BKM Ch 03 Answers w CFA

CHAPTER 3: HOW SECURITIES ARE TRADED 2.

Who sets the bid and asked price for a stock traded over the counter (OTC)? Would you expect the spread to be higher on actively or inactively traded stocks? OTC stock markets are dealer markets (as opposed to “exchange markets” like the NYSE). In dealer markets, the dealer buys the asset from the seller and then holds the assets until he or she is able find a buyer. The dealer’s profit comes from buying at the bid and selling at the ask. The difference between the bid and ask is called the spread. Since all transactions are between sellers and dealers or buyers and dealers, the prices are set by the dealers. Active stocks will have more dealers. To compete for business, dealers will decrease the profit margin and therefore quote smaller (tighter) spreads. Spreads will be larger for inactively traded stocks and smaller on actively traded stocks.

3.

Suppose you short sell 100 shares of IBM, now selling at $120 per share. (a) What is your maximum possible loss? Potential losses from a short position are unbounded, since the price can go infinitely high. (b) What happens to the maximum loss if you simultaneously place a stop-buy order at $128? The stop-buy order (also known as a “stop-loss buy order to go flat”) becomes a market buy order if the stock trades at or above $128. If the order is filled at $128, the maximum loss per share is $8. If the price of IBM shares goes above $128 before it is filled, the loss would be greater.

4.

A market order has: The answer is (a) – Price uncertainty but not execution uncertainty. A market order is an order to execute the trade immediately at the best possible or current market price. An advantage is immediate execution. The disadvantage is that the price at which it will be executed at is not known ahead of time (price uncertainty).

5.

Where would an illiquid security in a developing country most likely trade? Given these three choices, the answer is broker market. Brokers would mitigate search costs in illiquid markets by finding a counter party for the security. In the US, many illiquid bonds trade through broker markets. A portfolio manager will contact their representative at a bank with the desire to sell an issue. The broker will contact other clients to try to place the bond. The broker will either earn a commission or a spread or both. The broker can also mitigate information asymmetry in illiquid markets by only dealing in “reputable” securities. It might be the case that the bank representative acts a dealer and buys the security from the portfolio manager. Here the dealer is providing liquidity. The dealer is compensated by paying a lower price for the bond with the expectation of selling it later for a higher price (earning a large spread). The spread compensates the dealer for risk incurred while holding the bond and for the commitment of capital – having the money available to buy the bond and hold it in inventory. Dealers can also mitigate information asymmetry by only dealing in “reputable” securities. Electronic Limit-Order Markets (ELOM), such as the market for most stocks in the US, are markets which collect and sort by price and time priority limit orders placed by market participants. ELOM are useful in more liquid markets where many buyers and sellers are present and information costs are lower (buyers and sellers are informed about the securities). Continuous auctions with many market participants placing buy and sell limit orders creates tighter spreads than those typically found on broker or dealer markets. The ELOM charges a fee to transact on the market instead of earning the spread. The text uses the term “Electronic Crossing Networks” but the more common names are Electronic Communications Network (ECN) and Crossing Network. Both are more useful in liquid markets.

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Electronic Communications Network (ECN) is a broad term encompassing pretty much any market system that does not require placing an order with a person. So an ELOM is an ECN but some ECNs are not ELOM. For example, some ECNs (called “dark pools”) allow market participants to anonymously place an order for a stock. The order will be executed with a counter party on the ECN at a price equal to the average price traded for the stock on all the other markets over a five minute period. This can be useful because the market participant can execute large a order without affecting the public quote. For example, if a mutual fund wants to sell a large stock position and places a limit sell order on an ELOM book, the presence of that order might cause buyers to reconsider and lower the price at which the shares can be sold. The terms Alternative Trading System (ATS) is often used to describe ECNs that are not ELOMs. True broker markets still exist for small stocks in the US which do not meet NASDAQ or NYSE listing requirements. These stocks are traded on the OTCBB or Pink Sheet markets. They are illiquid and have high information asymmetry. 6.

