Engineering Economics Financial Decision Making for Engineers 5th Edition by Niall M. Fraser - Test Bank

Engineering Economics Financial Decision Making for Engineers 5th Edition by Niall M. Fraser – Test Bank

 

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Engineering Economics, 5e (Fraser)

Chapter 5   Comparison Methods: Part II

 

5.1   Multiple Choice Questions

 

1) The internal rate of return (IRR) is

1. A) the interest rate that allows an investor to recoup the initial investment.
2. B) the interest rate that ensures the positive cash flow of a project.
3. C) the interest rate that breaks even a project’s costs and benefits.
4. D) the interest rate that measures the return from operating costs
5. E) the interest rate that is set up by an investor to guarantee that the return on investment will be higher than from a bank interest rate.

Answer:  C

Diff: 1    Type: MC     Page Ref: 127

Topic:  5.2. Internal rate of return (IRR)

Skill:  Recall

User1:  Qualitative

 

2) A project pays $20 million right away, requires $10 million in investment in year 1, and pays $3 million in year 2. What is the approximate ERR of this project if the MARR is 10%??

1. A) 1.72%
2. B) 172%
3. C) 1.50%
4. D) 150%
5. E) 50%

Answer:  B

Diff: 1    Type: MC     Page Ref: 141

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

3) The fundamental idea behind comparison of mutually exclusive projects on the basis of incremental IRR is

1. A) different fractions of investments are associated with different levels of productivity.
2. B) all investments are non-simple.
3. C) some investments are not productive.
4. D) multiple IRRs.
5. E) high uncertainty.

Answer:  A

Diff: 2    Type: MC     Page Ref: 134-135

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Qualitative

 

 

4) The internal rate of return (IRR) is negative if

1. A) a project is losing money.
2. B) a cash inflow exceeds a cash outflow.
3. C) a project just breaks even.
4. D) a project is a simple investment.
5. E) IRR cannot be negative.

Answer:  A

Diff: 1    Type: MC     Page Ref: 128

Topic:  5.2. Internal rate of return (IRR)

Skill:  Recall

User1:  Qualitative

 

5) A project is represented by the following graphs:

 

 

What is the internal rate of return for this project?

1. A) 0%
2. B) 4%
3. C) 10%
4. D) 14%
5. E) 15%

Answer:  D

Diff: 1    Type: MC     Page Ref: 130-131

Topic:  5.2. Internal rate of return (IRR)

Skill:  Recall

User1:  Quantitative

 

6) Two mutually exclusive alternatives are being compared. We should choose the alternative that:

1. A) has a higher minimum acceptable rate of return assuming the lives of the alternatives are equal.
2. B) has a higher internal rate of return assuming the lives of the alternatives are equal.
3. C) has a higher internal rate of return regardless of the lives of the alternatives.
4. D) has an incremental investment with a rate of return equal to the minimum acceptable rate of return.
5. E) has an incremental investment with the rate of return exceeding minimum acceptable rate of return.

Answer:  E

Diff: 2    Type: MC     Page Ref: 132-136

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Qualitative

 

7) A project requires an initial investment of $100 000 and immediately pays $25 000. The next year this project requires an additional investment of $50 000 and does not pay anything. In the following year the project pays $150 000. The internal rate of return (i) for this project can be obtained by

1. A) using a present worth factor.
2. B) solving a quadratic equation.
3. C) calculating an external rate of return.
4. D) solving a system of two equations.
5. E) solving an ith degree polynomial equation.

Answer:  B

Diff: 3    Type: MC     Page Ref: 127

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Quantitative

 

8) What is the difference between the internal rate of return (IRR) and the external rate of return (ERR)?

