Fin 320F Application Questions Exam 1 Duvic

8. Understand human behavior

Individuals are motivated by incentives; Individuals are limited in resources, information and talent; humans are resourceful

36. Payment choice. Your company gives you the option of receiving your salary at the beginning of each month or at the end of each month. Which option should you choose? At the beginning of each month. At the end of each month. You really don't care.

$1 in salary at the beginning of each month is worth more to you than a dollar received at the end of the month. If you were to receive $1 at the beginning of the month you could invest it to earn interest. It would thus be worth more than a dollar at the end of the month, and would thus be preferable to receiving only $1 at the end of the month.

81. Time Value and student loans. On subsidized Stafford loans, a common source of financial aid for college students, interest does not begin to accrue until repayment begins. Who receives a bigger subsidy, a freshman or a senior? Explain.

A freshman does. The reason is that the freshman gets to use the money for much longer before interest starts to accrue. The subsidy is the present value (on the day the loan is made) of the interest that would have accrued up until the time it actually begins to accrue. So, it would be four years before the freshman had to make the first payment, but only one year before the senior had to begin writing the check. The problem is that the subsidy makes it easier to repay the loan, not obtain it. However, the ability to repay the loan depends on future employment, not current need. For example, consider a student who is currently needy, but is preparing for a career in a high-paying area (such as corporate finance!). Should this student receive the subsidy? How about a student who is currently has some funds, but is preparing for a relatively low-paying job helping disadvantaged youth?

1. Explain what conformation bias is.

A human trait in which we look for evidence to support our beliefs rather than countering them. While the scientific method involves stating hypotheses and then seeking out evidence that these hypotheses are false, with confirmation bias scientists often seek out information that confirms their existing beliefs

52. Given the project's opportunity cost and cash flows, determine the project's acceptability using Net Present Value.

As covered in Lesson 3, Net Present Value takes the economic value of the investment and subtracts the cost of the investment to get the additional wealth created (or destroyed!) if you were to make the investment. The NPV of the FastDrop investment is NPV = PVInflows - PVOutflows $2,727 = $80,000/1.10 - $70,000 When you state the present value of the benefits ($80,000 in one year) to what you'd have to pay today to receive those benefits ($70,000) you find that this is a wealth-increasing investment and should be adopted. Note that all we needed to do was to take FastDrop's economic value and subtract the price that the entrepreneur asked for the company. NPV analysis is just comparing what the investment is worth relative to how much you must pay for the investment. Also note that the decision reached using NPV is the same as with IRR. A word of caution: While this result works for many decisions, there are some very common situations where NPV and IRR may give conflicting advice, which we will cover later.

86. Interest Rates. What happens to the future value of an annuity if you increase the rate, r? What happens to the present value?

As explained in the Key Concepts, annuities are a series of regular cash flows. Each of the cash flows in the annuity acts in the same way as individual cash flows. Just as increasing the interest rate increases the future value of a cash flow and reduces the present value of the cash flow, assuming positive cash flows and a positive interest rate, the present value of an annuity will fall, and the future value of the annuity will rise.

29. Suppose Pharrell, Inc. had 35,000 shares of common stock outstanding. What is the earnings per share, or EPS, figure? What is the dividends per share figure?

As explained in the SB assignment, each of Pharrell's shareholders owns only a small part of the company, represented by the number of shares they hold. Individual shareholders are thus interested in the particular share of earnings and dividends they are entitled to, so we must convert total earnings and dividends to their per-share amounts. Earnings per share is the net income divided by the shares outstanding, so: EPS = Net income / Shares outstanding EPS = $154,050/35,000 EPS = $4.40 per share Dividends per share are the total dividends paid divided by the shares outstanding, so: DPS = Dividends / Shares outstanding DPS = $43,000/35,000 DPS = $1.23 per share We will use EPS and DPS when we calculate share prices in Unit 10.

101. Two distributions. You have two distributions available to you: a frequency distribution and a probability distribution. Please define each and identify which one you'd use to make your investment decision.

As seen in Unit 5, risk involves two returns: The expected return is future return, generally uncertain, that one expects to get from an investment. This is the return that is used in making most business decisions. The realized return is the return that is actually received at the end of the investment period. These distributions help determine the average/expected return and its relationship—variability—with possible realized returns. A frequency distribution presents a measure of how frequently historical returns have occurred over a given time period. From this distribution you can determine the average return earned over a given periods and how variable realized returns were from this average. To generalize, using a frequency distribution assumes that the future expected return will be the same as the historic average return. A probability distribution presents an estimate of the future. Possible rates of return are identified along with the likelihood of the returns. From the probability distribution we can calculate the expected return and how the realized return might vary from the expected return. Every decision we make involves looking into the future and we really don't know what is going to happen! While history has many important insights to provide us, the future is likely to be turbulent—remember creative destruction—so, while not ignoring historical returns, making the best estimates with probability distributions is probably the best course of action.

110. Determining Portfolio Weights. What are the portfolio weights for a portfolio that has 165 shares of Stock A that sell for $69 per share and 125 shares of Stock B that sell for $44 per share?

As the portfolio is a combination assets, its value is determined by two elements: the value of the assets in the portfolio, and the relative investment in these assets. Here we are given the values of Stocks A and B, and can thus determine the total value of the portfolio and then the proportion of wealth invested in each stock. Portfolio value. First, we will find the portfolio value, which is: Total value = 165($69) + 125($44) Total value = $16,885 Portfolio weights. The portfolio weight for each stock is determined by dividing the asset value by the total portfolio value: xA = [165($69)] / $16,885 = .6743 xB = [125($44)] / $16,885 = .3257

91. Calculating Annuity Cash Flows. For each of the following annuities, calculate the annual cash flow. FV/Years/Interest Rate $30,000 8 5% 1,200,000 40 7 625,000 25 8 125,000 13 4

As you can see, these problems are just giving you the opportunity to in each problem calculate a different variable. Here we have the FVA, the length of the annuity, and the interest rate. We want to calculate the annuity payment. Using the FVA equation: First annuity FVA = C{[(1 + r)^t - 1] / r} $30,000 = C[(1.05^8 - 1) / .05] C = $30,000 / 9.54911 C = $3,141.65 Second annuity FVA = C{[(1 + r)^t - 1] / r} $1,200,000 = C[(1.07^40 - 1) / .07] C = $1,200,000 / 199.63511 C = $6,010.97 Third annuity FVA = C{[(1 + r)^t - 1] / r} $625,000 = C[(1.08^25 - 1) / .08] C = $625,000 / 73.10594 C = $8,549.24 Fourth annuity FVA = C{[(1 + r)^t - 1] / r} $125,000 = C[(1.04^13 - 1) / .04] C = $125,000 / 16.62684 C = $7,517.97

85. Annuity Period. As you increase the length of time involved, what happens to the present value of an annuity? What happens to the future value?

Assuming positive cash flows and a positive interest rate, both the present and the future value will rise. This makes perfect sense when we realize that annuities are a stream of regular payments at regular intervals. When you add an additional period to an annuity, you're also adding an additional cash flows.

24. Bear Tracks, Inc. has current assets of $2,030, net fixed assets of $9,780, current liabilities of $1,640, and long-term debt of $4,490. What is the value of the shareholders' equity amount for this firm? How much is net working capital?

Balance Sheet Current Assets $2,030 Net Fixed Assets 9,780 Total Assets $11,810 Current Liabilities $1,640 Long-term debt 4,490 Total liabilities 6,130 Owners' equity 5,680 Total liabilities & Owners' Equity $11,810 Calculate shareholders' equity We can calculate total assets, which is the sum of the current assets and Net fixed assets. Now, recall that: Total assets = Total liabilities + Shareholder equity. With Total assets determined to be $11,810, we now know that the total for the right-hand side of the balance sheet, Total liabilities and shareholder equity, must also be $11,810. There is now only one number remaining: Owners' equity. The owners' equity is a plug variable. By this we mean that with the other items specified, there is only one number that will balance assets and total claims. We know that total assets must equal total liabilities and owners' equity. Total liabilities and owners' equity is the sum of all debt and equity, so if we subtract debt from total liabilities and owners' equity, the remainder must be the equity balance, so: Shareholder' equity = Total assets - Total liabilities = $11,810 - $6,130 = $5,680 Calculate Net working capital Now on to the second question. Net working capital is current assets minus current liabilities, so: NWC = Current assets - Current liabilities = $2,030 - $1,640 = $390

31. Under standard accounting rules, it is possible for a company's liabilities to exceed its assets. When this occurs, the owners' equity is negative. Can this happen with market values? Why or why not?

Book values can be negative, as they follow accounting principles. Market values can never be negative. Imagine a share of stock selling for -$20. This would mean that if you placed an order for 100 shares, you would get the stock along with the seller of the stock giving you a check for $2,000. How many shares do you want to buy? Given market's dependence on supply and demand, if an asset is worthless, it's worthless!

62. Investment Comparison. Suppose that when TMCC offered the security for $24,099, the U.S. Treasury had offered an essentially identical security. Do you think it would have had a higher or lower price? Why?

Building on our discussion in the previous problem, probably not! Both alternatives offer a future payment of $100,000 in 30 years. The Treasury security should be evaluated at the risk-free rate of return; the risky security should be evaluated at its appropriate risk-adjusted opportunity cost. Our risky security offers a 4.68% risk adjusted return at a price of $24,099. The treasury security should offer a lower rate of return, as there is no risk premium. To get this rate on an investment that will pay $100,000 with certainty you would accept a lower rate of return and would pay a higher price. If the risk-free rate is 1%, then the present value of the $100,000 would be: $100,000/(1.01)30 = $74,192. You would be willing to accept this much higher price because you would be getting a fair rate of return of 1%, which is appropriate for this risk-less investment. Note that the difference in these rates is magnified by the long time period of the investment! One of the very basic but very important relationships is the inverse relationship between price and rate of return. For a given future cash flow: If price rises the rate of return drops If the price drops the rate of return rises.

17. What is the agency problem? How does this affect corporations and what can be done to minimize agency costs?

Businesses must satisfy consumers in a competitive market: only those businesses that offer consumers good value will survive. These firms will survive only if they can organize themselves efficiently and if they can raise capital. Although the corporation faces substantial agency problems, it has several unique advantages that make it the dominant form or business organization in our economy. The agency problem. Unlike the proprietorship and partnership forms of organization, where ownership and control are centralized in the same individual/partners, the corporation is a separate legal being that can raise capital from individuals--stockholders--who play no direct role in running the company but rather entrust the role to professional managers. This creates a substantial agency problem in that the managers (agents) who have fiduciary responsibility to the stockholders (Principles) may engage in opportunistic behavior and seek to enrich/protect themselves at the expense of the stockholders. The impact on corporations: agency costs: Extract excessive perquisites and extract corporate wealth for their own use. Have a short planning horizon, in which they try to make the company look good in the short run—while they are managers with visible responsibilities—but not make important long-run investments that would benefit the shareholders but not the managers. Focus on size and other marks of prestige rather than the wealth of the shareholders. The remedy: Even though these advantages are substantial, they could be overshadowed by managerial opportunism. For the corporate form to survive, sufficient checks on managers must be in place. These agency control devices are of two types. Internal control devices that are contained in the structure of the firm. The board of directors is a major control devise, as they are the elected representatives of the shareholders. Compensation contracts that align the interests of managers with those of the shareholders. The corporations governing documents, the charter and by-laws, define managerial duties and place limits on managerial actions. Ambitious managers will rat out opportunistic manages and thus reduce the competition for promotion. External control devices in the firm's environment. Government regulations provide oversight and limits on managerial actions. Publicly-traded companies must have annual audits and reports to the shareholders. Shareholders may sue managers who violate their fiduciary duties. Large sophisticated institutional investors may have substantial proportion of shares in the company, which provides them influence over managerial actions. Managers who are lax or incompetent may cause the corporation to become a target of a hostile takeover, in which a group of outside investors makes an offer to existing shareholders to purchase control of the firm and eject the current managers.

45. Describe how NPV is calculated and describe the information this measure provides about a sequence of cash flows. What is the NPV criterion decision rule?

Calculation: NPV is simply economic cost-benefit analysis. All of the benefits (cash inflows) and costs (cost outflows) are identified. All amounts are taken to their present value using an appropriate discount rate, which is the project's opportunity cost. With all amounts stated at the same point in time the benefits and costs can be compared. Decision rule: If the present value of benefits exceed the present value of costs, then the project is wealth creating. If the present value of benefits is less than the costs, then the project would reduce wealth. Therefore, accept projects with positive NPVs and reject projects with negative NPVs. We would also accept projects with zero NPV, as they are offering us a fair rate of return. As we'll see later on in our course, earning a fair rate of return is actually a quite acceptable outcome!

