Deck 12: Dealing With Uncertainty and Risk

Question 1

A decision tree of a project is given as follows: What is the expected value of alternative A?

A)$4.98
B)$5.08
C)$5.91
D)$8.83
E)$9.66

Answer 1

B

Question 2

The break-even point is defined as the point at which

A)variable costs are equal to fixed costs.
B)the sum of variable and fixed costs is equal to total profit.
C)total income is just equal to the sum of fixed and variable costs.
D)profits are at a maximum.
E)profits are equal to variable costs.

Answer 2

C

Question 3

A decision tree of a project is given as follows: What is the expected value of alternative B?

A)$0
B)$4.5
C)$5.0
D)$5.2
E)$10.0

Answer 3

B

Question 4

The slope of a sensitivity graph of -5 with respect to operating costs means

A)a 1% increase in operating costs leads to a 5% decrease in PW of the project.
B)a 1% increase in operating costs leads to a $5 decrease in PW of the project.
C)a $1 increase in operating costs leads to a 5% decrease in PW of the project.
D)a $1 increase in operating costs leads to a $5 decrease in PW of the project.
E)a 1% increase in operating costs leads to a 5% increase in PW of the project.

Question 5

An engineering project involves reinforcing a concrete beam. From previous experience it is thought that the probability of corrosion is 1%. A diagnostic test is performed on the reinforced beam. If corrosion is present, then the probability that the test will reveal it is 80% while the probability that the test will miss it is 20%. The diagnostic never yields false positives-that is, it will never indicate corrosion if corrosion is not present. What is the probability of discovering corrosion?

A)0.001
B)0.008
C)0.09
D)0.8
E)0.002

Question 6

A pie company has two employees who each earn $30 000 a year, and it pays $10 000 rent every year. The ingredients for a pie, including the gas to cook it, cost $10 per pie. If pies are sold at $20 each, the break-even point for the company (calculated pre-tax)is

A)3 500 pies.
B)4 000 pies.
C)6 000 pies.
D)7 000 pies.
E)8 000 pies.

Question 7

A decision tree of a project is given as follows: What is the equivalent decision tree?

A)

B)

C)

D)

E)

Question 8

Suppose a discrete random variable X can take on these values with the following probabilities: What is the mean of the discrete random variable X?

A)0.25
B)0.50
C)0.75
D)1.00
E)1.25

Question 9

The sensitivity graph of a project is presented below: What is the least sensitive input of the project?

A)MARR
B)SV
C)FC
D)VC
E)O&M

Question 10

A graphical representation of the logical structure of a decision problem is usually

A)an event tree.
B)a decision tree.
C)a probability tree.
D)a risk tree.
E)an uncertainty tree.

Question 11

COOR Ltd. is buying a new sewing machine for $9 000. It can be sold at the end of its 10 year service life for $800. The firm's MARR is 10%. What is the minimum annual savings that the machine must yield in order to break even on the investment?

A)$2 012
B)$1 415
C)$1 815
D)$1 212
E)$1 692

Question 12

A pie company has two employees who each earn $30 000 a year, and it pays $10 000 rent every year. The ingredients for a pie, including the gas to cook it, cost $10 per pie. If the company is taxed at 50% and pies are sold at $20 each, the break-even point for the company (calculated after-tax)is

A)3 500 pies.
B)4 000 pies.
C)6 000 pies.
D)7 000 pies.
E)8 000 pies.

Question 13

Suppose you are asked to do a sensitivity analysis of a project when an economy is in recession, what assumptions do you need to make to evaluate the project?

A)Market share is low, variable costs are high, product price is high.
B)Market share is low, fixed costs are high, product price is low.
C)Market share is high, variable costs are high, product price is low.
D)Market share is low, variable costs are high, product price is low.
E)Market share is low, variable costs are low, product price is low.

Question 14

A company has developed a new product. Market price of the product is $10 per unit, variable costs are $6 per unit and total fixed costs are $100 000. Suppose that the company sets a target of $2 of profit per unit. How many units should be produced to meet the target?

