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 EGR 312 - 23

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 1978-2003 experienced 4.77% inflation) EGR 312 - 23

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.) EGR 312 - 23

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, EGR 312 - 23

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 EGR 312 - 23

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 EGR 312 - 23

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. EGR 312 - 23

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. EGR 312 - 23

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. EGR 312 - 23

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 = .04 + .03 + .04*.03 = 7.12% A = $20,000,000(A/P,7.12%,20) =1.906 million NOTE: if inflation is not considered, A = 1.471 million EGR 312 - 23