Dée Trader opens a brokerage account and purchases 300 shares of Internet Dreams at $40 per share. She borrows $4,000 from her broker to help pay for the purchase. The interest rate on the loan is 8% (a) What is the margin in Dée's account when she first purchases the stock The stock is purchased for 300  $40 = $12,000 The amount borrowed is $4,000. Therefore, the investor put up equity $8,000 The margin rate is 8,000/12,000 = 66.67% (b) If the share price falls to $30 per share by the end of the year, what is the remaining margin in her account? If the maintenance margin requirement is 30%, will she receive a margin call? If the share price falls to $30, then the value of the stock falls to $9,000. By the end of the year, the amount of the loan owed to the broker grows to: $4,000  1.08 = $4,320 Therefore, the remaining margin in the investor’s account is: $9,000  $4,320 = $4,680 The percentage margin is now: $4,680/$9,000 = 0.52 = 52% Therefore, the investor will not receive a margin call. (c) What is the rate of return on her investment? The rate of return on the investment over the year is: (Ending equity in the account  Initial equity)/Initial equity = ($4,680  $8,000)/$8,000 = 0.415 = 41.5%

7.

Old Economy Traders opened an account to short sell 1,000 shares of Internet Dreams from the previous problem. The initial margin requirement was 50%. (The margin account pays no interest.) A year later, the price of Internet Dreams has risen from $40 to $50, and the stock has paid a dividend of $2 per share. (a) What is the remaining margin in the account? (See the calculations below) The trader put up $20,000 The trader lost $10,000 in the share price move ($10 x 1000) The trader paid $2,000 in dividends ($2 x 1000) Ending Equity = $20,000 - $10,000 - $2,000 = $8,000 (b) If the maintenance margin requirement is 30%, will Old Economy receive a margin call? Margin Rate = Equity / Liability is: $8,000/$50,000 = 0.16 = 16% So there will be a margin call. (c) What is the rate of return on her investment? The equity in the account decreased from $20,000 to $8,000 in one year. 2

Return = -$12,000/$20,000 = -0.60 = -60% Calculations: Beginning of the Year: Assets Cash from Stock Sale = $40 x 1000 = $40,000 Margin Cash = $20,000 Total Assets = $60,000

Liabilities & Equity Value of Stocks Owed = 1000 x $40 = $40,000 Equity = $60,000 - $40,000 = $20,000

Margin Rate = Equity/Value of Stocks Owed = Equity/(Shares x P) Margin Rate = $20,000/(1000 x $40) = 0.50 End of the Year: Price = $50 Dividend Payable = 1000 x $2 = $2,000 Assets Cash from Stock Sale = $40 x 1000 = $40,000 Margin Cash = $20,000 Total Assets = $60,000

Liabilities & Equity Value of Stocks Owed = 1000 x $50 = $50,000 Div Payable = $2,000 Equity = $60,000 - $50,000 - $2,000 = $8,000

Once the Dividend is Paid: Assets Cash from Stock Sale = $40 x 1000 = $40,000 Margin Cash = $20,000 - $2,000 = $18,000 Total Assets = $58,000

Liabilities & Equity Value of Stocks Owed = 1000 x $50 = $50,000 Equity = $58,000 - $50,000 = $8,000

Margin Rate = Equity/Value of Stocks Owed = Equity/(Shares x P) Margin Rate = $8,000/(1000 x $50) = 0.16 8.

Consider the following limit-order book of a specialist. The last trade in the stock occurred at a price of $50. Limit Buy Orders Limit Sell Orders Price Shares Price Shares $49.75 500 $50.25 100 $49.50 800 $51.50 100 $49.25 500 $54.75 300 $49.00 200 $58.25 100 $48.50 600 (a) If a market buy order for 100 shares comes in, at what price will it be filled? At the best (lowest) limit-sell order price: $50.25 (b) At what price would the next market buy order (after the 100 shares in part (a)) be filled? At the next-best limit-sell order price: $51.50 (c) If you were the specialist, would you want to increase or decrease your inventory of this stock? You would want to increase your inventory. There is considerable buying demand at prices just below $50, indicating that downside risk is limited. In contrast, limit sell orders are sparse. If the assumption is that there is equal probability that the next order will be either a buy or sell, then the price is more likely to rise a lot since a moderate size buy order (501 shares) would result in a price increase to $58.25 while a moderate size sell order (501 shares) would cause the price to drop to $49.50. So the point of the question is to recognize that the sell-side of the limit-order book is very thin and the buy-side is deep. HOWEVER, how can the market maker increase his or her position in the stock without affecting the limit order book? That is not easily answered. 3

9.

