Chapter 8

Which of the following decision rules might best be used as a supplement to net present value (NPV) by a firm that favors liquidity? A) profitability index B) MIRR C) equivalent annual annuity D) payback period

D

The present value (PV) of an investment is ________. A) the amount that an investment would yield if the benefit were realized today B) the difference between the cost of the investment and the benefit of the investment in dollars today C) the amount you need to invest at the current interest rate to re-create the cash flow from the investment D) the amount by which the cash flow of an investment exceeds or falls

A

Which of the following best describes the Net Present Value rule? A) Take any investment opportunity where the net present value (NPV) is not negative; turn down any opportunity when it is negative. B) Take any investment opportunity where the net present value (NPV) exceeds the opportunity cost of capital; turn down any opportunity where the cost of capital exceeds the net present value (NPV) C) When choosing among any list of investment opportunities where resources are limited, always choose those projects with the highest net present value (NPV). D) If the difference between the present cost of an investment and the present value (PV) of its benefits after a fixed number of years is positive the investment should be taken, otherwise it should be rejected.

A

You are trying to decide between three mutually exclusive investment opportunities. The most appropriate tool for identifying the correct decision is ________. A) net present value (NPV) B) profitability index C) internal rate of return (IRR) D) incremental internal rate of return (IRR)

A

A firm has an opportunity to invest $95,000 today that will yield $109,250 in one year. If interest rates are 4%, what is the net present value (NPV) of this investment? A) $10,048 B) $11,053 C) $16,077 D) $14,250

A Explanation: A) $109,250 / (1 + 0.04) = $105,048.077 $105,048.077 - $95,000 = $10,048

A car dealership offers a car for $14,000 , with up to one year to pay for the car. If the interest rate is 5%, what is the net present value (NPV) of this offer to buyers who elect not to pay for the car for one year? A) $667 B) $1333 C) $13,333 D) $14,000

A Explanation: A) $14,000 / (1 + 0.05) = $13,333.3333 $14,000 - $13,333 = $667

Mary is in contract negotiations with a publishing house for her new novel. She has two options. She may be paid $100,000 up front, and receive royalties that are expected to total $26,000 at the end of each of the next five years. Alternatively, she can receive $200,000 up front and no royalties. Which of the following investment rules would indicate that she should take the former deal, given a discount rate of 8%? Rule I: The Net Present Value rule Rule II: The Payback Rule with a payback period of two years Rule III: The internal rate of return (IRR) Rule A) Rule I only B) Rule III only C) Rule II and III D) Rule I and II

A Explanation: A) Using a financial calculator, enter CF0 = 100,000, CF1 = 26,000, F1 = 5; calculate NPV for I = 8 = $203,810, which is greater than $200,000.

An orcharder spends $110,000 to plant pomegranate bushes. It will take four years for the bushes to provide a usable crop. He estimates that every year for 20 years after that he will receive a crop worth $10,500 per year. If the discount rate is 9%, what is the net present value (NPV) of this investment? A) -$42,098 B) -$21,049 C) $8420 D) $12,629

A Explanation: A) Using financial calculator, enter CF0 = -110,000 , CF1 = 0, F1 = 4, CF2 = 10,500 , F2 = 20; calculate NPV for I = 9% = -$42,098 .

An auto-parts company is deciding whether to sponsor a racing team for a cost of $1 million. The sponsorship would last for three years and is expected to increase cash flows by $570,000 per year. If the discount rate is 6.9%, what will be the change in the value of the company if it chooses to go ahead with the sponsorship? A) $498,597 B) $747,896 C) $797,756 D) $847,615

A NPV = -1,000,000 + 570,000 / (1 + 0.069 ) + 570,000 / (1 + 0.069 )2 + 570,000 / (1 + 0.069 )3 = $498,597

A lottery winner can take $6 million now or be paid $600,000 at the end of each of the next 16 years. The winner calculates the internal rate of return (IRR) of taking the money at the end of each year and, estimating that the discount rate across this period will be 4%, decides to take the money at the end of each year. Was her decision correct? A) Yes, because it agrees with the Net Present Value rule. B) Yes, because it agrees with the payback rule. C) Yes, because it agrees with both the Net Present Value rule and the payback rule. D) Yes, because it disagrees with the Net Present Value rule.

A planation: A) Using a financial calculator, enter PMT = 600,000, N = 16, I = 4%; calculate PV = $6,991,377 , which is greater than $6,000,000.

