Investments End of Chapter Questions 1-4

Which of the following correctly describes a repurchase agreement? a. The sale of a security with a commitment to repurchase the same security at a specified future date and a designated price. b. The sale of a security with a commitment to repurchase the same security at a future date left unspecified, at a designated price. c. The purchase of a security with a commitment to purchase more of the same security at a specified future date.

(a) A repurchase agreement is the sale of a security with a commitment to repurchase the same security at a specified future date and a designated price.

Suppose that XTel 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 XTel 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 XTel? b. If the maintenance margin is 25%, how can XTel's price fall before you get a margin call? c. How would your answer to (b) change if you had financed the initial purchase with only $10,000 if your own money? d. Qhat is the rate of return on your margined position (assuming again that you invested $15,000 of your own money) if XTel is selling after one year at (i) $44; (ii) $40; (iii) $36? What is the relationship between your percentage return and the percentage change in the price of XTel? Assume that XTel pays no dividends. e. Continue to assume that a year has passed. How low can XTel's price fall before you get a margin call?

(i) Net worth increases to: ($44 x 500) - $5,000 = $17,000 Percentage gain = (ii) With price unchanged, net worth is unchanged. Percentage gain = zero (iii)Net worth falls to ($36 x 500) - $5,000 = $13,000 Percentage gain = The relationship between the percentage return and the percentage change in the price of the stock is given by: % return = % change in price x (Total investment / Investor's initial equity) = % change in price x 1.3333 For example, when the stock price rises from $40 to $44, the percentage change in price is 10% (0.10), while the percentage gain for the investor is: % return = 0.10 x ($20,000 / $15,000) = 0.1333 or 13.33% b. The value of the 500 shares is 500P. Equity is (500P - $5,000). You will receive a margin call when: (500P－$5,000) / 500P = 0.25 or 25% à when P = $13.33 or lower. c. The value of the 500 shares is 500P. But now you have borrowed $10,000 instead of $5,000. Therefore, equity is (500P - $10,000). You will receive a margin call when: (500P －$10,000) / 500P = 0.25 or 25% à P = $26.67. With less equity in the account, you are far more vulnerable to a margin call. d. By the end of the year, the amount of the loan owed to the broker grows to: $5,000 x (1 + 0.08) = $5,400 The equity in your account is (500P - $5,400). Initial equity was $15,000. Therefore, the rate of return after one year is as follows: (i) ((500 x $44)－$5,400－ $15,000) / $15,000 = 0.1067 = 10.67% (ii) ((500 x $40)－$5,400－ $15,000) / $15,000 = -0.0267 = -2.67% (iii) ((500 x $36)－$5,400－ $15,000) / $15,000 = -0.1600 = -16.00% The relationship between the percentage return and the percentage change in the price of XTel is given by: % return = (% Δ in price x (Total investment / Investor's initial equity))−(8% x (Funds borrowed / Investor's initial equity)) For example, when the stock price rises from $40 to $44, the percentage change in price is 10% (0.10), while the percentage gain for the investor is: (.10 x ($20,000 / $15,000)) - (.08 x ($5,000 / $15,000)) = .1067 or 10.67% e. The value of the 500 shares is 500P. Equity is (500P - $5,400). I will receive a margin call when: (500P－$5,400) / 500P = 0.25 or 25% when P = $14.40 or lower.

What is a 12b-1 fee?

12b-1 fees are annual fees charged by a mutual fund to pay for marketing and distribution costs.

What is the difference between a call option and a long position in a futures contract?

A call option conveys the right to buy the underlying asset at the exercise price. A long position in a futures contract carries an obligation to buy the underlying asset at the futures price.

What is the difference between a primary asset and a derivative asset?

A primary (financial) asset has a claim on the real assets of a firm, whereas a derivative asset provides a payoff that depends on the prices of a primary asset but does not include the claim on the real assets.

What is the difference between a put option and a short position in a futures contract?

A put option conveys the right to sell the underlying asset at the exercise price. A short position in a futures contract carries an obligation to sell the underlying asset at the futures price.

What are agency problems? What are some approaches to solving them?

Agency problems are conflicts of interest between managers and stockholders. They can be addressed through corporate governance mechanisms, such as the design of executive compensation, oversight by the Board, and monitoring from the institutional investors

What is the difference between an IPO and an SEO?

An IPO is the first time a formerly privately-owned company sells stock to the general public. A seasoned equity offering (or seasoned issuance) is the issuance of stock by a company that has already undergone an IPO.

Where would an illiquid security in a developing economy most likely trade? a. Broker markets. b. Electronic crossing networks. C. Electronic limit-order markets.

An illiquid security in a developing country is most likely to trade in (a) broker markets.

Would you expect a typical open-end fxed-income mutual fund to have higher or lower operating expenses than a fxed-income unit investment trust? Why?

An open-end fund will have higher fees since they are actively marketing and managing their investor base. The fund is always looking for new investors. A unit investment trust need not spend too much time on such matters since investors find each other.

What are the differences between a limit order and a market order?

An order that specifies price at which an investor is willing to buy or sell a security is a limit order, while a market order directs the broker to buy or sell at whatever price is available in the market.

Preferred stock yields often are lower than yields on bonds of the same quality because of: a. Marketability b. Risk c. Taxation d. Call protection

Answer: c. Taxation

Corporate Fund started the year with a net asset value of $12.50. By year-end, its NAV equaled $12.10. The fund paid year-end distributions of income and capital gains of $1.50. What was the rate of return to an investor in the fund?

As the price of a close-end fund may deviate from its NAV, we instead use the price of the net asset value when we calculate the rate of return: a. Start of year price = $12.00 ´ (1+.02) = $12.24 End of year price = $12.10 ´ (1-.07) = $11.253 Although NAV increased, the price of the fund fell by $0.987. rate of return = (Δ(Price) ＋ Distributions) / Start of year price = (-$0.987 + $1.50) / $12.24 = 0.0419 = 4.19% b. An investor holding the same portfolio as the fund manager would have earned a rate of return based on the increase in the NAV of the portfolio: rate of return = (Δ(NAV) ＋ Distributions) / Start of year NAV = ($12.10 - $12 + $1.50) / $12 = 0.1333 = 13.33%

What is the difference between asset allocation and security selection?

