Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

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Unformatted text preview: is the value of the target minus the cost, we get: NPV NPV NPV NPV 14. a. * = VB – Cost = ∆ V + VB – Cost = ∆ V – (Cost – VB) = ∆ V – Merger premium The synergy will be the present value of the incremental cash flows of the proposed purchase. Since the cash flows are perpetual, the synergy value is: Synergy value = \$500,000 / .08 546 b. Synergy value = \$6,250,000 The value of Flash-in-the-Pan to Fly-by-Night is the synergy plus the current market value of Flash-in-the-Pan, which is: Value = \$6,250,000 + 10,000,000 Value = \$16,250,000 c. The value of the cash option is the amount of cash paid, or \$13 million. The value of the stock acquisition is the percentage of ownership in the merged company, times the value of the merged company, so: Stock acquisition value = .30(\$16,250,000 + 26,000,000) Stock acquisition value = \$12,675,000 d. The NPV is the value of the acquisition minus the cost, so the NPV of each alternative is: NPV of cash offer = \$16,250,000 – 13,000,000 NPV of cash offer = \$3,250,000 NPV of stock offer = \$16,250,000 – 12,675,000 NPV of stock offer = \$3,575,000 e. 15. a. The acquirer should make the stock offer since its NPV is greater. The number of shares after the acquisition will be the current number of shares outstanding for the acquiring firm, plus the number of new shares created for the acquisition, which is: Number of shares after acquisition = 30,000,000 + 12,000,000 Number of shares after acquisition = 42,000,000 And the share price will be the value of the combined company divided by the shares outstanding, which will be: New stock price = £720,000,000 / 42,000,000 New stock price = £17.14 b. Let α equal the fraction of ownership for the target shareholders in the new firm. We can set the percentage of ownership in the new firm equal to the value of the cash offer, so: α(£720,000,000) = £205,000,000 α = .2847 or 28.47% So, the shareholders of the target firm would be equally as well off if they received 28.47 percent of the stock in the new company as if they received the cash offer. The ownership percentage of the target firm shareholders in the new firm can be expressed as: Ownership = New shares issued / (New shares issued + Current shares of acquiring firm) .2847 = New shares issued / (New shares issued + 30,000,000) New shares issued = 11,941,748 547 To find the exchange ratio, we divide the new shares issued to the shareholders of the target firm by the existing number of shares in the target firm, so: Exchange ratio = New shares / Existing shares in target firm Exchange ratio = 11,941,748 / 20,000,000 Exchange ratio = .5971 An exchange ratio of .5971 shares of the merged company for each share of the target company owned would make the value of the stock offer equivalent to the value of the cash offer. 16. a. The value of each company is the sum of the probability of each state of the economy times the value of the company in that state of the economy, so: ValueBentley = .70(\$280,000) + .30(\$100,000) ValueBentley = \$226,000 ValueRolls = .70(\$250,000) + .30(\$70,000) ValueRolls = \$196,000 b. The value of each company’s equity is sum of the probability of each state of the economy times the value of the equity in that state of the economy. The value of equity in each state of the economy is the maximum of total company value minus the value of debt, or zero. Since Rolls is an all equity company, the value of its equity is simply the total value of the firm, or \$196,000. The value of Bentley’s equity in a boom is \$155,000 (\$280,000 company value minus \$125,000 debt value), and the value of Bentley’s equity in a recession is zero since the value of its debt is greater than the value of the company in that state of the economy. So, the value of Bentley’s equity is: EquityBentley = .70(\$155,000) + .30(\$0) EquityBentley = \$108,500 The value of Bentley’s debt in a boom is the full face value of \$125,000. In a recession, the value of the company’s debt is \$100,000 since the value of the debt cannot exceed the value of the company. So, the value of Bentley’s debt today is: DebtBentley = .70(\$125,000) + .30(\$100,000) DebtBentley = \$117,500 Note, this is also the value of the company minus the value of the equity, or: DebtBentley = \$226,000 – 108,500 DebtBentley = \$117,500 548 c. The combined value of the companies, the combined equity value, and combined debt value is: Combined value = \$226,000 + 196,000 Combined value = \$422,000 Combined equity value = \$108,500 + 196,000 Combined equity value = \$304,500 Combined debt value = \$117,500 d. To find the value of the merged company, we need to find the value of the merged company in each state of the economy, which is: Boom merged value = \$280,000 + 250,000 Boom merged value = \$530,000 Recession merged value = \$100,000 + 70,000 Recession merged value = \$170,000 So, the value of the merged company today is: Merged company value = .70(\$530,000) + .30(\$170,000) Merged company value = \$422,000 Since the merged company will still have \$125,000 in debt, the value of the equity in a boom is \$405,000, and the value of equity in a recession is \$45,000. So, the value of the merged company’s equity is: Merged equity value = .70(\$405,000) + .30(\$45,000) Merged equity value = \$297,000 The merged com...
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