1. A) The IRR is earned by a project whereas the ERR is earned outside of it
2. B) The ERR equals the difference between the IRR and the MARR
3. C) The IRR usually equals the MARR whereas the ERR is always higher than the MARR
4. D) The ERR is earned when a project’s return is used for the purpose of further reinvestment while the IRR is typically used for calculating the net return of a project
5. E) For a given explicit rate of return, a project can have more than one value for its ERR but can have only one value for its IRR

Answer:  A

Diff: 2    Type: MC     Page Ref: 140-142

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Qualitative

 

9) What economic concept is used as background for the external rate of return?

1. A) a present worth
2. B) a net cash flow
3. C) an internal rate of return
4. D) a payback period
5. E) an opportunity cost

Answer:  E

Diff: 3    Type: MC     Page Ref: 140

Topic:  5.1. Introduction

Skill:  Applied

User1:  Qualitative

 

 

10) A project requires no initial investment. It costs $4 000 a year from now and earns $8 000 two years from now. What is its internal rate of return?

1. A) 24%
2. B) 50%
3. C) 75%
4. D) 100%
5. E) 141%

Answer:  D

Diff: 1    Type: MC     Page Ref: 127

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

11) What assumption makes the external rate of return a proxy?

1. A) All receipts of a project are assumed to be invested at the minimum acceptable rate of return
2. B) Receipts that occur when a project balance is positive are assumed to be invested at the minimum acceptable rate of return
3. C) All receipts and disbursements of a project are assumed to be invested at the minimum acceptable rate of return
4. D) Receipts and disbursements that occur when a project balance is positive are assumed to be invested at the minimum acceptable rate of return
5. E) A project’s balance should be positive all the time

Answer:  A

Diff: 2    Type: MC     Page Ref: 141-142

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Qualitative

 

12) The external rate of return must be used if

1. A) there are multiple internal rates of return
2. B) a project involves only simple investments.
3. C) a project starts with cash outflow
4. D) a project requires multiple investments and generates multiple benefits
5. E) it is impossible to calculate the minimum acceptable rate of return.

Answer:  A

Diff: 2    Type: MC     Page Ref: 141-142

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Quantitative

 

 

13) A project is subject to the following cash flow diagram:

What rate of return would it be appropriate to use in this case?

1. A) ERR
2. B) IRR
3. C) MARR
4. D) Market rate of return
5. E) Explicit rate of return

Answer:  B

Diff: 2    Type: MC     Page Ref: 140-142

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Qualitative

 

14) What is the major advantage of the internal rate of return comparison method?

1. A) It gives an explicit measure of profit.
2. B) It has familiar meanings to decision makers.
3. C) It is very easy to calculate and therefore it is commonly used.
4. D) It takes into account the need to have capital recovered quickly.
5. E) It facilitates the comparison of projects of different size.

Answer:  E

Diff: 3    Type: MC     Page Ref: 147

Topic:  5.4. Rate of return and present/annual worth methods compared

Skill:  Recall

User1:  Qualitative

 

15) Which of the following statements is true with regard to the ERR?

1. A) The approximate ERR is just a proxy for the IRR.
2. B) The precise ERR is a proxy for the IRR.
3. C) For a simple investment, the precise ERR is greater than the IRR.
4. D) For a simple investment, the approximate ERR is greater than the IRR.
5. E) An acceptable project will earn at least the approximate ERR.

Answer:  E

Diff: 2    Type: MC     Page Ref: 141

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Qualitative

 

 

16) What is the major disadvantage of the internal rate of return method?

1. A) It complicates the comparison of projects of the different sizes.
2. B) It can produce more than one internal rate of return.
3. C) It discriminates against long-term projects.
4. D) It ignores the time value of money.
5. E) It ignores the expected service life.

Answer:  B

Diff: 3    Type: MC     Page Ref: 147

Topic:  5.4. Rate of return and present/annual worth methods compared

Skill:  Recall

User1:  Qualitative

 

17) A project is subject to the following cash flow diagram:

What is its rate of return?