46. What is the Internal Rate of Return? What is the IRR criterion decision rule?

Calculation: The IRR is the rate of return earned on an investment. The return is "internal" to the timeline as the calculation of the IRR does not involve the opportunity cost/discount rate. For simple one period time lines the calculation involves determining the difference between the ending and beginning value, and then dividing the beginning value into the difference: IRR = (Ending - Beginning)/ Beginning Even though you have a formula sheet, it's useful to understand the variables involved, and how they interact to produce a result. Decision rule: The IRR decision rule is to accept projects with IRRs greater than the discount rate, and to reject projects with IRRs less than the discount rate. This makes sense when you consider that the discount rate is the opportunity cost—the return required to compensate the investor for not investing in other projects equivalent to the one being evaluated. If a project's IRR = 9%, and the discount rate is 6%, the project is a good deal, as you are earning 3% more that you should expect to receive from the project given the other alternatives available to you.

12. What are the three types of financial management decisions? For each type of decision give an example of a business transaction that would be relevant.

Capital budgeting: What productive assets should the business invest in? Examples would include the following. Should a business invest in developing a new service such as self-driving trucks? Should the business invest in an assembly line with workers or one with robots? Should the company establish a call center in the US or in the Dominican Republic? Should the business invest in viral marketing or print advertising? Non-profits and governments also must invest in productive assets. A charity applying for a grant from the Bill and Melinda Gates Foundation must specify the resources needed to protect pregnant women from the Zika virus. Should Austin invest in a passenger rail system? Capital structure: How should a business raise the capital needed to invest in productive assets and finance its operations? Should managers issue financial securities—debt and equity—to raise capital? Is there an optimal mix of debt and equity? Instead of financial securities, should the business take out a bank loan? Issue equity and use the proceeds to retire outstanding debt? Working capital management: How can the company maintain its liquidity—its ability to ensure enough cash comes in on a daily basis to satisfy its short claims?While the capital budgeting and capital structure decisions involve the long-term focus of the business, working capital management focuses instead on the ability to run the business on a daily basis. Examples would be how the business manages it trade credit policy, its short-terms lines of credit, inventory levels, etc.

55. Compounding. What is compounding? What is discounting?

Compounding is the exponential increase in the value of an investment because interest earned is added to the principle, which produces an increased interest payment in the subsequent period. It is also the process of determining the future value of an investment. Discounting is the process of determining the value today of an amount to be received in the future. As many of financial decisions are made today, many problems involve taking present values and the rate used in time value calculations is often referred to as the "discount rate" whether or not you're taking present values or future values.

61. Time Value of Money: From the investor's point of view. Would you be willing to pay $24,099 today in exchange for $100,000 in 30 years? What would you consider in answering yes or no? Would your answer depend on who is making the promise to repay?

Consideration: Your key considerations would be based on opportunity cost. Is the rate of return implicit in the offer attractive relative to other, similar risk investments? The rates offered on investments reflect the perceived risk of the investments: i.e., how certain are we that we will actually get the $100,000? Few investments are riskless, where you will get exactly what you're promised. As we saw in Unit 5, the opportunity cost consists of the risk-free rate plus an appropriate risk premium based on the likelihood that the future payment will show up: Opportunity cost = risk free rate + risk premium. Decision: How would you decide? Calculate what you'd earn: the IRR. Investing $24,099 today and receiving $100,000 in thirty years produces and IRR of 4.86%. If other alternatives offer you less than 4.86% then take this investment. If another alternative offers you more than this investment's 4.86%, then take the alternative. The higher the risk premium the larger the interest rate and the lower the present values, as you don't value a highly risky future payment as much as an investment of lower risk. Final thought: The rate of return earned by the creditor is often less that the rate of the company that invests the borrowed funds in its capital budgeting projects, as the risk to the creditor is less than the risk of the company.

54. Your final choice. Given your financial situation, you can only make one investment. You want to consider both profitability and safety. You only have enough funds to invest in one of these attractive projects. Which investment should you choose? Hive Bliss FastDrop

Considering safety: Hive Bliss is the riskier investment, with a risk premium of 14%. FastDrop is safer, with a risk premium of only 6%. If you were thinking of safety, then FastDrop is the safest investment and should be chosen. Considering wealth: The NPV of FastDrop is $2,727; the NPV of Hive Bliss is $6,694. Thus, Hive Bliss would have a far greater positive impact on your wealth. Even though it is the riskier investment, Hive Bliss offers a better risk-return tradeoff. The higher risk of the Hive Bliss investment is taken into account in the discount rate that places a lower value on future cash flows. This discussion will make more and more sense as we go through our course.

105. Diversifiable and Nondiversifiable Risks. In broad terms, why is some risk diversifiable? Why are some risks nondiversifiable? Does it follow that an investor can control the level of unsystematic risk in a portfolio, but not the level of systematic risk?

Diversifiable risk: Things happen to companies: a great new product is introduced, a new CEO with an effective strategy is appointed, a restaurant chain suffers a series of well-publicized occurrences of food poisoning, etc. These events are unsystematic, in that they occur in a random pattern unconnected to the economy. Good events and bad events have a major impact on the companies involved; however, for an investor holding a large portfolio these events tend to cancel each other. The increased return of the company with the new product is balanced by the decreased return from the restaurant chain. With larger and larger portfolios these nonsystematic risks are reduced by diversification. By investing in a variety of assets, this unsystematic portion of the total risk can be eliminated at little cost. Nondiversifiable risk: Some events are systematic, in that they affect the entire economy. A rise in the price of oil, an increase in interest rates by the Federal Reserve, a major increase in tariffs as part of a "trade war" between countries will have a general impact on economic activity and most companies. For example, an increase in interest rates will increase the opportunity cost for most companies and reduce the desirability of their projects (their NPVs) As this impacts many companies, even a well-diversified portfolio will suffer a decline in its expected return. Investors can control the level of unsystematic risk in their portfolios by holding larger portfolios, which will reduce total volatility at low cost. They cannot diversify away systematic risk and will thus require a risk premium appropriate for the amount of systematic—nondiversifiable risk—in their portfolios.

19. One word continuously comes up in this course: efficiency. Please discuss efficiency in terms of how society organizes economic activity, how businesses are organized and why society allows corporations to focus on maximizing stockholder wealth.

Efficiency in society. Society must establish the economic system in which decisions are made on what to produce the right goods/services at the right time and in the right quantities. This decision is based on the allocation of property rights, which are the rights to use the asset, how the benefits are distributed and the ability to dispose of the assed. The two alternatives are socialism and capitalism. Efficiency in business organization: A business is an economic organization that draws on markets for resources that it can reconfigure to sell as goods and services in markets at a profit. There are three major forms of business organization: proprietorship, partnership, and corporation. These differ in their economic life, liabilities of owners and management structure. As business organizations compete in markets, each business organization must choose the organizational form that is most efficient in competing in their specific market. Efficiency in control of businesses. Society places the stockholders in control of the corporation. The stockholders in return are the residual holders of the corporation and enjoy profits. The stockholder-controlled firm benefits society in two ways. First, profits will occur only if the corporation is efficient in drawing in resources from society and in selling goods and services that members of the society actually want to buy. Thus, the corporation ensures that the resources of society are efficiently used to give a high standard of living to consumers. Second, this focus on profits for stockholders produces an efficient allocation of capital. Companies that produce profits will be able to raise capital. Companies that do not produce profits will have investors move capital from them to profitable firms.

38. Liquid investments. A friend offers you a Coke, a Pepsi, or a Diet Coke. You don't like Diet Coke, so you take the Pepsi. What is the opportunity cost of your choice? Zero, because the drink was free. The Pepsi. The Coke. The Coke plus the Diet Coke.

Eliminating undesirable choices. We here assume, as in many of the decisions we make, that we will consider only positive outcomes and reject outright undesirable outcomes. Sometimes the choice is among undesirable outcomes. "In the 36 states, the Federal Government, and U.S. Military that currently have death penalty statutes, five different methods of execution are prescribed: Lethal Injection, Electrocution, Lethal Gas, Firing Squad, and Hanging. All jurisdictions provide for execution by lethal injection. 16 jurisdictions provide for alternative methods of execution, contingent upon the choice of the inmate, the date of the execution or sentence, or the possibility of the method being held unconstitutional." (http://www.clarkprosecutor.org/html/death/methods.htm). So, if choosing to be shot or receive a lethal injection are the alternatives and you're really afraid of needles your best alternative might be the firing squad. Positive choices. Fortunately, in this example you do have some positive choices and would reject the drink you don't like, Diet Coke. Eliminating the undesirable alternative leaves your choice between Coke and Pepsi. As Opportunity Cost is defined as the best alternative foregone, if you chose Pepsi, you have chosen it rather than the best other alternative available, Coke.

104. Calculating asset expected returns and standard deviations. Based on the following information, calculate the expected return and standard deviation for the two stocks. State of Economy/Probability of State of Economy/Stock A/Stock B Recession .10 .02 -.30 Normal .50 .10 .18 Boom .40 .15 .31

Expected return. The expected return of an asset is the sum of the probability of each state occurring times the rate of return if that state occurs. So, the expected return of each asset is: E(RA) = .10(.02) + .50(.10) + .40(.15) = .1120, or 11.20% E(RB) = .10(-.30) + .50(.18) + .40(.31) = .1840, or 18.40% Variance and standard deviation. To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, and then sum. The result is the variance. So, the variance and standard deviation of each stock is: VarA = .10(.02 - .1120)^2 + .50(.10 - .1120)^2 + .40(.15 - .1120)^2 = .00150 SDA = .00150^(1/2) = .0387, or 3.87% VarB = .10(-.30 - .1840)^2 + .50(.18 - .1840)^2 + .40(.31 - .1840)^2 = .02978 SDB = .02978^(1/2) = .1726, or 17.26%

2. Why these experts might hold such opposing views

Experts develop a view of reality in their early years of study and, once held, may tend to seek out information that confirms their existing views, filter out information that does not support these views, and remember events that do support these views. Experts, like all humans, like to think of themselves as knowledgeable, and do not want to admit they are wrong. Also, as we discussed in class, if an expert is "wrong" he or she would suffer damage to reputation and career

67. Calculating Interest Rates. Solve for the unknown interest rate in each of the following: PV/Yrs/FV $715 11 $1,381 905 8 1,718 15,000 23 141, 832 70,300 16 312, 815

FV = $1,381 = $715(1 + r)^11 r = ($1,381 / $715)^(1/11) - 1 r = .0617, or 6.17% FV = $1,718 = $905(1 + r)^8 r = ($1,718 / $905)^(1/8) - 1 r = .0834, or 8.34% FV = $141,832 = $15,000(1 + r)^23 r = ($141,832 / $15,000)^(1/23) - 1 r = .1026, or 10.26% FV = $312,815 = $70,300(1 + r)^16 r = ($312,815 / $70,300)^(1/16) - 1 r = .0978, or 9.78%

65. Calculating Future Values. For each of the following, compute the future value: Present Vale/Yrs/Interest Rate $3,150 7 13% 8,453 16 7 89,305 19 9 227,382 26 5

FV = $3,150(1.13)^7 = $7,410.71 FV = $8,453(1.07)^16 = $24,954.64 FV = $89,305(1.09)^19 = $459,176.06 FV = $227,382(1.05)^26 = $808,495.97

68. Calculating the Number of Periods. Solve for the unknown number of years in each of the following: PV/Interest Rate/FV $195 9% $873 2,105 7 3,500 47,800 12 326,500 38,650 19 213,380

FV = $873 = $195 (1.09)^t t = ln($873 / $195) / ln 1.09 t = 17.39 years FV = $3,500 = $2,105(1.07)^t t = ln($3,500 / $2,105) / ln 1.07 t = 7.51 years FV = $326,500 = $47,800(1.12)^t t = ln($326,500 / $47,800) / ln1.12 t = 16.95 years FV = $213,380 = $38,650(1.19)^t t = ln($213,380 / $38,650) / ln 1.19 t = 9.82 years

64. Simple Interest versus Compound Interest. First City Bank pays 6 percent simple interest on its savings account balances, whereas Second City Bank pays 6 percent interest compounded annually. If you made a deposit of $8,100 in each bank, how much more money would you earn from your Second City Bank account at the end of 10 years?

First City Bank: The simple interest per year is: $8,100 × .06 = $486 So, after 10 years, you will have: $486 × 10 = $4,860 in interest. The total balance will be $8,100 + 4,860 = $12,960 Second City Bank: With compound interest, we use the future value formula to get the future value, which includes getting your deposit back plus the accumulated interest on interest. FV = PV(1 +r)t FV = $8,100(1.06)10 FV = $14,505.87 The difference between these two accounts is quite substantial. Difference = Second City Bank - First City Bank $1,545.87= $14,505.87 - 12,960. Second City's use of compound interest makes a big difference!

