Finance: Key Concepts in NPV, IRR, and Capital Budgeting

What is NPV?

NVP is the difference between the present value of future cash flows and the initial investment. Accept if NPV > 0.

How is NPV calculated?

NPV = Σ[CFt / (1+r)^t] − initial investment.

What is the payback period?

Time required for a project's cash flows to recover its initial cost; ignores time value of money.

How is the payback period calculated?

Add raw cash flows until they equal the initial investment.

What is the discounted payback period?

Time to recover initial cost using discounted cash flows; includes time value of money.

How is discounted payback calculated?

Discount cash flows, then accumulate until they equal initial cost.

What is the Average Accounting Return (AAR)?

Average Net Income ÷ Average Book Value; uses accounting data and ignores time value.

How is AAR calculated?

AAR = Average Net Income / Average Book Value.

What is IRR?

The discount rate that makes NPV = 0; accept if IRR > required return.

What problems occur with IRR?

Multiple IRRs with nonconventional cash flows; conflicts with NPV for mutually exclusive projects.

What are NPV profiles?

Graphs showing NPV at different discount rates; reveal IRR and comparison across projects.

What is a crossover rate?

The discount rate where two project NPVs are equal; found using IRR of cash-flow differences.

What is MIRR?

Modified IRR; assumes reinvestment at WACC and fixes IRR issues.

What is the Profitability Index (PI)?

PI = PV of future cash flows ÷ Initial Investment; accept if PI > 1.

What cash flows should be included in capital budgeting?

Incremental CFs, opportunity costs, side effects, NWC changes, taxes, depreciation tax shield.

What cash flows should be excluded from capital budgeting?

Sunk costs, financing costs, unrelated allocated overhead.

What is Net Working Capital?

NWC = Current Assets − Current Liabilities; invested early and recovered at end.

What is after-tax salvage value?

After-tax salvage = SP − (SP − BV)(Tax Rate).

What is straight-line depreciation?

Depreciation = (Cost − Salvage) ÷ Life.

What is MACRS depreciation?

IRS accelerated depreciation based on fixed percentages of the asset's cost.

What is the OCF formula?

OCF = (Sales − Costs − Dep)(1 − Tax Rate) + Dep.

What is the risk-return trade-off?

Higher risk requires higher expected return.

How do you calculate dollar returns?

Dollar return = Dividend + (End Price − Beginning Price).

How do you calculate percentage returns?

Holding period return = Dollar Return ÷ Beginning Price.

What is a risk premium?

Risk premium = Expected Return − Risk-free Rate.

Systematic vs. unsystematic risk?

Systematic = market-wide; unsystematic = firm-specific and diversifiable.

What is diversification?

Reducing unsystematic risk by holding many assets.

What does beta measure?

Beta measures sensitivity to market movements; β > 1 is more volatile.

What is the CAPM formula?

E(R) = Rf + β(Rm − Rf).

Forms of EMH?

Weak: past prices; Semi-strong: public info; Strong: all info.

What is marginal cost of capital?

The cost of raising additional capital today.

Dividend Growth Model formula?

Re = D1/P0 + g.

Cost of equity using CAPM?

Re = Rf + β(Rm − Rf).

Cost of preferred stock formula?

Rps = D / P0.

After-tax cost of debt formula?

Rate × (1 − Tax Rate).

What is WACC?

WACC = weRe + wdRd(1 −T) + wpsRps.

When is WACC used as the discount rate?

For average-risk firmwide projects.

What if a project has different risk than the firm?

Use divisional WACC, pure play beta, or project-specific discount rate.

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net present value

The difference between the present value of an investment’s future cash flows and its initial cost

Which statement concerning the net present value (NPV) of an investment or a financing project is correct?

Any type of project should be accepted if the NPV is positive and rejected if it is negative.

payback period

The length of time required for an investment to generate cash flows sufficient to recover the initial cost of the investment

An investment is acceptable if the payback period:

 

is less than some pre-specified period of time.

discounted payback period

The length of time required for a project's discounted cash flows to equal the initial cost of the project

The discounted payback rule states that you should accept an investment project if its discounted payback period:

 

is less than some pre-specified period of time.

internal rate of return

The discount rate that makes the net present value of an investment exactly equal to zero

profitability index

The present value of an investment's future cash flows divided by the initial cost of the investmen

an independent investment is acceptable if the profitability index (PI) of the investment is:

greater than 1

The primary reason that company projects with positive net present values are considered acceptable is that:

 

they create value for the owners of the firm.