1. A) 22%
2. B) 36%
3. C) 56%
4. D) 60%
5. E) 74%

Answer:  C

Diff: 2    Type: MC     Page Ref: 141

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

18) Unlike the internal rate of return method, the present and annual worth computations

1. A) are more complicated.
2. B) do not account for the time value of money.
3. C) give a direct measure of the profit provided by a project.
4. D) discriminate against long-term projects.
5. E) do not take into account expected service life of a project.

Answer:  C

Diff: 2    Type: MC     Page Ref: 147

Topic:  5.4. Rate of return and present/annual worth methods compared

Skill:  Recall

User1:  Qualitative

 

19) The following table summarizes information for five projects:

 

The data can be interpreted in the following way: The IRR on the incremental investment between project 5 and project 4 is 16%.

 

If all projects are independent and the company has at least $1 025 000 to invest, which projects should be undertaken if the MARR is 16%?

1. A) only 2
2. B) 2 and 4
3. C) 1, 3 and 5
4. D) 1, 3, 4 and 5
5. E) 1, 2, 3, 4 and 5

Answer:  D

Diff: 2    Type: MC     Page Ref: 129-131

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

20) The following table summarizes information for five projects:

 

The data can be interpreted in the following way: The IRR on the incremental investment between project 5 and project 4 is 16%.

 

If the projects are mutually exclusive, which projects should be undertaken if the MARR is 15%?

1. A) 3 only
2. B) 5 only
3. C) 3 and 5
4. D) 3, 4 and 5
5. E) 1, 3, 4, and 5

Answer:  B

Diff: 3    Type: MC     Page Ref: 132-136

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

21) Dealing with mutually exclusive projects, we start with some current alternative. How do we chose it?

1. A) the alternative with the highest internal rate of return
2. B) the alternative with a zero net benefit
3. C) the alternative with the benefit-cost ratio of one
4. D) the “do nothing” alternative
5. E) the alternative with the smallest first cost

Answer:  E

Diff: 1    Type: MC     Page Ref: 132-136

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Qualitative

 

22) What projects are called simple investments?

1. A) projects that consist of one inflow at the start followed by only one outflow
2. B) projects that have only two internal rates of return
3. C) projects that have a stream of revenues at the start followed by a stream of investments
4. D) projects that have one or more periods of outflows at the start followed by one or more periods of inflows
5. E) projects that require calculation of the external rate of return

Answer:  D

Diff: 1    Type: MC     Page Ref: 136-139

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Qualitative

 

23) Computation of the precise external rate of return can be a complex procedure because

1. A) positive balance earned by a project is to be invested outside this project at an unknown minimum acceptable rate of return.
2. B) of the difficulty in determining exactly when the explicit interest rate should be applied.
3. C) a project’s balance can be negative for the trial external rate of return.
4. D) the calculation requires a lot of experimenting with the trial external rate of return.
5. E) a project that requires this calculation is typically a simple investment project.

Answer:  B

Diff: 3    Type: MC     Page Ref: 140-142

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Qualitative

 

 

24) A two-year project has $100 million as initial investment and generates net savings of $60 million per year. What is the project’s IRR?

10. A) 10.1%
11. B) 11.1%
12. C) 12.1%
13. D) 13.1%
14. E) 14.1%

Answer:  D

Diff: 2    Type: MC     Page Ref: 127

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

25) The approximate ERR will always be

1. A) higher than the precise ERR.
2. B) lower than the MARR.
3. C) could be equal to precise ERR or MARR.
4. D) between the precise ERR and the MARR.
5. E) higher than both precise ERR and MARR.

Answer:  D

Diff: 2    Type: MC     Page Ref: 141

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Qualitative

 

26) For two mutually exclusive projects with equal lives, the one with

1. A) a higher IRR should be chosen.
2. B) a higher incremental PW at the MARR should be chosen.
3. C) a higher incremental FW at the MARR should be chosen.
4. D) a higher incremental IRR than the MARR should be chosen.
5. E) a higher incremental AW at the MARR should be chosen.