Asset allocation is the allocation of an investment portfolio across broad asset classes. Security selection is the choice of specific securities within each asset class.

Loaded-Up Fund charges a 12b-1 fee of 1% and maintains an expense ratio of .75%. Economy Fund charges a front-end load of 2%, but has no 12b-1 fee and has an expense ratio of .25%. Assume the rate of return on both funds' portfolios (before any fees) is 6% per year. How much will an investment in each fund grow to after: a. 1 year? b. 3 years? c. 10 years?

Assume a hypothetical investment of $100. The end value of the investment will be equal to I × (1 - front-end load) × (1 + r - true expense ratio)T Loaded-Up We add the 12b-1 fee to the operating expenses to obtain the true expense ratio: Expense ratio + (12b-1 fee) = 1% + 0.75% = 1.75% a. Year 1 = $100 ´ (1 + 0.06 - 0.0175) = $104.25 b. Year 3 = $100 ´ (1 + 0.06 - 0.0175)3 = $113.30 c. Year 10 = $100 ´ (1 + 0.06 - 0.0175)10 = $151.62 Economy fund a. Year 1 = $100 ´ 0.98 ´ (1 + 0.06 - 0.0025) = $103.64 b. Year 3 = $100 ´ 0.98 ´ (1 + 0.06 - 0.0025)3 = $115.90 c. Year 10 = $100 ´ 0.98 ´ (1 + 0.06 - 0.0025)10 = $171.41 Notice that if the investment horizon is 1 year, the investor does better under Loaded-Up Fund, but if the investment horizon is longer, the Economy fund outperforms.

Balanced funds and asset allocation funds each invest in both the stock and bond markets. What is the difference between these types of funds?

Balanced funds hold both equities and fixed-income securities in relatively stable proportions (e.g., Life-cycle funds and target-date funds). The proportion of debt and equity is a function of the investment goals of the client. On the other hand, asset allocation funds may dramatically vary the proportions allocated to each market in accord with the portfolio manager's forecast of the relative performance of each sector. Hence, these funds are engaged in market timing and are not designed to be low-risk investment vehicles.

A T-bill with face value $10,000 and 87 days to maturity is selling at a bank discount ask yield of 3.4%. a. What is the price of the bill? b. What is its bond equivalent yield?

Bank discount of 87 days: 0.034 x (87 days / 360 days) = 0.008217 a. Price: $10,000 x (1 - 0.008217) = $9,917.83 b. Bond equivalent yield = (Face value － Purchase price) / (Purchase price x T) = ($10,000 － $9,917.83) ($9,917.83 x (87 days / 365 days)) = 0.0348 or 3.48%

Why can closed-end funds sell at prices that differ from net value while open-end funds do not? What are some differences between a unit investment trust and a closed-end fund?

Close-end funds trade on the open market and are thus subject to market pricing. Open-end funds are sold by the mutual fund and must reflect the NAV of the investments.

What are the key differences between common stock, preferred stock, and corporate bonds?

Common stock is an ownership share in a publicly held corporation. Common shareholders have voting rights and may receive dividends (but are not contractually obligated to do so). Preferred stock represents nonvoting shares in a corporation, usually paying a fixed stream of dividends (but are not contractually obligated to do so). While corporate bonds are long-term debt issued by corporations, the bonds typically pay semi-annual coupons (and are contractually obligated to pay them) and return the face value of the bond at maturity.

Why are corporations more apt to hold preferred stock than other potential investors?

Corporations may exclude 50% of dividends received from domestic corporations in the computation of their taxable income.

What are the differences between equity and fixed-income securities?

Equity is a lower-priority claim on earnings (expressed as dividends) that represents an ownership share in a corporation. Fixed-income (debt) security is a higher-priority claim that legally obligates the issuer to pay the holder of the debt, but does not have an ownership interest. Fixed-income securities typically pay a specified cash flow at pre-contracted time intervals until the last payment on the maturity date. Shares of equity have an indefinite life.

A municipal bond carries a coupon rate of 2.25% and is trading at par. What would be the equivalent taxable yield of this bond to a taxpayer in a 35% combined tax bracket?

Equivalent taxable yield = Rate on municipal bond 1－ Tax rate = rm / (1－ t) = .02251 / (1－ 0.35) = .0346 or 3.46%

Oversight by large institutional investors or creditors is one mechanism to reduce agency problems. Why don't individual investors in the firm have the same incentive to keep an eye on management?

Even if an individual investor has the expertise and capability to monitor and improve the managers' performance, the payoffs would not be worth the effort, since his ownership in a large corporation is so small compared to that of institutional investors. For example, if the individual investor owns $10,000 of IBM stock and can increase the value of the firm by 5%, a very ambitious goal, the benefit would only be: $10,000 x 5% = $500. In contrast, a bank that has a multimillion-dollar loan outstanding to the firm has a big stake in making sure the firm can repay the loan. It is clearly worthwhile for the bank to spend considerable resources to monitor the firm.

Give an example of three financial intermediaries, and explain how they act as a bridge between small investors and large capital markets or corporations.

Even if the firm does not need to issue stock in any particular year, the stock market is still important to the financial manager. The stock price provides important information about how the market values the firm's investment projects. If the stock price rises considerably, managers might conclude that the market believes the firm's future prospects are bright (and generally supports the actions of management). This might be a useful signal to the firm to proceed with an investment such as an expansion of the firm's business. Since shares can be easily traded in the secondary market it makes them more attractive to investors since investors know that they will be able to sell their shares quickly. This makes investors more willing to buy shares in a primary offering, and thus improves the terms on which firms can raise money in the equity market.

What are the advantages and disadvantages of exchange-traded funds versus mutual funds?

Exchange-traded funds can be traded during the day, just as the stocks they represent. They are most tax effective, in that they do not have as many distributions. They have much lower transaction costs. They also do not require load charges, management fees, and minimum investment amounts. The disadvantages are that ETFs must be purchased from brokers for a fee and investors may incur a bid-ask spread when purchasing an ETF.

True or False: An ECN is a computer link used by security dealers primarily to advertise prices at which they are willing to buy or sell shares.

