By Yuriy Smirnov Ph.D.

Inflation affects capital budgeting analysis. It drives an increase in both revenue and costs, affecting future cash flows of a project. Inflation is also one of the components of interest rates, i.e., it is already included in the market cost of capital used as a discount rate.

The Fisher equation describes the relationship between the nominal interest rate, real interest rate, and expected inflation rate. This equation is also used in capital budgeting to calculate the inflation-adjusted discount rate. It can be written as follows:

1 + r_{n} = (1 + r_{r}) × (1 + i)

where r_{n} is the nominal discount rate, r_{r} is the real discount rate, and i is the expected inflation rate.

The nominal and real discount rates can be expressed as follows:

r_{n} = r_{r} + r_{r}×i + i

r_{r} = |
r_{n} - i |

1 + i |

Both nominal and real discount rates can be used in capital budgeting analysis depending on the method used to account for inflation.

Two methods can be used to account for inflation when expected cash flows of a project are discounted to calculate the net present value (NPV).

__Adjusting cash flows to nominal values__. This method implies that all expected cash flows are adjusted to nominal values, and the nominal discount rate is used to calculate their present value.__Adjusting cash flows to real values__. Expected cash flows of a project are adjusted to their real values and then discounted using the real discount rate.

Both methods bring the same result of project analysis, i.e., the net present value of a project will be the same regardless of which method is applied.

The relationship between the nominal cash flow value and the real cash flow value can be described using the following equation:

Nominal Cash Flow = Real Cash Flow × (1 + i)^{t}

Real Cash Flow = | Nominal Cash Flow |

(1 + i)^{t} |

where t is the number of periods (e.g., years if the annual inflation rate is applied).

Attention! The inflation rate has a different effect on components of future cash flows. For example, depreciation expense is not affected at all by inflation unlike the retail prices for products that directly affect the sales amount.

A company considers undertaking a capital project with an initial cost of $30,000,000 (required to buy new equipment) and a life span of 3 years. The other parameters of the project are as follows:

- The current sales price is $30 per unit, and expected sales by years are:
- 2,000,000 units in the first year
- 2,500,000 units in the second year
- 2,800,000 units in the third year

- The current variable cost is $21.60 per unit
- The current annual overhead cost is $5,000,000
- A company applies the straight-line depreciation method, with zero salvage value
- The market cost of capital is 12.50%
- The expected annual inflation rate is 2.5%
- The marginal tax rate is 30%

It is assumed that inflation will affect all the components of future cash flows except the depreciation expense.

The nonadjusted to inflation cash flows are shown in the table below.

Sales in Year 1 = 2,000,000 × $30 = $60,000,000

Sales in Year 2 = 2,500,000 × $30 = $75,000,000

Sales in Year 3 = 2,800,000 × $30 = $84,000,000

Total variable costs in Year 1 = 2,000,000 × $21.60 = $43,200,000

Total variable costs in Year 2 = 2,500,000 × $21.60 = $54,000,000

Total variable costs in Year 3 = 2,800,000 × $21.60 = $60,480,000

When the straight-line depreciation method is applied, the depreciation expense is the same in each year and amounts to $10,000,000.

Now we can calculate earnings before tax in each year by deducting total variable costs, overhead costs, and depreciation expense from the sales figures.

Earnings before tax in Year 1 = $60,000,000 - $43,200,000 - $5,000,000 - $10,000,000 = $1,800,000

Earnings before tax in Year 2 = $75,000,000 - $54,000,000 - $5,000,000 - $10,000,000 = $6,000,000

Earnings before tax in Year 3 = $84,000,000 - $60,480,000 - $5,000,000 - $10,000,000 = $8,520,000

The tax expense in each year is as follows:

Tax expense in Year 1 = $1,800,000 × 30% = $540,000

Tax expense in Year 2 = $6,000,000 × 30% = $1,800,000

Tax expense in Year 3 = $8,520,000 × 30% = $2,556,000

The net profit is calculated by deducting the tax expense from earnings before taxes.

Net profit in Year 1 = $1,800,000 - $540,000 = $1,260,000

Net profit in Year 2 = $6,000,000 - $1,800,000 = $4,200,000

Net profit in Year 3 = $8,520,000 - $2,556,000 = $5,964,000

The net cash flow is the sum of depreciation expense and net profit.

Net cash flow in Year 1 = $1,260,000 + $10,000,000 = $11,260,000

Net cash flow in Year 2 = $4,200,000 + $10,000,000 = $14,200,000

Net cash flow in Year 3 = $5,964,000 + $10,000,000 = $15,964,000

We should adjust cash flows to the inflation rate to calculate the inflation-adjusted NPV of a project. Cash flows adjusted to their nominal values are presented in the table below.

The real values of sales, total variable costs, and overhead should be adjusted to their nominal values at the end of each designated year.

Sales in Year 1 = $60,000,000×(1+0.025)^{1} = $61,500,000.00

Sales in Year 2 = $75,000,000×(1+0.025)^{2} = $78,796,875.00

Sales in Year 3 = $84,000,000×(1+0.025)^{3} = $90,458,812.50

Total variable costs and overhead costs are adjusted to nominal values in the same manner.

Depreciation expense is not affected by inflation; thus, its value is already nominal.

Now we can calculate the inflation-adjusted NPV of a project using the market cost of capital as the nominal discount rate because it already reflects the inflation.

NPV = -$30,000,000 + | $11,466,500 | + | $14,767,000 | + | $16,960,810.06 | = $3,772,316.53 |

(1+0.125)^{1} |
(1+0.125)^{2} |
(1+0.125)^{3} |

Let’s adjust all cash flows to their real value to prove that both methods bring the same NPV. Cash flows adjusted to their real values are given in the table below.

Since only depreciation expenses are given as nominal values, they should be adjusted to real values as follows:

Depreciation expense in Year 1 = | $10,000,000 | = $9,756,097.56 |

(1+0.025)^{1} |

Depreciation expense in Year 2 = | $10,000,000 | = $9,518,143.96 |

(1+0.025)^{2} |

Depreciation expense in Year 3 = | $10,000,000 | = $9,285,994.11 |

(1+0.025)^{3} |

We should also adjust the market cost of capital to the real value.

Real discount rate = | 12.50%-2.50% | = 9.76% |

1+0.025 |

NPV = -$30,000,000 + | $11,186,829.27 | + | $14,055,443.19 | + | $15,749,798.23 | = $3,772,316.53 |

(1+0.0976)^{1} |
(1+0.0976)^{2} |
(1+0.0976)^{3} |

As we have seen, both methods give the same net present value of a project. Thus, each method can be used in capital budgeting analysis provided cash flows and the discount rate are properly adjusted to the inflation rate.

Now we can claim with confidence that inflation affects capital budgeting analysis. It affects the values of future cash flows and the discount rate. To remove the impact of inflation, future cash flows and the discount rate should both be adjusted to either their real values or to nominal values. However, both ways lead to the same result, i.e., to the same figure of inflation-adjusted NPV. In other words, inflation has an effect on figures used in capital budgeting analysis, but it does not affect the result of analysis.

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