A)10 000
B)20 000
C)30 000
D)40 000
E)50 000

Question 15

In a sensitivity graph that examines the present worth of a project, the slope of a line shows

A)how sensitive a project's benefit-cost ratio is to changes in its inputs: the steeper, the more sensitive.
B)how sensitive a project's PW is to changes in its inputs: the steeper, the more sensitive.
C)how sensitive a project's benefit-cost ratio is to changes in its inputs: the flatter, the more sensitive.
D)how sensitive a project's PW is to changes in its inputs: the flatter, the more sensitive.
E)how sensitive the project's IRR is to changes in its inputs: the flatter, the more sensitive.

Question 16

In general, sensitivity analysis can be described as

A)establishing the range of variations in the key parameters of a project.
B)gaining a better understanding of how cash flows affect a project's performance.
C)predicting profitability of a project.
D)establishing the impacts of uncertainty in a project's inputs on its economic performance.
E)establishing the level of data errors.

Question 17

First cost of a construction project depends on weather. Historical weather data shows that in the fall weather is warm 20% of the time, it is cold 30% of the time and it is somewhat in between 50% of the time. During warm weather, first cost is expected to be $225 000, during cold weather $295 000 and $250 000 in between. What is the expected value of the first cost?

A)$225 000
B)$250 000
C)$252 000
D)$258 500
E)$295 000

Question 18

Below the results of a scenario analysis are presented: What is the expected value of total profit according to this analysis?

A)$2.8M
B)$3.2M
C)$3.6M
D)$4.2M
E)$4.4M

Question 19

Graphically, the break-even value for any one of the input parameters to a project is captured by

A)the slope of the project's sensitivity graph.
B)y-axis intercept of the graph of present worth as a function of that input parameter.
C)x-axis intercept of the graph of present worth as a function of that input parameter.
D)inverse of the slope of the graph of present worth as a function of that input parameter.
E)the ratio of the vertical intercept to horizontal intercept of the project's sensitivity graph.

Question 20

A firm decides to invest $5 million in a new food processing plant. The plant has an expected life of 20 years with expected sales of 6 million cans of food per year. Fixed annual costs are $2 million and annual variable costs are $1 per can. The product will be priced at $2 per can. Corporate tax rate is 40%, and the MARR is 10%. Ignoring tax impacts on the first cost, what is the project's PW under the base case scenario?

A)$25.6 million
B)$15.4 million
C)$46.1 million
D)$20.4 million
E)$29.0 million

Question 21

The expected value of the present worth of an engineering project is $103 015. It was evaluated on the basis of the following information on four potential outcomes:
If annual interest rate is 10%, and all the alternatives have equal probabilities of occurring, what is the annual savings under Alternative I?

Question 22

The decision tree of a project is represented by the following graph: What is the outcome of an alternative A if the expected monetary value of a project is $4.56?

A)$2.0
B)$2.5
C)$5.0
D)$8.4
E)$10.3

Question 23

Future annual revenue generated by a project is a random variable. Its probability distribution function is given as follows: What is the probability of annual revenue being higher than $30 000/year?

A)0.1
B)0.3
C)0.4
D)0.5
E)0.6

Question 24

If a decision tree shows the possible profits associated with each of several alternative decisions, what is the optimal decision strategy?

A)the strategy that has the maximum profit as one of its possible outcomes
B)the strategy that results in the highest expected value of profit
C)the strategy for which the sum of leaf-node values is a maximum
D)the strategy that minimizes the variance in profit
E)the strategy that minimizes the risk of obtaining the lowest possible profit

Question 25

New software has been developed, and $23 000 has been spent on its development. However, the implementation phase requires an additional $30 000. There is uncertainty about annual net revenue. Three potential scenarios with their probabilities of occurring were identified., as shown in the following table:
Assume a 10% MARR and use a decision tree to answer the following question: What is the expected PW for deciding whether or not to proceed?

Question 26

A firm's evaluation of all possible alternatives with respect to production costs produced the following results: Which alternatives should be eliminated from consideration?

