# Net Present Value (NPV) with Inflation

Net Present Value (NPV) is the difference between the present value of cash inflow and cash outflow of a project over a period of time. It uses to evaluate the investment proposal in order to select the most profitable project. It sums all the present value of cash outflow and expected cash inflow. If the balance is positive it means that the project will make a profit. On the other hand, if the result is negative, it will make losses in the future.

One main issue with NPV, it completely ignores inflation which decreases the value of future cash inflow. Inflation is the decreasing of currency value due to the decrease of purchase power. It the decrease of money value compare to the average price of goods and services over a period of time.

As the NPV is the tool to evaluate the project using future cash inflow, ignoring inflation will have a significant impact on the decision.

## Impact of Inflation on Cash Flow

The real cash flow (or current cash flow) is the cash flow that is not adjusted with the expected inflation.

Money or nominal cash flow is the cash flow that already adjusts with the expected inflation.

(1+i) = (1+r) (1+h) |

- i: money rate or nominal rate
- r: real rate
- h: inflation rate

## Include Inflation into NPV Calculation

There are two methods that can include the inflation into the NPV calculation:

### Using a Real Discount rate

Inflation is not considered in both future cash flow and discounted rates. It means that the future cash flow is the real cash flow which not yet adjust with expected inflation. The discounted rate is the real rate which also not taking into account inflation.

### Using Nominal rate

The difference from the first method, this method uses normal future cash flow and normal discounted rate to calculate the NPV. The expected future cash flow must be adjusted with inflation before discount. And the discounted rate must be the normal rate which already includes inflation.

## Example of Inflation with NPV

Company ABC is considering an investment proposal which requires making an initial investment of $ 40 million. The project expects to generate future cash of $10 million per year for 5 years. The nominal discounted rate is 5% and the inflation rate is 2% per year.

### Using Real Discounted Rate

Convert nominal rate to real discounted rate:

(1+i) = (1+r) (1+h)

(1+r) = (1+i)/(1+h)

(1+r) = (1+5%)/(1+2%)

(1+r)= 102.941%

r= 2.941 %

Year |
Cash Flow |
PV @ 2.941% |
PV of Cash Flow |

0 | (40,000,000) | 1.000 | (40,000,000) |

1 | 10,000,000 | 0.971 | 9,714,286 |

2 | 10,000,000 | 0.944 | 9,436,735 |

3 | 10,000,000 | 0.917 | 9,167,114 |

4 | 10,000,000 | 0.891 | 8,905,196 |

5 | 10,000,000 | 0.865 | 8,650,762 |

Total | 5,874,092 |

### Using Nominal Discounted Rate

The future cash flow must be adjusted with inflation before discounted to present value. We can use a nominal rate to discount as following:

Year |
Cash Flow |
Inflation (2%) |
PV @ 5% |
PV of Cash Flow |

0 | (40,000,000) | (40,000,000) | 1.000 | (40,000,000) |

1 | 10,000,000 | 10,200,000 | 0.952 | 9,714,286 |

2 | 10,000,000 | 10,404,000 | 0.907 | 9,436,735 |

3 | 10,000,000 | 10,612,080 | 0.864 | 9,167,114 |

4 | 10,000,000 | 10,824,322 | 0.823 | 8,905,196 |

5 | 10,000,000 | 11,040,808 | 0.784 | 8,650,762 |

Total | 5,874,092 |

Both methods will give the same result, if not there must something wrong with the calculation. As both calculations have included inflation with just different methods.