When comparing two projects with different lives, why do you compute an annuity with an equivalent present value (PV) to the net present value (NPV)? A) so that you can see which project has the greatest net present value (NPV) B) so that the projects can be compared on their cost or value created per year C) to reduce the danger that changes in the estimate of the discount rate will lead to choosing the project with a shorter timeframe D) to ensure that cash flows from the project with a longer life that occur after the project with the shorter life has ended are considered

B

Which of the following is NOT a limitation of the payback period rule? A) It does not account for the time value of money. B) It is difficult to calculate. C) It ignores cash flows after payback. D) It does not account for changes in the discount rate.

B

Which of the following statements is FALSE? A) The payback investment rule is based on the notion that an opportunity that pays back its initial investments quickly is a good idea. B) An internal rate of return (IRR) will always exist for an investment opportunity. C) A net present value (NPV) will always exist for an investment opportunity. D) In general, there can be as many internal rates of return (IRRs) as the number of times the projectʹs cash flows change sign over time.

B

A lawn maintenance company compares two ride-on mowersthe Excelsior, which has an expected working-life of six years, and the Grassassinator, which has a working life of four years. After examining the equivalent annual annuities of each mower, the company decides to purchase the Excelsior. Which of the following, if true, would be most likely to make them change that decision? A) Fuel prices are expected to rise and raise the annual running costs of all mowers. B) The mower is only expected to be needed for three years. C) The prices of equivalent mowers are expected to grow in the future as lawnmower manufacturers consolidate. D) The number of customers requiring lawn-mowing services is expected to sharply increase in the near future.

B

Peter has a business opportunity that requires him to invest $10,000 today, and receive $12,000 in one year. He can either use $10,000 that he already has for this investment or borrow the money from his bank at an interest rate of 10%. However, the $10,000 he has right now is needed for urgent repairs to his home, repairs that will cost at least $15,000 if he delays them for a year. What is the best alternative for Peter out of the following choices? A) No, since the net present value (NPV) of the investment, should he take it, is less than the net present value (NPV) of the home repairs if he delays them for one year. B) Yes, since he can borrow the $10,000 from a bank, repair his home, invest $10,000 in the business opportunity, which, since it has a NPV > 0 will mean he will still come out ahead after repaying the loan. C) Yes, since the net present value (NPV) of the investment is greater than zero he can invest the $10,000 in the business opportunity, and then next year use this money plus the benefit from this money to make the necessary home repairs. D) Yes, since the net present value (NPV) of the investment, should he take it, is greater than the net present value (NPV) of the home repairs if he delays them for one year.

B

Which of the following statements is FALSE? A) The payback rule is useful in cases where the cost of making an incorrect decision might not be large enough to justify the time required for calculating the net present value (NPV). B) The payback rule is reliable because it considers the time value of money and depends on the cost of capital. C) For most investment opportunities, expenses occur initially and cash is received later. D) Fifty percent of firms surveyed reported using the payback rule for making decisions.

B

A consultancy calculates that it can supply crude oil assaying services to a small oil producer for $115,000 per year for five years. There are some upfront costs the consultancy will require the oil producer to absorb. What is the maximum that these upfront costs could be, if the equivalent annual annuity to the oil company is to be under $160,000 , given that the cost of capital is 9%? A) $45,000 B) $175,034 C) $201,289 D) $160,000

B Explanation: B) Annual difference = $160,000 - $115,000 = $45,000 ; PV over 5 years at 9% = $175,034

The owner of a number of gas stations is considering installing coffee machines in his gas stations. It will cost $270,000 to install the coffee machines, and they are expected to boost cash flows by $120,536 per year for their five-year working life. What must the cost of capital be if this investment has a profitability index of 1? A) 1.89% B) 3.78% C) 7.55% D) 9.44%

B Explanation: B) Using a financial calculator, PMT = 120,536 , N = 5, PV = 540,000 , compute I = 3.78%.

