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.