99. Calculating EAR. First National Bank charges 10.1 percent compounded monthly on its business loans. First United Bank charges 10.3 percent compounded semiannually. As a potential borrower, which bank would you go to for a new loan?

For discrete compounding, to find the EAR, we use the equation: EAR = [1 + (APR / m)]^m - 1 First National Bank First National Bank charges an APR of 10.1%, but compounds monthly. EAR = [1 + (.101 / 12)]^12 - 1 = .1058, or 10.58% First United Bank First United Bank charges a higher APR of 10.3% EAR = [1 + (.103 / 2)]^2 - 1 = .1057, or 10.57% For a borrower, First United would be preferred since the EAR of the loan is lower. Notice that the higher APR does not necessarily mean the higher EAR. The number of compounding periods within a year will also affect the EAR. A difference of 10.58% - 10.57% = 0.01% seems like a small amount. However, if your company was borrowing $500,000, you'd be paying $5,000 more in interest. 0.01% is called a point. In markets this is not a trivial amount!

97. Calculating EAR. Find the EAR in each of the following cases: Stated Rate (APR)/# of Times Compounded 10% Quarterly 17 Monthly 13 Daily 9 Semiannually

For discrete compounding, to find the EAR, we use the equation: EAR = [1 + (APR / m)]^m - 1 APR of 10%, compounded quarterly EAR = [1 + (.10 / 4)]^4 - 1 = .1038, or 10.38% APR of 17%, compounded monthly EAR = [1 + (.17 / 12)]^12 - 1 = .1839, or 18.39% APR of 13%, compounded daily EAR = [1 + (.13 / 365)]^365 - 1 = .1388, or 13.88% APR of 9%, compounded semiannually EAR = [1 + (.09 / 2)]^2 - 1 = .0920, or 9.20%

79. Present Value. If you were an athlete negotiating a contract with a signing bonus of $1 million, would you want the signing bonus payable immediately, or divided into smaller payments over the duration of your contract? How about looking at it from the team's perspective?

From the athlete's point of view, if the total amount of the bonus is fixed, you want as much as possible as soon as possible. Spreading out the payments would make their present value smaller. The team (or, more accurately, the team owner) wants just the opposite. Given a fixed amount, splitting it up into future payments means that the present value is less, as the amounts paid out in the future have a smaller present value. These differences in perspectives makes sense when we know that a dollar received today is more valuable than a dollar received in the future. If you're the athlete receiving the funds, a higher present value is desirable. If you're the owner paying out, a smaller present value is desirable.

56. Values and Periods. As you increase the length of time involved, what happens to future values? What happens to present values?

Future values: Future values are positively related to the length of time of the investment, as each additional period additional interest is earned. This can be seen in the Future Value Factor = (1 + r)T, which is multiplied by the present value to get the future value. Present values: Present values are inversely related to the length of time of the investment. The Present Value Factor = 1/[(1 + r)T)] is the inverse of the Future Value Factor. This shows that discounting is the inverse of compounding.

7. Which provides a higher standard of living: command economies or market economies? Why?

Given the importance of incentives in guiding individual choice, market economies generally provide a better life for their citizens than alternative systems of economic organization because they accept human nature

11. Your good friend is a Libertarian who thinks that the only good government is no government. While you're not a Socialist, you do believe that governments have a role to play in a market economy. Explain to your friend the important roll played by government, and give an example of each.

Given your friend's beliefs, which might be to an extent reflect confirmation bias, may cause her to miss some of the ways that governments touch her and her family's lives. Enhance the welfare of its citizens. Limit opportunistic behavior. basis of this example.)Modify markets. You point out to your friend dozens of ways government structure economic activity. Given the imperfect nature of humans, and the real difficulties faced by those not blessed with good fortune, governments have a major rule to play in a market economy.

21. In preparing a balance sheet, why do you think standard accounting practices focuses on historic costs rather than market values?

Going back to our Key Concepts: Uses and Guiding Principles of Accounting, we defined the cost principle to record the purchase price of assets. Accounting uses historical costs, which canterm-18 be measured and reflect market values at the time the asset is obtained. Historical costs are thus considered more objective and not subject to estimation errors, or inflated by managers to make them look better. On the other hand, estimated market values for many assets are uncertain. For example, a firm may decide to sell a building. While the CFO may estimate what the building is worth, she will not know what the actual value is until the building is actually sold in a market transaction. As many homeowners found out in the Great Recession, what on thinks an asset is worth may be very different than what it actually might sell for! Estimated market values can be difficult to estimate, and different analysts would come up with different numbers. So, unless the accountant has a firm market transaction, where a buyer actually pays for the asset, book values reflect the historic cost of the asset and provide an objective, if imperfect, measure of value. This reliance on book values may mean that the balance sheet is not a true measure of current value. In Unit 5 we'll move to market values and the Economic Balance Sheet.

98. Calculating APR. Find the APR, or stated rate, in each of the following cases: # of Times Compounded/Effective Rate (EAR) Semiannually 14% Monthly 9 Weekly 8 Daily 13

Here we are given the EAR and need to find the APR. Using the equation for discrete compounding: EAR = [1 + (APR / m)]^m - 1 We can now solve for the APR. Doing so, we get: APR = m[(1 + EAR)^(1/m) - 1] EAR of 14%, compounded semiannually EAR = .14 = [1 + (APR / 2)]^2 - 1 APR = 2[(1.14)^(1/2) - 1] = .1354, or 13.54% EAR of 9%, compounded monthly EAR = .09 = [1 + (APR / 12)]^12 - 1 APR = 12[(1.09)^(1/12) - 1] = .0865, or 8.65% EAR of 8%, compounded weekly EAR = .08 = [1 + (APR / 52)]^52 - 1 APR = 52[(1.08)^(1/52) - 1] = .0770, or 7.70% EAR of 13%, compounded daily EAR = .13 = [1 + (APR / 365)]^365 - 1 APR = 365[(1.13)^(1/365) - 1] = .1222, or 12.22%

93. Calculating Annuity Values. If you deposit $5,000 at the end of each year for the next 20 years into an account paying 9.6 percent interest, how much money will you have in the account in 20 years? How much will you have if you make deposits for 40 years?

Here we need to find the FVA = C{[(1 + r)^t - 1] / r} FVA for 20 years = $5,000[(1.096^20 - 1) / .096] FVA for 20 years = $273,685.74 FVA for 40 years = $5,000[(1.096^40 - 1) / .096] FVA for 40 years = $1,985,526.07 Notice that because of compound interest, doubling the number of periods does not merely double the FVA, it increases it by over ($1,985,526 - $273,686)/$273,686 = 6.25 or 600%--an example of how compounding produces exponential growth!

121. Using CAPM: Market rate of return. A stock has an expected return of 10.9 percent, its beta is .85, and the risk-free rate is 2.8 percent. What must the expected return on the market be?

Here we need to find the expected return of the market, using the CAPM. Substituting the values given, and solving for the expected return of the market, we find: E(Ri) = Rf + [E(RM) - Rf] × Bi .109 = .028 + [E(RM) - .028](.85) E(RM) = .1233, or 12.33%

89. Calculating Annuity Cash Flows. For each of the following annuities, calculate the annual cash flow. PV/Years/Interest Rate $24,500 6 11% 19,700 8 7 136,400 15 8 285,650 20 6

Here we're given four variables and asked to solve for the annual payments. This is the same process used when you're taking out a loan to purchase a car: given what you've borrowed, how long your note will be, and what rate will you be charged, what are your monthly payments? Using the PVA equation and solving for the payment in each case, we find: First annuity PVA = C({1 - [1 / (1 + r)^t]} / r)) $24,500 = $C{[1 - (1 / 1.11)^6] / .11} C = $24,500 / 4.23054 C = $5,791.23 Second annuity PVA = C({1 - [1 / (1 + r)^t]} / r )) $19,700 = $C{[1 - (1 / 1.07)^8] / .07} C = $19,700 / 5.97130 C = $3,299.11 Third annuity PVA = C({1 - [1 / (1 + r)^t]} / r )) $136,400 = $C{[1 - (1 / 1.08)^15] / .08} C = $136,400 / 8.55948 C = $15,935.55 Fourth annuity PVA = C({1 - [1 / (1 + r)^t]} / r )) $286,650 = $C{[1 - (1 / 1 .06)^20] / .06} C = $286,650 / 11.46992 C = $24,904.27

92. Calculating Annuity Values. For each of the following annuities, calculate the future value. Annual Payment/Years/Interest Rate $1,900 10 8% 6,000 40 9 2,950 9 6 6,400 30 10

Here, we need to find the future value of an annuity. Using the FVA equation, we find: First annuity FVA = C{[(1 + r)^t - 1] / r} FVA = $1,900[(1.08^10 - 1) / .08] FVA = $27,524.47 Second annuity FVA = C{[(1 + r)^t - 1] / r} FVA = $6,000[(1.09^40 - 1) / .09] FVA = $2,027,294.67 Third annuity FVA = C{[(1 + r)^t - 1] / r} FVA = $2,950[(1.06^9 - 1) / .06] FVA = $33,899.38 Fourth annuity FVA = C{[(1 + r)^t - 1] / r} FVA = $6,400[(1.10^30 - 1) / .10] FVA = $1,052,761.75

122. Using CAPM: Riskfree rate. A stock has an expected return of 10.7 percent and a beta of .91, and the expected return on the market is 11.5 percent. What must the risk-free rate be?

Here, we need to find the risk-free rate, using the CAPM. Substituting the values given, and solving for the risk-free rate, we find: E(Ri) = Rf + [E(RM) - Rf] × Bi .1070 = Rf + (.1150 - Rf)(.91) .1070 = Rf + .10465 - .91Rf Rf = .0261, or 2.61%

47. What are the differences between the IRR and NPV? Are there any situations in which you might prefer one method over the other? Explain?

IRR, a measures the rate of return on an investment, answers the first question. Intuitively, the higher the rate the better; however, rates of return are a relative measure. Saying that you're earning 6% does not tell you whether or not 6% is a good return. To make effective decisions the IRR must be compared to the rate of return available from equivalent investments, the opportunity cost. The NPV, as cost/benefit analysis, answers the second question. NPV takes every aspect of economic value into account: the cash flows, their timing, and the opportunity cost. As there is a time value of money, amounts can be compared only when they occur at the same point in time. NPV therefore consolidates all cash flows today, and allow a proper comparison of inflows and outflows. NPV is a dollar measure of wealth created, stated in the current time. As the goal is to increase wealth, NPV is better than IRR. As the penny pitching example in the last Key Concepts shows, a high rate of return on a small investment will not benefit you as an investment with a higher NPV. Of course there are always complexities in the real world! In some situations these two decision rules may conflict. We'll discuss these special situations later in our course.

37. Interest rates and future values. As the interest rate rises, the present value of a future cash flow: Goes up. Goes down. Stays the same. Could either rise or fall.

If you expect to receive $10 in one year, the present value is $10/(1 + r). Note that the $10 is divided by (1+r). The higher the interest rate, the lower the present value, as you are discounting a future cash flow to get its value today, and your denominator just increased. Interest rates increase: Discounting $10 by 5% gives you $10/1.05) = $9.52. If the interest rate was to increase to 10%, then the present value would be $10/(1.10) = $9.09. An increase in the interest rate would cost you $9.09 - $9.52 = $0.43. Interest rates decrease: What if interest rates drop from 5% to 2%? The value of the future payment would be $10/(1 .02) = $9.80. You'd gain $9.80 - $9.52 = $0.55. So we've covered the what, now let's talk about the why. Any decision made concerning your $10 must be made with reference to the rates you could earn on other investments: the opportunity cost. In Unit 2 we examined how the government can use monetary policy to guide the economy. If the Fed increases interest rates, prices in the stock market generally drop, as the present value of future dividends drop. If the Fed decreases interest rates, stock prices generally increase. Fiscal and monetary policy are complex issues, but the foundation for understanding them is the time value of money! The interest rate used in our time value calculations is the opportunity cost which we'll develop in the next two units and use throughout our course.

44. Your little sister Tiffany is beginning to cause you some concern. She wants to borrow $480 from you today and promises to pay you $500 in one year. You earn 3% on your deposits. Disregarding what your 9 year-old sister would need $480 for, would this be a good loan for you to make?

