Question

Eddie’s Precision Machine Shop is insured for $700,000. The present yearly insurance premium is $1.00 per $100 of coverage. A sprinkler system with an estimated life of 20 years and no salvage value can be installed for $75,000. Annual maintenance costs for the sprinkler system are $1,700. If the sprinkler system is installed, the system must be included in the shop’s value for insurance purposes, but the insurance premium will reduce to $0.40 per $100 of coverage. Eddie uses a MARR of 15%/year.

1) What is the annual worth of this investment?

2) Is the filter economically justified?

Answer 1

1) Existing Insurance premium = ($700,000/$100)*$1.00 = $7,000

New Insurance Premium (after installing sprinkler) = [($700,000+$20,000)/$100]*$0.40 = $2,880

Saving in Insurance Premium = Existing Insursnce premium - New Insurance Premium

= $7,000 - $2,880 = $4,120 (this will be considered as annual cash flows)

Annual maintenance costs for sprinkler system = $1,700

Net annual cash inflows = Saving in Insurance Premium - Annual maintenance costs

= $4,120 - $1,700 = $2,420

Investment in Sprinkler system = $20,000

Present Worth of system = [Net Annual Cash Flows*PVAF(15%,20 yrs)] - Investment cost

= ($2,420*6.25933) - $20,000 = $15,147.58 - $20,000 = (-)$4,852.42

Annual Worth = Present Worth/[PVAF(15%,20 yrs)] = -$4,852.42/6.25933 = (-)$775.23

Hence annual worth of the given investment is negative (i.e. - $775.23).

2) As the present worth and annual worth of the investment is negative, the filter is not justified economically.