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# Opportunity Costs, Identification of Relevant Costs

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1. Why are historical or past data irrelevant to special decisions?

2. "Any future cost is relevant." Do you agree? Explain.

3. Paul and Paula Petroceli were trying to decide whether to go to the symphony or to the baseball game. They already have two nonrefundable tickets to "Pops Night at the Symphony" that cost \$40 each. This is the only concert of the season they considered attending because it is the only one with the type of music they enjoy. The baseball game is the last one of the season, and it will decide the league championship. They can purchase tickets for \$20 each.
The Petroceli will drive 50 miles round-trip to either event. Variables costs for operating their auto are \$1.4 per mile, and fixed costs average \$.13 per mile for the 18,000 miles they drive annually. Parking at the symphony is free, but it costs \$6 at the baseball game.
To attend either event, Paul and Paula will hire a baby-sitter at \$4 per hour. They expect to be gone 5 hours to attend the baseball game but only 4 hours to attend the symphony.

A. Compare the cost of attending the baseball game with cost of attending the symphony. Focus on relevant costs. Compute the difference in cost, and indicate which alternative is more costly to the Petroceli.

4. Valerie Monroe is an attorney employed by a large law firm at \$85,000 per year. She is considering whether to become a sole practitioner, which would probably generate annually \$320,000 in operating revenues and \$ 220,000 in operating expenses.

1. Present two tabulations of the annual income effects of these alternatives. The second tabulation should include the opportunity cost of Monroe's compensation as an employee.
2. Suppose Monroe prefers less risk and chooses to stay an employee. Show a tabulation of the income effects of rejecting the opportunity of independent practice.

5. Use the appropriate table to compute the following:

1. You have always dreamed of taking a trip to the Great Barrier Reef. What lump sum do you have to invest today to have the \$12,000 needed for the trip in three years? Assume that you can invest the money at

a. 4%, compounded annually
b. 10% compounded annually
c. 18% compounded annually

2. You are considering partial retirement. To do so you need to use part of your savings to supplement your income for the next five years. Suppose you need an extra \$15,000 per year. What lump sum do you have to invest now to supplement your income for five years? Assume that your minimum desired rate of return is

a. 4% , compounded annually
b. 10% compounded annually
c. 18% compounded annually

3. You just won a lump sum of \$400,000 in a local lottery. You have decided to invest the winnings and withdraw an equal amount each year 10 years. How much can you withdraw each year and have a zero balance left at the end of 10 years if you invest at

a. 5% compounded annually
b. 10% compounded annually

4. A professional athlete is offered the choice of two 4-year salary contracts, contract A for \$1.4 million and contract B for \$1.3 million:

Contract A Contract B

End of year 1 \$200,000 \$450,000
End of year 2 300,000 350,000
End of year 3 400,000 300,000
End of year 4 500,000 200,000
Total \$1,400,000 \$1,300,000

Which contract has the higher present value at 14% compounded annually? Show computations to support your answer.

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#### Solution Preview

1. Why are historical or past data irrelevant to special decisions?

Historical or past data is irrelevant to special decisions because they have already happened. So, they cannot be affected by a future decision.

2. "Any future cost is relevant." Do you agree? Explain.
A relevant cost or benefit is one that will be affected by the decision and be different for each alternative being considered. Variable costs can be relevant or irrelevant; fixed costs can be relevant or irrelevant. Whether or not each cost is relevant depends on the alternatives being considered.
3. Paul and Paula Petroceli were trying to decide whether to go to the symphony or to the baseball game. They already have two nonrefundable tickets to "Pops Night at the Symphony" that cost \$40 each. This is the only concert of the season they considered attending because it is the only one with the type of music they enjoy. The baseball game is the last one of the season, and it will decide the league championship. They can purchase tickets for \$20 each.
The Petroceli will drive 50 miles round-trip to either event. Variables costs for operating their auto are \$1.4 per mile, and fixed costs average \$.13 per mile for the 18,000 miles they drive annually. Parking at the symphony is free, but it costs \$6 at the baseball game.
To attend either event, Paul and Paula will hire a baby-sitter at \$4 per hour. They expect to be gone 5 hours to attend the baseball game but only 4 hours to attend the symphony.