False; An ECN (Electronic Communications Network) is a computer link used by all participants to advertise prices at which they are willing to buy or sell shares.

True or False: An investor who wishes to sell shares immediately should ask his or her broker to enter a limit order.

False; An investor who wishes to sell shares immediately should ask his or her broker to enter a market order.

True or False: An issue of additional shares of stock to the public by Microsoft would be called an IPO.

False; An issue of additional shares of stock to the public by Microsoft would be called an SEO (Seasoned Equity Offering).

True or False: Market orders entail greater time-of-execution uncertainty than limit orders.

False; Market orders entail less time-of-execution uncertainty than limit orders.

True or False: The ask price is less than the bid price.

False; The ask price is greater than the bid price.

For each transaction, identify the real and/or financial assets that trade hands. Are any financial assets created or destroyed in the transaction? a. Toyota takes out a bank loan to finance the construction of a new factory. b. Toyota pays off its loan. c. Toyota uses $10 million of cash on hand to purchase the additional inventory of spare auto parts.

Financial and Real Assets a. Toyota creates a real asset—the factory. The loan is a financial asset that is created in the transaction. b. When the loan is repaid, the financial asset is destroyed but the real asset continues to exist. c. The cash is a financial asset that is traded in exchange for a real asset, inventory.

How does a municipal revenue bond differ from a general obligation bond? Which would you expect to have a lower yield to maturity?

General obligation bonds are backed by the taxing power of the local governments, while revenue bonds have proceeds attached to specific projects. A revenue bond has fewer guarantees, it is riskier in terms of default, and, therefore, you expect it to have a higher yield.

What are some differences between hedge funds and mutual funds?

Hedge funds have much less regulation since they are part of private partnerships and free from most SEC regulation. They permit investors to take on many risks unavailable to mutual funds. Hedge funds, typically require higher fees (management fees and performance fees), are available only to accredited investors (investors with minimum net worth requirements), and provide less transparency to investors. This lack of transparency offers significant counter party risk and hedge fund investors need to be more careful about the funds they select. Mutual Funds Hedge Funds Management Fee Yes Yes Performance Fee No Yes SEC Regulation Heavy Light Initial Lock-up Periods No Frequent Leverage Minimal Unlimited Short Sales Not permitted Permitted Transparency to Investor High Low

What would happen to the divisor of the Dow Jones Industrial Average if FedEx, with a current price of around $115 per share, replaced Intel (with a current price of about $55 per share)?

In this case, the value of the divisor will increase by an amount necessary to maintain the index value on the day of the change. For example, if the index was comprised of only one stock, it would increase by ($115-%50)/$50 = 1.30

How does investment banking differ from commercial banking?

Investment bankers are firms specializing in the sale of new securities to the public, typically by underwriting the issue. Commercial banks accept deposits and lend the money to other borrowers. After the Glass-Steagall Act was repealed in 1999, some commercial banks started transforming to "universal banks" which provide the services of both commercial banks and investment banks. With the passage of the Dodd-Frank Wall Street Reform and Consumer Protection Act in 2010, Glass-Steagall was partially restored via the Volcker Rule (which generally prohibits commercial banks from conducting certain investment activities with their own accounts and investing in hedge funds and private equity funds). In 2018, Congress passed The Economic Growth, Regulatory Relief, and Consumer Protection Act established a threshold ($10 billion) for banks to be exempt from the Volcker Rule.

What is meant by limited liability?

Limited liability means that the most shareholders can lose in event of the failure of the corporation is their original investment (which differs from owners of unincorporated businesses).

Both a call and a put currently are traded on stock XYZ; both have strike prices of $50 and expirations of six months. a. What will be the profit to an investor who buys the call for $4 in the following scenarios for stock prices in six months? ( i ) $40; ( ii ) $45; ( iii ) $50; ( iv ) $55; ( v ) $60. b. What will be the profit in each scenario to an investor who buys the put for $6?

Long call for $4: Value of call at expiration Initial Cost Profit a. 0 4 -4 b. 0 4 -4 c. 0 4 -4 d. 5 4 1 e. 10 4 6 Long put for $6: Value of put at expiration Initial Cost Profit a. 10 6 4 b. 5 6 -1 c. 0 6 -6 d. 0 6 -6 e. 0 6 -6

Why have average trade sizes declined in recent years?

Many large investors seek anonymity for fear that their intentions will become known to other investors. Large block trades attract the attention of other traders. By splitting large transactions into smaller trades, investors are better able to retain a degree of anonymity.

How does buying on margin magnify both the upside potential and downside risk of an investment portfolio?

Margin is a type of leverage that allows investors to post only a portion of the value of the security they purchase. As such, when the price of the security rises or falls, the gain or loss represents a much higher percentage, relative to the actual money invested.

Why are money market securities often called "cash equivalents"?

Money market securities are referred to as "cash equivalents" because of their great liquidity. The prices of money market securities are very stable, and they can be converted to cash (i.e., sold) on very short notice and with very low transaction costs.

What features of money market securities distinguish them from other fixed-income securities?

Money market securities are short-term, relatively low risk, and highly liquid. Also, their unit value almost never changes.

What are the benefits to small investors of investing via mutual funds? What are the disadvantages?

Mutual funds offer many benefits: the ability to invest with small amounts of money, diversification, professional management, low transaction costs, tax benefits, and the ability to reduce administrative functions. The disadvantages associated with investing in mutual funds are generally operating expenses, marketing expenses, distribution charges, and loads. Loads are fees paid when investors purchase or sell the shares.

If the offering price of an open-end fund is $12.30 per share and the fund is sold with a front-end load of 5%, what is its net asset value?

NAV = Offering price ´ (1 - load) = $12.30 ´ 0.95 = $11.69

Why do financial assets show up as a component of household wealth, but not of national wealth? Why do financial assets still matter for the material well-being of an economy?

National wealth is a measurement of the real assets used to produce GDP in the economy. Financial assets are claims on those assets held by individuals. Financial assets owned by households represent their claims on the real assets of the issuers, and thus show up as wealth to households. Their interests in the issuers, on the other hand, are obligations to the issuers. At the national level, the financial interests and the obligations cancel each other out, so only the real assets are measured as the wealth of the economy. The financial assets are important since they drive the efficient use of real assets and help us allocate resources, specifically in terms of risk return trade-offs.

