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TECHNICAL PROBLEMS*1.For each one of the costs below, explain whether the resource cost is explicit or implicit, and give the annual opportunity cost for each one. Assume the owner of the business can invest money and earn 10 percent annually.a.A computer server to run the firm’s network is leased for $6,000 per year.b.The owner starts the business using $50,000 of cash from a personal savings account.c.A building for the business was purchased for $18 million three years ago but is now worth $30 million.d.Computer programmers cost $50 per hour. The firm will hire 100,000 hours of programmer services this year.e.The firm owns a 1975 model Clarke-Owens garbage incinerator, which it uses to dispose of paper and cardboard waste. Even though this type of incinerator is now illegal to use for environmental reasons, the firm can continue to use it because it’s exempt under a “grandfather” clause in the law. However, the exemption only applies to the current owner for use until it wears out or is replaced. (Note: The owner offered to give the incinerator to the Smithsonian Institute as a charitable gift, but managers at the Smithsonian turned it down.)2.During a year of operation, a firm collects $175,000 in revenue and spends $80,000 on raw materials, labor expense, utilities, and rent. The owners of the firm have provided32$500,000 of their own money to the firm instead of investing the money and earning a 14 percent annual rate of return.a.The explicit costs of the firm are $ _______. The implicit costs are $ _______. Total economic cost is $ _______.b.The firm earns economic profit of $ _______.c.The firm’s accounting profit is $ _______.d.If the owners could earn 20 percent annually on the money they have invested in the firm, the economic profit of the firm would be _______ (when revenue is $175,000).3.Over the next three years, a firm is expected to earn economic profits of $120,000 in the first year, $140,000 in the second year, and $100,000 in the third year. After the end of the third year, the firm will go out of business.a.If the risk-adjusted discount rate is 10 percent for each of the next three years, the value of the firm is $ _______. The firm can be sold today for a price of $ _______.b.If the risk-adjusted discount rate is 8 percent for each of the next three years, the value of the firm is $ _______. The firm can be sold today for a price of $ _______.4.Fill in the blanks:a.Managers will maximize the values of firms by making decisions that maximize _______ in every single time period, so long as cost and revenue conditions in each period are ______________.b.When current output has the effect of increasing future costs, the level of output that maximizes the value of the firm will be _______ (smaller, larger) than the level of output that maximizes profit in a single period.c.When current output has a positive effect on future profit, the level of output that maximizes the value of the firm will be _______ (smaller, larger) than the level of output that maximizes profit in the current period.APPLIED PROBLEMS1.At the beginning of the year, an audio engineer quit his job and gave up a salary of $175,000 per year in order to start his own business, Sound Devices, Inc. The new company builds, installs, and maintains custom audio equipment for businesses that require high-quality audio systems. A partial income statement for the first year of operation for Sound Devices, Inc., is shown below:RevenuesRevenue from sales of product and services$970,000Operating costs and expensesCost of products and services sold355,000Selling expenses155,000Administrative expenses45,000Total operating costs and expenses$555,000Income from operations$415,000Interest expense (bank loan)45,000Legal expenses to start business28,000Income taxes165,000Net income$177,00033To get started, the owner of Sound Devices spent $100,000 of his personal savings to pay for some of the capital equipment used in the business. During the first year of operation, the owner of Sound Devices could have earned a 15 percent return by investing in stocks of other new businesses with risk levels similar to the risk level at Sound Devices.a.What are the total explicit, total implicit, and total economic costs for the year?b.What is accounting profit?c.What is economic profit?d.Given your answer in part c, evaluate the owner’s decision to leave his job to start Sound Devices.2.A doctor spent two weeks doing charity medical work in Mexico. In calculating her taxable income for the year, her accountant deducted as business expenses her round-trip airline ticket, meals, and a hotel bill for the two-week stay. She was surprised to learn that the accountant, following IRS rules, could not deduct as a cost of the trip the $8,000 of income she lost by being absent from her medical practice for two weeks. She asked the accountant, “Since lost income is not deductible as an expense, should I ignore it when I make my