Net Present Value Rule (Video)

Vocabulary flashcards covering future value, present value, discount rate, NPVs, and the NPV decision rule as discussed in the net present value section.

Future Value (FV)

The value of a cash amount after growing at rate r; FV = PV × (1 + r). Example: $100 at 10% becomes $110.

Present Value (PV)

The value today of a cash flow C to be received in the future; PV = C ÷ (1 + r). Also called Present Discounted Value.

Present Discounted Value

An alternate name for Present Value (PV).

Discount Rate (r)

The interest rate used to discount future cash flows; typically nonnegative; affects PV and NPV calculations.

C0

The initial investment cash flow (usually negative) in the NPV formula.

C1

The payoff in one year (the cash flow in year 1) in the NPV formula.

Net Present Value (NPV)

NPV = C0 + C1 ÷ (1 + r); a measure of value added by an investment; positive NPV increases the firm's value.

NPV Rule

Choose projects with positive NPV to maximize the corporation's value; if NPV > 0, undertake the project.

Present Value vs Future Value relationship (r ≥ 0)

The present value of a future cash flow is less than or equal to the future amount; PV ≤ C, with equality only if r = 0; when r > 0, PV < C.

Cookie Jar Argument for r ≥ 0

Illustrates why we often assume nonnegative rates (risk-free storage appeal); crises can push rates to zero or negative, but typically r ≥ 0 holds.

Example NPV Calculation

With cost 0.5 million and payoff 0.54 million next year, NPV at r = 5% is ≈ 0.0143 million ($14,300), since NPV = -0.5 + 0.54/1.05.