John M. Watts, Jr., and Robert E. Chapman
Engineering economics is the application of economic techniques to the evaluation of design and engineering alternatives.1 The role of engineering economics is to assess the appropriateness of a given project, estimate its value, and justify it from an engineering standpoint. This chapter discusses the time value of money and other cash-flow concepts, such as compound and continuous interest. It continues with economic practices and techniques used to evaluate and optimize decisions on selection of fire safety strategies. The final section expands on the principles of benefit-cost analysis. An in-depth treatment of the practices and techniques covered in this compilation is available in the ASTM compilation of standards on building economics.2 The ASTM compilation also includes case illustrations showing how to apply the practices and techniques to investment decisions. A broader perspective on the application of engineering economics to fire protection engineering can be found in The Economics of Fire Protection by Ramachandran.3 This work is intended as a textbook for fire protection engineers and includes material and references that expand on several other chapters of this section of the SFPE handbook.
Time Value of Money
The following are reasons why $1000 today is “worth” more than $1000 one year from today: 1. Inflation 2. Risk 3. Cost of money Of these, the cost of money is the most predictable, and, hence, it is the essential component of economic analysis. Cost of money is represented by (1) money paid for the use of borrowed money, or (2) return on investment. Cost of money is determined by an interest rate. Time value of money is defined as the time-dependent value of money stemming both from changes in the purchasing power of money (inflation or deflation) and from the real earning potential of alternative investments over time.
It is difficult to solve a problem if you cannot see it. The easiest way to approach problems in economic analysis is to draw a picture. The picture should show three things: 1. A time interval divided into an appropriate number of equal periods 2. All cash outflows (deposits, expenditures, etc.) in each period 3. All cash inflows (withdrawals, income, etc.) for each period Unless otherwise indicated, all such cash flows are considered to occur at the end of their respective periods. Figure 5-7.1 is a cash-flow diagram showing an outflow or disbursement of $1000 at the beginning of year 1 and an inflow or return of $2000 at the end of year 5.
Cash flow is the stream of monetary (dollar) values— costs (inputs) and benefits (outputs)—resulting from a project investment. Dr. John M. Watts, Jr., holds degrees in fire protection engineering, industrial engineering, and operations research. He is director of the Fire Safety Institute, a not-for-profit information, research, and educational corporation located in Middlebury, Vermont. Dr. Watts also serves as editor of NFPA’s Fire Technology. Dr. Robert E. Chapman is an economist in the Office of Applied Economics, Building and Fire Research Laboratory, National Institute of Standards and Technology.
To simplify the subject of economic analysis, symbols are introduced to represent types of cash flows and 5–93
Fire Risk Analysis
F(2) C F(1) = F(1)(i) Interest is applied to the new sum:
0 1 2 3 4 5
C (F)(1)(1 = i) C P(1 = i)2 F (3) C F (2)(1 = i) C P(1 = i)3 and by mathematical induction, F(N) C P(1 = i)N Figure 5-7.1.
EXAMPLE: $100 at 10 percent per year for 5 yr yields F(5) C 100(1 = 0.1)5 C 100(1.1)5 C 100(1.61051) C $161.05 which is over 7 percent greater than with simple interest. EXAMPLE: In 1626 Willem Verhulst bought Manhattan Island from the Canarsie Indians for 60 florins ($24) worth of merchandise (a...