Open-end equity mutual funds commonly keep a small fraction of total investments in very liquid money market assets. Closed-end funds do not have to maintain such a position in "cash equivalent" securities. What difference between open-end and closed-end funds might account for their differing policies?

Open-end funds must honor redemptions and receive deposits from investors. This flow of money necessitates retaining cash. Close-end funds no longer take and receive money from investors. As such, they can be fully invested at all times.

What reforms to the financial system might reduce its exposure to systemic risk?

Passed in 2010, the Dodd-Frank Wall Street Reform and Consumer Protection Act proposed several mechanisms to mitigate systemic risk. The act attempts to limit the risky activities in which the banks can engage and calls for stricter rules for bank capital, liquidity, and risk management practices, especially as banks become larger and their potential failure becomes more threatening to other institutions. The act seeks to unify and clarify the lines of regulatory authority and responsibility in government agencies and to address the incentive issue by forcing employee compensation to reflect longer-term performance. It also mandates increased transparency, especially in derivatives markets.

What would you expect to be the relationship between securitization and the role of financial intermediaries in the economy? For example, what happens to the role of local banks in providing capital for mortgage loans when national markets in mortgage-backed securities become highly developed?

Progress in securitization facilitates the shifting of default risk from the intermediates to the investors of such a security. Since the intermediates no longer bear the default risk, their role and motivation in assessing and monitoring the quality of the borrowers is mitigated. For example, when the national market in mortgage-backed securities becomes highly developed, local banks can easily sell their claims on mortgages to the issuers of mortgage-backed securities and then use the money they receive to create more mortgages because the local banks make profits both from making loans and selling loans to the issuers of mortgage-backed securities. This way the local banks are incentivized by the volume of the loan that they lend out and not by the quality of the loan, and thus they become less cautious in originating subprime mortgages.

Suppose that in a wave of pessimism, housing prices fall by 10% across the entire economy. a. Has the stock of real assets of the economy changed? b. Are individuals less wealthy? c. Can you reconcile your answers to ( a ) and ( b )?

Real Estate as a Real Asset a. No. The real estate in existence has not changed, only the perception of its value has. b. Yes. The financial asset value of the claims on the real estate has changed, and thus the balance sheet of individual investors has been reduced. c. The difference between these two answers reflects the difference between real and financial asset values. Real assets still exist, yet the value of the claims on those assets or the cash flows they generate do change. Thus, there is the difference.

Lanni Products is a start-up computer software development firm. It currently owns computer equipment worth $30,000 and has cash on hand of $20,000 contributed by Lanni's owners. For each of the following transactions, identify the real and/or financial assets that trade hands. Are any financial assets created or destroyed in the transaction? a. Lanni takes out a bank loan. It receives $50,000 in cash and signs a note promising to pay back the loan over three years. b. Lanni uses the cash from the bank plus $20,000 of its own funds to finance the development of new financial planning software. c. Lanni sells the software product to Microsoft, which will market it to the public under the Microsoft name. d. Lanni accepts payment in the form of 1,000 shares of Microsoft stock. Lanni sells the shares of stock for $140 per share and uses part of the proceeds to pay off the bank loan.

Real and Financial Assets a. The bank loan is a financial liability for Lanni. Lanni's $50,000 IOU is the bank's financial asset. The cash Lanni receives is a financial asset. The new financial asset created is Lanni's promissory note held by the bank. b. The cash paid by Lanni (both the loan and its own cash) is the transfer of a financial asset to the software developer. In return, Lanni gets a real asset, the completed software. No financial assets are created or destroyed. Cash is simply transferred from one firm to another. c. Lanni sells the software, which is a real asset, to Microsoft. In exchange Lanni receives a financial asset, 1,000 shares of Microsoft stock. If Microsoft issues new shares in order to pay Lanni, that would be the creation of a new financial asset. d. In selling 1,000 shares of stock for $140,000, Lanni is exchanging one financial asset for another. In paying off the IOU with $50,000, Lanni is exchanging financial assets. The loan is "destroyed" in the transaction since it is retired when paid.

What are the differences between real and financial assets?

Real assets have productive capacity; they are assets used to produce goods and services. Real assets can be tangible (e.g., machinery) or intangible (e.g., a patent). Financial assets are claims on real assets or the income generated by them.

Why would you expect securitization to take place only in highly developed capital markets?

Securitization requires access to many potential investors. To attract these investors, the capital market needs: (1) Strong business laws; low probability of confiscatory taxation/regulation; (2) A well-developed investment banking industry; (3) A well-developed system of brokerage and financial transactions; (4) Well-developed media, particularly financial reporting. These characteristics are found in (and make for) a well-developed financial market.

Wall Street firms have traditionally compensated their traders with a share of the trading profits they generated. How might this practice have affected traders' willingness to assume risk? What agency problem can this practice can engender?

Since the traders benefited from profits but did not get penalized by losses, they were encouraged to take extraordinary risks. Since traders sell to other traders, there also existed a moral hazard since other traders might facilitate the misdeed. In the end, this represents an agency problem.

Examine the stocks listed in Figure 2.8 . For what fraction of these stocks is the 52-week high price at least 40% greater than the 52-week low price? What do you conclude about the volatility of prices on individual stocks?

Six of seven stocks have a 52-week high at least 40% above the 52-week low (and three out of seven are at 50% or more). It can be concluded that individual stocks are much more volatile than a group of stocks. 52-wk high 52-wk low Price ratio (High-Low)/Low 61.77 33.62 84% 161.58 99.15 63% 74.81 35.59 110% 17.27 12.09 43% 229.27 158.09 45% 31.04 22.87 36% 178.47 123.48 45%

Look at the futures listings for corn in Figure 2.11 . Suppose you buy one contract for December 2020 delivery. If the contract closes in December at a price of $4.00 per bushel, what will be your profit or loss? (Each contract calls for delivery of 5,000 bushels.)

The December maturity futures price is $3.9725 per bushel. If the contract closes at $4.00 per bushel in December, your profit / loss on each contract (for delivery of 5,000 bushels of corn) will8 be: ($4.00 - $3.9725) x 5000 = $ 137.50 gain.