An investor is considering a project that will generate $900,000 per year for four years. In addition to upfront costs, at the completion of the project at the end of the fifth year there will be shut-down costs of $400,000 . If the cost of capital is 4.4%, based on the MIRR, at what upfront costs does this project cease to be worthwhile? A) $2.62 million B) $2.91 million C) $3.21 million D) $3.50 million

B lanation: B) Bring all negative cash flows to time 0; thus, PV shut-down cost = -400,000 / (1 + 0.044 )5 = -$322,520.63 ; FV positive cash flows at time 5 = $4,013,810.7 ; PV of positive cash flows at time 0 = $3,139,085; NPV at 4.4% = 2.91 million

A firm is considering several mutually exclusive investment opportunities. The best way to choose between them is which of the following? A) profitability index B) payback period C) net present value (NPV) D) internal rate of return (IRR)

C

According to Graham and Harveyʹs 2001 survey (Figure 8.2 in the text), the most popular decision rules for capital budgeting used by CFOs are ________. A) NPV, IRR, MIRR B) MIRR, IRR, Payback period C) IRR, NPV, Payback period D) Profitability index, NPV, IRR

C

Which of the following is NOT a limitation of the payback rule? A) It does not consider the time value of money. B) Lacks a decision criterion that is economically based. C) It is difficult to calculate. D) It does not consider cash flows occurring after the payback period.

C

Which of the following is true regarding the profitability index? A) It does not use the net present value (NPV) to assess benefits. B) It is very simple to compute. C) Attention must be taken when using it to make sure that all of the constrained resource is utilized. D) It is unreliable when used for choosing between different projects.

C

Martin is offered an investment where for $6000 today, he will receive $6180 in one year. He decides to borrow $6000 from the bank to make this investment. What is the maximum interest rate the bank needs to offer on the loan if Martin is at least to break even on this investment? A) 1% B) 2% C) 3% D) 4%

C Explanation: C) ($6180 - $6000 )/$6000 = 3%

A delivery service is buying 600 tires for its fleet of vehicles. One supplier offers to supply the tires for $80 per tire, payable in one year. Another supplier will supply the tires for $20,000 down today, then $45 per tire, payable in one year. What is the difference in PV between the first and the second offer, assuming interest rates are 8.1%? A) -$860 B) -$229 C) -$574 D) $860

C Explanation: C) -$80 × 600 = $48,000 PV1 = 48,000 / (1 + 0.081 ) = $44,403.3302 -$45 × 600 = $27,000 PV2 = -20,000 + $27,000 / (1 + 0.081 ) = $44,976.8733 PV1 - PV2 = $44,403.3302 - $44,976.8733 = -$574 THIS MATH IS WRONG

A farmer sows a certain crop. It costs $240,000 to buy the seed, prepare the ground, and sow the crop. In one yearʹs time it will cost $93,200 to harvest the crop. If the crop will be worth $350,000 , and the interest rate is 7%, what is the net present value (NPV) of this investment? A) $240,000 B) $87,103 C) $0 D) $567,103

C Explanation: {(350,000 - $93,200 )/(1 + 0.07)} - 240,000 = $0

Two mutually exclusive investment opportunities require an initial investment of $7 million. Investment A pays $2.0 million per year in perpetuity, while investment B pays $1.4 million in the first year, with cash flows increasing by 4% per year after that. At what cost of capital would an investor regard both opportunities as being equivalent? A) 3% B) 7% C) 13% D) 15%

C Explanation: C) -7 + 2.0 / r = -7 + 1 / (r - 0.04); r = 13%

A mining company plans to mine a beach for rutile. To do so will cost $14 million up front and then produce cash flows of $7 million per year for five years. At the end of the sixth year the company will incur shut-down and clean-up costs of $6 million. If the cost of capital is 13.0%, then what is the MIRR for this project? A) -60.97% B) -78.39% C) -87.10% D) -95.81%

C Explanation: C) Bring all negative cash flows to time 0; thus, PV shut-down cost = -6 / (1 + 0.13)6 = 2.88191116 ; FV positive cash flows at time 6 = 51.2589405 ; MIRR of the project = -87.10%.

A local government awards a landscaping company a contract worth $1.5 million per year for five years for maintaining public parks. The landscaping company will need to buy some new machinery before they can take on the contract. If the cost of capital is 6%, what is the most that this equipment could cost if the contract is to be worthwhile for the landscaping company? A) $5.69 million B) $6.00 million C) $6.32 million D) $6.63 million

C Explanation: C) Using a financial calculator, enter PMT = 1.5, N = 5, I = 6%; calculate PV = $6.32 million.

