Deck 4: Comparison Methods: Part I

Question 1

For the purpose of comparison, what alternative should be used in assessing an independent project?

A)the "do nothing" alternative
B)other projects, earning MARR or higher interest rate
C)putting money into a bank to earn a bank interest rate
D)investing money in an alternative project that can recoup the investment
E)investing money in an alternative project, which can earn the same interest rate as an independent project

Answer 1

A

Question 2

If project A has present worth of -$27 000 and project B has present worth of -$26 000, then

A)project B should be accepted on the basis of maximum benefits
B)project A should be accepted because it has larger absolute value.
C)project B should be accepted on the basis of minimum costs.
D)the situation requires additional assessment since some of the costs or benefits might not be considered.
E)the decision cannot be made because of uncertainty.

Answer 2

C

Question 3

The annual worth of a project is measured in terms of

A)dollars.
B)dollars per unit.
C)dollars per year.
D)dollars per unit per year.
E)percentage.

Answer 3

C

Question 4

A project requires $10 000 as initial investment and will earn a revenue of $2 000 per year over the next seven years. The interest rate is 5.0% per year. What is the present worth of the project's costs?

A)$1 573
B)$2 000
C)$8 681
D)$10 000
E)$11 573

Question 5

What is the basis for decision-making using the present worth comparison method?

A)to maximize the present worth of a project at the minimum acceptable rate of return
B)to maximize the benefits of a project at the minimum acceptable rate of return
C)to minimize the costs of a project at the minimum acceptable rate of return
D)to maximize the difference between the project's benefits and costs at the minimum acceptable rate of return
E)to minimize the difference between the project's costs and benefits at the minimum acceptable rate of return

Question 6

Two projects are mutually exclusive if

A)the expected costs and benefits of one project do not depend on whether or not the other project is chosen.
B)the expected costs and benefits of one project depend on whether the other project is chosen.
C)if it is impossible to do both at the same time
D)in the process of choosing one project at least one other project is chosen for comparison.
E)the possibility of the implementation of one project directly depends on whether or not the other one is implemented.

Question 7

What is the payback period?

A)a period of time over which an initial investment can be recovered fully assuming market interest rate to be equal to the MARR
B)a period of time after which a project starts generating profit
C)a period of time over which an initial investment cannot be recovered
D)a period of time over which an initial investment can be recovered fully
E)a period of time over which an initial investment can be recouped assuming zero interest rate

Question 8

The minimum acceptable rate of return (MARR)is

A)an interest rate, which is equal to a current bank interest rate.
B)the least interest rate among all alternative projects.
C)a highest interest rate among all alternative projects.
D)an interest rate that allows an investor to recoup the investment.
E)an interest rate that must be earned for a project to be accepted.

Question 9

What is the present worth of an independent project that requires initial investment of $50 000 and annual maintenance costs of $4 000 for 10 years at a 4% minimum acceptable rate of return?

A)-$4 000
B)-$32 444
C)-$54 000
D)-$82 444
E)-$17 556

Question 10

A project is marginally acceptable if

A)it earns positive present worth at the minimum acceptable rate of return.
B)it earns negative present worth at the minimum acceptable rate of return.
C)the present worth of a project is zero at the minimum acceptable rate of return.
D)it earns more than the minimum acceptable rate of return.
E)the difference between project's costs and benefits is positive at the minimum acceptable rate of return.

Question 11

A project requires $10 000 as initial investment and will earn a revenue of $3 000 per year over the next five years. Annual interest rate is 5.4%. What is the present worth of the project's benefits?

A)$2 846
B)$6 348
C)$7 154
D)$10 000
E)$12 846

Question 12

The annual worth method is

A)similar to the present worth method but transforms all annuities to a uniform series at the minimum acceptable rate of return.
B)similar to the present worth method but transform all annuities to arithmetic gradient series at the minimum acceptable rate of return.
C)methodologically different from the present worth method since it does not convert all annuities to the present worth at the minimum acceptable rate of return.
D)similar to the present worth method since it transforms all annuities to the present worth as a single payment.
E)similar to the present worth method except that all payments are converted into a geometric gradient series.