What is the LIBOR rate? The federal funds rate?

The London Interbank Offer Rate (LIBOR)—a key reference rate in the money market—is the rate at which large banks in London are willing to lend money among them. The Federal funds rate is the rate of interest on very short-term loans among financial institutions in the U.S.A.

An investor is in a 30% combined federal plus state tax bracket. If corporate bonds offer 9% yields, what yield must municipals offer for the investor to prefer them to corporate bonds?

The after-tax yield on the corporate bonds is: 0.09 x (1 - 0.30) = 0.063 or 6.3%. Therefore, the municipals must offer at least 6.3% yields.

Why are high-tax-bracket investors more inclined to invest in municipal bonds than are lowbracket investors?

The coupons paid by municipal bonds are exempt from federal income tax and from state tax in many states. Therefore, the higher the tax bracket that the investor is in, the more valuable the tax-exempt feature to the investor.

What are some different components of the effective costs of buying or selling shares of stock?

The effective price paid or received for a stock includes items such as bid-ask spread, brokerage fees, commissions, and taxes (when applicable). These reduce the amount received by a seller and increase the cost incurred by a buyer.

The New Fund had average daily assets of $2.2 billion in the past year. The fund sold $400 million and purchased $500 million worth of stock during the year. What was its turnover ratio?

The excess of purchases over sales must be due to new inflows into the fund. Therefore, $400 million of stock previously held by the fund was replaced by new holdings. So turnover is: Turnover rate = Value of stocks sold or replacedValue of assets = $400,000,000/$2,200,000,000 = 0.1818 = 18.18%

What problems would confront a mutual fund trying to create an index fund tied to an equally weighted index of a broad stock market?

The fund would require constant readjustment since every change in the price of a stock would bring the fund asset allocation out of balance.

What are the major components of the money market?

The major components of the money market are Treasury bills, certificates of deposit, commercial paper, bankers' acceptances, Eurodollars, repos and reverses, federal funds, and brokers' calls.

An open-end fund has a net asset value of $10.70 per share. It is sold with a front-end load of 6%. What is the offering price?

The offering price includes a 6% front-end load, or sales commission, meaning that every dollar paid results in only $0.94 going toward the purchase of shares. Therefore: Offering price = NAV/(1-load) = $10.70/(1-0.06) = $11.38

What is the difference between a primary and a secondary market?

The primary market is the market where newly-issued securities are sold, while the secondary market is the market for trading existing securities. After firms sell their newly-issued stocks to investors in the primary market, new investors purchase stocks from existing investors in the secondary market.

How do security dealers earn their profits?

The primary source of income for a securities dealer is the bid-ask spread. This is the difference between the price at which the dealer is willing to purchase a security and the price at which they are willing to sell the same security.

On January 1, you sold short one round lot of Snow's stock at $21 per share. On March 1, a dividence of $3 per share was paid. On April 1, you covered the short sale by buying the stock at a price of $15 per share. You paid 50 cents per share in commissions for each transaction. What is the value of your account on April 1?

The proceeds from the short sale (net of commission) were: ($21 x 100) - $50 = $2,050. A dividend payment of $300 was withdrawn from the account. Covering the short sale at $15 per share costs (and $.50 per share commission): $1500 + $50 = $1550. Therefore, the value of your account is equal to the net profit on the transaction: $2,050 - $300 - $1,550 = $200. Noted that the profit of $200 equals (100 shares x profit per share of $2), your net proceeds per share were: $21 Selling price of stock -$15 Repurchase price of stock -$ 3 Dividend per share -$ 1 2 trades x $0.50 commission per share = $ 2

What would you expect to happen to the spread between yields on commercial paper and Treasury bills if the economy were to enter a steep recession?

The spread will widen. Deterioration of the economy increases credit risk, that is, the likelihood of default. Investors will demand a greater premium on debt securities subject to default risk.

Find the after-tax return to a corporation that buys a share of preferred stock at $40, sells it at year-end at $40, and receives a $4 year-end dividend. The firm is in the 21% tax bracket.

The total before-tax income is $4.00. The corporations may exclude 50% of dividends received from domestic corporations in the computation of their taxable income; the taxable income is therefore: $4.00 x 50% = $2.00. Income tax in the 30% tax bracket: $2.00 x 21% = $0.42 After-tax income = $4.00 - $0.42 = $3.58 After-tax rate of return = $3.58/$40.00 = 0.0895 or 8.95%

Why do call options with exercise prices higher than the price of the underlying stock sell for positive prices?

There is always a chance that the option will expire in the money. Investors will pay something for this chance of a positive payoff.

Using the data in the previous problem, calculate the first-period rates of return on the following indexes of the three stocks: a. A market value-weighted index b. An equally weighted index

Total market value at t = 0 is: ($90 x 100) + ($50 x 200) + ($100 x 200) = $39,000 Total market value at t = 1 is: ($95 x 100) + ($45 x 200) + ($110 x 200) = $40,500 Rate of return = V1/V0 － 1 = ($40,500/$39,000) - 1 = 0.0385 or 3.85% b. The return on each stock is as follows: RA = V1/V0 － 1 = ($95/$90) - 1 = 0.0556 or 5.56% RB = V1/V0 － 1 = ($45/$50) - 1 = -0.10 or -10.00% RC = V1/V0 － 1 = ($110/$100) - 1 = 0.10 or 10.00% The equally-weighted average is (5.56%+(-10.00%)+10.00%)/3 = 1.85%

Firms raise capital from investors by issuing shares in the primary markets. Does this imply that corporate financial managers can ignore the trading of previously issued shares in the secondary market?

Treasury bills serve a purpose for investors who prefer a low-risk investment. The lower average rate of return compared to stocks is the price investors pay for predictability of investment performance and portfolio value.

True or False: Market orders entail greater price uncertainty than limit orders.

True

What is the role of an underwriter? A prospectus?

Underwriters purchase securities from the issuing company and resell them. A prospectus is a description of the firm and the security it is issuing; it can be viewed as a marketing tool for the underwriter.

In what circumstances are private placements more likely to be used than public offerings?