decision next year to go to Mexico for charity work?” Can you give the doctor some advice on decision making?3.When Burton Cummings graduated with honors from the Canadian Trucking Academy, his father gave him a $350,000 tractor-trailer rig. Recently, Burton was boasting to some fellow truckers that his revenues were typically $25,000 per month, while his operating costs (fuel, maintenance, and depreciation) amounted to only $18,000 per month. Tractor-trailer rigs identical to Burton’s rig rent for $15,000 per month. If Burton was driving trucks for one of the competing trucking firms, he would earn $5,000 per month.a.How much are Burton Cummings’s explicit costs per month? How much are his implicit costs per month?b.What is the dollar amount of the opportunity cost of the resources used by Burton Cummings each month?c.Burton is proud of the fact that he is generating a net cash flow of $7,000 (= $25,000 – $18,000) per month, since he would be earning only $5,000 per month if he were working for a trucking firm. What advice would you give Burton Cummings?4.Explain why it would cost Rafael Nadal or Venus Williams more to leave the professional tennis tour and open a tennis shop than it would for the coach of a university tennis team to do so.5.An article in The Wall Street Journal discusses a trend among some large U.S. corporations to base the compensation of outside members of their boards of directors partly on the performance of the corporation. “This growing practice more closely aligns the director to the company. [Some] companies link certain stock or stock-option grants for directors to improved financial performance, using a measure such as annual return on equity.”How would such a linkage tend to reduce the agency problem between managers and shareholders as a whole? Why could directors be more efficient than shareholders at improving managerial performance and changing their incentives?6.An article in The Wall Street Journal reported that large hotel chains, such as Marriott, are tending to reduce the number of hotels that they franchise to outside owners and increase the number the chain owns and manages itself. Some chains are requiring34private owners or franchisees to make upgrades in their hotels, but they are having a difficult time enforcing the policy. Marriott says this upgrading is important because “we’ve built our name on quality.”a.Explain the nature of the agency problem facing Marriott.b.Why would Marriott worry about the quality of the hotels it doesn’t own but franchises?c.Why would a chain such as Marriott tend to own its hotels in resort areas, such as national parks, where there is little repeat business, and franchise hotels in downtown areas, where there is a lot of repeat business? Think of the reputation effect and the incentive of franchises to maintain quality.7.Fortune magazine reported that SkyWest, an independent regional airline, negotiated a financial arrangement with Delta and United to provide regional jet service for the two major airlines. For its part of the deal, SkyWest agreed to paint its jets the colors of Delta Connection and United Express and to fly routes specified by the two airlines. In return, Delta and United agreed to pay SkyWest a predetermined profit margin and to cover most of the regional airline’s costs. Fortune explained that while the deal limited the amount of profit SkyWest could earn, it also insulated the smaller airline from volatility in earnings since Delta and United covered SkyWest’s fuel costs, increased its load factor (the percentage of seats occupied), and managed its ticket prices.Fortune suggested that Wall Street liked the deal because SkyWest’s market valuation increased from $143 million to $1.1 billion after it began its service with the two major airlines. Explain carefully how this arrangement with Delta and United could have caused the value of SkyWest to increase dramatically even though it limited the amount of profit SkyWest could earn.MATHEMATICAL APPENDIXReview of Present Value CalculationsThe concept of present value is a tool used to determine the value of a firm, which is the present value of expected future profits to be earned. In Chapters 1 and 13 of this text, you will find it useful to be able to calculate present values. Even if you have not already studied present value analysis in your finance or accounting classes, this short presentation will provide you with the basic computational skills needed to calculate the present value of a stream of expected profit to be received in future periods.Present Value of a Single Payment in the FutureThe payment you would accept today rather than wait for a payment (or stream of payments) to be received in the future is called the present value (PV) of that future payment (or stream of payments). Suppose, for example, that a trustworthy person promises to pay you $100 a year from now. Even though you are sure you will get the $100 in a year, a dollar now is worth more than a dollar a year