1. Effects of Inflation
Inflation – the increase in the amount of money necessary to obtain the same amount of product or service before the inflated prices was present.
Let f represent the inflation rate per period (year), then for n periods in the future:
today’s dollars = future dollars
(1+f)n
future dollars = today’s dollars * (1+ f)n
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2. Effects of Inflation Example 1978 – hamburger, coke and fries ($0.99).
$0.99 = $3.99
(1+f)25
f = 5.7%
Using fast-food as a basis, the inflation rate over the 25 year period was 5.7%.
Note: the Consumer Price Index does essentially the same thing, but uses a combination of food, housing, transportation, health, and a variety of other costs. (in reality, the CPI says the period from experienced 4.77% inflation)
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3. Effects of Inflation Definitions
Real or inflation-free interest rate (i) – the rate at which interest is earned without considering the effects of changes in the value of currency.
Inflation adjusted interest rate if – the interest rate that has been adjusted to take inflation into account (the market interest rate). This rate is a combination of the real interest rate (i) and the rate of inflation (f).
Inflation adjusted interest rate if – the interest rate that has been adjusted to take inflation into account (the market interest rate). This rate is a combination of the real interest rate (i) and the rate of inflation (f). Note: when you place money in a bank, the bank is paying a market interest rate. (That is, it changes as the inflation rate changes.)
NOTE: THESE DEFINITIONS ARE DIFFERENT THAN YOU MIGHT SEE ELSEWHERE (THAT’S WHY WHEN PEOPLE WRITE ABOUT IT, THEY’RE USUALLY CAREFUL TO SAY “ADJUSTED FOR INFLATION” OR “WITHOUT INFLATION”, ETC.)
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4. Effects of Inflation Present Worth Adjusted for Inflation
Recall PW given some Future value:
If F is a future-dollar amount with inflation built in, then:
or,
where,
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5. Effects of Inflation Example
A 10-year, $10,000 bond with a 10% dividend rate paid quarterly, is expected to return 8% per year, compounded quarterly. Find the PW assuming no inflation.
I = _______________
PW = ___________________________
Find the PW assuming a 6% annual inflation rate, compounded quarterly.
if = ___________________________
PW = ___________________________________________
i = 2.5% * $10,000 = $250.
PW = $250(P/A,2%,40) + $10,000(P/F,2%,40) = $11,367
if = 2% + 6%/4 +2.5%(6%/4) = 3.53%
PW = $250(P/A,3.53%,40) + $10,000(P/F,3.53%,40)
= $7875
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6. Effects of Inflation Future Worth
Case 1: Actual Amount Accumulated – when trying to determine the actual amount of accumulated money after some time period, use the market interest rate. or
Assumption here is that the “market interest rate” includes inflation
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7. Effects of Inflation Future Worth
Case 2: Constant value with purchasing power – to determine the purchasing power of future dollars, first calculate the future dollar value using if , then discount the effects of inflation. or
For example, if you invest now in order to buy a house in 5 years. The numerator tells you how much money you have “in the bank” (assuming the interest rate takes inflation into account), but F tells you how much house you will be able to buy.
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8. Effects of Inflation Future Worth
Case 3: Future amount required, no interest – this is the case when one wants to know the future cost of an item, such as a hamburger, fires and coke.
or,
Example: this tells you how much you can expect the house to cost in 5 years.
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9. Effects of Inflation Future Worth
Case 4: Inflation and Real Interest – this is the case when a MARR is established that accounts for a desired earned interest rate, and also account for inflation.
If an interest of i is desired, and inflation is running at a rate of f, then the MARRf is set to:
MARRf = if = i + f + if
or,
This is how you set your MARR knowing that inflation is going to affect buying power.
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10. Effects of Inflation Capital Recovery
Because capital recovery analysis tends to span a significant number of years, the effects of inflation are particularly important.
Example: A toll bridge is built for $20 million. How much must be recovered in tolls if the bridge is to last for 20 years. Assume a MARR of 4% and an inflation rate of 3%.
if = MARRf = ________________________
A = _________________________
if = *.03 = 7.12%
A = $20,000,000(A/P,7.12%,20) =1.906 million
NOTE: if inflation is not considered, A = million
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