If you made the loan you would receive $500 in one year. Given your interest rate of 3%, the present value of this payment is: $500/(1 + r) = $500/(1.03) = $485.43. This is a good deal. You would give Tiffany $480, but receive a future cash flow that has a present value of $485.43. Economically, you're better off by $485.43 - $480 = $5.44, a comparison we'll make more explicit when we introduce Net Present Value Analysis in Lesson 2. Of course, Tiffany is eventually going to figure this out, so you might want to keep your bedroom door locked at night.

25. Why is it that the revenue and cost figures shown on a standard income statement may not be representative of the actual cash inflows and cash outflows that occurred during a period?

In Key Concepts: Uses and Guiding Principles of Accounting we show that accounting follows the accrual/matching principle, which calls for revenues and the costs associated with producing those revenues, to be "booked" when the revenue process is essentially complete, not necessarily when the cash is collected or bills are paid. This matching of revenues and expenditures is quite logical, as the firm is not likely to spend/invest money unless they expect to get revenue from the expenditure. However, the accrual/matching principle uses revenues, not actual cash inflows, and expenses, not actual cash outflows. While the focus on accounting-defined flows rather than cash flows is quite useful in making short-term working capital decisions, it may not be a good guide for measuring net cash flow (cash in minus cash out) for capital budgeting and financing decisions, which should be based on expected future cash flows. We'll discuss cash flow analysis later in this Unit. All of the methods defined in this Key Concept are adopted to serve the major purpose of accounting: to provide useful and objective information to decision makers.

9. Your sister strongly supports nationalization of the US health care sector. She feels that politicians and government administrators would do a better job of using scarce resources to serve the health needs of the US. Please evaluate her argument, giving your own examples to support your conclusions.

In a command economy: Property rights are controlled by the government. The government allocates resources as it thinks best for society and the consumption of goods are be determined by rationing. A government-run health care system thus allocates only a limited amount of resources to health care based on the government's determination of what the best interests of society are. The following results may occur: cosmetic services might be restricted to free up funds for health care for the poor; medical tests, such as breast cancer screenings, may be denied to some patients as not being cost effective; the amount spent private health treatment may be find that we are spending too much on health care relative to education, and close down some health-related activities to provide more student loans. Thus, the scarce resources of society are directed as the health-care administrators think best. This may produce suboptimal results as we have seen in our course. We can examine this issue in more depth by using the points in Why Government can't run a business. 1. Governments are run by politicians, not businessmen 2. Politicians need headlines 3. Governments use other people's money 4. Government does not tolerate competition 5. Government enterprises are almost always monopolies 6. Successful corporations are run by benevolent despots 7. Government is regulated by government

95. Calculating Perpetuity Values. In the previous problem, suppose Curly's told you the policy costs $645,000. At what interest rate would this be a fair deal?

In this problem we're given all of the cash flows and asked to calculate the interest rate. Here we need to find the interest rate that equates the perpetuity cash flows with the PV of the cash flows. Using the PV of a perpetuity equation we can now solve for the interest rate as follows: PV = C / r $645,000 = $30,000 / r r = $30,000 / $645,000 = .0465, or 4.65%

58. Future Values. Suppose you deposit a large sum in an account that earns a low interest rate and simultaneously deposit a small sum in an account with a high interest rate. Which account will have the larger future value?

It depends on the length of time involved. The large deposit will have a larger future value for some period, but after time, the smaller deposit with the larger interest rate will eventually become larger due to the effect of compound interest. The length of time for the smaller deposit to overtake the larger deposit depends on the amount deposited in each account and the interest rates.

32. Suppose a company's operating cash flow was negative for several years running. Is this necessarily a good sign or a bad sign?

It's probably not a good sign for an established company. As cash balances go down, the company faces insolvency, where it does not have the underlying value to continue operations. A company that has several years of negative cash flow would eventually run out of cash and cease to exist. On the other hand, a start-up would likely face negative cash flow for several years. The negative cash flow would be a sign of growth as the company develops its concepts into a viable product. While substantial cash inflows would not come from sales, the company would use cash provided by angle investors and venture capitalist, a process we'll discuss later in our course. Two comments. First, we've seen two terms that look similar but do reflect different concepts that you should understand. Liquidity: Can the firm pay its short-term obligations, such as paying workers or its accounts payable. Solvency: Is the firm a viable company: can it meet its long-term financial obligations: meeting its long-term contractual interest payments to its bondholders. A solvent company's assets are greater than the claims against those assets. Second, cash flow analysis is crucial for making managerial decisions and involves not only the size of the cash flows, but also their timing and risks. While we'll introduce these analytical techniques in the remaining units of Part II, you'll not really understand them unless you have a decent foundation in accounting!

20. What does liquidity measure? Explain the trade-off a firm faces between high-liquidity and low-liquidity levels.

Liquidity measures how quickly and easily an asset can be converted to cash without significant loss in value. A liquid asset can easily and quickly be converted to cash, whereas an illiquid asset is difficult to convert to cash. By converting we mean selling, and here are two examples. A share of Apple stock is liquid. You can sell it instantly, face a low transaction cost, and loose none of your share's value. A condo is not liquid. If you were to sell your condo you'd list it for sale, which might take a few weeks to find a buyer and additional time to close the sale. You could certainly sell quickly, but would have to accept a much lower cost. And, there's the Realtor who helps you with the transaction and would be paid a commission, perhaps as much as 6% of the sales price. So, if you might need the funds quickly, investing in the apple stock is the way to go. Liquidity is not an either or situation. You would certainly like an illiquid asset—the condo—to provide shelter, as a stock certificate does not provide adequate shelter in a rainstorm. You would therefore invest some of your wealth in shelter, some in investments, and have sufficient cash on hand to handle regular expenses as they occur, and also a liquid reserve to handle unexpected major expenses, such as a blown transmission or a broken leg. Similarly, it's desirable for firms to have sufficient liquidity so that they can more safely meet short-term creditor demands. However, liquidity for a firm has an opportunity cost. Firms need to invest in long-term, illiquid productive assets to satisfy their customers. Also, these long term assets reap higher returns than very liquid assets such as cash or marketable securities. It's up to the firm's financial management staff to find a reasonable compromise between these opposing needs.

57. Values and Interest Rates. What happens to a future value if you increase the rate, r? What happens to a present value?

Major determinants of value are the amount of time, as seen in question 2, and interest rates. Future values are positively related to interest rates, as the higher the interest rate, the higher the amount of interest earned in each period. Present values are inversely related to interest rates, as calculating present values involves dividing (1 + r)^T. These questions show the mirror image of calculating future values and present values. While this seems like a simple, even boring statement, it's surprising how many students end up mismanaging these calculations. Remember: future values increase with longer time periods and higher interest rates; present values decrease with longer time periods and higher interest rates.

6. Mixed Economy

Many economies have government control over some areas of economic activity but leave most economic decisions to markets. For example, Austin Energy is owned by the City of Austin

4. Define and contrast market economies and command economies.

Market Economies: allows people to control property rights: to hold and dispose of assets as they desire through markets. Market participants act on incentives to maximize their welfare. Resources are allocated based on the cumulative trade of market participants Command Economies: Property rights are controlled by the government. The government will allocate resources as it thinks best for society. The consumption of goods will be determined by rationing. This is also called Socialism

106. Information and Market Returns. Suppose the government announces that, based on a just-completed survey, the growth rate in the economy is likely to be 2 percent in the coming year, as compared to 5 percent for the year just completed. Will security prices increase, decrease, or stay the same following this announcement? Does it make any difference whether or not the 2 percent figure was anticipated by the market? Explain.

Market prices reflect information. Investors will look for information that will impact stock prices. If new favorable information on a stock reaches the market investors will want to buy the stock and the price will increase. If investors receive unfavorable information on the stock they will sell the stock and the price will drop. Information impacting the market as a whole—systematic information—will affect all securities. In this case, if the market expected the growth rate in the coming year to be 2 percent, then there would be no change in security prices if this expectation had been fully anticipated and priced. However, if the market had been expecting a growth rate different than 2 percent and the expectation was incorporated into security prices, then the government's announcement would most likely cause security prices in general to change; prices would typically drop if the anticipated growth rate had been more than 2 percent, and prices would typically rise if the anticipated growth rate had been less than 2 percent.

16. What goal should always motivate the actions of the firm's financial manager?

Maximizing the wealth of its shareholders, with wealth measured by the share price set in competitive stock markets. This focus on profitability as measured by markets can lead to (1) the efficient use of society's scarce resources and (2) the raising of large amounts of capital, thus leading to a higher standard of living for society. This goal is measurable! The stock price reflects the performance of the corporation. A successful company that produces value for society will see its stock price increase. One that doesn't will see the stock price decrease and, if profits continue to decline, the corporation will cease to exist. I stress that this goal, unlike those of government and nonprofit organizations, takes human nature into account. Our elected politicians are our agents with the explicit goal of providing a society that benefits all of its members. One of the measure of political success in our current presidential race is how much money the candidates can raise. This is a very limited way of measuring how beneficial their policies will be if elected.

30. What accounting item differentiates accounting net income from net cash flow?

Net income: Accounting rules guide how revenues and expenditures are recognized and thus provide objective information to decision makers. One of the major expenses is the use of the firm's productive assets--for example, a major robotic lathe is used to produce a complex artificial heart valve. This asset is"used up" over time and thus loses value in exactly the same why that your car loses value of the years that you drive it. Accounting convention and tax laws define this wearing out as Depreciation. The firm is allowed to deduct a depreciation expense from revenues. This is a non-cash deduction that also requires adjustments made in asset book values in accordance with the matching principle in financial accounting. Net cash flow: Net cash flow is the cash flow produced by the company. As depreciation is not a cash expense it is not part of net cash flow. However, depreciation is a tax shield that reduces taxable income and thus the taxes paid, which are a cash flow.

23. Given the balance sheets calculated in Question 3, what was the change Rasputin's in net working capital in 2019?

Net working capital is a major part of the balance sheet. Companies must have liquidity—the ability to pay their bills on a daily basis. As the cash coming in on a daily basis will not usually match the cash going out, they need a positive balance to serve as cushion. Working capital involves short-term assets, which are expected to turn into cash within a year, and short-term claims, which must be paid for in cash within a year. Net Working Capital (NWC) measures the difference between these short-term and long-term items and should be positive. However, a change in NWC could be favorable or unfavorable. Increase: An increase in NWC indicates that the company is more liquid: that it has more current assets vs. current liabilities and is thus better able to meet its current obligations. However, companies can have more NWC than needed. Excess NWC takes cash away for more productive activities. For example, you may carry a balance in your checking account to cover your checks. Having $10,000 in your checking account is probably not efficient, as you could invest a large part of this cash in stocks that would provide a much higher rate of return. Reduction: A reduction in NWC in given year could actually be beneficial. For example, if a company were to become more efficient in inventory management, the amount of inventory needed would decline. The same might be true if it becomes better at collecting its receivables. In general, anything that leads to a decline in ending NWC relative to beginning NWC would have this effect. Of course, a declining NWC could also be bad news if it reflected a decline in cash due to a decline in sales, or an increase in labor costs not matched by an increase in sales. To calculate the change in NWC we must first determine the NWC for each year. 2018: NWC = Current assets - Current liabilities = $2,140 - $994 = $1,146 2019: NWC = Current assets - Current liabilities = $2,346 - $1,126 = $1,220. The change in NWC is thus $1,220 - $1,146 = $74. This means that Rasputin invested more in short-term assets than it took on short-term liabilities. Its NWC cushion increased, giving it more liquidity.

107. Expected Portfolio Returns. If a portfolio has a positive investment in every asset, can the expected return on the portfolio be greater than that on every asset in the portfolio? Can it be less than that on every asset in the portfolio? If you answer yes to one or both of these questions, give an example to support your answer.

No to both questions. The portfolio expected return is a weighted average of the asset returns, so it must be less than the largest asset return and greater than the smallest asset return. This is not a trivial question, as it does require an understanding of what an average return really is!

66. Calculating Present Values. For each of the following, compute the present value: Yrs/Interest Rate/FV 15 7% $17,328 8 11 41,517 13 10 790,382 25 13 647,816

PV = $17,328 / (1.07)^15= $6,280.46 PV = $41,517 / (1.11)^8 = $18,015.33 PV = $790,382 / (1.10)^13 = $228,945.51 PV = $647,816 / (1.13)^25= $30,513.40

27. Pharrell, Inc. has sales of $634,000, costs of$328,000, depreciation expense of $73,000, interest expense of $38,000, and a tax rate of 21 percent. What is the net income for this firm?