When a firm is a willing buyer of securities and wishes to avoid the extensive time and cost associated with preparing a public issue, it may issue shares privately.

Why do most professionals consider the Wilshire 5000 a better index of the performance of the broad stock market than the Dow Jones Industrial Average?

While the DJIA has 30 large corporations in the index, it does not represent the overall market nearly as well as the approximate 3,500 stocks contained in The Wilshire 5000 index. The DJIA is simply too small.

The average rate of return on investments in large stocks has outpaced that on investments in Treasury bills by about 8% since 1926. Why, then, does anyone invest in Treasury bills?

You should be skeptical. If the author actually knows how to achieve such returns, one must question why the author would then be so ready to sell the secret to others. Financial markets are very competitive; one of the implications of this fact is that riches do not come easily. High expected returns require bearing some risk, and obvious bargains are few and far between. Odds are that the only one getting rich from this book is its author.

Reconsider Lanni Products from Problem 9. a. Prepare its balance sheet just after it gets the bank loan. What is the ratio of real assets to total assets? b. Prepare the balance sheet after Lanni spends the $70,000 to develop its software product. What is the ratio of real assets to total assets? c. Prepare the balance sheet after Lanni accepts the payment of shares from Microsoft. What is the ratio of real assets to total assets?

a. Assets Cash $70,000 Computers 30,000 Total $100,000 Liabilities and Shareholders' Equity Bank Loan $50,000 Shareholders Equity 50,000 Total $100,000 Ratio of real to total assets = $30,000/$100,000 = 0.3 b. Assets Software Product $70,000 Computers 30,000 Total 100,000 Liabilities and Shareholders' Equity Bank Loan $50,000 Shareholder Equity 50,000 Total $100,000 Ratio of real to total assets = $100,000/$100,000 = 1.0 c. Assets Microsoft shares (70/share) $140,000 Computers 30,000 Total $170,000 Liabilities and Shareholders' Equity Bank Loan $50,000 Shareholders Equity 50,000 Total $100,000 Ratio of real to total assets = $30,000/$155,000 = 0.2 Conclusion: When the firm starts up and raises working capital, it will be characterized by a low ratio of real to total assets. When it is in full production, it will have a high ratio of real assets. When the project "shuts down" and the firm sells it, the percentage of real assets to total assets goes down again because the product is again exchanged into financial assets.

Discuss the advantages and disadvantages of the following forms of managerial compensation in terms of mitigating agency problems, that is, potential conflicts of interest between managers and shareholders. a. A fixed salary. b. Stock in the firm that must be held for five years. c. A salary linked to the firm's profits.

a. A fixed salary means compensation is (at least in the short run) independent of the firm's success. This salary structure does not tie the manager's immediate compensation to the success of the firm, and thus allows the manager to envision and seek the sustainable operation of the company. However, since the compensation is secured and not tied to the performance of the firm, the manager might not be motivated to take any risk to maximize the value of the company. b. A salary paid in the form of stock in the firm means the manager earns the most when shareholder wealth is maximized. When the stock must be held for five years, the manager has less of an incentive to manipulate the stock price. This structure is most likely to align the interests of managers with the interests of the shareholders. If stock compensation is used too much, the manager might view it as overly risky since the manager's career is already linked to the firm. This undiversified exposure would be exacerbated with a large stock position in the firm. c. When executive salaries are linked to firm profits, the firm creates incentives for managers to contribute to the firm's success. However, this may also lead to earnings manipulation or accounting fraud, such as divestment of its subsidiaries or unreasonable revenue recognition. That is what audits and external analysts will look out for.

What are some comparative advantages of investing your assets in the following: a. Unit investment trusts. b. Open-end mutual funds. c. Individual stocks and bonds that you choose for yourself.

a. A unit investment trust offers low costs and stable portfolios. Since they do not change their portfolios, investors know exactly what they own. They are better suited to sophisticated investors. b. Open-end mutual funds offer higher levels of service to investors. The investors do not have any administrative burdens and their money is actively managed. These are better suited for less knowledgeable investors. c. Individual securities offer the most sophisticated investors ultimate flexibility. Investors can save money since they are only charged the expenses they incur. All decisions are under the control of the investor.

Consider the three stocks in the following table. P t represents the price at time t, and Q t represents shares outstanding at time t. Stock C splits two-for-one in the last period. P 0 Q 0 P 1 Q 1 P 2 Q 2 A 90 100 95 100 95 100 B 50 200 45 200 45 200 C 100 200 110 200 55 400 a. Calculate the rate of return on a price-weighted index of the three stocks for the first period ( t = 0 to t = 1). What must happen to the divisor for the price-weighted index in year 2? b. Calculate the rate of return of the price-weighted index for the second period ( t = 1 to t = 2).

a. At t = 0, the value of the index is: ($90 + $50 + $100)/3 = 80 At t = 1, the value of the index is: ($95 + $45 + $110)/3 = 83.33 The rate of return is: V1/V0 － 1 = (83.33/80) - 1 = 0.0417 or 4.17% b. In the absence of a split, stock C would sell for $110, and the value of the index would be the average price of the individual stocks included in the index: ($95 + $45 + $110)/3 = $83.33. After the split, stock C sells at $55; however, the value of the index should not be affected by the split. We need to set the divisor (d) such that: $83.33 = ($95 +$45 + $55) / d d = 2.34

an Impressive Fund had excellent investment performance last year, with portfolio returns that placed it in the top 10% of all funds with the same investment policy. a. Do you expect it to be a top performer next year? Why or why not? b. Suppose instead that the fund was among the poorest performers in its comparison group. Would you be more or less likely to believe its relative performance will persist into the following year? Why?

a. Empirical research indicates that past performance of mutual funds is not highly predictive of future performance, especially for better-performing funds. While there may be some tendency for the fund to be an above average performer next year, it is unlikely to once again be a top 10% performer. b. On the other hand, the evidence is more suggestive of a tendency for poor performance to persist. This tendency is probably related to fund costs and turnover rates. Thus if the fund is among the poorest performers, investors would be concerned that the poor performance will persist.

