FINA 469 Calculation problems

Assume you purchased 500 shares of XYZ common stock on margin at $40 per share from your broker. If the initial margin is 60%, the amount you borrowed from the broker is:

$8,000 Stock Value = 500*$40 = $20,000 Initial Margin = 60% Max can be borrowed = Stock Value*(1-IMR)

The Hydro Index is a price weighted stock index based on the 5 largest boat manufacturers in the nation. The stock prices for the five stocks are $10, $20, $80, $50 and $40. The price of the last stock was just split 2 for 1 and the stock price was halved from $40 to $20. What is the new divisor for a price weighted index?

4.50 Index(0) = ($10+$20+$80+50+$40)/5 = 40 Index(1) = ($10+$20+$80+$50+$20)/X = 40 X = 4.50

An investor purchases one municipal bond and one corporate bond that pay rates of return of 5% and 6.4%, respectively. If the investor is in the 15% tax bracket, his after-tax rates of return on the municipal and corporate bonds would be, respectively:

5% and 5.44% After-tax return on municipal bond = .05 After-tax return on corporate bond = .064(1 - .15) = .0544 = 5.44%

A benchmark index has three stocks priced at $23, $43, and $56. The number of outstanding shares for each is 350,000 shares, 405,000 shares, and 553,000 shares, respectively. If the market value weighted index was 970 yesterday and the prices changed to $23, $41, and $58 today, what is the new index value?

975 Index = {[($23*350,000)+($41*405,000)+($58*553,000)] / [($23*350,000)+($43*405,000)+($56*553,000)]} * 970 = 975

Buying On Margin Stock Price = $100 50% initial Margin Interest rate on loan 9% 200 shares purchased Case 1: Stock price rises to $130 after 1 year what is your return? Case 2: Stock Price Lowers to $70 after 1 year what is your return?

Initial Position Market Value = $20,000 Borrowed = $10,000 Equity = $10,000 Case 1: Market Value = $26,000 Borrowed = $10,000 Equity = $16,000 Interest Due = $10,000*9% Return = 51% Case 2: Market Value = $14,000 Borrowed = $10,000 Equity = $4,000 Interest Due = $10,000*9% Return = -69% Return = End Account Balance / Initial Investment by Borrower

You short-sell 200 shares of Tuckerton Trading Co., now selling for $50 per share. What is your maximum possible gain, ignoring transactions cost?

Tuckerton could go bankrupt making the share price $0. You could keep entire proceeds from the short sale Maximum Gain = Proceeds - Minimum possible replacement cost Maximum Gain = (200*$50) - (200*$0)

You sell short 200 shares of Doggie Treats Inc. that are currently selling at $25 per share. You post the 50% margin required on the short sale. If your broker requires a 30% maintenance margin, at what stock price will you get a margin call? (You earn no interest on the funds in your margin account, and the firm does not pay any dividends.)

Account at the time of short sale: Cash from SS = $5,000 Cash for Equity = $2,500 Total Assets = $7,500 Liability = $5,000 Equity = $2,500 Total Liability + Equity = $7,500 Account as prices change: Cash from SS = $5,000 Cash for Equity = $2,500 Total Asset = $7,500 Liability = 200P Equity = $7,500 - 200P Total Liability + Equity = $7,500 Margin Call if Equity/Market Value = 0.30 0.30=($7,500-200P)/200P P=$28.85

You short-sell 200 shares of Rock Creek Fly Fishing Co., now selling for $50 per share. If you want to limit your loss to $2,500, you should place a stop-buy order at

Amount received from short sale = 200 * $50 = $10,000 Loss = $2,500 = 200P-$10,000 P = $62.50

An investor buys $8,000 worth of a stock priced at $40 per share using 50% initial margin. The broker charges 6% on the margin loan and requires a 30% maintenance margin. In 1 year the investor has interest payable and gets a margin call. At the time of the margin call the stock's price must have been

