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

Effects of Inflation Example 1978 – hamburger, coke and fries ($0.99) hamburger, coke and fries ($3.99). $0.99 = $3.99 (1+f) 25 f = 5.7% Using fast-food as a basis, the inflation rate over the last 25 years was 5.7%.

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 i f – 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.

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,

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 = 2.5% * $10,000 = $250. PW = $250(P/A,2%,40) + $10,000(P/F,2%,40) = $11367 Find the PW assuming a 6% annual inflation rate, compounded quarterly. i f = 2% + 6%/4 +2.5%(6%/4) = 3.53% PW = $250(P/A,3.53%,40) + $10,000(P/F,3.53%,40) = $7875

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

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 i f, then discount the effects of inflation. or

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,

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 MARR f is set to: MARR f = i f = i + f + if or,

Effects of Inflation Capital Recovery Because capital recovery analysis tends to span a significant number of years, the effects of inflation are particularly important. 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%. i f = *.03 = 7.12% A = $20,000,000(A/P,7.12%,20)