Which of the following decision rules is best defined as the amount of time it takes to pay back the initial investment? A) internal rate of return (IRR) B) profitability index C) net present value (NPV) D) payback period

D

A convenience store owner is contemplating putting a large neon sign over his store. It would cost $50,000, but is expected to bring an additional $24,000 of profit to the store every year for five years. Would this project be worthwhile if evaluated using a payback period of two years or less and if the cost of capital is 10%? A) Yes, since it will pay back its initial investment in two years. B) Yes, since the value of the cash flows into the store, in present dollars, are greater than the initial investment. C) Yes, since the cash flows after two years are greater than the initial investment. D) No, since the value of the cash flows over the first two years are less than the initial investment.

D

A security firm is offered $80,000 in one year for providing CCTV coverage of a property. The cost of providing this coverage to the security firm is $74,000, payable now, and the interest rate is 8.5%. Should the firm take the contract? A) Yes, since net present value (NPV) is positive. B) It does not matter whether the contract is taken or not, since NPV = 0. C) Yes, since net present value (NPV) is negative. D) No, since net present value (NPV) is negative.

D

Most corporations measure the value of a project in terms of which of the following? A) discount value B) discount factor C) future value (FV) D) present value (PV)

D

Which of the following is NOT a valid method of modifying cash flows to produce a MIRR? A) Discount all of the negative cash flows to time 0 and leave the positive cash flows alone. B) Leave the initial cash flow alone and compound all of the remaining cash flows to the final period of the project. C) Discount all of the negative cash flows to the present and compound all of the positive cash flows to the end of the project. D) Turn multiple negative cash flows into a single negative cash flow by summing all negative cash flows over the projectʹs lifetime.

D

Which of the following is a disadvantage of the Net Present Value rule? A) can be misleading if inflows come before outflows B) not necessarily consistent with maximizing shareholder wealth C) ignores cash flows after the cutoff point D) relies on accurate estimate of the discount rate

D

Which of the following situations can lead to IRR giving a different decision than NPV? A) delayed investment B) multiple IRRs C) differences in project scale D) All of the above can lead to IRR giving a different decision than NPV.

D

You are opening up a brand new retail strip mall. You presently have more potential retail outlets wanting to locate in your mall than you have space available. What is the most appropriate tool to use if you are trying to determine the optimal allocation of your retail space? A) internal rate of return (IRR) B) payback period C) net present value (NPV) D) profitability index

D

A janitorial services firm is considering two brands of industrial vacuum cleaners to equip their staff. Option A will cost $1,500, require servicing of $200 per year, and it will last five years. Option B will cost $1,000, require servicing of $100 per year, and it will last three years. If the cost of capital is 8%, which is the better option, given that the firm has an ongoing requirement for vacuum cleaners? A) Option A, since it has a lower equivalent annual annuity. B) Option B, since it has a lower equivalent annual annuity. C) Option A, since it has a greater equivalent annual annuity. D) Option B, since it has a greater equivalent annual annuity.

D Answer: D Explanation: D) Using a financial calculator, NPV(A) = -$2,298.54 equivalent annual annuity (A) = -$575.68 NPV(B) = -$1257.71 equivalent annual annuity (B) = -$488.03

An investor has the opportunity to invest in four new retail stores. The amount that can be invested in each store, along with the expected cash flow at the end of the first year, the growth rate of the concern, and the cost of capital is shown for each case. It is assumed each investment will operate in perpetuity after the initial investment. Which investment should the investor choose? A) Initial investment: $100,000; Cash flow in year 1: $12,000; Growth Rate: 1.25%; Cost of Capital: 9.1% B) Initial investment: $90,000; Cash flow in year 1: $10,000; Growth Rate: 1.50%; Cost of Capital: 9.3% C) Initial investment: $80,000; Cash flow in year 1: $8,000; Growth Rate: 1.75%; Cost of Capital: 8.0% D) Initial investment: $60,000; Cash flow in year 1: $6,000; Growth Rate: 2.50%; Cost of Capital: 7.2%

D Explanation: D) NPV project D= -60,000 + 6,000 / (0.072 - 0.025) = $67,660 NPV project A = -100,000 + 12,000 / (0.091 - 0.0125) = $52,866 NPV project B = -90,000 + 10,000 / (0.093 - 0.015) = $38,205 NPV project C = -80,000 + 8,000 / (0.08 - 0.0175) = $48,000

Which of the following statements is FALSE? A) In general, the difference between the cost of capital and the internal rate of return (IRR) is the maximum amount of estimation error in the cost of capital estimate that can exist without altering the original decision. B) The internal rate of return (IRR) can provide information on how sensitive your analysis is to errors in the estimate of your cost of capital. C) If you are unsure of your cost of capital estimate, it is important to determine how sensitive your analysis is to errors in this estimate. D) If the cost of capital estimate is more than the internal rate of return (IRR), the net present value (NPV) will be positive.