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

Question 27

There are three alternatives for producing a needed resource. The table below presents mean costs and variance of costs for each of them. If mean-variance dominance is applied to these alternatives then

A)A dominates B.
B)B dominates C.
C)C dominates A.
D)B dominates A.
E)A dominates C.

Question 28

MMM Consulting is considering three scenarios of building a bridge. Data collected by the firm's experts are presented below:
Probability of the best case scenario is 10% while probability of the expected and the worst case scenarios is 70% and 20% respectively. Assuming zero inflation and 10% annual interest rate, should the bridge be built?

Question 29

The probability of heavy traffic on a provincial highway is 20%, while the probabilities of low and medium traffic are 50% and 30% respectively. It was estimated that annual maintenance costs of the highway are $20 000 in the case of low traffic, $30 000 in the case of medium traffic and $100 000 in the case of heavy traffic. Calculate the expected value of the annual maintenance costs.

Question 30

The Kisu Company has just spent $100 000 to install a new technological line to produce kitchen knives. Estimates and probabilities for net annual savings, depreciation rates, CCA rates and useful life are given below:
Kisu pays a 30% corporate tax rate. Calculate the expected value of the annual worth of the line if the after-tax MARR is 10%.

Question 31

You are offered a chance to buy a ticket in a lottery. You have a one in ten chance of winning this lottery. If you win, your name will be entered along with 399 other winners as an entrant in a second lottery. All the entrants in the second lottery have an equal chance of winning the single prize, a sportscar valued at $400 000. What is the most it would be rational for you to pay for a ticket in the first lottery?

A)$10
B)$40
C)$100
D)$400
E)$1 000

Question 32

NB TECH is evaluating a dam-building project. The following estimates for probable cashflows were obtained:
NB TECH uses a discount rate of 5%. If the life of a dam is 10 years and it has no salvage value thereafter, should it be built?

Question 33

You have a contract with a company in the remote country of Placidia which guarantees you a profit of 100 000 Placidos in five years time. At the moment, one Placido is equal to one Canadian dollar. However, there is about to be an election in Placidia, and if the Placidia First candidate gets in, it is expected that there will be 10% annual inflation in Placidia over the next five years. As far as you can tell, each of the two candidates has an equal chance of being elected. If your MARR is 10%, what is the expected present value to you of the contract, in Canadian dollars?

A)$38 554
B)$50 323
C)$62 091
D)$82 645
E)$86 777

Question 34

As a rule, potential values of a random variable in a decision tree are represented by

A)chance nodes.
B)decision nodes.
C)terminal positions.
D)branches.
E)links.

Question 35

You are experimenting with a new process for manufacturing high-energy-density batteries. Your technical staff tell you that the process should only produce 25% defectives. However, the first three batteries produced by the process all turn out to be defective. What are the odds on this happening if your technical staff are telling the truth?

A)1.6%
B)8.3%
C)12.5%
D)18.6%
E)22%

Question 36

The host of a TV show offers you a chance to pick one of four boxes. Three are empty, one contains $1 000. If you pick an empty box, you can pay $250 for a second pick from the remaining three boxes. If you pick another empty box, you can pay $500 for a third pick from the two remaining boxes. If you pick wrong a third time, you are out of the game. What is your expected gain (or loss)from playing this game?

A)$250
B)$310
C)$330
D)$350
E)$500

Question 37

In general, an increase in salvage value ________ and an increase in the interest rate ________ the present worth of a project.

A)increases, increases
B)increases, decreases
C)decreases, increases
D)decreases, decreases
E)does not change, decreases

Question 38

You are experimenting with a process for producing high-energy-density batteries. You have a contract with the government to deliver a batch of 20 batteries, due today. If you deliver them on time and they are all functional, you will get $100 000. Each battery has a 1% chance of being defective, and if any of them are defective, the government will not pay you the $100 000, but will fine you $10 000. What is the expected value to you of your contract with the government?