from now. How much money would you accept now rather than wait one year for a guaranteed payment of $100? Because of the time value of money, you will be willing to accept less than $100; that is, the present value of a $100 payment one year from now is less than $100. The process of calculating present value is sometimes referred to as discounting since the present value of a payment is less than the dollar amount of the future payment.To properly discount the $100 future payment, you must first determine the opportunity cost of waiting for your money. Suppose that, at no risk, you could earn a return of 6 percent by investing the money over a one-year period. This 6 percent return is called the risk-free discount rate since it determines the rate at which you will discount future dollars to determine their present value, assuming you bear no risk of receiving less than the promised amount. In Chapter 15, we will show you how to determine35the appropriate risk premium to add to the risk-free discount rate when the future payment involves a degree of risk. For now, you need not be concerned about adjusting for risk.Given that you can earn 6 percent (with no risk) on your money, how much money do you need nowlet’s denote this amount as $Xin order to have exactly $100 a year from now? Since $X(1.06) is the value of $X in one year, set this future value equal to $100:$X(1.06) = $100It follows that the amount you must invest today ($X) is $94.34 (= $100/1.06) in order to have $100 in a year. Thus the present value of $100 to be received in one year is $94.34 now. In other words, you would accept $94.34 now, which will grow to $100 in one year (at a 6 percent annual discount rate).Now suppose that the $100 payment comes not in one year but after two years. Investing $X at 6 percent would yield $X(1.06) at the end of year 1 and [$X(1.06)] (1.06) = $X(1.06)2 at the end of year 2. For an investment to be worth $100 in two years,$X(1.06)2 = $100The amount you must invest today in order to have $100 at the end of two years is $89 [= $100/(1.06)2]. Thus the present value of $100 in two years with a discount rate of 6 percent is $89.Clearly a pattern is emerging: The present value of $100 in one year at 6 percent isPV=$100(1.06)=$94.34The present value of $100 in two years at 6 percent isPV=$100(1.06)2=$89Therefore, the present value of $100 to be received in t years (t being any number of years) with a discount rate of 6 percent isPV=$100(1.06)tThis relation can be made even more general to determine the present value of some net cash flow (NCF) to be received in t years at a discount rate of r. Net cash flow is the cash received in time period t, net of any costs or expenses that must be paid out of the cash inflow. Also note that if the discount rate is 6 percent, for example, r is expressed as 0.06, the decimal equivalent of 6 percent.RelationThe present value (PV) of $NCF to be received in t years at a discount rate of r isPV=$NCF(1+r)tAs illustrated above, the present value of a cash flow declines the further in the future it is to be receivedfor example, the present value of $100 at 6 percent was $94.34 in one year and only $89 in two years. As should be evident from the more general statement of present value, the present value of a cash flow is inversely related to the discount ratefor example, the present value of $100 to be received in two years is $89 with a discount rate of 6 percent but only $85.73 [= $100/(1.08)2] with a discount rate of 8 percent.RelationThere is an inverse relation between the present value of a cash flow and the time to maturity: The present value of a cash flow to be received in t years is greater than that for the same cash flow to be received in t + i years. There is an inverse relation between the present value of a cash flow and the discount rate.Present Value of a Stream of PaymentsSo far we have considered the present value of a single payment. We now extend present value analysis to consider the value of a stream of payments in the future. Suppose your trustworthy friend promises to pay you $100 in one year and $100 in two years. Using 6 percent as the risk-free discount rate for the first year, the present value of the first payment would bePV=$100(1.06)=$94.34At the 6 percent discount rate, the present value of the second payment would bePV=$100(1.06)2=$8936Thus the present value of the two-period stream of cash flows isPV=$100(1.06)+$100(1.06)2=$94.34+$89=$183.34From the preceding, you should be able to see that the present value of a stream of net cash flows is equal to the sum of the present values of the net cash flows. We can state this more precisely in the following:RelationThe present value of a stream of cash flows, where $NCFt is the cash flow received or paid in period t, is given byPV=$NCF1(1+r)=$NCF2(1+r)2+$NCF3(1+r)3+…+$NCFT(1+r)T=r=1T$NCFt(1+r)twhere r is the discount rate, and T is the life span of the stream of cash flows.

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