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Unformatted text preview: ale proceeds, including flotation costs is: X(1 – .08) = $35,000,000 X = $38,043,478 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 = $38,043,478/$31 = 1,227,209 6. This is basically the same as the previous problem, except we need to include the $900,000 of expenses in the amount the company needs to raise, so: X(1 – .08) = $35,900,000 X = $39,021,739 required total proceeds from sale. Number of shares offered = $39,021,739/$31 = 1,258,766 7. 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: 413 Net amount raised = (8,000,000 shares)($22.10) – 950,000 – 250,000 = $175,600,000 The company received $175,600,000 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 $24 per share, and the company received $22.10 per share. The difference, which is the underwriters spread, is also a direct cost. The total direct costs were: Total direct costs = $950,000 + ($24 – 22.10)(8,000,000 shares) = $16,150,000 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 = $250,000 + ($29.50 – 24)(8,000,000 shares) = $44,250,000 This makes the total costs: Total costs = $16,150,000 + 44,250,000 = $60,400,000 The flotation costs as a percentage of the amount raised is the total cost divided by the amount raised, so: Flotation cost percentage = $60,400,000/$175,600,000 = .3440 or 34.40% 8. The number of rights needed per new share is: Number of rights needed = 100,000 old shares/20,000 new shares = 5 rights per new share. Using PRO as the rights-on price, and PS as the subscription price, we can express the price per share of the stock ex-rights as: PX = [NPRO + PS]/(N + 1) a. b. c. 9. PX = [5($80) + $80]/6 = $80.00; PX = [5($80) + $75]/6 = $79.17; PX = [5($80) + $65]/6 = $77.50; No change. Price drops by $0.83 per share. Price drops by $2.50 per share. In general, the new price per share after the offering will be: P= Current market value + Proceeds from offer Old shares + New shares The current market value of the company is the number of shares outstanding times the share price, or: Market value of company = 30,000($40) Market value of company = $1,200,000 414 If the new shares are issued at $40, the share price after the issue will be:
$1,200,000 + 8,000($40) 30,000 + 8,000 P = $40.00 P= If the new shares are issued at $20, the share price after the issue will be:
$1,200,000 + 8,000($20) 30,000 + 8,000 P = $35.79 P= If the new shares are issued at $10, the share price after the issue will be:
$1,200,000 + 8,000($10) 30,000 + 8,000 P = $33.68 P= Intermediate 10. a. The number of shares outstanding after the stock offer will be the current shares outstanding, plus the amount raised divided by the current stock price, assuming the stock price doesn’t change. So: Number of shares after offering = 8,000,000 + $40,000,000/$65 = 8,615,385 Since the par value per share is $1, the old book value of the shares is the current number of shares outstanding. From the previous solution, we can see the company will sell 615,385 shares, and these will have a book value of $65 per share. The sum of these two values will give us the total book value of the company. If we divide this by the new number of shares outstanding. Doing so, we find the new book value per share will be: New book value per share = [8,000,000($20) + 615,385($65)]/8,615,385 = $23.21 The current EPS for the company is: EPS0 = NI0/Shares0 = $11,500,000/8,000,000 shares = $1.44 per share And the current P/E is: (P/E)0 = $65/$1.44 = 45.22 If the net income increases by $600,000, the new EPS will be: EPS1 = NI1/shares1 = $12,100,000/8,615,385 shares = $1.40 per share 415 Assuming the P/E remains constant, the new share price will be: P1 = (P/E)0(EPS1) = 45.22($1.40) = $63.51 The current market-to-book ratio is: Current market-to-book = $65/$20 = 3.25 Using the new share price and book value per share, the new market-to-book ratio will be: New market-to-book = $63.51/$23.21 = 2.7357 Accounting dilution has occurred because new shares were issued when the market-to-book ratio was less than one; market value dilution has occurred because the firm financed a negative NPV project. The cost of the project is given at $40 million. The NPV of the project is the new market value of the firm minus the current market value of the firm, or: NPV = –$40,000,000 + [8,615,385($63.51) – 8,000,000($65)] = –$12,869,565 b. For the price to remain unchanged when the P/E ratio is constant, EPS must remain constant. The new net income must be the new number of shares outstanding times the current EPS, which gives: NI1 = (8,615,385 shares)($1.44 per share) = $12,384,615 11. The current ROE of the company is: ROE0 = NI0/TE0 = $630,000/($6,500,000 – 2,600,000) = .1620 or 16.20% The new net income will be the...
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