Pharrell, Inc. Income Statement Sales $634,000 Costs 328,000 Depreciation 73,000 EBIT $233,000 Interest 38,000 Taxable income $195,000 Taxes (21%) 40,950 Net income $154,050 1. Calculate EBIT. Revenues are the "Top Line" reflecting revenues from Pharrell's sales of goods and services. From these we subtract the operating costs incurred to produced goods and services, the depreciation expense that represents the use of the capital assets. This produces the Earnings Before Interest and Taxes (EBIT) which reflect the operating profitability of Pharrell, Inc. 2. Subtract the interest expense. Interest is the cost of borrowing money from creditors/bondholders and is a tax-deductible financing expense. 3. In determining EBIT and then subtracting the interest expense, you have subtracted all of the tax deductible expenses and thus the profit that is exposed to income tax. Subtracting this tax gives us the Net Income. It is the "Bottom Line" of the company and measures the accounting profits that accrue to Pharrell's shareholders.

113. Returns and Standard Deviations. Consider the following information: State of Economy/Probability of State of Economy/Stock A/Stock B/Stock C Boom .60 .15 .02 .34 Bust .40 .03 .16 -.08 What is the expected return on an equally weighted portfolio of these three stocks? What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C?

Portfolio expected return with equal investment in the three assets: To find the expected return of the portfolio, we need to find the return of the portfolio in each state of the economy. In this case all three assets have the same weight. To find the expected return in an equally weighted portfolio, we can sum the returns of each asset and divide by the number of assets, so the expected return of the portfolio in each state of the economy is: Boom: Rp = (.15 + .02 + .34) / 3 = .17, or 17% Bust: Rp = (.03 + .16 + .08) / 3 = .0367, or 3.67% The expected return of the portfolio is calculated by multiplying the returns in Boom and Bust states by the likelihood of those states occurring. E(Rp) = .60(.17) + .40(.0367) = .1167, or 11.67% Portfolio variance with unequal investment in the three assets: In this part of the question the portfolio does not have an equal weight in each asset. The portfolio return in Boom and Bust must be computed by multiplying the returns of each security by its proportional weight in the portfolio. To do this, multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get: Boom: Rp = .20(.15) +.20(.02) + .60(.40) = .2380, or 23.80% Bust: Rp = .20(.03) +.20(.16) + .60(.08) = -.0100, or -1.00% The expected return of the portfolio is:E(Rp) = .60(.2380) + .40(-.0100) = .1388, or 13.88%

22. Based on the following information for Rasputin Corporation, prepare a balance sheets for 2018 and 2019 Use a 21 percent tax rate. 2018 2019 Sales $3,790 $3,990 COGS 2,043 2,137 Deprec. expense 975 1,018 Interest 225 267 Dividends 200 225 Current assets 2,140 2,346 Net fixed assets 6,770 7,087 Current liabilities 994 1,126 Long-term debt 2,869 2,956

Rasputin Corporation Balance Sheets as of December 31, 2018 and 2019 2018/2019 Current assets 2,140 2,346 Net fixed assets 6,770 7,087 Total Assets 8,910 9,433 2018/2019 Current liabilities 994 1,126 Long-term debt 2,869 2,956 Total Liabilities & Shared Equity 8,190 9,433 The first step is to enter the appropriate accounts in the balance sheet. Note that while most of the items are given, there was no number for equity. However, we know from the major accounting balance sheet identity Total assets = Total liabilities + Shareholder equity Solving for 2019 equity we get $9,433 = $4,082 + Equity Equity = $9,433 - $4,082 = $5,351 There are three items that are not part of the balance sheet. Dividends are payments to shareholders. They are very important but are not part of the balance sheet. Interest expense is an expense listed in the income statement. While you are given the tax rate, this rate should be applied to income, which is in the income statement.

26. Based on the following information for Rasputin Corporation prepare an income statement for 2019. Please use a 21% corporate tax rate. 2018/2019 Sales $3,790 $3,990 Cost of goods sold 2,043 2,137 Depreciation expense 975 1,018 Interest 225 267 Dividends 200 225 Current assets 2,140 2,346 Net fixed assets 6,770 7,087 Current liabilities 994 1,126 Long-term debt 2,869 2,956

Rasputin Corporation Income Statement Sales $3,990 COGS 2,137 Deprec. Expense 1,018 EBIT $835 Interest 267 Taxable Inc $568 Taxes 119 Net Income $449

18. The stockholders have the legal right to control the firm and to receive dividends and potential capital gains in return. How can this arrangement benefit society as a whole?

Residually, Efficient production, Efficient capital allocation, This system therefore results in the efficient production of the goods and services which the members of society (the consumers) want, while making best use of society's scarce capital. However, to accomplish ends which will benefit not only the stockholders but society as a whole, the system must have: A system of government regulations to protect society from negative externalities, Competition to insure that the consumer faces a fair price. Control of opportunistic behavior on the part of corporate managers.

10. Define self-interest and opportunism? Which do markets follow? Explain.

Self-interest: Seeking to benefit oneself while still respecting the rights of others: seeking a fair deal. Opportunism: Seeking an immoral gain from others via deception, deceit, theft. Actions would improperly harm others. Markets on average are guided by self-interest. Market-based businesses are generally guided by their self-interest to provide in an efficient manner the goods and services that consumers want. Only by satisfying consumer demand will profits be received. While imperfect, market economies accept human nature as it is and provide, through consumer choice and government regulation, limits on opportunistic behavior. Corrective actions: Market participants can engage in opportunistic behavior; however the ability of other market participants to choose not to deal with these misbehaving participants provides a disciplining force that corrects the bad behavior. Business scandals are a sign of the system correcting itself, and are generally of much shorter duration than non-business scandals.

117. Corporate Downsizing. In recent years, it has been common for companies to experience significant stock price changes in reaction to announcements of massive layoffs. Critics charge that such events encourage companies to fire longtime employees and that Wall Street is cheering them on. Do you agree or disagree?

Such layoffs generally occur in the context of corporate restructurings. To the extent that the market views a restructuring as value-creating, stock prices will rise. So, it's not the layoffs per se that are being cheered on but the cost savings associated with the layoffs. Nonetheless, Wall Street does encourage corporations to take actions to create value, even if such actions involve layoffs. These layoffs may also be the result of creative destruction, which is increasingly affecting higher level jobs.

60. Time Value of Money: From the company's point of view. Why would TMCC be willing to accept such a small amount today ($24,099) in exchange for a promise to repay about four times that amount ($100,000) in the future

TMCC borrows money because it hopes to earn a higher rate of return in its capital budgeting projects than the rate payed to their creditors. If the creditors lend $24,099 and receive $100,000 in thirty years they would earn an IRR of 4.86%. If TMCC takes the $24,099 and invests it wisely in projects that produce desirable products for its customers it would earn more than the 4.86% they pay to the creditors. If rate of return on TMCC's projects was 6%, the borrowed $24,099 would grow to an inflow $138,412. In thirty years, TMCC's investment would be worth $138,412. After paying off the debt, they would have $38,412 ($138,412 - $100,000) that they would not otherwise have. This ability to use borrowed funds to create wealth is one of the basic rationales for businesses borrowing funds.

48. Project IRR. A firm evaluates all of its projects by applying the IRR rule. If the required rate of return is 14 percent, should the firm accept a project that requires an investment today of $158,500 and has an expected cash flow in one year of $175,000?

The IRR is the rate of return earned on an investment. For our simple one-period investment the IRR is: IRR = (Ending value - Beginning value)/ Beginning value = ($175,000 -$158,500)/ $158,500 = $16,500/$158,500 = 10.41% The required rate of return—the opportunity cost offered on equivalent investments—is 14%, the IRR does not compare well with other equivalent investments, so this investment should be rejected. In Unit 6 we'll see how calculating IRR with multiple periods is more complex and will require a financial calculator

49. Project NPV. For the investment in the previous problem, suppose the firm uses the NPV decision rule. At the same required rate of return of 14 percent, should the firm accept the project? What if the required rate of return was 8 percent?

The NPV of a project is the PV of the outflows minus by the PV of the inflows. The equation for the NPV of this project at a 14 percent opportunity cost/discount rate is: NPV = -$158,500 + $175,000 /1.14 = -$158,500 + $153,509 = -$4,991 At a 14 percent required return, the NPV is negative, so we would reject the project. The equation for the NPV of the project at an 8% percent required return is: NPV = -$158,500 + $175,000 /1.08 = -$158,500 + $162,037 = $3,537. At an 8 percent required return, the NPV is positive, so we would accept the project. While this is a simple computational problem, it demonstrates some major economic relationships. The opportunity cost: Economic decisions are comparisons of alternatives. We evaluate investments or other economic decisions using the opportunity cost, which is the rate we should earn on equivalent investments, with equivalent being largely based on risk, which we'll look at in Lesson 3. The opportunity cost is directly used in calculating NPV. The opportunity cost is not used in calculating IRR: the IRR is compared to the opportunity cost to reach a decision. The opportunity cost is often called the required rate of return, as it is the minimum rate of return that is acceptable. Economic value: We calculate how much the future cash flows of an investment are worth to us today-- their present value--which takes into account the amount of the cash flows, when they occur, and their risk. The present value of inflows is the economic value. NPV: Note that the PVInflows, a major component of the NPV calculation is, by the previous definition, the economic value of the benefits (expected future cash flows to be received from the investment). NPV thus calculates the economic value of an investment and then subtracts the amount you'd have to pay to get the future cash flows (economic value) of the investment. If the economic value exceeds the cost, it's a good investment. A good deal is a good deal: In this example we saw that at an opportunity cost of 14% the project is a bad investment, and both the NPV and IRR decision rules agreed that we should reject it. When the opportunity cost dropped to 8%, then both the NPV and IRR decision rules changed their recommendations to accept. For many projects these two decision rules will give the same decision; however, there are some situations that we'll see in Unit 11 where this equivalence does not hold. As this brief example shows, accounting (Unit 4), economic decision making (Unit 5) and time value of money (Unit 6) are the foundation for everything else in the course, and also in your professional and personal decisions upon graduation.

34. In problem 4, what is the average tax rate? What is the marginal tax rate?

The average tax rate is the total taxes paid divided by taxable income, so using the information from Question 4 gives us: Average tax rate = Total tax / Taxable income = $78,020 / $243,000 = .3211, or 32.11% With a progressive tax system the marginal and average taxes paid will differ. With a flat tax rate system the marginal and average tax rates, and thus the amounts paid, are the same. Please keep the differences between marginal and average taxes in mind. Personal taxes are still computed using a progressive tax system. And it's likely that we will see corporate marginal tax rates reappear in the future!

119. Calculating Portfolio Betas. You own a stock portfolio invested 15 percent in Stock Q, 25 percent in Stock R, 40 percent in Stock S, and 20 percent in Stock T. The betas for these four stocks are .75, .87, 1.26, and 1.76, respectively. What is the portfolio beta?

The beta of a portfolio is the sum of the weight of each asset in the portfolio times the beta of each asset. So, the beta of the portfolio is: Bp = .15(.75) + .25(.87) + .40(1.26) + .20(1.76) = 1.19 Note that this calculation involves only market risk: there is no reduction in risk due to diversification because there is no unique risk in the asset betas, so the portfolio beta is just sum of the betas of the three assets in the portfolio. The risk of the portfolio is influenced in how wealth is allocated among the three assets. Increasing the relative investment in the low beta asset (Bp = .75) by reducing the investment in the high beta asset (Bp= 1.76) will reduce the portfolio beta.

80. Present Value. Suppose two athletes sign 10-year contracts for $80 million. In one case, we're told that the $80 million will be paid in 10 equal installments. In the other case, we're told that the $80 million will be paid in 10 installments, but the installments will increase by 5 percent per year. Who got the better deal?

The better deal is the one with equal installments. Given that the total value of both annuities must be the same, $80 million, the second annuity's first payment would have to be rather small to have the payments on the second annuity grow at 5% per year. The pattern of payments is an important part of a contract. Many companies offering individuals credit use consumer ignorance of time value to extract additional wealth from their customers!

112. Portfolio Expected Return. You own a portfolio that is 15 percent invested in Stock X, 40 percent in Stock Y, and 45 percent in Stock Z. The expected returns on these three stocks are 10 percent, 13 percent, and 15 percent, respectively. What is the expected return on the portfolio?

The expected return of a portfolio is the sum of the expected return of each asset weighted by its proportion in the portfolio. So, the expected return of the portfolio is: E(Rp) = .15(.10) + .45(.13) + .45(.15) = .1345, or 13.45%

111. Portfolio Expected Return. You own a portfolio that has $2,750 invested in Stock A and $3,900 invested in Stock B. If the expected returns on these stocks are 9 percent and 14 percent, respectively, what is the expected return on the portfolio?

