# 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 of money and increase in the nominal value of revenue (i.e. cash inflows) and expenses (cash outflows).

Since the net present value is mostly calculated for projects with duration of more than one year, the drop in purchasing power due to inflation is significant. It is important to correctly reflect this phenomenon in the capital budgeting process.

## Methods

There are two ways in which inflation can be accounted for in NPV calculation: nominal method and real method. The basic pricinple is to discount cash flows which contain the effect of inflation (i.e. nominal cash flows) using nominal discount rate and discount cash flows with do not contain the effect of inflation (i.e. real cash flows) using real discount rate. Both of these methods result in the same net present value.

### Nominal Method: Nominal Cash-Flows at Nominal Discount Rate

In the nominal method, nominal project cash flows are discounted at nominal discount rate.

Nominal net cash flows are project cash flows for Period Y which are measured in Period Y dollar values. It means that any cash flow estimates prepared based on the prices that prevailed in time 0 are adjusted for the effect of inflation depending on the expected inflation.

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}**

Nominal discount rate is the discount rate which incorporates the expected inflation rate. Inflation rate is based on consumper price index (CPI), core inflation or GDP deflator.

**Nominal Discount Rate
= (1 + Real Discount Rate)(1 + Inflation Rate) – 1
≈ Real Discount Rate + Inflation Rate**

This is the equation for Fisher effect: the relationship between real and nominal discount rate.

### Real Method: Real Cash Flows at Real Discount Rate

Under the real method of NPV calculation, cash flows for all periods are measured in time 0 dollars and discounted using the real discount rate i.e. a discount rate which doesn't contain the effect of any expected inflation. In other words, in the real method, inflation is excluded from both cash flows and discount 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.

by Obaidullah Jan, ACA, CFA and last modified on

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