# NPV and Inflation

Net present value (NPV) is a technique that involves estimating future net cash flows of an investment, discounting those cash flows using a discount rate reflecting the risk level of the project and then subtracting the net initial outlay from the present value of the net cash flows. It helps in identifying whether a project adds value or not.

Inflation is a phenomenon that results in decrease in purchasing power and results in increases in revenue and costs. It affects estimates of future cash flows. In order to make better decision, accurate capital budgeting calculations are important, which are possible only when all the financial variables are taken care of.

## Methods

There are two ways in inflation can be accounted for while calculating net present value:

**Nominal method:**converting real cash flows to nominal cash flows and discounting them using nominal discount rate**Real method:**estimating real cash flows and discounting them using real discount rate

The final net present value is same under both methods.

Under the nominal method, net cash flows in time t are calculated by the following formula:

Nominal Cash Flows at Time t = Real Cash Flows at Time t × (1 + Inflation Rate)^{t}

Under the real method, real cash flows and real discount rate are used.

Relationship between nominal discount rate, real discount rate and inflation is given below:

Nominal Discount Rate

= (1 + Real Discount Rate)(1 + Inflation Rate) – 1

≈ Real Discount Rate + Inflation Rate

## Examples

**Example 1:** Inflation adjustment using nominal cash flows

M2 SWF is considering a project that is expected to generate $10 million at the end of each year for 5 years. The initial outlay required is $25 million. A nominal discount rate of 9.2% is appropriate for the risk level. Inflation is 5%.

You are the company’s financial analyst. The company’s CFO has asked you to calculate NPV using a schedule of future nominal cash flows.

__Solution__

Nominal cash flows are calculated for each year as follows:

Year 1 = $10 million × (1+5%)^{1} = $10.5 million

Year 2 = $10 million × (1+5%)^{2} = $11.3 million

Year 3 = $10 million × (1+5%)^{3} = $11.58 million

Year 4 = $10 million × (1+5%)^{4} = $12.16 million

Year 5 = $10 million × (1+5%)^{5} = $12.76 million

These nominal cash flows are to be discounted using nominal discount rate, which is 9.2%

All amounts are USD in million.

Year | 1 | 2 | 3 | 4 | 5 | Total |

Nominal cash flows | 10.50 | 11.03 | 11.58 | 12.16 | 12.76 | |

PV discount rate @ 9.2% nominal | 0.916 | 0.839 | 0.768 | 0.703 | 0.644 | |

PV of cash flows | 9.62 | 9.25 | 8.89 | 8.55 | 8.22 | 44.52 |

Net present value = $44.52 – $25 million = $19.52 million

**Example 2:** Inflation adjustment using real cash flows and real discount rate

Under the real method, we discount real cash flows using real discount rate.

The relationship between nominal discount rate, real discount rate and inflation can be rearranged as follows:

Real discount rate

= (1 + nominal discount rate) ÷ (1+inflation rate) – 1

≈ nominal discount rate – inflation rate

= (1+ 9.2%) ÷ (1+5%) – 1

= 4%

Year | 1 | 2 | 3 | 4 | 5 | Total |

Real cash flows | 10.00 | 10.00 | 10.00 | 10.00 | 10.00 | |

PV discount rate @ 4% real | 0.962 | 0.925 | 0.889 | 0.855 | 0.822 | |

PV of cash flows | 9.62 | 9.25 | 8.89 | 8.55 | 8.22 | 44.52 |

Net present value = $44.52 million – $25 million = $19.52 million

You can see that the net present value is consistent under both methods.

Written by Obaidullah Jan, ACA, CFAhire me at