Every decision made by a company involves money and the goal of these decisions is to add value to the company. Engineering economy owns a crucial role of analyzing expected economic results based on each decision.
These expected economic results consist of four essential elements: Cash flows, Occurrences times of cash flows, Interest rates for time value of money, and Measure of economic worth for selecting an alternative.
One essential aspect in the engineering economy is the time value of money, the fact that money makes money over time, hence it must be taken into consideration while performing engineering economy projects.
Changes in the value of money in a given one period (i.e., one year, one month, etc.) is called interest and for more than one interest period, simple rate and compound interest become relevant. Simple interest calculates based on the initial money or principal and ignoring any interest that occurred during the preceding interest periods.
For example, a company takes a loan of €100.000 for 3 years with 5% simple interest. The interest for each year:
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟 = €100.000 × 5% = €5.000
Total amount due after 3 years:
𝑇𝑜𝑡𝑎𝑙 𝐷𝑢𝑒 = €100.000 + (3 × €5.000) = €115.000
Compounded Interest, however, calculate every interest accumulated in all periods. In other words, this method calculates the interest from the previous interest. Here is the calculation gave the same example with compounded interest.
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑌𝑒𝑎𝑟 1 = €100.000 × 5% = €5.000
𝑇𝑜𝑡𝑎𝑙 𝐷𝑢𝑒 𝑌𝑒𝑎𝑟 1 = €100.000 + €5.000 = €105.000
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑌𝑒𝑎𝑟 2 = €105.000 × 5% = €5.250
𝑇𝑜𝑡𝑎𝑙 𝐷𝑢𝑒 𝑌𝑒𝑎𝑟 2 = €105.000 + €5.250 = €110.250
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑌𝑒𝑎𝑟 3 = €110.250 × 5% = €5.762,5
𝑇𝑜𝑡𝑎𝑙 𝐷𝑢𝑒 𝑌𝑒𝑎𝑟 3 = €110.250 + €5.762,5 = €115.762,5
The example above is also called the single-payment compound amount factor, or F/P factor for short (this notation means find F, given P). F/P Factor can be calculated by the following formula:
𝐹 = 𝑃(1 + 𝑖) 𝑛
Where F, P, I, and n represent the future value, present value, interest rate, and a number of years respectively. The inverse factor of F/P is P/F Factor, or find P given F factor and has the following formula:
For example, given the known example above we can easily calculate the present value:
P/F and F/P factors are the most basic concept in the engineering economy and they help determine which investments to pick since they provide how the money changes over a period of time. These concepts also important in Industrial Engineering field since one of the core factors in problem-solving also involves money.
Comments