Answer:  D

Diff: 2    Type: MC     Page Ref: 132-136

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Qualitative

 

27) The problem of multiple IRRs arises whenever

1. A) IRR > ERR.
2. B) IRR = ERR.
3. C) a project is a simple investment.
4. D) a project starts with net savings followed by investments.
5. E) a project starts with first cost followed by net annual savings for the rest of the project’s service life.

Answer:  D

Diff: 2    Type: MC     Page Ref: 136-139

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Qualitative

 

 

28) In general, the IRR comparison method and the PW comparison method

1. A) produce the same results for independent projects but not for mutually exclusive projects.
2. B) produce the same results for mutually exclusive projects but not for independent projects.
3. C) produce different results for both independent projects and mutually exclusive projects.
4. D) produce the same results for independent projects and mutually exclusive projects with unequal lives.
5. E) produce the same results for independent projects and mutually exclusive projects with equal lives.

Answer:  E

Diff: 3    Type: MC     Page Ref: 143-147

Topic:  5.4. Rate of return and present/annual worth methods compared

Skill:  Recall

User1:  Qualitative

 

29) External rate of return is used for

1. A) projects with unequal lives.
2. B) projects which are non-simple investments.
3. C) projects with large capital costs but small operating costs.
4. D) projects with small capital costs but large operating costs.
5. E) projects that start with cash outflows followed by cash inflows.

Answer:  B

Diff: 1    Type: MC     Page Ref: 140

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Qualitative

 

30) You are going to buy a new car worth $14 500. A car dealer computes your monthly payment to be $267 for 7-year financing. What is the dealer’s effective annual rate of return on this loan?

9. A) 9.33%
10. B) 9.77%
11. C) 10.23%
12. D) 10.67%
13. E) 11.33%

Answer:  B

Diff: 2    Type: MC     Page Ref: 126-127

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

31) A project involves an immediate expenditure of $1 000, and will require additional expenditures of $100 a year for the next ten years, starting one year from now.  After ten years it yields an income of $3 000. What is its rate of return?

3. A) 3.5%
4. B) 4.5%
5. C) 5.5%
6. D) 6.5%
7. E) 7.5%

Answer:  C

Diff: 2    Type: MC     Page Ref: 129-142

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

32) A project involves an immediate expenditure of $2 000, and will require additional expenditures of $150 a year for the next ten years, starting one year from now. After ten years it yields an income of $8 000, but a year later a further expenditure of $1 000 will be required to close down the project. What is its rate of return?

1. A) 9%
2. B) 10%
3. C) 11%
4. D) 12%
5. E) 13%

Answer:  A

Diff: 2    Type: MC     Page Ref: 129-142

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

33) I sign a contract that guarantees me an immediate payment of $2 000, but then I have to invest $800 a year for ten years.  At the end of the tenth year I get a further payment of $8 000. What is my internal rate of return on the contract?

1. A) There are two solutions: 8% and 16%.
2. B) There are two solutions: 13% and 25%.
3. C) There are two solutions, 15% and 30%.
4. D) There are two solutions: 18% and 24%.
5. E) There is a single solution: about 22%.

Answer:  B

Diff: 2    Type: MC     Page Ref: 129-142

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

34)  I sign a contract that guarantees me an immediate payment of $2 000, but then I have to invest $800 a year for ten years.  At the end of the tenth year I get a further payment of $8 000. If I can invest money at 10% interest, what is my approximate external rate of return on the contract?

1. A) about 9%
2. B) about 10%
3. C) about 11%
4. D) about 12%
5. E) There are two solutions, about 8% and about 12%.

Answer:  C

Diff: 2    Type: MC     Page Ref: 140-142

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

 

35) What is the IRR corresponding to this cashflow diagram?

 

 

1. A) about 9%
2. B) about 12%
3. C) about 19%
4. D) about 22%
5. E) about 25%

Answer:  C

Diff: 2    Type: MC     Page Ref: 129-139

Topic:  5.2. Internal rate of return (IRR)

Skill:  Applied

User1:  Quantitative

 

36) What is the IRR corresponding to this cashflow diagram?