Payback is frequently used to analyze independent projects because:

its easy and quick to calculate

One characteristic of the payback method of project analysis is the:

 

bias towards liquidity.

profitability index

If you want to review a project from a benefit-cost perspective, you should use the _______ method of analysis.

NPV

Project A is opening a bakery at 10 Center Street. Project B is opening a specialty coffee shop at the same address. Both projects have unconventional cash flows, that is, both projects have positive and negative cash flows that occur following the initial investment. When trying to decide which project to accept, given sufficient funding to accept either, you should rely most heavily on the _____ method of analysis.

payback

If a firm is more concerned about the quick return of its initial investment than it is about the amount of value created, then the firm is most apt to evaluate a capital project using the _____ method of analysis.

No matter how many forms of investment analysis you employ:

the actual results from a project may vary significantly from the expected results.

discounted payback and payback

Which of the following methods of project analysis are biased towards short-term projects?

The payback method of analysis:

has a timing bias

The discounted payback method:

considers the time value of money

the payback method:

 

requires an arbitrary choice of a cutoff point.

Using the internal rate of return method, a conventional investment project should be accepted if the internal rate of return is:

greater than the discount rate

The internal rate of return for an investment project is best defined as the:

 

discount rate that causes the NPV to equal zero.

The elements that cause problems with the use of the IRR in projects that are mutually exclusive are referred to as the:

timing and scale problems

You must know the discount rate to:

 

compute the NPV but you can compute the IRR without having a discount rate.

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sunk cost

A cost that has already been paid, or the liability to pay has already been incurred

opportunity cost

The most valuable investment given up if an alternative investment is chosen

MACRS

The depreciation method currently allowed under U.S. tax law governing the accelerated write-off of property under various lifetime classifications is called _____ depreciation.

depreciation tax shield

The depreciation method currently allowed under U.S. tax law governing the accelerated write-off of property under various lifetime classifications is called _____ depreciation.

One purpose of identifying all of the incremental cash flows related to a proposed project is to:

eliminate any cost which has previously been incurred so that it can be omitted from the analysis of the project

Sunk costs include any cost that:

has previously been incurred and cannot be changed

sunk

You spent $500 last week fixing the transmission in your car. Now, the brakes are acting up and you are trying to decide whether to fix them or trade the car in for a newer model. In analyzing the brake situation, the $500 you spent fixing the transmission is a(n) _____ cost.

Which one of the following should be excluded from the analysis of a project?

sunk costs

All of the following are anticipated effects of a proposed project. Which of these should be considered when computing the cash flow for the final year of a project?

 operating cash flow, net working capital recovery, salvage values

The net working capital of a firm will decrease if there is:

 

a decrease in accounts receivable.

A company which uses the MACRS system of depreciation:

 will write off the entire cost of an asset over the asset's class life.

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An efficient capital market is one in which:

 

security prices reflect all available information.

The notion that actual capital markets, such as the NYSE, are fairly priced is called the:

 

efficient market Hypothesis (EMH).

strong

The hypothesis that market prices reflect all available information of every kind is called _____ form efficiency.

semistrong

The hypothesis that market prices reflect all publicly available information is called _____ form efficiency.

Financial markets fluctuate daily because they:

 

are continually reacting to new information.

Insider trading does not offer any advantages if the financial markets are:

strong form efficient

What is the primary characteristic of Treasury bills (T-bills) that makes their return the risk-free benchmark?

 

Virtually no default risk

What does the term "risk premium" refer to in financial investments?

 

The additional return required for investing in a risky asset

What is a key assumption of behavioral finance regarding financial participants?

 

They are not perfectly rational and self-controlled

What is a key focus of behavioral finance studies?

 

Understanding the influence of psychological biases

Which of the following is an example of a behavioral financial aspect?

loss/risk aversion

What is a key argument against the efficient market theory?

 

It does not incorporate irrational emotional behavior