To move cash flow forward in time:
Future Compounded Value of a Cash Flow

FV=

To move cash flow backwards in time:
Present Discounted Value of a Cash Flow

PV =

Because we need to compare values at the same point in time, if there are different streams:
Present Value of Cash Flow Stream:

PV = → + + …+ Future Value of a Cash Flow Stream with a Present Value of PV:

(See other iterations) Perpetuities ­ when a constant cash flow will occur at regular intervals indefinitely (no time frame, so no FV) Present Value of a Perpetuity:

PV =

Present Value of a Growing Perpetuity: Expected amount of perpetual payment increase at a constant rate (g) G < R always

This looks like Period 1: C; Period 2: discount it as:

; Period 3:

… so we

PV =

or

Annuities ­ when a constant cash flow will occur at regular intervals for a finite number of N periods (bc a timeline is defined, both a PV and FV exist) General Formula Present Value of an Annuity: These have interim Cash Flows, coming every period, same CFs, same R, set N

PV =

=

PV = + +

Future Value of an Annuity: Finite time, same R, same CFs

+ … +

FV = = Present Value of a Growing Annuity: Annuities can have g > r or g < r (unlike Perpetuities) PV =

Loan or Annuity Payment:

Cash flow =

If you know the PV of CF but not the Internal Rate of Return (the Interest Rate that sets NPV of
CF equal to zero): PV (positive flows) – PV (negative flows)
IRR → PV (positive flows) = PV (negative flows)

NPV → determines whether risk is worth the reward… High Rate, the more likely to reject project bc cash flows will be lower. Rate can be higher due to uncertainty and difficulty calculating future cash flows. IRR > Cost of Capital (or NPV > 0) ACCEPT

IRR < Cost of Capital (or NPV > 0) REJECT
IRR = Cost of Capital (or NPV > 0) INDIFFERENT The IRR rule usual answers the NPV rule, if stand alone project’s negative CFs precede positive
CFs. NPV is always best and never misleading, especially when choosing a project. IRR cannot just be doubled when a project size is doubled, unlike NPV. IRR conflicts with NPV if Delayed Investments (conflicts with