Chapter 8: Net Present Value

The NPV formula can be defined as:

PV - required investment

A company has the opportunity to invest in one of two mutually exclusive projects. Project A has an initial cost of $1.2 million and cash flows with a present value of $4.5 million. Project B has an initial cost of $2 million and cash flows with a present value of $5 million. Which project should the firm choose to invest in?

Project A because it has a higher net present value Reason: Project A has a higher NPV and is the correct choice: $4.5 million - $1.2 million = $3.3 million. The NPV for Project B is only $5 million - $2 million = $3 million

True or false: When choosing among mutually exclusive projects, choose the one that offers the highest NPV.

True

The net present value rule states that managers increase shareholder wealth by:

accepting all projects with a positive NPV.

A positive NPV investment _________ while a negative NPV investment __________.

builds shareholder value; destroys shareholder value

The relationship between the NPV profile and the discount rate is

declining

The internal rate of return (IRR) is also called the:

discounted cash flow (DCF) rate of return

The ___________ method of project selection asks, "How long must the project last in order to offer a positive net present value?"

discounted-payback

The rate of return rule states that the rate of return is the discount rate at which NPV:

equals 0

The cash flow per period with the same present value as the cost of buying and operating a machine is called the:

equivalent annual annuity

Since a risky dollar is worth less than a safe one, returns for risky projects must be ________ than those of a risk-free investment.

higher

The IRR rule specifies that a firm should select any project whose IRR is __________ the firm's ___________.

higher than; opportunity cost of capital

Select which of the following relationships is correct:

if the opportunity cost of capital is less than a project's rate of return, then the NPV of the project is positive

If choices you make today do not affect future investment opportunities, then

it is enough simply to compare the NPV of the projects.

If two projects (investments) A and B are said to be mutually exclusive then we know that the firm ______________.

must choose to invest in either A or B, but not both.

Which two investment criterion methods are most used by firms?

net present value internal rate of return

The rate of return rule states that a firm should invest in any project offering a rate of return that is higher than the:

opportunity cost of capital

A project's IRR measures the _________ whereas the opportunity cost of capital is equal to the ____________.

profitability of a project; return offered by equivalent-risk investments in the capital market

Under which of the following situations should the IRR decision rule be avoided?

project NPV does not decline smoothly as discount rate increases selection of mutually exclusive projects a project with multiple rates of return

The opportunity cost of capital is determined by the ______ of a project.

risk

When comparing investments in assets with different lives you should:

select the project with the lowest equivalent annual annuity of costs

Under which of the following situations should the IRR decision rule be avoided?

selection of mutually exclusive projects a project with multiple rates of return project NPV does not decline smoothly as discount rate increases

Which of the following are problems that managers may encounter when deciding between mutually exclusive projects?

the choice between short and long-lived equipment the timing of investments when equipment should be replaced

The Internal Rate of Return (IRR) can best be defined as:

the discount rate at which the NPV equals zero

The opportunity cost of capital can best be described as:

the expected rate of return given up by investing in a project rather than in the capital market

When evaluating a single project for acceptance, the NPV and IRR decision rules will give the same result when _________.

the graph of NPV versus discount rate declines smoothly as discount rate increases

When considering mutually exclusive projects, the project that adds most to shareholder wealth is the one with:

the highest NPV

The payback period for a project can best be defined as:

the length of time before you recover your initial investment

The discount rate used to value capital investments is often referred to as ____.

the opportunity cost of capital

True or false: IRR is essentially the same as the opportunity cost of capital.

False

True or false: the payback rule states that a project should be accepted if its payback period is greater than a specified cutoff period.

False

Which of the three limitations of the Payback Rule can be overcome with a modification to it?

Gives equal weight to all cash flows arriving before the cutoff period

The single variable of interest for the investment timing problem is

NPV

Which of the following is the capital investment decision criterion that will always lead management to make the value-maximizing choice?

NPV

Which mutually exclusive project should a manager select?