10. A) About 10.5%
11. B) About 11.5%
12. C) About 12.5%
13. D) About 13.5%
14. E) About 14.5%

Answer:  E

Diff: 2    Type: MC     Page Ref: 129-139

Topic:  5.2. Internal rate of return (IRR)

Skill:  Applied

User1:  Quantitative

 

 

37) If you can invest money at 10% interest, what is the approximate ERR corresponding to this cashflow diagram?

 

 

1. A) 15%
2. B) 20%
3. C) 25%
4. D) 30%
5. E) 35%

Answer:  C

Diff: 2    Type: MC     Page Ref: 140-142

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

5.2   Short Answer Questions

 

1) What is the difference between the internal rate of return and the minimum acceptable rate of return?

Answer:  The minimum acceptable rate of return (MARR) is a lower limit for investment acceptability. The MARR is usually set by a business evaluating an investment project. Frequently market interest is used as the MARR. The internal rate of return (IRR) is that interest rate at which the present worth of all costs is equal to the present worth of all benefits associated with an investment project.  For a project to be accepted, the IRR of the project must exceed the MARR.

Diff: 1    Type: SA     Page Ref: 127-128

Topic:  5.2. Internal rate of return (IRR)

Skill:  Recall

User1:  Qualitative

 

 

2) You can buy a car for $40 000 paying cash now or you can finance it through a bank loan paying $700 per month for 5 years. What is the IRR of the financing option in annual terms?

Answer:  By definition, the IRR equates present worth of costs and present worth of benefits. If you choose financing then $40 000 is your benefit while $700 per month for 60 months is your cost. Equating the two values with the help of the present worth of equal payments factor :

 

40 000 = 700 * [(1+IRR)60 – 1)/IRR/(1 + IRR)60]

 

and solving for IRR, we obtain 0.001615 by trial and error in a spreadsheet.  This is the effective monthly IRR, so the effective annual IRR is:

 

1.00161512 – 1 = 0.0196 or 1.96%

Diff: 2    Type: SA     Page Ref: 127-128

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

3) When does the problem of multiple IRRs arise and what are possible solutions to the problem?

Answer:  If a project is not a simple investment, there may be more than one value of IRR satisfying the condition PW(Costs) = PW (Benefits).  Such projects are usually characterized by one or more cash inflows at the start, followed by cash outflows. In such a case, application of the precise or approximate External Rate of Return (ERR) can resolve the problem.

Diff: 1    Type: SA     Page Ref: 136-138

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Qualitative

 

4) You have two ways to invest $1 000 000 you won in a lottery: (i) to buy government bonds that earn 4% annually, or (ii) to buy an apartment building that brings you $100 000 per year in revenues. Compare the two options in terms of their internal rates of return.

Answer:  The IRR of the first option is 4%. The IRR of the second option can be calculated as follows:

Initial Investment = Present Worth of infinite equal annual revenues at an unknown IRR

or 1 000 000 = 100 000/IRR.

IRR = 0.1 or 10%. It turns out that the second option is better since it results in a higher rate of return.

Diff: 2    Type: SA     Page Ref: 127-128

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

 

5) You are considering the following project: It pays you $5 000 at the end of the first year, costs $10 000 by the end of the second year and brings $4 000 next year. What is the project’s internal rate of rate, external rate of return and the approximate external rate of return if current market interest rate is 25%? Comment on the project acceptability on the basis of the given information.

Answer:  The IRR is calculated from PW(Costs) = PW (Benefits) evaluated at the unknown IRR:

 

10 000/(1 + IRR)2 = 5 000/(1 + IRR) + 4,000/(1 + IRR)3

 

from which we can deduce that IRR = 0.447 or 44.7%.

