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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.

#### 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