A)-$1 821
B)$79 970
C)$81 791
D)$82 645
E)$86 777

Question 39

The host of a TV show offers you a choice of ten closed boxes. Some of them contain money, some are empty. The total amount of money in them is $1 000. The host offers, for a price, to tell you how many are empty. How much is this offer worth?

A)It's not worth anything.
B)$10
C)$12.50
D)$100
E)$250

Question 40

The host of a TV show offers you a choice of five closed boxes. One contains $1 000, one contains $500, one contains $100, and two are empty. He offers, for a price, to remove one of the empty boxes and let you choose among the remaining four. How much is this offer worth?

A)It's not worth anything, because you still might choose the other empty box.
B)$80
C)$320
D)$400
E)$1 600

Question 41

A coal mine extracts 100 000 tons of coal annually using mining equipment that costs $10 million. Operating and maintenance costs are $3 million per year. Define the break-even price of coal over planning horizon of six years under a 8% annual interest rate if the equipment's salvage value is $200 000.

Question 42

BC Power has just purchases a $0.5 million turbine. The turbine will allow it to produce 10 000 kilowatt hours (KWH)of electricity per day for twenty years. Afterwards the turbine's scrap value is expected to be negligible. Current price of electricity is $0.06/KWH. Operating costs of the turbine are $100 000 per year. Now BC Power pays a 40% corporate tax rate on its annual income. Depending on the outcome of the provincial elections, it is expected that the tax rate can either increase by 10% or decrease by 10%. Given this information and assuming a 5% annual interest rate and a 20% CCA rate, perform a sensitivity analysis on the company's after-tax profit in the turbine's first year of operation with respect to the expected changes in the corporate tax rate.

Question 43

This decision tree represents the expected profits and the standard deviations associated with three decisions facing a mobile phone producer (All figures are in millions of dollars). The root node (the one on the left)represents the decision of whether to produce the phones in China or North America. The second pair of nodes represent the decision of whether to market the phones in China or North America; and the final nodes represent the choice of selling price: if the phones are sold in China, they will be sold for either $30 or $40, whereas if they are sold in North America, they will be sold for either $40 or $50. Based on the calculated values, what is the company's best strategy?

Question 44

Describe the backward induction procedure used in decision tree analysis.

Question 45

New equipment was bought by an engineering firm for $5 million. For the base case, assume a 7% interest rate, a 20% depreciation rate and service life of four years. Construct a sensitivity graph for the PW of the equipment's salvage value with respect to a variation of 20% in its depreciation rate.

Question 46

A new technological line to produce shoes is being designed. It costs $100 000 and operating costs are expected to be $30 000 per year. Planned annual production is 800 pairs and the price of a pair of shoes is $80. The line's service life is five years, the depreciation rate is 20%. Assuming a 10% annual interest rate for the base case, perform a sensitivity analysis with respect to the interest rate in the interval [-20%, +20%] in terms of present worth. Comment on your results briefly.

Question 47

A manager of a manufacturing enterprise is considering whether to produce an intermediate good in house or to buy it from another firm. If the good is produced in house, three potential outcomes are possible: (i)if production is done in one shift, then expected profit is -$30 000 per year, (ii)if production is done in two shifts, then expected profit is $10 000, and (iii)if production is done in three shifts, then expected profit is $55 000. Probabilities associated with these outcomes were estimated as 35%, 45% and 20% respectively. However, if the good is purchased, two potential outcomes arise: (i)on-time delivery of the good results in $20 000 of expected profit, (ii)delays in delivery result in an expected loss of -$17 000. Probabilities of these outcomes are 60% and 40% respectively. Draw a decision tree, and execute it to make a decision.

Question 48

The first cost of a highway project is $1.5 million. Operating and maintenance costs were estimated at $50 000 per year. There will be zero salvage value of the highway after 20 years. As a result of this project, a recreational facility worth $10 000 per year in benefits will be destroyed. Assuming a 4% social discount rate, what is the break-even value of time savings to the highway users? How would this value change if social discount rate increased to 10%?