 

The exact ERR can be obtained by calculating net benefits each year, and moving benefits at the current interest rate. For example, at the end of year 2, benefit of $5 000 becomes 5 000 x (1+0.25) = $6 250. Since cost that year is $10 000, net benefit at the end of year 2 is 6 250 – 10 000 = -$3 750 which is actually net cost. Now it is possible to set the following equation:

 

3 750 x (1+ERR) = 4 000

 

from which we can deduce that ERR = 0.067 or 6.7%.

 

In order to calculate the ERRapp it is necessary to take all benefits at the current interest rate to the end of year 3 and to equate the result to all costs taken to the same year at the unknown ERRapp:

5 000 x (1 + 0.25)2 + 4 000 = 10 000 x (1 + ERRapp)

and ERRapp = 0.181 or 18.1%

 

The project would be accepted on the basis of the IRR, but rejected on the basis of the ERR and ERRapp.

 

Diff: 3    Type: SA     Page Ref: 140-142

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

 

6) Suppose that a project pays $5 000 on odd years and costs $5 000 on even years. If the life of the project is 6 years, what is its approximate external rate of return if the MARR is 10%? Would you accept or reject such a project?

Answer:

PW of all benefits at the 10% interest rate at the end of year 6 is:

 

5 000(1.1)5 + 5 000(1.1)3 + 5 000(1.1) = $20 207.55

 

PW of all costs at the unknown ERR at the end of year 6 is:

 

5 000(1+ERR)4 + 5 000(1 + ERR)2 + 5 000

 

Therefore, the following equation arises:

 

20 207.55 = 5 000(1 + ERR)4 + 5 000(1 + ERR)2 + 5 000

 

or  (1 + ERR)4 + (1 + ERR)2 – 3.04151 = 0

 

Solution to this equation is ERR = 0.146 or 14.6%. Since the ERR is greater than the market interest rate, the project should be accepted.

Diff: 3    Type: SA     Page Ref: 141-142

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

7) If you invest $1 000 now, you will receive this amount back in two years plus dividends of $200 each year. What is the IRR of this investment?

Answer:  We set up the following equation:

 

1 000 = 1 000/(1 + IRR)2 + 200/(1 + IRR) + 200/(1 + IRR)2

 

Solving for IRR results in 20% internal rate of return.

 

Diff: 2    Type: SA     Page Ref: 127-128

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

 

8) Suppose that Maria borrowed $5 000 from a bank to be repaid in five equal annual payments of $1 250. What is the IRR of this transaction?

Answer:  The underlying equation for the transaction is 5 000 = 1 250(P/A, IRR, 5). It can be simplified to:

 

(P/A, IRR, 5) = 4

 

From tables, 9% < IRR < 10%. Interpolating:

 

IRR = 0.09 + 0.01(4.0264 – 4.0)/(4.0264 – 3.9347) = 0.00929 or 9.29%

 

where (P/A, 9%, 5) = 4.0264 and (P/A, 10%, 5) = 3.9347.

Diff: 1    Type: SA     Page Ref: 129-131

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

9) What are the advantages and disadvantages of the comparison method based on the IRR against the present worth comparison method?

Answer:  IRR’s advantages: facilitates comparison of projects of different sizes; commonly used.

IRR’s disadvantages: relatively difficult to calculate; multiple IRRs.

PW’s advantages: gives explicit measure of profit contribution; difficult to compare projects of different sizes.

Diff: 1    Type: SA     Page Ref: 147

Topic:  5.4. Rate of return and present/annual worth methods compared

Skill:  Recall

User1:  Qualitative

 

10) Assume that Stan takes a student loan of $5 000 at the beginning of his first year at Miskatonic University and graduates at the end of year 5. After graduation, a 7% interest rate on the debt is applied. If Stan makes four equal annual payments to re-pay the debt in four years after graduation, what is the IRR on his loan?

