Question

The two mutually exclusive alternatives, as security systems for a local visitor center, are under consideration. The data related to these systems is as follows:

	System 1	System 2
First Cost, $	$350,000	$275,000
Annual O&M, $/year	$7,000	$5,000
Benefits, $/year	$125,000	$105,000
Disbenefits, $/year	$15,000	$20,000
Savage value, $	$10,000	$7,000
Useful life	25	20

Which security system do you recommend based on a B-C ratio analysis? The interest rate is 7% per year.

Answer 1

Arranging alternative in increasing order of initial cost

DN < 2 < 1

B/C of (2-DN) = (105000 - 20000) / (275000*(A/P,7%,20) + 5000 - 7000*(A/F,7%,20))

= (105000 - 20000) / (275000*0.094393 + 5000 - 7000*0.024393)

= 2.76

As incremental B/C is more than 1, system 2 is selected

B/C of (1 - 2) = ((125000-15000) - (105000 - 20000)) / ((350000*(A/P,7%,25) + 7000 - 10000*(A/F,7%,25)) - (275000*(A/P,7%,20) + 5000 - 7000*(A/F,7%,20)))c

= ((125000-15000) - (105000 - 20000)) / ((350000*0.085811 + 7000 - 10000*0.015811) - (275000*0.094393 + 5000 - 7000*0.024393))

= 4.11

As incremental B/C is more than 1, system 1 is selected

Finally system 1 must be selected