The expected return of a portfolio is the sum of the expected returns of the assets comprising the portfolio weighted by the relative weight of each asset in the portfolio. Total value. The total value of the portfolio is: Total value = $2,750 + 3,900 = $6,650 Expected return. The expected return of this portfolio is: E(Rp) = ($2,750/$6,650) x .09 + ($3,900/$6,650) x .14 = .1193, or 11.93%

50. FastDrop economic value. You are planning to place your money in safe government securities, which currently offer a 4% risk less rate of return. Before making this investment, an entrepreneur approaches you and asks you to purchase her new business venture, FastDrop, a delivery service for legal documents that would produce a single cash inflow of $80,000 at the end of the year. You have determined that 6% is an appropriate risk premium for this investment. How much would you be willing to pay for Fast Drop?

The first step is to calculate the opportunity cost. R = risk-free rate + risk premium 10% = 4% + 6% Given the opportunity cost of 10%, you can determine that the economic value of this investment is: $80,000/1.10 = $72,727 $72,727 is the value of the expected future cash flow and thus the economic value of the investment in FastDrop.

87. Annuity Present Values. Tri-State Megabucks Lottery advertises a $10 million grand prize. The winner receives $500,000 today and 19 annual payments of $500,000. A lump sum option of $5 million payable immediately is also available. Is this deceptive advertising?

The lottery is just one example of the many annuities we see in daily life. The headline doesn't really specify the fact that it's an annuity, but the payments fit the definition of an annuity due. In this example we'll see how to use a calculator to evaluate these alternatives. Lottery face values are the total payments, in this case $10,000,000. This is a nominal value and not a cash flow. The fine print specifies that the payment will be split into equal annual payments, which give $10,000,000/20 = $500,000. You would receive a cash payment of $500,000 every year. These payments do indeed add up to $10,000,000, so the lottery statement is not deceptive; however, it does not take time value into account. Your choices are: Take annual payments of $500,000. Take the lump sum of $5,000,000 today. The problem, in stating that you'll receive the first payment today and nineteen subsequent payments at the end of each year, fits the definition of a 20-period annuity due. In setting these payments, the lottery assumed a discount rate. You can use the calculator to determine this rate and thus make your decision.

120. Using CAPM: Beta. A stock has an expected return of 11.4 percent, the risk-free rate is 3.7 percent, and the market risk premium is 7.1 percent. What must the beta of this stock be?

The next three problems work through the calculation of each variable in the CAPM. We are given the values for the CAPM except for the B of the stock. We need to substitute these values into the CAPM, and solve for the B of the stock. One important thing we need to realize is that we are given the market risk premium. The market risk premium is the expected return of the market minus the risk-free rate. We must be careful not to use this value as the expected return of the market. Using the CAPM, we find: E(Ri) = Rf + [E(RM) - Rf] × Bi .114 = .037 + .071Bi Bi = 1.08

53. You are very popular with entrepreneurs! Just as you are ready to finalize your deal with FastDrop, another entrepreneur offers you another business deal: Hive Bliss, a company that sells home bee hives as a personal source of honey. Hive Bliss would require an investment of $95,000 and offers a cash inflow of $120,000 at the end of the year. An apiculture consultant advises that this is a fairly risky investment and suggests a risk premium of 14%. What is its NPV?

The opportunity cost: Hive Bliss has more risk than FastDrop, as you are more uncertain of getting the promised payment of $120,000 in one year. Its opportunity cost is Opportunity cost = Risk-free rate + Risk premium 18% = 4% + 14%. Note that while the risk premium changes from one investment to another, the risk-free rate of return is the same for both of these investments. The NPV: Given the opportunity cost of 18%, Hive Bliss's NPV is: NPV = PVinflows - PVoutflows = $120,000/(1.18) - $95,000 = $101,695 - $95,000 = $6,694 The decision: When all the dust settles, this project costs you $95,000 but offers expected cash flows with a present value of $101,695. NPV is cost/benefit analysis and Hive Bliss offers benefits that exceed its costs and is thus a wealth-increasing project that should be accepted.

51. FastDrop Internal Rate of Return. In question 1 you determined the economic value of FastDrop Delivery Service, given its end-of-year cash inflow of $80,000 and its opportunity cost of 10%. In further negotiations the entrepreneur offers to sell you the business for $70,000. Calculate the IRR of this offer and decide if this is an acceptable investment.

The opportunity cost: the rate of return earned on equivalent investments—is 10%. This discount rate is adjusted for the general time value of money—the risk-free rate of return—and the risk of the cash flows. The IRR: The Internal Rate of Return is the rate of return of a project given its cash flows. In this unit we're using a simple one-period equation for the IRR. In Unit 6 we'll see how to calculate the IRR for multiple periods. 𝐼𝑅𝑅=(𝐸𝑛𝑑𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒-𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒)/𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒 The IRR for the FastDrop investment, using our simple one-period equation, is 𝐼𝑅𝑅=($80,000-$70,000)/$70,000 = $10,000/$70,000 = 0.1429 or 14.29% The decision: The IRR rule states that the rate of return earned from the project's cash flows must at least equal the rate of return offered on equivalent investments. IRR = 14.29% Opportunity cost = 10% As this investment offers a rate of return higher than the opportunity cost it is a wealth-increasing investment and should be adopted.

5. Economic Activity

The process by which a society produces and allocates the goods and services that are necessary to support human life. Property rights are the right to control an asset: how it is used, how the benefits from this use are distributed, and the ability to dispose of the asset. . In a simplified sense, there are two ways to organize economic activity based on control of property rights

100. Calculating APR. Vandermark Credit Corp. wants to earn an effective annual return on its consumer loans of 14.2 percent per year. The bank uses daily compounding on its loans. What interest rate is the bank required by law to report to potential borrowers? Explain why this rate is misleading to an uninformed borrower.

The reported rate is the APR, so we need to convert the EAR to an APR as follows: Algebraically convert the EAR equation to solve for the APR EAR = [1 + (APR / m)]^m - 1 APR = m[(1 + EAR)^(1/m) - 1] = 365[(1.142)^(1/365) - 1] = .1328, or 13.28% This is deceptive because the borrower is actually paying annualized interest of 14.2 percent per year, not the 13.28 percent reported on the loan contract. If you were borrowing $2,000: You think, given the APR that you're paying $2,000 x 13.28% = $265. You're actually paying $2,000 x 14.2% = $284.

15. In a large corporate, what are the two distinct groups that report to the chief financial officer? What group is the focus of corporate finance?

The treasurer's office and the controller's office are the two primary organizational groups that report directly to the chief financial officer. The controller's office handles many of the functions that help control the corporation's operations, including cost and financial accounting, tax management, and management information systems. The treasurer's office is more focused on the corporation's outside activities, especially those involving raising and deploying capital, including cash and credit management, capital budgeting, and financial planning. Our course focuses on the capital budgeting and capital structure decisions and will thus focus more on the functions of the treasurer's office. (Chapter 1, 1.4)

69. Calculating Rates of Return. Assume the total cost of a college education will be $295,000 when your child enters college in 18 years. You presently have $53,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child's college education?

To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)^t Solving for r, we get: r = (FV / PV)^(1 / t) - 1 = ($295,000 / $53,000)^(1/18) - 1 = .1001, or 10.01%

102. Why the heck do we have two measures of volatility?

The variance measures how much the realized returns might vary from the expected return. Given that the expected return is an average of the possible returns, it's likely that if we just add up the possible returns they'd sum to near zero: the returns above the expected value and the returns below the expected value would cancel each other out—not very useful! To eliminate this canceling the differences are squared, eliminating negative signs and emphasizing larger differences between the realized and expected returns. Thus, the variance formula: 𝑉𝑎(𝑅) = ∑[𝑝(𝑟𝑒𝑡𝑢𝑟𝑛)𝑥(𝑅−𝐸(𝑅) 2 ] While very useful, the variance is measured in squared percents:%2. We have a problem here, in that the expected value is measured in percents: %. 𝑅 = ∑(𝑝(𝑟𝑒𝑡𝑢𝑟𝑛)𝑥𝑟𝑒𝑡𝑢rn Just as you can't add feet and square feet when measuring a room for a carpet, you can't directly combine expected return and variance. So, we take the square root of the variance to get the standard deviation. The SD, like the expected return, is measured in percents: %. We can thus add and subtract the SD from the expected value to give an indication of the amount of dispersion of realized returns around the expected return.

14. What is the primary disadvantage of the corporate form of organization? Name at least two of the advantages of corporate organization.

Their disadvantages include the following. Double taxation. Corporations, as separate legal entities from their owners, are taxed. Any profits distributed to their owners—shareholders—are then taxed as personal income. Agency problems: The corporate structure separates owners from managers, allowing managers to pursue their own interests to the potential harm of shareholders, customers, and society in general. Despite these disadvantages, corporations dominate economic activity because of their substantial advantages. Limited liability: Shareholders face the potential loss of their investment in the company, but to not put all of their assets at risk to poor decisions on the part of the corporation's managers. Unlimited life: The corporation, as a separate legal entity from its owners, is not subject to the requirement to be reorganized upon the death of an owner. Ease of transferability: Ownership interests are valued as shares, which can be easily transferred among investors in the stock market. Ease of raising capital: As you can see, these three advantages of corporations are the mirror image of the disadvantages of the proprietorship/partnership organizational form. Corporations can attract external investors because these investors, do not risk their whole wealth, can depend on a corporation being around for a long time period, and can easily sell their investment. Just about the most important decision on making an investment is having a clear exit available! Specialization: The Key Concepts: The Forms of Business Organizations stressed the separation of ownership and management, which leads to specialization, which leads to increased efficiency.

90. Calculating Annuity Values. For each of the following annuities, calculate the present value. Annuity Payment/Years/Interest Rate $2,100 7 5% 1,095 9 10 11,000 18 8 30,000 28 14

There are only five variables that most of the problems in These Applications use. Here we must calculate the present value of four annuities. Using a calculator makes quick work of this task. Here we need to find the present value of an annuity. Using the PVA equation, we find First annuity PVA = C({1 - [1 / (1 + r)^t]} / r) PVA = $2,100{[1 - (1 / 1.05^)7] / .05} PVA = $12,151.38 Second annuity PVA = C({1 - [1 / (1 + r)^t]} / r) PVA = $1,095{[1 - (1 / 1.10)^9 ] / .10} PVA = $6,306.13 Third annuity PVA = C({1 - [1 / (1 + r)^t]} / r) PVA = $11,000{[1 - (1 / 1.08)^18 ] / .08} PVA = $103,090.76 Fourth annuity PVA = C({1 - [1 / (1 + r)^t]} / r) PVA = $30,000{[1 - (1 / 1.14)^28] / .14} PVA = $208,819.87

123. Using the CAPM: The opportunity cost. Jackne Business Services (JBS) provides IT, procurement, shipping and financial services to small retail companies in Central Texas. Their controller wants to calculate the discount rate to use in their capital budgeting projects. She's determined that the risk-free rate is 0.41%, the market rate of return is 7.25, and JBS' beta is 1.2. What is JBS' discount rate?

There are two steps to this problem: First, set up the Security Market Line. Second, determine JBS' discount rate. Set up the Security Market Line (SML). The SML is a visual representation of the CAPM. We'll build the SML on a step-by-step basis. First, set up the axes. Beta on x-axis, E(R) on y-axis Second, enter the market information. Third, draw the Security Market Line. E(RM) - Rf = 7.25% - 0.41% 6.84% The SML is a visual representation of the risk-return relationship in the market. It is a straight-line connecting the risk-free rate and the market rate of return on the Y-axis with their appropriate betas--0 for the risk-free rate and 1 for the market portfolio—on the X-axis. The risk premium for bearing one unit of market risk is E(RM) - RF. For this problem this market risk premium would be 7.25% -0 0.41% = 6.84%. Given the risk-return relationship in the market we can calculate the discount rate for any asset—all we need is the asset's beta. Assets that are less risky than the market have a beta less than one and will thus have a discount rate less than the market return of 7.25%. Assets that are riskier than the market have a beta greater than one and will thus have a discount rate greater than the market return of 7.25%. Determine JBS' discount rate. JBS' beta is 1.2. This makes its stock risker that the average stock in the market so it should earn a higher rate of return that the market portfolio. We can use the CAPM to determine that JBS should use a discount rate of: E(Ri) = Rf + [E(RM) - Rf] × Bi = 0.0041 + [0.0684] x 1.2 = 0.0041 + 0.0821 = 0.0862. As we previously calculated, the risk premium for one unit of market risk is 6.84%.The risk premium for JSB is 8.21%, which gives its discount rate of 8.62%. This is the appropriate discount rate given the current market. If conditions were to change, such as the Fed changing interest rates or economic activity changing then the SML would shift and SBS' discount rate would change.