Answer:  The first step is to define the size of the annual payment after graduation

A = 5 000 x (A/P, 7%, 4) = $1 476.14/year

 

Now the following equation with respect to year 5 can be introduced:

5 000 x (F/P, IRR, 5) = 1 476.14 x (P/A, IRR, 4)

 

Solution to the equation is IRR = 0.0225 or 2.25%.

Diff: 3    Type: SA     Page Ref: 127-129

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

 

11) Suppose that you can buy a car now for $20 000. On the other hand, you can lease it at $350 per month for 60 months. If you buy a car now, then you will be able to sell it at the end of the fifth year for $8 000. If you choose to lease, what is the monthly and annual IRR of the lease compared to the buying a car now?

Answer:  If you choose to lease, you forgo $20 000 of costs now (which is your benefit) and $8 000 of benefits in five years time (which is your cost) plus you pay $350 per month for 60 months, which is also your cost.

 

Let IRRm be the monthly internal rate of return. Then:

 

20 000 = 8 000 x (P/F, IRRm, 60) + 350 x (P/A, IRRm, 60)

 

Solution to this equation is IRRm = 0.0102 or 1.02% per month.

So the effective annual IRR = 1.0112 – 1 = 12.68%

Diff: 3    Type: SA     Page Ref: 127-129

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

12) Explain how you would compare two mutually exclusive projects on the basis of the internal rate of return.

Answer:  First calculate the IRR for both alternatives. Reject any alternative for which IRR < MARR.  Next calculate the incremental IRR of upgrading from the cheaper to the more expensive project. An alternative with a higher investment (first cost) is accepted only if it meets the criterion:

 

IRR of incremental investment > MARR

 

Otherwise, the alternative with lower investment is checked against MARR. It is accepted if its

IRR > MARR.

Diff: 2    Type: SA     Page Ref: 132-136

Topic:  5.3. Internal rate of return comparisons

Skill:  Recall

User1:  Qualitative

 

13) There are two options to buy a plot of land for construction: (i) upfront payment of $250 000, or

(ii) four equal payments of $50 000 in years 1-4 and the fifth payment of $150 000 in year 5. What is the implied IRR of choosing the second option over the first?

Answer:  If the second option is chosen, then $250 000 is a benefit since it is payment avoided.  Since the IRR equates the present worth of benefits and costs, the following equation arises:

 

250 000 = 50 x (P/A, IRR, 4) + 150 x (P/F, IRR, 5)

 

and IRR = 10.21%.

Diff: 2    Type: SA     Page Ref: 127-129

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

 

14) Steve is a professional web-site designer. He just bought a powerful computer for $5 000. According to the existing market, he will be able to sell this computer for $1 000 three years from now. In order for Steve to get 10% internal rate of return on his computer, what annual revenue should he generate over the three-year period?

Answer:  It is possible to set up the following equation based on the definition of the IRR:

 

5 000 = 1 000 * (P/F, 10%, 3) + X * (P/A, 10%, 3)

 

Solving this equation for X produces $1 708.46 per year.

 

Diff: 2    Type: SA     Page Ref: 127-129

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative

 

15) YVY Consulting group received a contract to evaluate a new technological line to produce shoes. The project is subject to the following cash flows:

 

Cash flow	Value
Purchase price	$100 000
Annual operating costs	$20 000/year
Annual production	800 pairs/year
Service life	5 years

 

If the market price of a pair of shoes is $70 and the MARR is 15%, is this a good investment on the basis of the IRR?

Answer:  It is necessary to calculate the IRR of this investment and compare it with the MARR = 15%. However, first it is necessary to find annual revenue as follows:

 

Annual Revenue = $70 * 800 = $56 000/year

 

The IRR of this investment can be calculated from:

 

100 000 = (56 000 -20 000) x (P/A, IRR, 5)

 

IRR comes to 23.4% by trial and error in a spreadsheet. Since the IRR is greater than the MARR, this is a good investment.

Diff: 2    Type: SA     Page Ref: 127-129

Topic:  5.3. Internal rate of return comparisons

Skill:  Applied

User1:  Quantitative