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 $20.5 million to be purchased by BSW Inc. The two firms currently have cumulative total cash flows of $1 million that are growing at 3 percent annually. Managers of EAG estimate that because of synergies the merged firm's cash flows will increase by an additional 4 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 8 percent. Managers of BSW Inc. agree that cash flows should grow at an additional 4 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 determine the NPV of the merger, we need to calculate the present value (PV) of all the cash flows associated with the merger, including the price of $20.5 million that BSW Inc. would pay to acquire EAG Corp.

PV of cash flows in years 0-3:

CF(0-3) = $1,000,000 x (1.03)^0 + $1,040,000 x (1.03)^1 + $1,081,600 x (1.03)^2 + $1,124,864 x (1.03)^3 = $4,347,816

PV of cash flows after year 3:

CF(4-infinity) = $1,168,711 x (1.02)/(0.08 - 0.02 - 0.04) = $64,236,065

PV of price paid for EAG Corp.:

Price = $20.5 million

PV = $20,500,000 / (1.08)^0 = $20,500,000

Thus, the total PV of cash flows associated with the merger is:

Total PV = $4,347,816 + $64,236,065 + (-$20,500,000) = $48,083,881

To make this a positive NPV project, the present value of expected cash flows must exceed the amount that BSW Inc. would pay for EAG Corp., or $20.5 million.

Solving for the growth rate after year 3 that makes the total PV equal to $20.5 million:

$20,500,000 = $4,347,816 x (1.08)^3 + $64,236,065 x (1+g)^3

$20,500,000 = $59,303,310 + $64,236,065 x (1+g)^3

$4,932,755 = $64,236,065 x (1+g)^3

1+g = (4,932,755 / 64,236,065)^(1/3)

1+g = 0.934

g = -0.066

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:

g = 2% (the long-term growth rate estimated by EAG) + 4% (additional growth rate for the first three years) + 2% (minimum growth rate needed after year 3) = 8%

However, since the managers of BSW Inc. are unsure of the long-term growth rate estimated by EAG, we need to solve for the minimum growth rate that would make the merger a positive NPV project for any long-term growth rate:

$20,500,000 = $4,347,816 x (1.08)^3 + $64,236,065 x (1+g)^3

$20,500,000 = $59,303,310 + $64,236,065 x (1+g)^3

$4,932,755 = $64,236,065 x (1+g)^3

1+g = (4,932,755 / 64,236,065)^(1/3)

1+g = 0.934

g = -0.066

Therefore, the minimum growth rate needed after the first three years such that BSW Inc. would see this merger as a positive NPV project for any long-term growth rate is:

g = 2% (minimum growth rate needed after year 3) = 2.82%

Hence, the answer is B.

Valuation of a Merger the Managers of BSW Inc