You are bullish on Telecom stock. The current market price is $50 per share, and you have $5,000 of your own to invest. You borrow an additional $5,000 from your broker at an interest rate of 8% per year and invest $10,000 in the stock. (a) What will be your rate of return if the price of Telecom stock goes up by 10% during the next year? The stock currently pays no dividends. Increase in share value = 10% x $10,000 = $1,000 Interest Expense = 8%  $5,000 = $400 Return = ($1,000 - $400)/$5,000 = 0.12 = 12.00% (b) How far does the price of Telecom stock have to fall for you to get a margin call if the maintenance margin is 30%? Assume the price fall happens immediately. The value of the Assets is the value of the 200 shares (200P). Liabilities = Loan amount = $5,000 Margin Rate = Equity/Assets = (Assets – Liabilities)/Assets = (200P – $5,000)/200P You will receive a margin call if Margin Rate < 0.30 Margin Call if (200P – $5,000)/200P < 0.30 Solve for P: Margin call if P < $35.71

10. You are bearish on Telecom and decide to sell short 100 shares at the current market price of $50 per share. (a) How much in cash or securities must you put into your brokerage account if the broker's initial margin requirement is 50% of the value of the short position? Initial Margin = 50% x 100 x $50 = $2,500. (b) How high can the price of the stock go before you get a margin call if the maintenance margin is 30% of the value of the short position? Total assets are $7,500 ($5,000 from the sale of the stock and $2,500 put up for margin). Liabilities are 100P. Equity is ($7,500 – 100P). A margin call if ($7,500 – 100P)/200P < 0.30 P > $57.69 11. Suppose that Intel currently is selling at $40 per share. You buy 500 shares using $15,000 of your own money, borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 8%. (a) What is the percentage increase in the net worth of your brokerage account if the price of Intel immediately changes to: (i) $44; (ii) $40; (iii) $36? What is the relationship between your percentage return and the percentage change in the price of Intel? Assets = $40  500 = $20,000 Liability = $5,000 Equity = $15,000. (i)

(ii)

(iii)

Price to $44 Equity = Assets – Liabilities = ($44  500) – $5,000 = $17,000 Return = $17,000/$15,000 – 1 = 0.1333 = 13.33% Price at $40 Equity = Assets – Liabilities = ($40  500) – $5,000 = $15,000 Return = $15,000/$15,000 – 1 = 0% Price at $36 Equity = Assets – Liabilities = ($36  500) – $5,000 = $13,000 Return = $13,000/$15,000 – 1 = -0.1333 = -13.33% 4

The relationship between the Margin Return and the Stock Return is given by: Margin Return = Stock Return  Assets/Equity Assets/Equity is a leverage measure so the stock’s return (the asset’s return) is increased by the leverage ratio. For example, when the stock price rises from $40 to $44, the stock return is 10% The Equity Return = 10%  ($20,000/$15,000) = 10%  1.333 = 13.33% 1.333 is the leverage measure. (b) If the maintenance margin is 25%, how low can Intel's price fall before you get a margin call? The value of the Assets is the value of the 500 shares (500P). Liabilities = Loan amount = $5,000 Margin Rate = Equity/Assets = (Assets – Liabilities)/Assets = (500P – $5,000)/500P You will receive a margin call if Margin Rate < 0.25 Margin Call if (500P – $5,000)/500P < 0.25 Solve for P: Margin call if P < $13.33 (c) How would your answer to (b) change if you had financed the initial purchase with only $10,000 of your own money? The value of the Assets is the value of the 500 shares (500P). Liabilities = Loan amount = $10,000 Margin Rate = Equity/Assets = (Assets – Liabilities)/Assets = (500P – $10,000)/500P Margin Call if (500P – $10,000)/500P < 0.25 Margin call if P < $26.67 With less equity, more levered, more vulnerable to a margin call. (d) What is the rate of return on your margined position (assuming again that you invest $15,000 of your own money) if Intel is selling after 1 year at: (i) $44; (ii) $40; (iii) $36? What is the relationship between your percentage return and the percentage change in the price of Intel? Assume that Intel pays no dividends. At the end of 1 year, the loan amount (liability) = $5,000(1 + 0.08) = $5,400 (i) Price to $44 Equity = Assets – Liabilities = ($44  500) – $5,400 = $16,600 Return = $16,600/$15,000 – 1 = 0.1067 = 10.67% (ii) Price at $40 Equity = Assets – Liabilities = ($40  500) – $5,400 = $14,600 Return = $14,600/$15,000 – 1 = -0.0267 = -2.67%% (iii) Price at $36 Equity = Assets – Liabilities = ($36  500) – $5,400 = $12,600 Return = $12,600/$15,000 – 1 = -0.1600 = -16.00% The relationship between the Margin Return and the Stock Return is given by: Margin Return = (Stock Return  Assets/Equity) – (Loan Rate x Liabilities/Equity) For example, when the stock price rises from $40 to $44, the stock return is 10% Equity Return = (10%  ($20,000/$15,000)) – (8%  ($5,000/$15,000)) = (10%  1.333) – (8%  0.333) = 13.33% – 2.67% = 10.67% (e) Continue to assume that a year has passed. How low can Intel's price fall before you get a margin call? The value of the Assets is the value of the 500 shares (500P). Liabilities = Loan amount x 1.08 = $5,400 Margin Rate = Equity/Assets = (Assets – Liabilities)/Assets = (500P – $5,400)/500P 5

