Handbook of Civil Engineering Calculations

DETERMINATION OF MANUFACTURING

BREAK-EVEN POINT

A manufacturing firm has a choice between two machines to produce a product. The rele-

vant data are as follows:

Machine A Machine B

First cost, $ 20,000 28,000

Salvage value, $ 2,000

Life, years 10 6

Annual operating cost, $ 3,000 + 5.00 per unit 2,500 + 1.50 per unit

If money is worth 7 percent, what annual production is required to justify purchase of ma-
chine B?

Calculation Procedure:

1. Compute the annual cost of the first machine
   Let x denote the number of units produced annually. Then, by using the capital-recovery
   factor, A = ($20,000 - $2000)(0.14238) + $2000(0.07) + $3000 + 5 = $5703 + 5 for ma-
   chine A.


2. Compute the annual cost of the second machine
   Using the same procedure for machine B gives A = ($28,000)(0.20980) + $2500 + 1.5 =
   $8374+1.5.


3. Equate the annual costs, and solve for the unknown
   Substituting the annual costs from steps 1 and 2 yields $5703 + 5jc = $8374 + 1.5*; x =
   763 units.
   This is the break-even point at which the costs of each machine are equal. If produc-
   tion is expected to exceed this volume, machine B is the economical choice.

COST COMPARISON WITH NONUNIFORM

OPERATING COSTS

Two alternative machines have the following data:

Machine A Machine B

First cost, $ 6,800 12,000

Salvage value, $ ... 1,000

Life, years 6 10

For machine A, the estimated annual operating cost is $1240. For machine B, it is $800
for the first 4 years, $1200 for the next 3 years, and $1500 for the remaining 3 years. De-
termine which machine is more economical, using an 8 percent interest rate.