An office building and its equipment are insured for $2,500,000. The present ann
ID: 3687398 • Letter: A
Question
An office building and its equipment are insured for $2,500,000. The present annual insurance premium is $1.25 per $100 of coverage. A sprinkler system with an estimated life of 15 years and no salvage value can be installed for $100,000. Annual maintenance and operating cost is estimated to be $1,500. The premium will be reduced to $0.60 per $100 coverage if the sprinkler system is installed.
i) Find the rate of return if the sprinkler system is installed.
ii) With interest at 5 %, find the payout period for the sprinkler system.
Explanation / Answer
An office building and its equipment are insured for $2,500,000.
The present annual insurance premium is $1.25 per $100 of coverage.
A sprinkler system with an estimated life of 15 years and no salvage value can be installed for $100,000.
Annual maintenance and operating cost is estimated to be $1,500.
The premium will be reduced to $0.60 per $100 coverage if the sprinkler system is installed.
i) Find the rate of return if the sprinkler system is installed.
ii) With interest at 5 %, find the payout period for the sprinkler system.
The building is insured for an amount of: $2,500,000.
Premium amount is: $1.25 per $100. So, the premium amount being paid is: $31250.
Sprinkler system cost is: $100,000 for 15 years.
Maintenance cost of the sprinkler per year is: $1,500.
So, for 15 years, $22,500 is the maintenance cost.
Total cost of the sprinkler sytem is: $101,500, for 15 years.
The premium will be reduced to $.60 per $100 coverage if the sprinkler system is installed.
So, now the premium amount is: $.60 per $100. So, the new premium amount being paid is: $15,000.
The savings on the insurance amount being paid per year is: $31250 - $15,000 = $16,250.
For 15 years, the total savings will accumulate to: 243,750, which is far higher than the total amount spent on sprinkler system.
And the rate of return is therefore, 243,750 - 101,500 = 142,250 in total, and the per year profit is: $9483.33.
With interest at 5%, the payout period for the sprinkler system is:
$101,500 * .05 = $5,075 per year. And 101,500 / 5075 = 20 years.