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

Answer:  Annual Worth = Present Worth÷[PV(15%,20 yrs)]

= -$4,852.42÷6.25933

= (-)$775.23

Here, the annual worth of the given system is negative (i.e. - $775.23).

The filter is not justified economically, this is because the present worth and annual worth of the system(investment) is negative,

Explanation:

In order to calculate the annual worth, we'll first compute the existing insurance premium and new insurance premium using the following formula.

i.e. Existing Insurance premium = ($700,000÷$100)×$1.00 = $7,000

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

Now, evaluating Savings in insurance premium.

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

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

Given :

Annual maintenance costs for sprinkler system = $1,700

Investment in Sprinkler system = $20,000

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

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

Now, Present worth of the system is given as :

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

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

Annual Worth = Present Worth÷[PV(15%,20 yrs)]

= -$4,852.42÷6.25933

= (-)$775.23

Here, the annual worth of the given system is negative (i.e. - $775.23).

2)  The filter is not justified economically, this is because the present worth and annual worth of the system(investment) is negative,