NPV = $1,800, Total Cash Flow = $9,000

A firm plans to invest $10,000,000 in a new factory that will generate annual cash flows to the firm of $3,000,000 for 5 years, then will be scrapped. If the appropriate opportunity cost of capital for this investment is 8.0 percent, what is its NPV?

$1,978,130 $1,978,130 = -10,000,000 + 3M/(1.08) + 3M/(1.08)2 + 3M/(1.08)3 + 3M/(1.08)4 + 3M/(1.08)5

Machines A and B are mutually exclusive and have the following investment and operating costs. Machine A has a life of 3 years while Machine B has a 2 year life. Year: 0 1 2 3 A $5,000 $800 $900 $1,000 B $6,000 $850 $900 -- Assume the discount rate is 9 percent. The equivalent annual annuity of machine A is ______. The equivalent annual annuity of machine B is ______.

$2,477.53; $4,399.74 For Machine A, the PV of costs at 9% is $7,263.64. To find the equivalent annual annuity, set the PV of costs for 3 years to $7,263.64. You will see that an equivalent annual annuity of $2,869.53 works out: $2,869.53/(1.09)1 + $2,869.53/(1.09)2 + $2,869.53/(1.09)3 = $7,263.63 For Machine B, the PV of costs at 9% is $7,537.33. To find the equivalent annual annuity, set the PV of costs for 2 years to $7,537.33. You will see that an equivalent annual annuity of $4,284.74 works out: $4,284.74/(1.09)1 + $4,284.74/(1.09)2 = $7,537.33.

A machine that costs $20,000 today has annual operating costs of $1,500, $1,600, $1,700 and $1,800 in each of the next four years. The discount rate is 10 percent. The PV of costs is ________ and the equivalent annual annuity is _______.

$25,192.61; $7,947.53

What is the NPV of a project with an initial investment of $95, a cash flow in one year of $107, and a discount rate of 6%? (Be sure to record the initial investment as a negative number.)

$5.94

A firm plans to invest $300,000 in a new high-efficiency furnace that will reduce it's energy bill by $100,000 in years 1 and 2, $75,000 in years 3,4,5 and $50,000 in year 6. If the appropriate discount rate is 7.5%, the NPV of this project is ________.

$80,729 50000/(1.075)6 + 75000/(1.075)5 + 75000/(1.075)4 + 75000/(1.075)3 + 100000/(1.075)2 + 100000/(1.075) - 300000

A project has an initial investment of $5 million and cash flows for 6 years of $1.5 million per year. What is the project's internal rate of return (IRR)? Hint: use your financial calculator or financial spreadsheet to answer this question. Or, use trial and error to see which discount rate below offers an NPV closest to zero.

19.9% Reason: An IRR of 19.9% gives an NPV of $673.16, which is the closest figure to zero.

A project has an initial investment of $1.4 million and a present value of cash flows totaling $4 million. What is the project's net present value (NPV)?

2.6 Million NPV=initial investment + PV of cash flows= -$1.4 million + 4 million = $2.6 million

A project has an initial investment of $125,000 and cash flows of $50,000 per year for 3 years. What is the project's internal rate of return (IRR)? Hint: use your financial calculator or financial spreadsheet to answer this question. Or, use trial and error to see which discount rate below offers an NPV closest to zero.

9.7% A discount rate of 9.7% gives an NPV of $2.27, which is the closest to zero.

Which of the following is the correct definition of the Equivalent Annual Annuity (EAA)?

A stream of cash flows or payments that have the same present value as a project or investment's cash flows.

Which of the following are three limitations of the Payback Rule for accepting projects?

Biases the firm against long-term projects in favor of short-term ones Does not consider cash flows after the payback period Gives equal weight to all cash flows arriving before the cutoff period

Making the choice to invest today or to postpone that investment to a future date is a choice between mutually exclusive projects. When making this choice, what is the correct criterion to use?

Choose the investment date that produces the highest NPV today.

Which capital budgeting decision method finds the present value of each cash flow before calculating a payback period?

Discounted payback period

When comparing investments in assets with different lives, which project is best?

EAA = -$3,000; NPV = -$10,000 elect the project with the lowest equivalent annual annuity of costs