Engineering economics Interest Time value of money Evaluating economic alternatives Breakeven economics

Interest Interest = total amount owed – principal amount (12.1) (12.2) Interest = (principal)(number of interest periods)(interest rate) = Pni (12.3)

Single payment compound amount F = ? 1 2 3 4 n-2 n-1 n P period (12.4) (12.5)

Single payment present worth F 1 2 3 4 n-2 n-1 n P=? period (12.6)

Uniform series compound amount 1 2 3 4 n-2 n-1 n A period (12.7)

Capital recovery P 1 2 3 4 n-2 n-1 n A=? period A (12.8)

Nominal interest i = effective interest rate r = nominal interest rate m = interest periods per year y = number of years (12.9) (12.10)

Uniform series compound amount 1 2 3 4 n-2 n-1 n A period (12.11) (12.12)

Uniform series sinking fund 1 2 3 4 n-2 n-1 n A=? period A (12.13)

Gradient series (12.14) (12.15) (12.16) P = ? 1 2 3 4 n-2 n-1 n A 1 2 3 4 n-2 n-1 n A period A+2G A+4G A+3G A+(n-2)G A+(n-1)G A+(n-3)G (12.14) (12.15) (12.16)

Present worth method (12.17) (12.18)

Least common multiple $30,000 $45,000 years 1 2 3 4 5 6 least common 1 2 3 4 5 6 least common multiple

Future worth method (12.19) (12.20) (12.21)

Equivalent annual worth method (12.22) (12.23)

Rate of return method (12.24)

Simple payback period (12.25)

Discounted payback period (12.26)

Breakeven analysis breakeven point R Cost Profit TC Loss FC q q* Breakeven quantity Loss Profit breakeven point

Summary Engineering economic analyses should consider the time value of money Interest factor formulas and tables are useful in evaluating alternatives The PW and FW methods can be used to evaluate alternatives having different lives by using the least common multiple of years. The EUAW method is preferred because it has the advantage of not requiring the use of the least common multiple. The breakeven point is that level of production (and sales) that results in a zero profit