Inflation

Inflation is a general rise in the price level (the average amount of money needed to buy the same basket of goods and services) over time. Deflation is the opposite, prices falling. Both are measured as the percentage change in some price index, most commonly the CPI, over a defined period.

A 3% annual inflation rate means that, on average, the same basket of consumer goods costs 3% more this year than last year. Equivalently, a dollar buys 3% less. Money has lost some purchasing power.

CPI is the Consumer Price Index: a number set to 100 at some reference year, tracking the cost of a representative consumer basket relative to that base. The percentage change in CPI from one year to the next is the inflation rate:

$f_t=\frac{{\text{CPI}}_t-{\text{CPI}}_{t-1}}{{\text{CPI}}_{t-1}}.$

Inflation matters for engineering economic analysis in two places.

Cash flows themselves. Future cash flows stated in today’s dollars don’t reflect what those amounts will actually buy. A $10,000 contract payment 20 years from now, at 3% inflation, will buy only about $5,500 worth of today’s goods. Comparing nominal dollar amounts across time without inflation-adjustment is misleading.

Interest rates. Rates already include compensation for inflation. The nominal (or actual) interest rate is what’s quoted; the real rate is what you’d earn after stripping out inflation. The Fisher relation links them.

Two ways to keep the accounting straight:

• Actual dollars (also called current or nominal dollars). The money that will actually change hands at the future date. Purchasing power varies year-to-year because of inflation.

• Real dollars (also called constant dollars). Expressed in the purchasing power of a reference year, commonly today. Inflation has been stripped out; the amount represents what the cash flow is “really” worth in today’s terms.

Conversion: if $A_N$ is an actual-dollar amount in year $N$ and $f$ is the average inflation rate over the period, the equivalent real-dollar amount referenced to year 0 is

$R_{0,N}=\frac{A_N}{(1+f{)}^N}.$

Same math as discounting at rate $f$, since inflation behaves like a discount on purchasing power.

The rule: match real with real and actual with actual. Real cash flows get discounted at the real MARR, actual cash flows at the actual MARR. Mixing the two (real cash flows discounted at actual MARR, say) double-counts inflation and gives a wrong PW.

The two equivalent calculations:

1. PW of actual dollars at the actual MARR.
2. PW of real dollars at the real MARR.

Both should give the same answer (up to rounding). Pick whichever framing makes the cash flows easier to estimate.

In different contexts:

• Contract escalation. Long-term contracts often include CPI escalation clauses so the payment keeps pace with inflation. Minimum-wage indexing works the same way.

• Industry-specific inflation. Different sectors inflate at different rates. Construction costs often outpace consumer inflation; oil prices fluctuate independently. A project-specific index (e.g. the construction cost index for a building project) usually gives better estimates than economy-wide CPI.

• Hyperinflation. Rates of dozens or hundreds of percent per year. Distinct enough from “normal” inflation that engineering-economic models need rework, but rare in stable economies.

See Real interest rate for the corresponding interest rate and Cost index for price indices.