Inflation

Summary

$Inflation=\frac{CPI\left(n\right)-CPI\left(n-1\right)}{CPI\left(n-1\right)}\cdot 100$

This is a percentage of increase or decrease (inflation vs deflation), where CPI = “Consumer Price Index” wherethe cost to purchase a standard basket of goods and services is computed periodically.

You can find the CPI by $CPI=\frac{\text{Weighted average @ year 1}}{\text{Weighted aveage @ year 2}}\ast 100$

Definitions

• $f$: inflation
• $i^{\prime }$: Real interest rate (inflation free)
• $i$: Market (actual) interest rate
• $R_N$: Real dollars (the real value of a goof or service) which uses a real interest rate and represents purchasing power at a base year (inflation free dollars)
• $C_N$: Actual dollars uses an actual / market interest rate, these are inflated dollars

Real and actual dollars cannot be combined in the same context. You need to convert from one to the other $R_N=\frac{C_N}{{\left(1+f\right)}^N}$

The relationship between the market (actual) and real interest rate
Purchasing power depends on real dollar value…

Consider the value of \M$investedforoneyearat$i$,$M\left(1+i\right)$attheendoftheyear.Iftheinflationrateoverthenextyearisf,therealvalueofourcashflowis:$\frac{M\left(1+i\right)}{1+f}$

This definition can be used to define the real interest rate:
$M\left(1+i^{\prime }\right)=\frac{M\left(1+i\right)}{1+f}\to i^{\prime }=\frac{1+i}{1+f}-1$

An investor who wishes to get a real rate of 𝑖′ and who expects inflation at a rate 𝑓 will require a current interest rate of: $i=i^{\prime }+f+i^{\prime }f$

The Effect of Inflation on the MARR
Similarly, $MAR{R}_A=MAR{R}_R+f+MAR{R}_R\ast f$
For small values of $MAR{R}_R$, ignore the third term

The Effect of Inflation on the IRR
$IR{R}_a=IR{R}_r+f+IRRr\ast f$

• Note that you can solve for the real IRR by computing present wroth, setting it to 0, and using $IR{R}_R$ as your i in P/F factors and stuff like that

Here, we see the actual MARR and IRR and related in the same way to their real counterparts. Therefore, correctly anticipated inflation has no effect on project evaluation. If the base year for the real dollars is year 0 for PW, the numerical value of PW is the same either way.

For each question, we need to figure out what kind of dollars we are working with:

• Actual → need actual interest rate
• Real → real interest rate
• If its a mix, convert one to the other for consistency

Note

• ”Based on todays prices” → real dollars
• Actual dollars are when this is not mentioned (contracts, etc)