# Rate of Return

Rate of return is, by definition, the interest rate at which the present worth of the net cash flow is zero. Com-putationally, this method is the most complex method of comparison. If more than one interest factor is involved,

the solution is by trial and error. Microcomputer programs are most useful with this method.

The calculated interest rate may be compared to a discount rate identified as the “minimum attractive rate of return” or to the interest rate yielded by alternatives. Rate-of-return analysis is useful when the selection of a number of projects is to be undertaken within a fixed or limited capital budget.

EXAMPLE:

An industrial fire fighting truck costs \$100,000. Sav-ings in insurance premiums and uninsured losses from the acquisition and operation of this equipment is esti-mated at \$60,000/yr. Salvage value of the apparatus after 5 yr is expected to be \$20,000. A full-time driver during operating hours will accrue an added cost of \$10,000/yr. What would the rate of return be on this investment?

@ 40% present worth

=  + F (P/, 40%, 5)+ A(P/A, 40%, 5)

=  -\$100,000 + \$20,000(0.18593)

+  (\$60,000 – 10,000)(2.0352)

= \$5,478.60

@50% present worth

=  = F (P/F, 50%, 5)= A(P/A, 50%, 5)

=  -\$100,000 + \$20,000(0.13169)

=  (\$60,000 – \$10,000)(1.7366)

= – \$10,536.40

By linear interpolation, the rate of return is 43 percent.