The New Fund (from Problem 22) had an expense ratio of 1.1%, and its management fee was 0.7% a. What were the total fees paid to the fund's investment managers during the year? b. What were the other administrative expenses?

a. Fees paid to investment managers were: 0.7% × $2.2 billion = $15.4 million. b. Since the total expense ratio was 1.1% and the management fee was 0.7%, we conclude that 0.4% must be for other expenses. Therefore, other administrative expenses were: 0.004 × $2.2 billion = $8.8 million

Examine the balance sheet of commercial banks in Table 1.3. a. What is the ratio of real assets to total assets? b. What is that ratio for nonfinancial firms ( Table 1.4 )? c. Why should this difference be expected?

a. For commercial banks, the ratio is: $184.2/$18090.1 = 0.0102 b. For non-financial firms, the ratio is: $23,907/$45,643 = 0.5238 c. The difference should be expected since the business of financial institutions is to make loans that are financial assets.

Suppose that you sell short 500 shares of XTel, 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 one year if XTel stock is selling at (i) $44; (ii) $40; (iii) $36? Assume that XTel pays no dividends. b. If the maintenance margin is 25%, how high can XTel's price rise before you get a margin call? c. Redo parts (a) and (b), but now assume that XTel 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.

a. Given the $15,000 invested funds and assuming the gain or loss on the short position is (-500 x DP), we can calculate the rate of return using the following formula: Rate of return = (-500 x DP)/15,000 Thus, the rate of return in each of the three scenarios is: (i) Rate of return = (-500 x $4) / $15,000 = -.1667 = 16.67% (ii) Rate of return = 0% (iii)Rate of return = (-500 x (-4) / $15,000 = 0.1333 = 13.33% Total assets on margin are the sum of the initial margin and the proceeds from the sale of the stock: $20,000 + $15,000 = $35,000. Liabilities are 500P. A margin call will be issued when: ($35,000－500P) / 500P = 0.25 or 25% à P = $56 or higher. b. With a $1 dividend, the short position must now pay on the borrowed shares: ($1/share x 500 shares) = $500. Rate of return is now: [(-500 x DP) - 500]/15,000 (i) Rate of return = (-500 x $4 - $500) / $15,000 = 0.1667 = 16.67% (ii) Rate of return = (-500 x $0 - $500) / $15,000 = 0.0333 = 3.33% (iii)Rate of return = (-500 x (-$4) - $500) / $15,000 = 0.1000 = 10% Total assets are $35,000, and liabilities are (500P + 500). A margin call will be issued when: ($35,000－500P－500) / 500P = 0.25 or 25% à P = $55.20 or higher.

DRK, Inc., has just sold 100,000 shares in an initial public offering. The underwriter's explicit fees were $60,000. The offering price for the shares was $40, but immediately upon issue, the share price jumped to $44. a. What is your best guess as to the total cost of the equity issue? b. Is the entire cost of the underwriting a source of profit to the underwriters?

a. In addition to the explicit fees of $60,000, we should also take into account the implicit cost incurred to DRK from the underpricing in the IPO. The underpricing is $4 per share, or a total of $400,000, implying total costs of $460,000. b. No. The underwriters do not capture the part of the costs corresponding to the underpricing. However, the underpricing may be a rational marketing strategy to attract and retain long-term relationships with their investors. 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.

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? 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?

a. Initial margin is 50% of $5,000, which is $2,500. b. Total assets are $7,500 ($5,000 from the sale of the stock and $2,500 put up for margin). Liabilities are 100P. Therefore, net worth is ($7,500 - 100P). Solving ($7,500－100P) / 100P = 0.30, we get P = $57.69. A margin call will be issued when the stock price reaches $57.69 or higher.

What options position is associated with: a. The right to buy an asset at a specified price? b. The right to sell an asset at a specified price? c. The obligation to buy an asset at a specified price? d. The obligation to sell an asset at a specified price?

a. Long call b. Long put c. Short put d. Short cal

The Investments Fund sells Class A shares with a front-end load of 6% and Class B shares with 12b-1 fees of 0.5% annually as well as back-end load fees that start at 5% and fall by 1% for each full year the investor holds the portfolio (until the ffth year). Assume the portfolio rate of return net of operating expenses is 10% annually. a. If you plan to sell the fund after four years, are Class A or Class B shares the better choice for you? b. What if you plan to sell after 15 years?

a. Suppose you have $1000 to invest. The initial investment in Class A shares is $940 net of the front-end load. After 4 years, your portfolio will be worth: $940 x (1.10)4 = $1,376.25 Class B shares allow you to invest the full $1,000, but your investment performance net of 12b-1 fees will be only 9.5%, and you will pay a 1% back-end load fee if you sell after 4 years. Your portfolio value after 4 years will be: $1,000 x (1.095)^4 = $1,437.66 After paying the back-end load fee, your portfolio value will be: $1,437.66 x 0.99 = $1,423.28 Class B shares are the better choice if your horizon is 4 years. b. With a 15-year horizon, the Class A shares will be worth: $940 x (1.10)^15 = $3,926.61 For the Class B shares, there is no back-end load in this case since the horizon is greater than 5 years. Therefore, the value of the Class B shares will be: $1,000 x (1.095)^15 = $3,901.32 At this longer horizon, Class B shares are no longer the better choice. The effect of Class B's 0.5% 12b-1 fees cumulates over time and finally overwhelms the 6% load charged to Class A investors

Marabel bid price is $67.95, and ask is $68.05. a. You have placed a limit order to sell at $68. What are you telling your broker? b. Given market prices, will your order be executed?

a. The broker is instructed to attempt to sell your Marabel stock as soon as the Marabel stock trades at a bid price of $68 or less. b. The broker will attempt to execute but may not be able to sell at $68, since the bid price is now $67.95. The price at which you sell may be more or less than $68 because the stop-loss becomes a market order to sell at current market prices

Turn to Figure 2.8 and look at the listing for Home Depot. a. What was the firm's closing price yesterday? b. How many shares can you buy for $5,000? c. What would be your annual dividend income from those shares? d. What must be Home Depot's earnings per share?

a. The closing price today is $224.15, which is $1.44 above yesterday's price. Therefore, yesterday's closing price was: $224.15 － $1.44 = $222.71. b. You would buy 22 shares: $5,000/$224.15 = 22.31 (round down for 22 shares) c. Your annual dividend income on 22 shares would be 22 x $5.44 = $119.68. d. Earnings per share can be derived from the price-earnings (PE) ratio: Given price/Earnings = 22.36 and Price = $224.15, we know that Earnings per Share = $224.13/22.36 = $10.02