You will receive a margin call if Margin Rate < 0.25 Margin Call if (500P – $5,400)/500P < 0.25 Solve for P: Margin call if P < $14.40 12. Suppose that you sell short 500 shares of Intel, currently selling for $40 per share, and give your broker $15,000 to establish your margin account. (a) If you earn no interest on the funds in your margin account, what will be your rate of return after 1 year if Intel stock is selling at: (i) $44; (ii) $40; (iii) $36? Assume that Intel pays no dividends. Assets = Invested Cash + Proceeds from Short Sale = $15,000 + ($40  500) = $35,000 Liability = Value of 500 Shares Owed = 500P Equity = Assets – Liabilities = $35,000 – 500P (i)

(ii)

(iii)

Price to $44 Equity = Assets – Liabilities = $35,000 – ($44  500) = $35,000 – $22,000 = $13,000 Return = $13,000/$15,000 – 1 = -0.1333 = -13.33% Price at $40 Equity = Assets – Liabilities = $35,000 – ($40  500) = $35,000 – $20,000 = $15,000 Return = $15,000/$15,000 – 1 = 0% Price at $36 Equity = Assets – Liabilities = $35,000 – ($36  500) = $35,000 – $18,000 = $17,000 Return = $17,000/$15,000 – 1 = 0.1333 = 13.33%

(b) If the maintenance margin is 25%, how high can Intel's price rise before you get a margin call? Assets = Invested Cash + Proceeds from Short Sale = $15,000 + ($40  500) = $35,000 Liability = Value of 500 Shares Owed = 500P Equity = Assets – Liabilities = $35,000 – 500P Margin Rate = Equity/Liabilities = ($35,000 – 500P)/500P You will receive a margin call if Margin Rate < 0.25 Margin Call if ($35,000 – 500P)/500P < 0.25 Margin call if P > $56.00 (c) Redo parts (a) and (b), but now assume that Intel also has paid a year-end dividend of $1 per share. The prices in part (a) should be interpreted as ex-dividend, that is, prices after the dividend has been paid. The dividend is either payable to the entity from which the short borrowed the shares – in which case the liability is greater by the dividend amount or the dividend has been paid to the entity from which the short borrowed the shares – in which case the assets (cash) is lower. Assets = Invested Cash + Proceeds from Short Sale – Dividend = $15,000 + ($40  500) – ($1  $500) = $34,500 Liability = Value of 500 Shares Owed = 500P Equity = Assets – Liabilities = $34,500 – 500P (i)

(ii)

(iii)

Price to $44 Equity = Assets – Liabilities = $34,500 – ($44  500) = $34,500 – $22,000 = $12,500 Return = $12,500/$15,000 – 1 = -0.1333 = -13.33% Price at $40 Equity = Assets – Liabilities = $34,500 – ($40  500) = $34,500 – $20,000 = $14,500 Return = $14,500/$15,000 – 1 = -3.33% Price at $36 Equity = Assets – Liabilities = $34,500 – ($36  500) = $34,500 – $18,000 = $16,500 Return = $16,500/$15,000 – 1 = 15%