Initial Position Stock Value = $8,000 Total Asset = $8,000 Loan = $4,000 Equity = $4,000 Loan + Equity = $8,000 After one year Stock Value = 200P Total Assets = 200P Loan = $4,000 Interest Due (0.06*$4,000) = $240 Equity = Current Position - Borrowed + additional Cash = 200P - $4,000 + (-240) The stock price for a Margin Call at 30% will be: Equity/Market Value < MMR (200P-$4,000-$240)/200P < 0.30 60P < 200P - $4240 P<$30.29 per share

An investor buys $16,000 worth of a stock priced at $20 per share using 60% initial margin. The broker charges 8% on the margin loan and requires a 35% maintenance margin. The stock pays a $.50-per-share dividend in 1 year, and then the stock is sold at $23 per share. What was the investor's rate of return?

Initial investment by investor = 0.60 * $16,000 = $9,600 Value of stock in 1 year = $18,400 Dividends received = 400 Interest Due = 512 Loan Payoff = (1-0.60)*16,000 = 6,400 Ending account balance = $18,400+400-512-6,400 = $11,888 Return = Ending account balance / Initial investment by investor = $11,888 / $9,600 = 23.86%

The margin requirement on a stock purchase is 25%. You fully use the margin allowed to purchase 100 shares of MSFT at $25. If the price drops to $22, what is your percentage loss?

Loss = (22-25)*100 = -$300 Amount Invested = 0.25*$25*100 = $625 Return = $300/$625 = -48%

Assume that you have just purchased some shares in an investment company reporting $500 million in assets, $50 million in liabilities, and 50 million shares outstanding. What is the net asset value (NAV) of these shares?

NAV = (Assets-Liabilities)/Outstanding shares NAV = $9

A T-bill quote sheet has 90-day T-bill quotes with a 4.92% bank discount rate (in other words 4.86% bid). If the bill has a $10,000 face value, an investor could buy this bill for:

P = $9,878.50 0.0486 = [((10,000 - P)/10,000) * (360/90)]

Buying on Margin: X Corp stock price = $70 50% initial margin 40% maintenance margin 1000 shares purchased a) What is your initial position? b) What is your position if stock falls below $60 per share c) How far can price fall before margin call d) To restore IMR what is the new equity level?

a) Initial Position: Market Value of stock = $70*10,000 = $70,000 Borrowed = 0.50 * $70,000 = $35,000 Equity = 0.50 * $70,000 b) New Position @ $60 per share: Market Value = $60 * 10,000 = $60,000 Borrowed = $35,000 Equity = Position Value - Borrowing + Additional Cash = $60,000 - $35,000 + $0 = $25,000 Margin = Equity in account/Value of stock = $25,000/$60,000 = 41.67% No Margin Call yet c) Stock Price Margin Call of 40% will occur at: Margin Call occurs: Market Value = Borrowed / (1-MMR) Market Value = $35,000 / (1-0.40) Market Value = $58,333 Margin Call will occur when stock price drops below $58.33 per share Position at Margin Call Market Value = $58,333 Borrowed = $35,000 Equity = $23,000 d) to restore IMR Equity must be 50% of market value: Equity = 0.50*Market Value = 0.50*$58,333 = $29,166.50 must be in account equity Must add = $29,166.50 - $23,333 = $5.833.50

Short Sale 1,000 shares of Dot Bomb stock at $100 per share IMR = 50% MMR = 30% a) How much do you have in your broker's account? b) What is your percentage margin? c) what price does the stock have to rise to for a margin call

a) account with the broker after short sale will be: Assets: Cash: $100,000 from Short Sell Your own cash: $50,000 Liabilities: Owe Dot Bomb Stock: $100,000 = 1,000 shares * $100 per share Equity: $50,000 b) Percentage Margin = Equity/Value of stock owed Percentage Margin = $50,000/$100,000 = 50% c) MMR of 30%: Position at Margin Call Assets: $100,000 Cash in account: $50,000 Total Assets: $150,000 Liabilities: Owe DB stock: 1000P Equity: $150,000-1000P Total Liabilities + Equity = $150,000 Margin call occurs when: Equity/Value of shares = 0.30 ($150,000 - 1,000P)/1,000P = 0.30 P = $115.38 for a margin call