15: Solution
Chapter Raising Capital Page 505 Questions: 1, 3, 4, 5, 7 1. a. The new market value will be the current shares outstanding times the stock price plus the rights offered times the rights price, so: New market value = 500,000($81) + 60,000($70) = $44,700,000 b. The number of rights associated with the old shares is the number of shares outstanding divided by the rights offered, so: Number of rights needed = 500,000 old shares/60,000 new shares = 8.33 rights per new share c. The new price of the stock will be the new market value of the company divided by the total number of shares outstanding after the rights offer, which will be: PX = $44,700,000/(500,000 + 60,000) = $79.82 d. The value of the right Value of a right = $81.00 79.82 = $1.18 e. A rights offering usually costs less, it protects the proportionate interests of existing share-holders and also protects against underpricing.
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Using the equation we derived in Problem 2, part c to calculate the price of the stock ex-rights, we can find the number of shares a shareholder will have ex-rights, which is: PX = $74.80 = [N($81) + $40]/(N + 1) N = 5.613 The number of new shares is the amount raised divided by the per-share subscription price, so: Number of new shares = $20,000,000/$40 = 500,000 And the number of old shares is the number of new shares times the number of shares ex-rights, so: Number of old shares = 5.613(500,000) = 2,806,452
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4.
If you receive 1,000 shares of each, the profit is: Profit = 1,000($7) 1,000($5) = $2,000 Since you will only receive one-half of the shares of the oversubscribed issue, your profit will be: Expected profit = 500($7) 1,000($5) = $1,500 is This an example of the winners curse.
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Using X to stand for the required sale proceeds, the equation to calculate the total sale proceeds, including flotation costs is: X(1 .09) = $60,000,000 X = $65,934,066 required total proceeds from sale. So the number of shares offered is the total amount raised divided by the offer price, which is: Number of shares offered = $65,934,066/$21 = 3,139,717
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We need to calculate the net amount raised and the costs associated with the offer. The net amount raised is the number of shares offered times the price received by the company, minus the costs associated with the offer, so: Net amount raised = (10,000,000 shares)($18.20) 900,000 320,000 = $180,780,000 The company received $180,780,000 from the stock offering. Now we can calculate the direct costs. Part of the direct costs are given in the problem, but the company also had to pay the underwriters. The stock was offered at $20 per share, and the company received $18.20 per share. The difference, which is the underwriters spread, is also a direct cost. The total direct costs were: Total direct costs = $900,000 + ($20 18.20)(10,000,000 shares) = $18,900,000 We are given part of the indirect costs in the problem. Another indirect cost is the immediate price appreciation. The total indirect costs were: Total indirect costs = $320,000 + ($25.60 20)(10,000,000 shares) = $56,320,000 This makes the total costs: Total costs = $18,900,000 + 56,320,000 = $75,220,000
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The flotation costs as a percentage of the amount raised is the total cost divided by the amount raised, so: Flotation cost percentage = $75,220,000/$180,780,000 = .4161 or 41.61%
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