for g using a financial calculator or trial and error, we get g = 6.925%.

Therefore, the minimum growth rate needed after the first three years would be 6.925% to make this merger a positive NPV project for BSW Inc.

Valuation of a Merger the Managers of BSW Inc