D Explanation: D) If the cost of capital estimate is more than the internal rate of return (IRR), the NPV will be negative.

A florist is buying a number of motorcycles to expand its delivery service. These will cost $78,000 but are expected to increase profits by $3000 per month over the next four years. What is the payback period in this case? A) 10.40 months B) 15.60 months C) 19.50 months D) 26.00 months

D Explanation: D) Payback period = 78,000 / 3000 = 26.00 months

Tanner is choosing between two investment options. He can invest $500 now and get (guaranteed) $550 in one year, or invest $500 now and get (guaranteed) $531.40 back later today. The risk-free rate is 3.5%. Which investment should Tanner prefer? A) $531.40 later today, since $1 today is worth more than $1 in one year. B) $550 in one year, since it is $50 more than he invested rather than $31.40 more than he invested. C) Neither - both investments have a negative NPV. D) Tanner should be indifferent between the two investments, since both are equivalent to the same amount of cash today.

D Explanation: D) The NPVs are equal, so that each is the same as $31.40 today.

Jenkins Security has learned that a rival has offered to supply a parking garage with security for ten years for $45,000 up front and a further $15,000 per year. If Jenkins Security offers to provide security for eight years for an upfront cost of $60,000 and a separate yearly payment, by what maximum amount can this yearly payment be over $20,000, so that Jenkinsʹ offer matches the equivalent annual annuity of their rivalʹs offer? (Assume a cost of capital of 5%.) A) -$89 B) -$94 C) -$100 D) -$111

D Explanation: D) Using a financial calculator, spreading $45,000 over 10 years = $5827.70587 ; thus, EAA = $9172.29413 ; spreading $60,000 over 8 years = $9283.30882 ; thus, the difference = -$111 .

The owners of a chain of fast-food restaurants spend $25 million installing donut makers in all their restaurants. This is expected to increase cash flows by $11 million per year for the next five years. If the discount rate is 5.3%, were the owners correct in making the decision to install donut makers? A) No, as it has a net present value (NPV) of -$4.45 million. B) No, as it has a net present value (NPV) of -$2.22 million. C) Yes, as it has a net present value (NPV) of $13.34 million. D) Yes, as it has a net present value (NPV) of $22.23 million.

D Explanation: D) Using financial calculator, enter CF0 = -25,000,000 , CF1 = 11,000,000 , F1 = 5; calculate NPV for I = 5.3% = $22,231,874.40 .

T OR F: Internal rate of return (IRR) can reliably be used to choose between mutually exclusive projects.

FALSE

T OR F: When different projects put different demands on a limited resource, then net present value (NPV) is always the best way to choose the best project.

FALSE

T OR F: When using equivalent annual annuities to compare the costs of projects with different lives, you should not consider any changes in the expected replacement cost of equipment.

FALSE

T or F: Preference for cash today versus cash in the future in part determines net present value (NPV).

False

T or F: The internal rate of return (IRR) rule will agree with the Net Present Value rule even when positive cash flows precede negative cash flows.

False

T OR F When an alternative decision rule disagrees with the net present value (NPV), the NPV should be followed.

TRUE

T OR F: Net present value (NPV) is usefully supplemented by internal rate of return (IRR), since IRR gives a good indication of the sensitivity of any decision made to changes in the discount rate.

TRUE

T OR F: The profitability index can break down completely when dealing with multiple resource restraints.

TRUE

T OR F: When comparing mutually exclusive projects which have different scales, you must know the dollar impact of each investment rather than percentage returns.

TRUE

T OR F: When different investment rules give conflicting answers, then decisions should be based on the Net Present Value rule, as it is the most reliable and accurate decision rule.

TRUE

T OR F: You can evaluate alternative projects with different lives by calculating and comparing their equivalent annual annuity.

TRUE

T or F: Net present value (NPV) is the difference between the present value (PV) of the benefits and the present value (PV) of the costs of a project or investment.

True

T or F: The Net Present Value rule implies that we should compare a projectʹs net present value (NPV) to zero.

True

T or F: The payback rule is based on the idea that an opportunity that pays back its initial investment quickly is a worthwhile opportunity.

True