Question 13

Two mutually exclusive projects with the same service lives of 2 years are characterized by first costs of $100 million and $120 million respectively and annual savings of $60 million and $70 million respectively. If the MARR is 10%, which one should be chosen on the basis of the present worth comparison method?

A)The second one because it has higher annual savings.
B)The first one because its present worth is higher.
C)The second one because its present worth is higher.
D)The first one because incremental present worth is positive.
E)Neither because both produce negative present worth.

Question 14

Christine Robichaud, an engineer at Opus Ltd., has a $70 000 budget for upgrading the company's warehouse. She has calculated that the improvements could be completed in three months from now and would consume the entire budget. Due to these improvements the company saves $9 000 by the end of the first year, $14 000 by the end of the second year, and $35 000 by the end of the third year, $54 000 by the end of the fourth year and $17 000 by the end of the fifth year. What is the payback period for this project?

A)1
B)2
C)3
D)4
E)5

Question 15

For comparison purposes, in order to evaluate alternatives with unequal lives one should

A)repeat service life of each alternative at least three times.
B)assume some certain study period for evaluation by introducing salvage values for each alternative.
C)assume that the service life of each project is indefinite.
D)apply only annual worth comparison method for each alternative.
E)apply only present worth comparison method for each alternative.

Question 16

The best way to compare two projects with unequal lives is the

A)payback period.
B)present worth comparison method.
C)annual worth comparison method.
D)study period method.
E)incremental present worth comparison method.

Question 17

Mutually exclusive projects can be compared in terms of present worth if

A)they have the same service life.
B)they have the same costs.
C)they have the same benefits.
D)they have the same rate of return.
E)they have the same depreciation rate.

Question 18

A contingent project is an example of

A)independent projects.
B)mutually exclusive projects.
C)related but not mutually exclusive projects.
D)public projects.
E)incremental projects.

Question 19

If one project cannot be done by itself, a second project can be done alone, and both of them can be done together then the first project is said to be

A)independent from the second project.
B)related but not mutually exclusive to the second project.
C)mutually exclusive to the second project.
D)contingent on the second project.
E)interrelated with the second project.

Question 20

An investor wants to invest in the trucking business. To run this business, 10 trucks should be acquired. The market price of a truck is $50 000. It is also necessary to pay $390 000 per year as wages to the truck drivers. Vehicle repair and maintenance costs are $10 000 per year. What is the annual worth of the project's costs at 5% MARR over a 10-year period?

A)$400 000
B)$406 475
C)$454 750
D)$464 750
E)$551 800

Question 21

I can invest for a pension in either the Senex or the Geriatrix pension plan. Senex requires me to invest $1500 a year for the next 15 years (beginning one year from now), whereas Geriatrix requires an immediate deposit of $5 000 and 15 subsequent annual investment of $1 200 a year (also starting one year from now ). If my MARR is 15%, how much greater is the equivalent uniform annual cost to me of the series of payments I would make to Geriatrix versus the series of payments I would make to Senex?

A)$333
B)$444
C)$555
D)$666
E)$777

Question 22

Consider the following investment alternatives: If MARR is 20%, which one is the best based on PW comparison method?

A)A
B)B
C)C
D)D
E)E

Question 23

Jim is considering new software to design web pages. Currently there are three brands on the market: SUMY, ROVNO and PSEL. Based on the software manuals, Jim evaluated his productivity in terms of pages designed per year and put this information in a table:
If Jim receives $10 per page designed, evaluate these alternatives in terms of their payback period.