A. Compare the cost of attending the baseball game with cost of attending the symphony. Focus on relevant costs. Compute the difference in cost, and indicate which alternative is more costly to the Petroceli.

Note: Relevant costs must relate to the future and be different for each alternative being considered. Therefore, we will consider only the cost of ticket, parking fee, and baby-sitter expense.
Symphony Baseball game

Tickets (40 x 2) = 80 (20 x 2) = 40
Parking fee 0 6
Baby-sitter expense (4 x 4) = 16 (4 x 5) = 20
Total cost 96 66

The cost different is \$96 - \$66 = \$30. Going to the symphony is more costly to the Petroceli.

4. Valerie Monroe is an attorney employed by a large law firm at \$85,000 per year. She is considering whether to become a sole practitioner, which ...

#### Solution Summary

This solution is comprised of a detailed explanation to answer why are historical or past data irrelevant to special decisions, explain if any future cost is relevant, compare the cost of attending the baseball game with cost of attending the symphony, calculate the opportunity cost of Monroe's compensation as an employee, and calculate how much to invest today to have the \$12,000 needed for the trip in three years.

\$2.19
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## An Illustration of Relevant Costs for Decision Making

An Illustration of Relevant Costs for Decision-Making

ABSTRACT
The concepts of incremental cost, opportunity cost, sunk cost, and cost allocation are identified and discussed in the context of early U.S. foreign policy. The case is derived from an authentic exchange of views between Thomas Jefferson and John Adams on how the United States should protect its merchant shipping against the Barbary Pirates. Both men compare the cost of waging war against the pirates with the cost of paying ransom for captured U.S. seamen and bribes to protect future shipping. Adams quantifies the opportunity cost associated with not taking any action against the pirates. Jefferson articulates an incremental costing argument, on the assumption that the U.S. should build a navy regardless of U.S. policy towards the Barbary States. The case constitutes a brief introduction to management accounting by illustrating different cost concepts, and also lends itself to a discussion of the historical origins of management accounting.

The beginning of wisdom in using accounting for decision-making is a clear understanding that the relevant costs and revenues are those which as between the alternatives being considered are expected to be different in the future. It has taken accountants a long time to grasp this essential point.
&#61485;R. H. Parker (1969, 15)

BACKGROUND
The Barbary Pirates
Throughout the 17th and 18th centuries, the North African Barbary States of Morocco, Algiers, Tunis and Tripoli engaged in piracy of European merchant shipping. The Barbary pirates routinely captured and confiscated ships and cargo, and enslaved or ransomed their crews and passengers. England, France and Spain entered into treaties with the Barbary States, in effect, paying "protection money" for their merchant shipping. These powerful European nations preferred bribery to war, because they perceived an economic benefit from the threat the pirates posed to the merchant shipping of other European nations.
Until the Revolutionary War, merchant ships from the American Colonies were protected by the British Royal Navy and by the treaties between England and the Barbary States. American shipping lost this protection in 1783, and within the next two years three American ships were captured, one by Morocco and two by Algiers. Morocco soon freed the American crew in exchange for a ransom of 5,000 pounds sterling (about \$25,000).1 The crews held by the Algerians were captive throughout 1786 and for some time thereafter.

