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Unformatted text preview: pany will have a value greater than the face value of debt in both states of the economy, so the value of the company’s debt is $125,000. e. There is a wealth transfer in this case. The combined equity value before the merger was $304,500, but the value of the equity in the merged company is only $297,000, a loss of $7,500 for stockholders. The value of the debt in the combined companies was only $117,500, but the value of debt in the merged company is $125,000 since there is no chance of default. The bondholders gained $7,500, exactly the amount the stockholders lost. If the value of Bentley’s debt before the merger is less than the lowest firm value, there is no coinsurance effect. Since there is no possibility of default before the merger, bondholders do not gain after the merger. f. 549 Challenge 17. a. To find the value of the target to the acquirer, we need to find the share price with the new growth rate. We begin by finding the required return for shareholders of the target firm. The earnings per share of the target are: EPSP = $640,000/500,000 = $1.28 per share The price per share is: PP = 10($1.28) = $12.80 And the dividends per share are: DPSP = $380,000/500,000 = $0.76 The current required return for Palmer shareholders, which incorporates the risk of the company is: RE = [$0.76(1.04)/$12.80] + .04 = .1018 The price per share of Palmer with the new growth rate is: PP = $0.76(1.06)/(.1018 – .06) = $19.30 The value of the target firm to the acquiring firm is the number of shares outstanding times the price per share under the new growth rate assumptions, so:
* VT = 500,000($19.30) = $9,647,904.19 b. The gain to the acquiring firm will be the value of the target firm to the acquiring firm minus the market value of the target, so: Gain = $9,647,904.19 – 500,000($12.80) = $3,247,904.19 c. The NPV of the acquisition is the value of the target firm to the acquiring firm minus the cost of the acquisition, so: NPV = $9,647,904.19 – 500,000($13) = $3,147,904.19 d. The most the acquiring firm should be willing to pay per share is the offer price per share plus the NPV per share, so: Maximum bid price = $13 + ($3,147,904.19/500,000) = $19.30 Notice that this is the same value we calculated earlier in part a as the value of the target to the acquirer. 550 e. The price of the stock in the merged firm would be the market value of the acquiring firm plus the value of the target to the acquirer, divided by the number of shares in the merged firm, so: PFP = ($40,600,000 + 9,647,904.19)/(1,000,000 + 150,000) = $43.69 The NPV of the stock offer is the value of the target to the acquirer minus the value offered to the target shareholders. The value offered to the target shareholders is the stock price of the merged firm times the number of shares offered, so: NPV = $9,647,904.19 – 150,000($43.69) = $3,093,829.73 f. g. Yes, the acquisition should go forward, and Plant should offer cash since the NPV is higher. Using the new growth rate in the dividend growth model, along with the dividend and required return we calculated earlier, the price of the target under these assumptions is: PP = $0.76(1.05)/(.1018 – .05) = $15.42 And the value of the target firm to the acquiring firm is:
* VP = 500,000($15.42) = $7,710,144.93 The gain to the acquiring firm will be: Gain = $7,710,144.93 – 500,000($15.42) = $1,310,144.93 The NPV of the cash offer is now: NPV cash = $7,710,144.93 – 500,000($13) = $1,210,144.93 And the new price per share of the merged firm will be: PFP = [$40,600,000 + 7,710,144.93]/(1,000,000 + 150,000) = $42.01 And the NPV of the stock offer under the new assumption will be: NPV stock = $7,710,144.93 – 150,000($42.01) = $1,408,821.68 Even with the lower projected growth rate, the stock offer still has a positive NPV. However, the NPV of the stock offer is now higher. Plant should purchase Palmer with a stock offer of 150,000 shares. 551 18. a. To find the distribution of joint values, we first must find the joint probabilities. To do this, we need to find the joint probabilities for each possible combination of weather in the two towns. The weather conditions are independent; therefore, the joint probabilities are the products of the individual probabilities. Possible states Rain-Rain Rain-Warm Rain-Hot Warm-Rain Warm-Warm Warm-Hot Hot-Rain Hot-Warm Hot-Hot Joint probability .1(.1) = .01 .1(.4) = .04 .1(.5) = .05 .4(.1) = .04 .4(.4) = .16 .4(.5) = .20 .5(.1) = .05 .5(.4) = .20 .5(.5) = .25 Next, note that the revenue when rainy is the same regardless of which town. So, since the state "Rain-Warm" has the same outcome (revenue) as "Warm-Rain", their probabilities can be added. The same is true of "Rain-Hot" / "Hot-Rain" and "Warm-Hot" / "Hot-Warm". Thus the joint probabilities are: Possible states Rain-Rain Rain-Warm Rain-Hot Warm-Warm Warm-Hot Hot-Hot Joint probability .01 .08 .10 .16 .40 .25 Finally, the joint values are the sums of the values o...
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