94. Calculating Perpetuity Values. Curly's Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $30,000 per year forever. If the required return on this investment is 5 percent, how much will you pay for the policy?

This cash flow is a perpetuity. To find the PV of a perpetuity, we use the equation: PV = C / r PV = $30,000 / .05 PV = $600,000.00 This is a simple calculation, but you can use your calculator if you wish. As I mentioned in an earlier solution in this Application, perpetuities are similar to annuities but have no end. The present value of this infinite payment stream is finite because we are not adding the payments, but rather adding the present value of the payments.

40. Future value. You receive $750 today and deposited it in your savings account that has an interest rate of 3%. What will your savings account balance be in one year?

This problem asks you to find the future value of a present value. If you deposit $750 today, you get your $750 back in one year plus the interest earned on the deposit: 1 + r. In this problem we have: Future value = $750 x (1 + r) = $750 + ($750 x r) = $750 + ($750 x 0.03) = $750 + $22.50 = $773. Our simple equation simplifies this calculation. Future value = $750 x (1 + r) = $750 x (1.03) = $773. Note that calculating future value--multiplying by (1 + r)--is the mirror image of calculating present values--dividing by (1 + r). The basic relationship of present values, future values time and interest rates is the time value of money! Unit 6 will introduce many specific time value calculations, but all of these are just iterations of this basic relationship.

41. The bribe. As an incentive for you to stay in school your Uncle Henry offers to pay you $5,000 in one year. If the interest rate is 4%, how much is the $5,000 payment worth to you today?

This problem involves discounting--finding the value today of a future payment. Given the interest rate of 4%, what amount deposited today would grow to $5,000, which would be equivalent to the $5,000 in one year that your uncle has kindly offered you. This involves dividing the $5,000 by (1 + r). $5,000/(1.04) = $4,807.69. If you were to deposit $4,807.69 in your account today it would grow to $5,000 in one year. You would thus be indifferent to these two alternatives, which would have the same value on one year of $5,000. Conversely, they would both have the same value today: $4,807.69. Now, this is for one period. These calculations get a bit more complex for multiple periods of multiple cash flows, as we will see in Unit 6. P.S. Be sure to send Uncle Henry a nice birthday card.

28. Suppose Pharrell, Inc. paid out $43,000 in cash dividends. What is the addition to retained earnings?

This question continues our examination of Pharrell's incomes statement by asking what happens to net income, which represents the profit made by Pharrell in a given year. A portion of this profit may be paid out to shareholders in the form of a dividend, or it may be retained by the company to invest in productive assets. Net income = Dividends + Addition to retained earnings You can rearrange the above to solve for the amount of profit that Pharrell is retaining. Additions to retained earnings = Net income - Dividends Addition to retained earnings = $154,050 - $43,000 Addition to retained earnings = $111,050 Pharrell made a profit of $154,050. It paid out dividends of $43,000. The remaining $111,050 went into a balance sheet account called retained earnings, which represents all profit (net income) not paid out to the shareholders over the life of the company. Owners' equity in the balance sheet thus includes the funds that shareholders have invested in the company by purchasing stock and all profits that have been retained in the company. As part of the shareholders' wealth, retained earnings must be accounted for in the balance sheet. Owner's equity Common stock and paid-in surplus Retained earnings Total. This question shows that elements of the income statement and balance sheet are interconnected. In addition to retained earnings, another example is depreciation, which occurs as an expense in the income statement and also appears as accumulated depreciation in the balance sheet to adjust fixed assets into net fixed assets.

42. The piggy bank. Your little sister Tiffany has received a special Piggy bank with a $20 bill in it. This is a special locked Piggy and will unlock itself in one year. Tiffany has offered to sell you Piggy today. Unfortunately, this nice Piggy bank will completely destroy itself in one year and have no value, so plan on getting only the $20! If your savings rate is 5%, how much is the $20 in Piggy worth to you today if you can't get at it for a year?

This question highlights how to use economic value. You would offer Tiffany the present value of the $20. $20/(1+r) = $20/1.05) = $19.05. This is the economic value of the Piggy bank: the maximum amount that you'd pay. A bad deal: paying more than economic value. Tiffany asks you to pay $19.50 today. You would decline, as you would lose money on the deal. You could instead invest $19.50 today at 5% and have $20.48 in your pocket instead of $20 in the Piggy. You would lose the difference between what you pay and what you get, with both numbers being stated in one year. FV of piggy - FV of alternate investment = loss $20.00 - $20.48 = -$0.48 A good deal--paying less than economic value. If you were a ratty brother and offered Tiffany $18 for the bank today, and she accepted, you would be much better off. The payment of $18 would be worth $18 x (1.05) = $18.90 in one year which is less than the $20 in Piggy's stomach. FV of piggy - FV of your payment = gain $20.00 - $18.90 = $1.10

108. Diversification. True or false: The most important characteristic in determining the expected return of a well-diversified portfolio is the variances of the individual assets in the portfolio. Explain.

This statement is false. Variance is a measure of total risk: the sum of the differences between the portfolio returns at different states relative to the portfolio's expected return. This total risk is the combination of two types of risk. Variance = Unsystematic risk + Systematic risk Variance can also be defined as: Variance = Diversifiable risk + Nondiversifiable risk The variance and expected return on a well-diversified portfolio are functions of systematic risk only, as the diversifiable risk is reduced by diversification.

78. Calculating Rates of Return. Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, Sotheby's sold the Edgar Degas bronze sculpture Petite Danseuse de Quatorze Ans at auction for a price of $10,311,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,377,500. What was his annual rate of return on this sculpture?

To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)^t Solving for r, we get: r = (FV / PV)^(1 / t) - 1 = ($10,311,500 / $12,377,500)^(1/4) - 1 = -.0446, or -4.46%

76. Calculating Growth Rates and Future Values. In 1895, the first U.S. Open Golf Championship was held. The winner's prize money was $150. In 2014, the winner's check was $1,620,000. What was the annual percentage increase in the winner's check over this period? If the winner's prize increases at the same rate, what will it be in 2045?

To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)^t Solving for r, we get: r = (FV / PV)^(1 / t) - 1 = ($1,620,000 / $150)^(1/119) - 1 = .08117, or 8.117% Given the interest rate of 10.23%, we can find the FV of the future first prize in 2045, we use: FV = PV(1 + r)^t FV = $1,620,000(1.08117)^31 = $18,206,589

77. Calculating Rates of Return. In 2014, an Action Comics No. 1, featuring the first appearance of Superman, was sold at auction for $3,207,852. The comic book was originally sold in 1938 for $.10. What was the annual increase in the value of this comic book?

To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)^t Solving for r, we get: r = (FV / PV)^(1 / t) - 1 = ($3,207,852 / $.10)^(1/76) - 1 = .2554, or 25.54%

71. Calculating Rates of Return. In 2014, an 1874 $20 double eagle sold for $15,000. What was the rate of return on this investment?

To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula: FV = PV(1 + r)^t Solving for r, we get: r = (FV / PV)^(1 / t) - 1 r = ($15,000 / $20)^(1/140) - 1 r = .0484, or 4.84%

72. Calculating the Number of Periods. You're trying to save to buy a new $150,000 Ferrari. You have $35,000 today that can be invested at your bank. The bank pays 2.1 percent annual interest on its accounts. How long will it be before you have enough to buy the car?

To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula: FV = PV(1 + r)^t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) FV = $150,000 = $35,000(1.021)^t t = ln($150,000 / $35,000) / ln 1.021 t = 70.02 years

35. Hailey, Inc., has sales of $38,530, operating costs of $12,750, depreciation expense of $2,550, and interest expense of $1,850. If the tax rate is 21%, what is the Net cash flow?

To calculate the NCF, we first need to construct an income statement. The income statement starts with revenues and subtracts costs to arrive at NI. We then add back depreciation, which is not a cash outflow, to get NCF. Income Statement Sales $38,530 Costs $12,750 Depreciation $2,550 EBIT $23,230 Interest $1,850 Taxable Income $21,380 Taxes (21%) $4,490 Net income $16,890 + Depreciation $2,550 Net cash flow $19,440

75. Calculating Future Values. Your coin collection contains fifty 1952 silver dollars. If your grandparents purchased them for their face value when they were new, how much will your collection be worth when you retire in 2063, assuming they appreciate at an annual rate of 4.3 percent?

To find the FV of a lump sum, we use: FV = PV(1 + r)^t FV = $50(1.043)^111 = $5,352.15

73. Calculating Present Values. Imprudential, Inc., has an unfunded pension liability of $730 million that must be paid in 25 years. To assess the value of the firm's stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 5.5 percent, what is the present value of this liability?

To find the PV of a lump sum, we use: PV = FV / (1 + r)^t PV = $730,000,000 / (1.055)^25 PV = $191,430,603.85

74. Calculating Present Values. You have just received notification that you have won the $1 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you're around to collect), 80 years from now. What is the present value of your windfall if the appropriate discount rate is 7.25 percent?

To find the PV of a lump sum, we use: PV = FV / (1 + r)^t PV = $1,000,000 / (1.0725)^80 = $3,700.12

83. Present Value and Multiple Cash Flows. Investment X offers to pay you $3,400 per year for nine years, whereas Investment Y offers to pay you $5,200 per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 6 percent? If the discount rate is 22 percent?

To find the PVA, we use the equation: PVA = C({1 - [1/(1 + r)^t]} / r ) At an interest rate of 6 percent: Present value of X: $23,125.75 = $3,400{[1 - (1/1.06)^9] / .06 } Present value of Y $21,904.29 = $5,200{[1 - (1/1.06)^5] / .06} At an interest rate of 22 percent: Present value of X: $12,873.37 = $3,400{[1 - (1/1.22)^9] / .22} Present value of Y: $14,890.93 = $5,200{[1 - (1/1.22)^5] / .22} Notice that: At 6% discount rate the PV of Investment X is greater than the present value of Investment Y The reason is that X has a greater number of total cash flows. At a lower interest rate, the total cash flow is more important since the cost of waiting (the interest rate) is not as great. At 22% discount rate the PV of Investment Y is greater than the present value of Investment X At a higher interest rate, Y is more valuable since it has larger annual payments. At a higher interest rate, getting these payments early are more important since the cost of waiting (the interest rate) is so much greater.

88. Calculating Annuity Present Values. An investment offers $5,430 per year for 15 years, with the first payment occurring one year from now. If the required return is 8 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever?

To find the Present value of Annuity (PVA), we use the equation: PVA = C({1 - [1/(1 + r)^t]} / r) $5,430 for 15 years PVA = $5,430{[1 - (1/1.08)^15] / .08} = $46,478 $5,430 for 40 years PVA = $5,430{[1 - (1/1.08)^40] / .08} = $64,751 $5,430 for 75 years PVA = $5,430{[1 - (1/1.08)^75] / .08} = $67,664 As with individual payments, the longer the payment stream the higher the future value. As the length of the annuity payments increases, the present value of the annuity approaches the present value of the perpetuity. A perpetuity is a stream of payments that goes on (technically) forever. To find the PV of a perpetuity, we use the equation: PV = C / r PV = $5,430 /.08 PV = $67,875 Note that the difference between the present value of the 75-year annuity and the present value of the perpetuity is only $67,875 - $67,664 = $211.

70. Calculating the Number of Periods. At 4.7 percent interest, how long does it take to double your money? To quadruple it?

To find the length of time for money to double, triple, etc., the present value and future value are irrelevant as long as the future value is twice the present value for doubling, three times as large for tripling, etc. To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)^t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) Double your money FV = $2 = $1(1.047)^t t = ln 2 / ln 1.047 t = 15.09 years Quadruple your money FV = $4 = $1(1.047)^t t = ln 4 / ln 1.047 t = 30.18 years

43. Your friend wants to pay back the money she borrowed from you. She offers you $300 today or $315 in one year. If you could save at 6%, which one should you choose?

To make this comparison we must move these amounts to the same point in time. We could do this by moving the $300 to the future, or the $315 to the present. Using present values: The value of the payment today is $300. The present value of the future payment of $315 is $315/(1+r) = $315/(1.06) = $297.17. So, you could receive $300 today, or "receive" $297.17, the PV of the future payment of $315. You should grab the offer of $300 today. Using future values. You could invest the $300 received today at 6% and have $300 x (1.06) = $318 in one year. The value of the future payment of $315 in one year is, naturally, $315. So receiving $300 today would be worth $318 in one year, which is better that receiving $315 in one year, so take the payment today. The bottom line: $300 today is a better deal than $315 in one year given your interest rate of 6%. Using present values and future values will give you the same decision!!