Question 24

I can invest for a pension in either the Senex or the Geriatrix pension plan. Senex requires me to invest $1500 a year for the next 15 years (beginning one year from now), whereas Geriatrix requires an immediate deposit of $5 000 and 15 subsequent annual investment of $1 200 a year (also starting one year from now ). Senex pays 10% on my investments, whereas Geriatrix pays 9%. How much more money will I have in my pension plan in 15 years time if I invest in Geriatrix?

A)$1 500
B)$3 380
C)$10 610
D)$5 790
E)I will have less money than if I had invested in Senex.

Question 25

I can buy a Grapefruit laptop computer for $3 000, or a Doors laptop for $2 500. The Grapefruit has an expected life of five years, whereas the Doors is only expected to last four years. Both provide equivalent service. A four-year-old Grapefruit has a salvage value of $200. If my MARR is 10%, what is the present cost of choosing the Grapefruit over the Doors?

A)$300
B)$315
C)$363
D)$383
E)$636

Question 26

What is the exact payback period for a 10-year project that requires $12 000 in initial investment, $1 000 in annual maintenance costs and generates annual revenue of $2 600 per year under 5% MARR?

A)7.5 years
B)7.9 years
C)8.4 years
D)9.2 years
E)10 years

Question 27

Suppose that cash flows of a project are given as follows: It is known that MARR is 10%. What is the project's payback period?

A)one year
B)two years
C)three years
D)four years
E)The project does not pay back.

Question 28

I spend $15 per week on bus fares to work. One day I decide to buy a mountain bike for $2000 and to ride to work instead. Assuming I work 50 weeks in a year, what is the payback time for this investment?

A)two years five months
B)two years seven months
C)two years eight months
D)two years nine months
E)two years ten months

Question 29

How is the payback period defined and what is its economic interpretation?

Question 30

For an independent project to be accepted

A)the PW of the project evaluated at MARR should be positive.
B)the PW of the project evaluated at MARR should be equal to zero.
C)the PW of the project evaluated at the MARR should be equal or greater than zero.
D)the PW of the project should be positive at the market interest rate.
E)the PW of the project should be equal to zero at the market interest rate.

Question 31

Annual worth comparison method

A)should be used widely because it does not have to assume a fixed minimum acceptable rate of return over the duration of a project.
B)can be preferable to the payback period method because the latter discriminates over the short-term projects.
C)should be used whenever it requires less calculations than the present worth method since the two methods lead to the same result for projects with equal lives.
D)can provide more accurate estimates of a project worth for the related but not mutually exclusive projects then other methods.
E)is always preferred to the present worth method for comparison of two projects with the same service lives.

Question 32

A municipality decided to build a new bridge to accommodate the city's growing traffic across the river. It has to pay $200 000 to construct the bridge plus $15 000 per year for its maintenance. Assuming that the bridge will have an infinite service life, calculate the present worth of the project at 10% interest rate.

A)$201 500
B)-$215 000
C)$280 000
D)$350 000
E)-$350 000

Question 33

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

A)a lower PW at the MARR should be chosen.
B)a higher AW at the MARR should be chosen.
C)a lower FW at the MARR should be chosen.
D)a higher incremental PW at the MARR should be chosen.
E)a higher incremental AW at the MARR should be chosen.

Question 34

By using the payback period method a decision-maker

A)equally treats short- and long-term projects.
B)takes into account the timing of cash flows.
C)accounts for time value of money.
D)disregards the need for a fast capital recovery.
E)favours long-term projects over the short-term projects.

Question 35

Explain how related but not mutually exclusive projects are compared in terms of the present worth and the annual worth comparison methods

Question 36

I can invest for a pension in either the Senex or the Geriatrix pension plan. Senex requires me to invest $1500 a year for the next 15 years (beginning one year from now), whereas Geriatrix requires an immediate deposit of $5 000 and 15 subsequent annual investment of $1 200 a year (also starting one year from now ). If my MARR is 15%, how much greater is the present cost to me of the series of payments I would make to Geriatrix versus the series of payments I would make to Senex?