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Note that if we assume the dividend is still payable to the entity from which the short borrowed the shares, then assets and liabilities each increase by $500 – so equity is unchanged. Assets = Invested Cash + Proceeds from Short Sale – Dividend = $15,000 + ($40  500) – ($1  $500) = $34,500 Liability = Value of 500 Shares Owed = 500P Equity = Assets – Liabilities = $34,500 – 500P Margin Rate = Equity/Liabilities = ($34,500 – 500P)/500P You will receive a margin call if Margin Rate < 0.25 Margin Call if ($34,500 – 500P)/500P < 0.25 Margin call if P > $55.20 14. The bid on Fincorp is $55.25 and the ask is $55.50. (a) Suppose you have submitted an order to your broker to buy at market. At what price will your trade be executed? $55.50 (the best ask) (b) Suppose you have submitted an order to your broker to sell at market. At what price will your trade be executed? $55.25 (the best bid) (c) Suppose you have submitted a limit order to sell at $55.62. What will happen? Your order will not be executed immediately. It will be placed in the limit order book behind the best ask of $55.50. (d) Suppose you have submitted a limit order to buy at $55.37. What will happen? Your order will not be executed immediately. It will be placed in the limit order book ahead of the $55.25 and become the best bid. 16. You've borrowed $20,000 on margin to buy shares in Disney, which is now selling at $40 per share. Your account starts at the initial margin requirement of 50%. The maintenance margin is 35%. Two days later, the stock price falls to $35 per share. (a) Will you receive a margin call? Initial Margin = Equity/Assets = 50% The means you put up the same amount that you borrowed so Equity = $20,000 Liabilities = $20,000 Assets = $40,000 = 1,000 shares x $40 Margin Rate = Equity/Assets = (Assets – Liabilities)/Assets = (1,000P – $20,000)/1,000P = [(1,000 x $35) - $20,000]/(1,000 x $35) = 0.4286 = 42.86% > 35% So no margin call (b) How low can the price of Disney shares fall before you receive a margin call? Margin Call if (1,000P – $20,000)/1,000P < 0.35 Solve for P: Margin call if P < $30.77

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Extra Margin and Short Position Questions 1.

An investor puts up $20,000 to take a long position in a stock with a price of $50.

(a) If the initial margin rate on the position is 80%, how many shares can the investor purchase? What dollar amount the investor is borrowing from the brokerage firm? Number of Shares = (Dollars invested/Margin Rate)/P 0 = ($20,000/0.80)/$50 = 500 shares Loan Amount = $20,000/0.80 – $20,000 = $5,000 Assets

Liabilities & Equity

Stock = $50 x 500 = $25,000

Loan = $5,000 Equity = $25,000 - $5,000 = $20,000

(b) Assume the investor will receive a margin call if the margin rate drops below 30%. Below what price will the investor receive a margin call? (Assume the price change is immediate so you can ignore the dividend yield and interest on the loan.) Margin Rate = Equity/Stock Value = (Stock Value – Loan)/Stock Value = (Shares x P – Loan)/(Shares x P) Solve for P and plug in values: P = Loan/[Shares x (1 – Margin Rate)] = $5,000/[500 x (1 – 0.30)] = $14.29 Check Margin rate at P = 14.29: Margin Rate = (Shares x P – Loan)/(Shares x P) = (500 x $14.29 - $5,000)/(500 x $14.29) = $2,145/$7,145 = 30% (c) Calculate the return on the stock at the margin call price. Calculate the return on the investor’s equity at the margin call price. Calculate the ratio of the return on the stock to the return on the investor’s equity. How does this ratio compare to the initial margin rate? Stock Return = $14.29/$50 – 1 = -71.42% Investor’s Equity Return = $2,145/$20,000 – 1 = -89.28% Stock Return/Equity Return = -71.42%/-89.28% = 80% The ratio equals the initial margin rate. (d) Assume the stock pays a single annual dividend of $1.50 one year from today. If, at the end of the year, the stock’s price is $45, calculate the total return on the stock over the year. Stock Return = (P1 + Div)/P0 – 1 = ($45 + 1.50)/$50 – 1 = $46.50/$50 – 1 = -7.00% Note that this is equal to the capital gain return plus the dividend yield: Cap Gain Return = 45/50 – 1 = -10% and Dividend Yield = $1.50/$50 = 3% Stock Return = -10% + 3% = 7% (e) If the investor’s broker charges 8% on margin loans, calculate the return on the investor’s equity over the year. First calculate the new Equity: Assets

Liabilities & Equity

Stock = $45 x 500 = $22,500

Loan = $5,000(1.08) = $5,400

Div Cash = $1.50 x 500 = $750

Equity = $23,250 - $5,400 = $17,850

Total Assets = $23,250 Investor’s Equity Return = $17,850/$20,000 – 1 = -10.75%

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2.

