# Handy formulas for discounted cash flows

Keep this set of formulas handy if you are studying ACCA F9, P4 or P5 or CIMA P1 and F3. These formulas will frequently crop up so it’s a great idea to learn them now so you may recall them throughout your studies and exams.

'Yr n' is the number of years that the cash flow is received for.

Discounting a single cash flow

PV = Cash flow x discount factor

## Annuities – cash flows that occur annuity for a finite time period

Discounting an annuity starting in one year’s time

PV = Annual Cash flow x annuity factor yr n

Discounting an annuity starting immediately

PV = (Annual Cash flow x annuity factor yr n-1) + annual cash flow

Discounting an annuity starting in year 4

PV = (Annual cash flow x annuity factor yr n) x discount factor for the yr before the annuity starts

## Perpetuities – cash flows that continue into the foreseeable future

Discounting a perpetuity starting in one year’s time

PV = Annual Cash flow / discount rate

Discounting a perpetuity starting immediately

PV = (Annual Cash flow / discount rate) + annual cash flow

Discounting a perpetuity starting in year 4

PV = (Annual cash flow / discount rate) x discount factor for the yr before the perpetuity starts