The present value (PV) is the present discounted value of future cash flows. For assets, it is the present discounted value of future net cash inflows that an asset is expected to produce. For liabilities, it represents the present discounted value of future net cash outflows that are expected to be required to settle the liability.

**Present value formula and its example calculation**

The present value represents the present nominal of the money we would receive in the future. We can calculate it with the following formula:

This concept is widely applied in various fields of finance. For example, when you target to have Rp1,000 in the next five years and invest in assets with a return of 12% per year (or 1% per month), then you must now invest as much as:

**PV = 1000/((1+1%)^60) = Rp550.45**

In excel, we can calculate it using the PV formula:

**= PV(rate, nper, pmt, [fv], [type])**

**RATE**is the interest rate per period (1%)**NPER**is the number of periods (60 months)**PMT**is the payment for each period and cannot change during the annuity period (0)**FV**is the future value (Rp1000)**TYPE**refers to when payments are due (0 at the end and 1 at the beginning, in this case, 0).

The above formula assumes we get a monthly return on investment of 1%. If we get annual returns instead of monthly, the values we need to invest now are:

**PV = 1000 / ((1 + 12%)^5) = Rp567.43**

The value is slightly different due to differences in interest and number of periods. PV uses the concept of interest on interest – or compound interest, i.e. ((1+r%)^N) – so that the value is sensitive to the percentage discount rate and the number of periods. A higher the discount rate leads to a lower the present value of future cash flows. Likewise, the longer the period, the smaller the present value of future cash flows. The following are simulations for the different number of periods and discount rates:

PV (r=1%, FV =1000) | Number of periode (r=1%) | PV (nper=60, FV=1000) | r |

408.4 | 90 | 421.6 | 1.45% |

451.1 | 80 | 460.7 | 1.30% |

498.3 | 70 | 503.6 | 1.15% |

550.4 | 60 | 550.4 | 1.00% |

608.0 | 50 | 601.8 | 0.85% |

671.7 | 40 | 658.0 | 0.70% |

741.9 | 30 | 719.6 | 0.55% |

819.5 | 20 | 787.0 | 0.40% |

905.3 | 10 | 860.9 | 0.25% |