An investor puts up $30,000 and takes a SHORT position in a stock with a price of $100.

(a) If the initial margin rate is 50%, how many shares can the investor short? Number of Shares = (Dollars invested/Margin Rate)/P 0 = ($30,000/0.50)/$100 = 600 shares Assets

Liabilities & Equity

Cash from Stock Sale = $100 x 600 = $60,000

Value of Stocks Owed = 600 x $100 = $60,000

Margin Cash = $30,000

Equity = $90,000 - $60,000 = $30,000

Total Assets = $90,000 Margin Rate = Equity/Value of Stocks Owed = Equity/(Shares x P) Margin Rate = $30,000/(600 x $100) = 0.50 (b) Assume the investor will receive a margin call if the margin rate drops below 30%. ABOVE what price will the investor receive a margin call? (Assume the price change is immediate so you can ignore the dividend yield and interest expense.) Margin Rate = Equity/Value of Stocks Owed = (Total Assets – Shares x P)/(Shares x P) Solve for P and plug in values: P = Total Assets/[Shares x (1 + MR)] = 90,000/[600(1 + 0.30)] = $115.38 Check Margin rate at P = $115.38: Margin Rate = Equity/Value of Stocks Owed = (Total Assets – Shares x P)/(Shares x P) Margin Rate = ($90,000 – 600 x $115.38)/(600 x $115.38) = ($90,000 – $69,228)/$69,228 Margin Rate = $20,772/$69,228 = 30% (c) Calculate the return on the stock at the margin call price. Calculate the return on the investor’s equity at the margin call price. Calculate the ratio on the return on the stock to the return on the investor’s equity. How does this ratio compare to the margin rate? Stock Return = $115.38/$100 – 1 = 15.38% Investor’s Equity Return = $20,772/$30,000 – 1 = -30.76% Stock Return/Equity Return = 15.38%/-30.76% = -50% The ratio equals the negative of the margin rate. (d) Assume the stock pays a single annual dividend of $4.00 one year from today. If, at the end of the year, the stock’s price is $90, calculate the total return on the stock over the year. Stock Return = (P1 + Div)/P0 – 1 = ($90 + $4)/$100 – 1 = $94/$100 – 1 = -6.00% (e) Assume the broker charges 5% on borrowed shares (calculated on the initial value of the position) and you earn 2% on the margin cash in the account. Calculate the return on the investor’s equity over the year. First calculate the new equity: Assets

Liabilities & Equity

Cash from Stock Sale = $60,000

Current Value of Stocks Owed = 600 x $90 = $54,000

Margin Cash = $30,000(1.02) = $30,600

Interest Payable on Borrowed Stocks = $60,000(0.05) = $3,000

Total Assets = $90,600

Dividend Payable = 600 x $4 = $2,400 Equity = $90,600 - $54,000 - $3,000 - $2,400 = $31,200

Note that I have listed the Interest and Dividends as “payable” liabilities. Once paid, the amount of cash decreases so Equity does not change. Investor’s Equity Return = $31,200/$30,000 – 1 = 4.00% The price dropped 10% and the investor was levered 2 to 1, but the cost of the short decreased the profit to 4.00%. 9

CFA PROBLEMS 1.

a.

In addition to the explicit fees of $70,000, FBN appears to have paid an implicit price in underpricing of the IPO. The underpricing is $3 per share, or a total of $300,000, implying total costs of $370,000.

b.

No. The underwriters do not capture the part of the costs corresponding to the underpricing. The underpricing may be a rational marketing strategy. Without it, the underwriters would need to spend more resources in order to place the issue with the public. The underwriters would then need to charge higher explicit fees to the issuing firm. The issuing firm may be just as well off paying the implicit issuance cost represented by the underpricing.

2.

(d)

The broker will sell, at current market price, after the first transaction at $55 or less.

3.

(d)

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