# How Does Inflation Affect Net Present Value Appraisals?

Inflation has an inverse relationship with interest rates. It lowers the present value of future cash flows. Thus, it can affect the net present value calculations as well.

Let us discuss what is net present value and how does inflation affects it.

## What is Net Present Value?

Net present value (NPV) represents the sum of all future cash flows over the entire life of a project or investment that is discounted to the present day.

In other words, NPV is the estimate of the worth of future cash flows in today’s terms. It tells analysts how much the future flows will be worth if received today.

The net present value method can be used in several ways to determine the financial feasibility of a project, viability of an investment, business valuation, and so on.

Usually, analysts use a risk-free interest rate to discount the cash flows to present terms. However, companies use more specific discount rates (cost of capital or WACC) to discount future cash flows and calculate the NPV.

The net present value is the sum of all future cash flows. The net amount can be a negative or positive figure. If it is positive, an investment or project is considered profitable.

## How to Calculate Net Present Value?

The net present value of a project or an investment can be calculated by discounting all future cash flows to the present day. These cash flows should include cash outflows as well as cash inflows.

If there is only one cash flow arising in one year, the simple formula for NPV will be:

Net Present Value = Cash Flow / (1 + i) t    – Initial Investment

Where i= interest rate and, t= time in years

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If there are several cash flows then the formula can be written as:

NPV = C1/(1+r)1 + C2/(1+r)2 + C3/(1+r)3 + …. Cn/(1+r)n– Xo

Where r is the discount rate and c1, c2, up to Cn represent cash flows for respective years and Xo is the initial investment.

Let us consider a simple working example of NPV calculations.

Suppose a company ABC expects the following cash flows from a real estate investment for the next five years. It uses a discount rate of 10% and the initial investment is \$ 100,000.

We can discount the cash flows using the discount factors for these cash flows to calculate the NPV of the project.

We have ignored the inflation and tax effects from our calculations. The cash flows discounted to present value offer a positive NPV.

## How Does Inflation Affect Net Present Value Appraisals?

The NPV method is useful in appraising investment options and business valuations. Analysts need to use a suitable discount rate to estimate the viability of the investment.

Inflation is the increase of prices that generally leads to a decline in the value of money. It means inflation decreases the purchasing power. Thus, \$ 100 today will be worth less than it in 5 years due to inflation effects.

Inflation and interest rates are inversely related. It means a higher inflation rate means a lower interest rate and vice versa.

Using a higher discount rate means a lower present value of a cash flow. It means when future cash flows are discounted with a higher discount rate, the net present value of the future cash flows decreases.

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The net present value of all future cash flows can be affected by several factors. However, keeping other factors constant, inflation will decrease the interest rates. The purchasing power of investors will decrease and they will demand higher returns.

Conversely, inflation will lower the interest rates and the weighted average cost of capital (WACC) of a company. Most companies use WACC as a discount rate for NPV appraisals. Thus, inflation will indirectly increase the NPV amount keeping all other factors constant.

## Impact of Inflation on Cash flows

When cash flows have not been adjusted (increased) for inflation, they are called real or current cash flows. When these cash flows take into account the effect of inflation, they are called nominal or money cash flows.

Inflation affects different components of the financial statements of a company differently. The individual impact on all items is not uniform. Therefore, cash flows also get affected differently. Generally, inflation will decrease the value of future cash flows.

The general relationship between the real interest rate, nominal interest rate, and inflation can be described using Fisher’s equation.

(1 + i) = (1 + r) × (1 + h)

Where i = money rate            r = real rate                  h = inflation rate

Suppose the real interest rate is 5% and the inflation rate is 8%. The nominal interest rate can be calculated using the equation above.

(1 + i) = (1 + r) × (1 + h)

(1+i) = (1+5%) × (1+ 8%) = 1.134

Therefore, i = 0.134 or 13.4%

We can use the same equation to determine the inflation rate, real interest rate, or nominal interest rate when the other two components are known.

## Discounting Cash Flows with Real and Nominal Interest Rates

NPV appraisals can be evaluated using a nominal or real interest rate. Discounting cash flows with different discount rates give different values.

For consistency, an investment should be appraised using the same methods across different calculations. If you use a nominal interest rate, you should first discount future cash flows for the inflation effect.

However, when using a real interest rate, you’ll need to use the real cash flows without adjusting them for inflation. This way, you’ll receive consistent appraisal value of future cash flows.

Let us understand the concept using an example.

## Working Examples

Suppose ABC company is considering a project that is expected to generate \$10 million at the end of each year for 5 years. The initial investment required is \$20 million.

The nominal interest rate is 9.2% and the inflation rate currently is 5%.

We can use the NPV of this project by discounting the future cash flows to their present value terms and by adjusting them for inflation.

Nominal cash flows are calculated for each year as follows:

Year1 = \$10 million × (1+5%)1 = \$10.5 million
Year2 = \$10 million × (1+5%)2 = \$11.3 million
Year3 = \$10 million × (1+5%)3 = \$11.58 million
Year4 = \$10 million × (1+5%)4 = \$12.16 million
Year5 = \$10 million × (1+5%)5 = \$12.76 million

Now we can discount these cash flows in present value terms using the 10% nominal interest rate.

We can calculate the real discount rate by using Fisher’s equation:

(1+I) = (1+r) × (1+h)

Or (1+r) = (1+9.2%) / (1+5%)

r = 4.0%

When we use real interest rate, we will also use real cash flows. Therefore, the NPV of the investment can be calculated as:

As you can see the NPV for the investment using both interest rates are the same. The key here is to remain consistent when choosing the cash flows for discounting to the present values.

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