82. Present Value and Multiple Cash Flows. Eulis Co. has identified an investment project with the following cash flows. If the discount rate is 10 percent, what is the present value of these cash flows? What is the present value at 18 percent? At 24 percent? Year/Cash Flow 1 $680 2 490 3 975 4 1,160

To solve this problem, we must find the future values of each cash flow and add them. To find the PV of a lump sum, we use: PV = FV / (1 + r)^t Present value at 10% $2,547.97 = $680 / 1.10 + $490 / 1.10^2 + $975 / 1.10^3 + $1,160 / 1.10^4 Present value at 18% $2,119.91 = $680 / 1.18 + $490 / 1.18^2 + $975 / 1.18^3 + $1,160 / 1.18^4 Present value at 24% $1,869.09 = $680 / 1.24 + $490 / 1.24^2 + $975 / 1.24^3 + $1,160 / 1.24^4

84. Future Value and Multiple Cash Flows. Booker, Inc., has identified an investment project with the following cash flows. If the discount rate is 8 percent, what is the future value of these cash flows in Year 4? What is the future value at an interest rate of 11 percent? At 24 percent? Year/Cash Flow 1 $985 2 1,160 3 1,325 4 1,495

To solve this problem, we must find the future values of each cash flow and then sum them at N = 4. To find the future value of a lump sum, we use: FV = PV(1 + r)^t Future value at 8% $5,519.84 = $985(1.08)^3 + $1,160(1.08)^2 + $1,325(1.08) + $1,495 Future value at 11% $5,742.10 = $985(1.11)^3 + $1,160(1.11)^2 + $1,325(1.11) + $1,495 Future value at 24% $6,799.64 = $985(1.24)^3 + $1,160(1.24)^2 + $1,325(1.24) + $1,495 Notice, since we are finding the value at Year 4, the cash flow at Year 4 is added to the FV of the other cash flows. In other words, we do not need to compound this cash flow. As with an individual cash flow, the future value of a series of cash flows increases as the interest rate increases.

63. Length of Investment. The TMCC security is traded on an exchange. If you looked at the price today, do you think the price would exceed the $24,099 original price? Why? Holding all economic and risk factors constant, if you looked in 2028, do you think the price would be higher or lower than today's price? Why?

Today: We would say that the price in the market would be the same as the economic value calculated. $24,099. This because the U.S. capital markets are reasonably efficient. For now we'll just accept this statement, but will examine market efficiency in Unit 14. In ten years: We're making some major assumptions about the economy and the company being static for a decade!!! We cannot be sure that interest rates will remain constant or that TMCC's financial position will not change—or for that matter if they will still be in existence! However, given these assumption, the price would be higher because as time passes the price of the security will tend to rise toward $100,000. This increase is just a reflection of the time value of money. As time passes, the time until receipt of the $100,000 grows shorter, and the present value rises.

39. A coat of paint. Your house needs a new coat of paint. You could hire a painter for $1,200 or spend $300 for materials and devote 8 hours of your time to the project. (It's a small house!). If you normally make $200/hour at your consulting job, what is the opportunity cost of having the house painted by the professional painter?

Understanding the opportunity cost. In this question you are the homeowner. If you are considering using the professional painter, your other alternative--your opportunity cost--is painting the house yourself. So we must determine the cost of painting the house yourself and then use that cost to evaluate the deal offered by the professional painter. Computing the opportunity cost. If you choose to paint the house yourself, you must pay the materials cost of $300 and also invest your time. As you are a skilled consultant, you could devote your time to your professional work and earn $200 per hour. So, if you spend 8 hours of your valuable time painting your house, you would forego 8 x $200 = $1,600 hours in income. The cost of painting the house yourself is thus $300 + $1,600 = $1,900. Using the opportunity cost. Professional painter: $1,200 Do it yourself: $1,900. The painter, being a professional, is more efficient at painting and it would be economically beneficial for you to let her do the work. You'd be better off by: $1,900 - $1,200 = $700. Opportunity cost is a major concept and is used in many ways. While we will mostly use opportunity cost as a discount/compound rate in time value, it can be used to compare almost anything. Remember Dan Ariely's TED Talk. We have limited opportunity sets and make comparisons among these opportunities. And, one of the most valuable of our assets is our time!

13. What are the four primary disadvantages to the sole proprietorship and partnership forms of business organization? What benefits are there to these types of business organizations as opposed to the corporate form?

Unlimited liability: The owners' wealth is exposed to losses in the business. If the assets of the business are insufficient to meet the claims on the business, creditors will seize the personal assets of the owners. This, as you can, imagine, limits the interest of outsiders to invest in the business. Limited life: Formally the proprietor/partner is the business. They die, the business legally also dies. Difficulty in transferring ownership: A proprietor or partner desiring to exit the business must find someone who would wish to buy them out. This transfer of ownership is a complex, expensive and time-consuming process. It is also made difficult by the lack of an external market price that would help value the business. Difficult to raise capital funds: This disadvantage is the result of the other three disadvantages. Proprietorships/partnerships will not attract many outside investors. Anyone wanting to invest, but not be an active manager, faces risk to their entire wealth, would have to invest in a business that would legally die if an owner dies, and would find it difficult to get out of the investment. Proprietorships and partnerships also have advantages that make them ideally suited for some types of business activity. You'll understand these advantages better when we look at corporations in the next question. Simple to establish: They have a much simpler structure to establish and run. Less regulation: They face less regulation than corporations. No Agency conflict: The owners are the managers, so there is not an inherent agency conflict. Taxes: This is a biggie! Profits are taxed as personal income of the owners.

33. The SGS Co. had $243,000 in taxable income. Assuming that corporations face marginal tax rates, use these rates to calculate SGS's income tax. Table 2.3 Corporate Tax Rates Taxable Income Tax Rate $ 0 - 50,000 15% 50,001 - 75,000 25% 75,001 - 100,000 34% 100,001 - 335,000 39% 335,001 - 10,000,000 34% 10,000,001 - 15,000,000 35% 15,000,001 - 18,333,333 38% 18,333,334+ 35%

Using Table 2.3, we can see the marginal tax schedule. The first $50,000 of income is taxed at 15 percent, the next $25,000 is taxed at 25 percent, the next $25,000 is taxed at 34 percent, and the next $143,000 is taxed at 39 percent. So, the total taxes for the company will be: Taxes = .15($50,000) + .25($25,000) + .34($25,000) + .39($243,000 - 100,000) Taxes = $78,020 Marginal tax rates are called progressive, as the more you earn the larger the percent you pay on higher marginal dollars of income.

103. Calculating asset expected return. Based on the following information, calculate the expected return. State of Economy/Probability of State of Economy/Rate of Return of State Occurs Recession .30 -.11 Boom .70 .21

We are given the following types of information in this probability distribution: There are two possible states of the economy: recession and boom. Given these economic states we can estimate the rate of return earned in each state. The expected return of an asset is the sum of the probability of each state occurring times the rate of return if that state occurs. So, the expected return of asset is: E(R) = .30(-.11) + .70(.21) = .1140, or 11.40% Note: developing a probability distribution (at least, one that you'd want to use) takes great insights into economics and how companies would respond given the state of the economy. In a booming economy we'd expect a company to earn a higher rate of return. In a recession we'd likely see a lower rate of return.

3. Why this is important to a business decision maker?

We depend on expert and, while they do provide essential knowledge, they are subject to errors in understanding and we must take that into account when using expert-provided information

116. Beta and CAPM. Is it possible that a risky asset could have a negative beta? What does the CAPM predict about the expected return on such an asset? Can you give an explanation for your answer?

Yes, it is possible to have a negative beta; the return would be less than the risk-free rate. A negative beta asset would carry a negative risk premium because of its value as a diversification instrument, so adding it to a portfolio would actually reduce portfolio beta. One example of a negative beta would be gold or other countercyclical asset. I practice there are very few negative beta assets.

109. Portfolio Risk. If a portfolio has a positive investment in every asset, can the standard deviation on the portfolio be less than that on every asset in the portfolio?

Yes, the standard deviation of the portfolio can be less than that of every asset in the portfolio. Standard deviation is nothing more that the square root of the variance, and is thus a measure of total risk. Diversification reduces the unique, or diversifiable, risk. With imperfectly correlated returns some of the variability of the individual assets is cancelled out.

96. APR and EAR. Should lending laws be changed to require lenders to report EARs instead of APRs? Why or why not?

Yes, they should. APRs generally don't provide the relevant rate. The only advantage is that they are easier to compute, but, with modern computing equipment, that advantage is not very important. Also, the APR's on debt generally look more attractive that the true rate charged. You'll find that, as a consumer, your understanding of the difference will save you money on anything—clothing car, house—that you buy on credit!

118. Measures of risk. Your friend in this course uses variance as a measure of risk in her other courses and doesn't see why she has to bother with beta, yet another measure of risk she doesn't think is important. Would you agree or disagree with your friend?

You should explain to your friend that she should not ignore beta. You can convince her that beta is important by reviewing the definitions of variance, diversification, beta and opportunity cost. Variance is a summary measure derived from probability distributions. Probability distributions give the possible returns and their likelihood of occurring. Variance measures the dispersion of realized returns from the expected return, and is thus a measure of the total volatility—risk—of the asset. Diversification is the process of reducing the risk of a portfolio by holding assets whose returns are not perfectly correlated. Returns of different assets, which can be in different industries, different countries, have varying quality of management, etc., do not move exactly together through time. The imperfect correlation of returns of assets in a portfolio thus tend to dampen the movement of the portfolio return, making the risk of the portfolio less than the sum of the risk of the assets in the portfolio. Limits of diversification: As more and more assets are added to a portfolio the portfolio variance does drop; however, after a number of assets have been added the variance ceases to drop. This occurs because the variance reflects two types of risk. Unique risk is the risk unique to an asset in the portfolio. It is this risk that is being diversified. Market risk is the risk of the asset that is correlated to the market-the economy. If a major economic event occurs, such as a change in interest rates, expectations about future difficulties in the economy, a trade war, new technological developments, etc., all asset returns will be affected. This economy-wide risk can't be diversified away. Given the two risks, investors will diversify unique risk but must bear market risk. Beta measures the market risk in an asset. As this risk can't be diversified away, investors will demand a risk premium appropriate for the amount of market risk they bear. As the markets are controlled by large investors who use diversification, the appropriate risk premium for the opportunity cost is based on beta.

115. Systematic versus Unsystematic Risk. Indicate whether the following events might cause stocks in general to change price, and whether they might cause Big Widget Corp.'s stock to change price. a. The government announces that inflation unexpectedly jumped by 2 percent last month. b. Big Widget's quarterly earnings report, just issued, generally fell in line with analysts' expectations. c. The government reports that economic growth last year was 3 percent, which generally agreed with most economists' forecasts. d. The directors of Big Widget die in a plane crash. 3. Congress approves changes to the tax code that will increase the top marginal corporate tax rate. The legislation had been debated for the previous six months.

a. This is a systematic risk: the increase in inflation will be reflected in interest rates and opportunity costs. Market prices in general will most likely decline and Big Widget will be along for the ride down. b. This is a firm specific risk; as the report just reflects the expectations of investors, the company price will most likely stay constant. c. This is a systematic risk; as with an individual company, if economic activity is as expected market prices in general will most likely stay constant. However, if the growth rate turns out to be different from what was expected market prices would change. d. This is a firm specific risk; the company price will most likely decline. Of course, if the directors were felt to be incompetent, the price could rise. e. This is a systematic risk; market prices in general will most likely stay constant. In this case market participants, following the debate, likely saw that the tax increase would occur and had already adjusted prices to reflect their beliefs.

114. Systematic versus Unsystematic Risk. Classify the following events as mostly systematic or mostly unsystematic. Is the distinction clear in every case? a. Short-term interest rates increase unexpectedly. b. The interest rate a company pays on its short-term debt borrowing is increased by its bank. c. Oil prices unexpectedly decline. d. An oil tanker ruptures, creating a large oil spill. e. A manufacturer loses a multimillion-dollar product liability suit. f. A Supreme Court decision substantially broadens producer liability for injuries suffered by product users.

a. systematic: Interest rate changes impact all elements of the economy and thus cannot be diversified away. b. unsystematic: This interest rate change likely reflects a change in the risk of the individual company. As this interest rate change is unique to the company it can be diversified away in a large portfolio. c. both; probably mostly systematic: Oil prices change the cost of energy in the economy as would thus be systematic; however, not all companies would be equally impacted. d. unsystematic: This would affect the company, and a lot of fish, but would not impact the entire economy. e. unsystematic: Again, bad news for the company, but the settlement impacts only the cash flow of this company. f. systematic: This would impact many companies and likely have some impact on the economy and security markets.