Question

4. A business has an annual premium of $7050 for a fire insurance if no sprinkler system is installed. If a fire occurs, it is expected that the business will have unrecoverable losses of $375,000 without a sprinkler system. If a sprinkler system is installed, the annual premium will decrease to $2700 and the unrecoverable losses will be reduced to $187,500. Annual maintenance costs for a sprinkler system are 1% of the purchase price. Use a minimum rate of return of 10%, what is the maximum justifiable cost of a sprinkler system. Assume the sprinkler system will last 20 years with no salvage value. Also, in a given year, the probability of a fire is 0.01

Answer 1

In this Sum they given two benefits when you install the Sprinkler Systems Benefit No. 1, if fire occur, Unrecoverable loss of 3,75,000/- will reduce unto 1,87,500/- Benefit No. 2, Annual Insurance premium will reduce unto 2,700/- P.A. Conclusion over Benefit determination. In the Scenario 1.) they gave 187500 benefit arise if you installed sprinkler system, but the probity of fire occur is 0.01%. Sprinkler life spam is 20 years. So consolidated primality over the year is (20*0.01%=0.20%). But its very very less so we can ignore benefit no.1 In the Scenario 2.) they give 2700 yearly benefit arise weather fire occur or not. So, We can take second benefit to determine the sprinkler purchase value To Determine sprinkler value, Expenses because of the sprinkler should not exceed the benefits arise from the sprinkler 2700 Particulars Amount Annual Benefits from Sprinkler & Maximum allowable sprinkler expenses Expenses of Sprinkler Maintenance Cost @1% of sprinkler Interest Cost @10% of Sprinkler Depreciation (100%/20=5%) 1% 10% 5% 16% Assume 16% of sprinkler cost 100% sprinkler cost (2700*100/16)=16875 2700 16875 Amount 16875 Particulars if sprinkler cost Annual Expenses Maintenance Cost @1% of sprinkler Interest Cost @10% of Sprinkler Depreciation (100%/20=5%) 168.75 1687.5 843.75 2700

Hence

Maximum Justifiable Sprinkler cost is 16,875/- with monthly expenses of 2700/-