Historical Background
The capture of American ships by the Barbary pirates created an early and important foreign policy crisis for the United States. The U.S. response to the Barbary crisis was strongly influenced by two factors, one military and the other financial. The military consideration was that the U.S. had no navy. The Continental Navy of the Revolutionary War was disbanded in 1784, and the navy was not reestablished until 1798. During the intervening years, the United States had minimal naval power. Disbanding the Continental Navy was primarily a cost-savings measure. However, there were also important non-financial arguments for and against the navy. Some Americans who favored reestablishing close ties with England feared that the presence of a U.S. navy on the high seas would lead to confrontations with the British Navy. Other Americans, including John Adams, viewed a strong navy as the best national defense against foreign threats. Many Americans preferred the prospect of building a navy over an army due to their general distrust of standing armies?the result of their experience with the British occupation in America during the latter part of the Colonial Era.
The financial factor that influenced the U.S. response to the Barbary pirates was that any effective response would require a significant expense relative to the government's available funds. The U.S. government found itself in a precarious financial condition in the years immediately following the Revolutionary War. The Continental Congress and individual states borrowed over \$40 million to finance the war, including about \$6 million from France. From 1781 to 1788, the period during which the United States operated under the Articles of Confederation, the federal government did not have the power to tax its citizens, levy tariffs, or regulate commerce. The cost of operating the government during this time was about \$500,000 annually, not including funding the debt (Hicks et al. 1970, 103). Some income was generated by the post office and from sales of public lands, but the two principal revenue sources available to the government were requesting support from the states and issuing paper money. State contributions to the federal government constituted only a small fraction of what was needed, and issuing paper money was an inflationary measure that had already been used extensively during the Revolutionary War. The financial plight of the new nation was sufficiently acute that during this period, the government borrowed from foreign sources just to meet the interest obligations on existing foreign debt.
The ratification of the Constitution in 1788 greatly enhanced the powers of the Federal government, and allowed the new Congress to levy and collect duties and taxes. However, the ability of the new government to actually enact and enforce revenue-generating measures was untested, and evolved over time. In 1786, during the Confederation period, and again in 1794, during Washington's presidency, popular opposition to taxation led to civil unrest. The first incident, Shays' Rebellion, arose in Massachusetts when the State Legislature levied taxes to pay off the war debt. The second incident, the Whiskey Rebellion, occurred in Western Pennsylvania when the federal government imposed an excise tax on distilled liquor. Also, although the Federal government had more potential resources under the Constitution than under the Articles of Confederation, it soon had more obligations. In 1790, under a plan advanced by Secretary of the Treasury Alexander Hamilton, the federal government assumed the remaining war debts that were owed by the individual states.
However, despite financial tribulations at both the state and federal levels, economic conditions in the United States during this period were generally good. A short recession that occurred after the Revolutionary War was followed by a period of economic growth. The strong economy led to increased federal revenues, and that fact, combined with the success of American leaders in keeping the nation out of the growing conflict between England and France, enabled the government to become current on its obligations under the national debt during Jefferson's administration.

The Adams-Jefferson Correspondence
In 1786, John Adams was the leading U.S. diplomat in London, and Thomas Jefferson was the U.S. ambassador to France. A few years earlier, in 1784, the Continental Congress had authorized Adams and Jefferson to negotiate treaties with the Barbary States (Kitzen 1993, 10). Consequently, the responsibility to negotiate the release of the captured American seamen, and to establish U.S. foreign policy that would protect U.S. shipping in the Mediterranean, fell largely to these two men. Against this backdrop, Adams sent Jefferson a letter that included the following analysis:

Adams to Jefferson
Grosvenor Square, June 6, 1786

Dear Sir

... The first Question is, what will it cost us to make Peace with all five [Barbary States]? Set it if you will at five hundred Thousand Pounds Sterling, tho I doubt not it might be done for Three or perhaps for two.
The Second Question is, what Damage shall we suffer, if we do not treat.
Compute Six or Eight Per Cent Insurance upon all your Exports, and Imports.
Compute the total Loss of all the Mediterranean and Levant Trade.
Compute the Loss of half your Trade to Portugal and Spain.
These computations will amount to more than half a Million sterling a year.
The third Question is what will it cost to fight them? I answer, at least half a Million sterling a year without protecting your Trade, and when you leave off fighting you must pay as much Money as it would cost you now for Peace.
The Interest of half a Million Sterling is, even at Six Per Cent, Thirty Thousand Guineas a year. For an Annual Interest of 30,000 pounds sterling then and perhaps for 15,000 or 10,000, we can have Peace, when a War would sink us annually ten times as much. (Cappon 1959, 133-134)

In the last paragraph of the excerpt, Adams states interest expense in terms of guineas. A guinea was worth about one pound sterling. Jefferson responded to Adams a few weeks later:
Jefferson to Adams
Paris, July 11, 1786I need some help with the questions at the end of the case study.

(See attached file for full problem description)

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