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Engineering Economy, 5/e

Leland Blank, Texas A&M University
Anthony Tarquin, University of Texas - El Paso

Rate of Return Analysis: Multiple Alternatives

Sample FE Exam Questions

How to use this section: This section includes questions and problems like those on a typical FE exam. For organization purposes only, they are presented in chapter order of the text Engineering Economy, 5^th edition, by Blank and Tarquin.

It is recommended that you read through each question carefully.

In an incremental investment rate of return analysis of multiple mutually exclusive alternatives that have different lives, the incremental investment cash flow must extend through:

The life of the longer of the two alternatives under consideration

The least common multiple of the lives of the two alternatives under consideration

The longest life of all of the alternatives under consideration

The least common multiple of the lives of all of the alternatives under consideration

Alternative A has a first cost of $10,000, an annual operating cost of $5,000 and a salvage value of $2,000. Alternative B has an initial cost of $25,000, an annual operating cost of $1,000 and a salvage value of $12,000. If both alternatives have a five-year life, the equation that will yield the rate of return on the incremental investment is:

0 = -$15,000 - 4,000(P/A,i,5) + 10,000(P/F,i,5)

0 = -$15,000 + 4,000(P/A,i,5) - 10,000(P/F,i,5)

0 = -$15,000 + 4,000(P/A,i,5) + 12,000(P/F i,5)

0 = -$15,000 + 4,000(P/A,i,5) + 10,000(P/F,i,5)

Alternative X has a first cost of $5 million and an annual maintenance cost of $200,000. Alternative Y has a first cost of $7 million, a maintenance cost of $40,000 and periodic expenditures of $100,000 every five years. If both alternatives have infinite lives, the equation that will yield the rate of return on the incremental investment is:

0 = -$2 million + 160,000/i + 100,000(P/F,i,5)

0 = -$2 million + 160,000/i + 100,000(A/F,i,5)/i

0 = -$2 million + 160,000/i - 100,000(A/F,i, )/i

0 = -$2 million + 160,000/i + 100,000(A/F,i,5)

Questions 4 through 7 are based on the following statement:

Two mutually exclusive alternatives, A and B, are to be evaluated by the rate of return (ROR) method. The initial investment for alternative B is greater than that of alternative A.

If the overall ROR of alternative A is less than the MARR and the overall rate of return of alternative B is greater than the MARR, then:

Alternative B should be compared incrementally to alternative A.

Alternative B should be selected.

The ROR on the increment of investment between A and B is between the ROR on alternative A and the ROR of alternative B.

Alternative A should be selected because it has a lower initial investment cost.

If the overall ROR of both alternatives, A and B, is greater than the MARR, then:

Select alternative A because it has a lower initial investment cost.

Select alternative B because it has a higher initial investment cost.

Conduct an incremental analysis and select A if the ROR on the increment exceeds the MARR.

Conduct an incremental analysis and select B if the ROR on the increment exceeds the MARR.

If the overall ROR of both alternatives, A and B, is greater than the MARR and the ROR of B is greater than that of A, then:

Select alternative B, even without an incremental analysis.

The ROR on the increment between A and B exceeds the MARR.

The ROR on the increment between A and B exceeds the overall rate of return for alternative A.

All of the above.

If the overall ROR for alternative A exceeds the MARR and the ROR for alternative B is less than the MARR, then:

An incremental analysis is not necessary; select A

The ROR on the increment between A and B is less than the MARR.

The ROR on the increment between A and B is less than the overall rate of return on B.

All of the above.

Questions 8 through 10 are based on the following information:

Alternative	Initial Investment,$	Alternative Overall Rate of Return, %	Incremental Rate Of Return in % When Compared with Alternative
-----------	-------------	---------------	A	B	C
-----------	-------------	---------------	----------------------
A	- 40,000	29
B	- 75,000	15	1
C	-100,000	16	7	20
D	-200,000	14	10	13	12

If the alternatives are independent, which should be selected if the company's MARR is 15% per year?

Only alternative A

Alternatives A and B

Alternatives A and C

Alternatives A, B, and C

If the alternatives are mutually exclusive and the company's MARR is 11% per year, which alternative(s) should be selected?

A, B, C, and D

Only A

Only D

Only A and C

If the alternatives are mutually exclusive and the company's MARR is 10% per year, which alternative(s) should be selected?

A, B, C, and D

Only, A, B, and C

Only A

Only D

If the projects are independent, the ones that should be selected are:

A and B

A, B, and C

Only A

Only B

If the projects are mutually exclusive, the ones that should be selected are:

Only A

Only B

Only C

A, B, and C

Alternative I, which requires an initial investment of $20,000, will yield a rate of return of 25% per year. Alternative C, which requires a $30,000 investment, will yield 20% per year. Which of the following statements is true about the rate of return on the $10,000 increment?

It is greater than 20% per year

It is exactly 20% per year

It is between 20% and 25% per year

It is less than 20% per year

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