Ec 1745 Problem Set 7

Tarun Singh Worked with Richard Gong Ec 1745 Problem Set 7 1. A) Since the total value of assets is $250 million and the market value of the existing debt decreases by $30 million so therefore the equity increases by $30 million to $180 million. Price = Equity/# of shares Price = $180 million/ 15 million → Price = $12 per share B) At a market price of $12 per share the company can buy back ($60 million/ $12)= 5 million shares. C) Market Value = Equity + Debt Equity: The company bought back 5 million shares, so there are only 10 million shares in the market @ $12 per share so equity is worth (10 million x $12) = $120 million. Debt: The market value of the existing debt went down to $70 million and the company issued $60 million more in debt so there is now ($70 million + $60 million) = $130 million in debt. Thus the market value of the company is ($120 million + $130 million) = $250 million; the market value remains unchanged. D) Debt ratio = Debt/(Debt + Equity) $130 million/$250 million = .52 E) Shareholders gain $30 million from the price increase in the stock while existing debt holders actually lose $30 million from the market value of the existing debt falling from $100 million to $70 million. 2. A) Equity = $80 with 50% chance and $40 with 50% chance Debt = $0 L = max (0, ((($80+$40)/2)/2)) = $30 B) L = max (0, ((($80-$50)/2)/2)) + max (0, ((($40-$50)/2)/2)) = $7.50 C) L = max (0, ((($100-$59)/2)/2)) + max (0, ((($60-$59)/2)/2)) = $10.50 The firm would take the project as it increases the firm’s value D) L = max (0, ((($80-$30)/2)/2)) + max (0, ((($40-$30)/2)/2)) = $15 w/ project: L = max (0, ((($100-$39)/2)/2)) + max (0, ((($60-$39)/2)/2)) = $20.50 The firm would still take the project as it increases the firm’s value

E) This problem shows that with less debt companies are able to obtain higher value because the debt does not exceed all the vale in these cases meaning there is more value left over. 3. A) P = 100p+40(1-p)+1 = 60p+41 Shareholders retain: (1-(.5/(60p+41)))(100+1) Shareholders have to retain > 100 if a VH firm issues equity, otherwise it will send a negative signal to shareholders and shareholders will think the firm is actually a VL firm. → (1-(.5/(60p+41)))(101)>100 (1-(.5/(60p+41)))>(100/101) → 60p>9.5 → p>.1583 B) A VL firm will issue equity if issuing equity will cause shareholders to retain >40 since it’s real value is only 40. p=.05 → P=60(.05)+41 =44 Shareholders retain: (1-(.5/44))(41) = 40.534 Since 40.534>40 the VL firm will issue equity C) At p=.1 the VL firm issues equity but the VH firm does not. The VH firm needs p>.1583 to issue equity. p=.1 → P0=60(.1)+40 = 46 By issuing equity when p=.1 investors will know that the firm is a V L firm and thus p=0 in which case the value of the firm P1=60(0)+40+1=41 Thus the value of the firm goes from 46 to 41, a change of -5 4. A) P0= $20 million/1 million shares = $20 per share → $20 million=$1million/(r-.05) → r=.10 Total Equity=$1.05million/(.10-.05)=$21 million Total Equity= (P1(1 million+X shares)) = $21 million P1 million + XP= $21 million We know XP = $1 million → P1 million= $20 million so P1=$20 B) $1 million/$20 per share = 50,000 shares The firm would have to issue 50,000 new shares C) Including the 50,000 new shares, the total dividends will be divided up into 1.05 million shares. Since the total dividends at t=2 will be $1.05 million, the dividends per share will be $1 and will increase by 5% each year. D) Current shareholders get $2 per share in year one and $1 per share in year two which then grows at 5%. PV = ($2 million/1.1) + ($1 million/((.1-.05)(1.10))) = $20 million