A)$2 457
B)$3 246
C)$3 863
D)$4 127
E)$4 222

Question 37

I have 3 possible choices for a lawnmower. They have expected working lives of 3, 4 and 5 years. If I expect lawnmower technologies to be stable for the foreseeable future, over what period of time should I compare the equivalent uniform annual costs of the three choices?

A)12 years
B)20 years
C)30 years
D)45 years
E)60 years

Question 38

I spend $60 per month on bus fares to work. One day I decide to buy a mountain bike for $1680 and to ride to work instead. Assuming I work 12 months in a year, and my MARR is 1% per month, compounded monthly, what is the discounted payback time for this investment?

A)two years five months
B)two years seven months
C)two years eight months
D)two years nine months
E)two years ten months

Question 39

A manager is considering two technological lines to produce candies. The first one requires $1 million in initial investment and produces 150 kilograms (kg)of candies per day. The second one requires $1.3 million of initial investment and produces 200 kg of candies per day. Assuming the same service life of six years for both lines, a 5% annual interest rate and the price of candies of $4/kg, which line should the manager acquire?

Question 40

If you have reliable economic forecast for five years only, and you would like to evaluate two alternatives with five and six years service lives, the best method to do so is

A)the repeated lives method.
B)the study period method.
C)Both repeated lives method and study period method produce the same result.
D)to choose the alternative with the highest FW.
E)to choose the alternative with the highest PW.

Question 41

MMM Consulting is evaluating two oil pumps with the same operating costs. The first pump lasts three years and costs $12 000. The second one lasts 4 years and costs $15 000. Current market interest rate is 8%. Compare the two using the repeated lives method.

Question 42

Explain when the repeated lives comparison method should be applied and how it works.

Question 43

MJ Consulting is doing a feasibility study on a new technological line to produce shoes. Experts identified three mutually exclusive alternatives. Information on all of them is presented in the following table:
If the price of a pair of shoes is $100, the annual interest rate is 7% and service life is 5 years for all alternatives, which one is the best?

Question 44

REMAX Development owns a parcel of land in a city and wants to sell it to the highest bidder. One of the requirements is that REMAX will be involved in the construction and maintenance on that land. Three bidders submitted their proposals. From a standpoint of REMAX information is as follows:
Evaluate these projects on the basis of their present worth if the interest rate is 12% and the assessment horizon is 25 years.

Question 45

The present worth of a 4-year project is $145 million. It has a first cost of $76.8 million, annual savings and operating costs, and salvage value of $44 million at the end of its service life. What is the project's annual net savings if its MARR is 4%?

Question 46

It was discovered by geologists that an oil deposit can produce oil commercially for 5 years. In order to develop this deposit $100 million is required in initial investment with the sale value of the equipment of $20 million at the end of the deposit's life. In addition, $4 million annually is required for operating and maintenance costs. Current price of oil is $90 per barrel. How much oil must this deposit produce per year in order to cover all the costs under 2% interest rate?

Question 47

Suppose that cash flows of a project are given as follows:
What is the project's payback period?

Question 48

NB Power wants to assess the opportunity to install and use a photovoltaic system to produce electricity from solar energy. The unit cost of electricity currently produced by the thermal power plant is $0.06 per kilowatt-hour. The photovoltaic system is characterized by the following:
Batteries must be replaced every 5 years while power control is replaced every 10 years.
Assuming a service life of 20 years, annual interest rate of 10%, capacity of the photovoltaic system of 30 kilowatt-hours per day and ignoring the installation cost, should NB Power implement the system?

Question 49

How is the study period comparison method different from the repeated lives comparison method?

Question 50

Morris paid $500 per month for 20 years to pay off a bank mortgage on his house. If his down payment was $5 000, and the interest rate was 6% compounded monthly, how much did his house cost?

Question 51

A new computer system costs $20 000 and saves $5 000 per year over a five year service life. Resale value of the computer is estimated at $5 000 at the end of its service life. If the MARR is 4%, what is the annual net benefits of the computer system?