Which security should sell at a greater price? a. A 10-year Treasury bond with a 5% coupon rate or a 10-year T-bond with a 6% coupon. b. A three-month expiration call option with an exercise price of $40 or a three-month call on the same stock with an exercise price of $35. c. A put option on a stock selling at $50 or a put option on another stock selling at $60. (All other relevant features of the stocks and options are assumed to be identical.)

a. The higher coupon bond: The 10-year T-bond with a 6% coupon b. The call with the lower exercise price: The call with the exercise price of $35 c. The put option on the lower priced stock: The put on the stock selling at $50

See 17 on page 56 for table: a. if a market buy order for 100 shares comes in, at what price will it be filled? b. At what price would the next market buy order be filled? c. If you were a security dealer, would you want to increase or decrease your inventory of this stock?

a. The market-buy order will be filled at $49.80, the best price of limit-sell orders in the book. b. The next market-buy order will be filled at $49.85, the next-best limit-sell order price. c. As a security dealer, 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, indicating that a moderate buy order could result in a substantial price increase.

Dee 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 Dee's account when she first purchases the stock? b. If the share price falls to $30 a share, what is the remaining margin in her account? c. If the maintenance margin requirement is 30%, will she receive a margin call? d. What is the rate of return on her investment?

a. The stock is purchased for $40 x 300 shares = $12,000. Given that the amount borrowed from the broker is $4,000, Dee's margin is the initial purchase price net borrowing: $12,000 - $4,000 = $8,000. b. 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: Principal ´ (1 + Interest rate) = $4,000 x (1 + 0.08) = $4,320. The value of the stock falls to: $30 x 300 shares = $9,000. The remaining margin in the investor's account is: $9,000 - $4,320 = $4680 c. Margin on long position = Equity in account / Value of stock. = ($9,000 － $4,320) / $9,000 = 0.52 = 52% d. Rate of return = (Ending equity in account － Initial equity in account) / Initial equity in account = ($4,680 － $8,000) / $8,000 = - 0.4150 = - 41.50%

Suppose that short-term municipal bonds currently offer yields of 4%, while comparable taxable bonds pay 5%. Which gives you the higher after-tax yield if your combined tax bracket is: a. Zero b. 10% c. 20% d. 30%

a. The taxable bond. With a zero tax bracket, the after-tax yield for the taxable bond is the same as the before-tax yield (5%), which is greater than the 4% yield on the municipal bond. b. The taxable bond. The after-tax yield for the taxable bond is: 0.05 x (1 - 0.10) = 0.045 or 4.50%. c. Neither. The after-tax yield for the taxable bond is: 0.05 x (1 - 0.20) = 0.04 or 4%. The after-tax yield of taxable bond is the same as that of the municipal bond. d. The municipal bond. The after-tax yield for the taxable bond is: 0.05 x (1 - 0.30) = 0.035 or 3.5%. The municipal bond offers the higher after-tax yield for investors in tax brackets above 20%.

Fincorp bid is $55.25, and 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? b. Suppose you have submitted an order to sell at market. At what price will your trade be executed? c. Suppose you have submitted a limit order to sell at $55.62. What will happen? d. Suppose you have submitted a limit order to buy at $55.37. What will happen?

a. The trade will be executed at $55.50. b. The trade will be executed at $55.25. c. The trade will not be executed because the bid price is lower than the price specified in the limit-sell order. d. The trade will not be executed because the asked price is higher than the price specified in the limit-buy order.

You've borrowed $20,000 on margin to buy shares in Ixnay, 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? b. How low can the price of Ixnay shares fall before you receive a margin call?

a. You will not receive a margin call. You invest in 1,000 shares of Ixnay at $40 per share with $20,000 in equity and $20,000 from borrowing. At $35 per share, the value of the stock becomes $35,000. Therefore, the equity decreases to $15,000: Equity = Value of stock - Debt = $35,000 - $20,000 = $15,000 Percentage margin = Equity in account / Value of stock = $15,000 / $35,000 = 0.4286 or 42.86% The percentage margin still exceeds the required maintenance margin. b. Solving (1,000P－$20,000) / 1,000P = 0.35 or 35%, we get P = $30.77 You will receive a margin call when the stock price falls to $30.77 or lower.

Turn back to Figure 2.3 and look at the Treasury bond maturing in February 2039. a. How much would you have to pay to purchase one of these bonds? b. What is its coupon rate? c. What is the current yield (i.e., coupon income as a fraction of bond price) of the bond?

a. You would have to pay the asked price of: 128.212 = 128.212% of par = $1,282.12 b. The coupon rate is 3.500%, implying coupon payments of $35.00 annually or, more precisely, $17.50 (= 35.00/2) semiannually. c. Given the asked price and coupon rate, we can calculate current yield with the formula: Current yield = Annual coupon incomePrice = 3.5128.212 = 0.0273 = 2.73%

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? (Ignore the expected dividend.) 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.

a. Your initial investment is the sum of $5,000 in equity and $5,000 from borrowing, which enables you to buy 200 shares of Telecom stock: Initial investment / Stock price = $10,000 / $50 = 200 shares The shares increase in value by 10%: $10,000 x 0.10 = $1,000. You pay interest of = $5,000 x 0.08 = $400. The rate of return will be: ($1,000 － $400) / $5,000 = 0.12 = 12% b. The value of the 200 shares is 200P. Equity is (200P - $5,000), and the required margin is 30%. Solving (200P －$5,000) / 200P = 0.30, we get P = $35.71. You will receive a margin call when the stock price falls below $35.71.

Find the equivalent taxable yield of the municipal bond in Problem 14 for tax brackets of: a. Zero b. 10% c. 20% d. 30%

a. r = 0.041 － 0 = 0.04 or 4.00% b. r = 0.041 － 0.10 = 0.0444 or 4.44% c. r = 0.041 － 0.20 = 0.05 or 5.00% d. r = 0.041 － 0.30 = 0.0571 or 5.71%