Question
An office building and its equipment are insured to $710,000.
The present annual insurance premium is $0.85 per $100 of coverage.
A sprinkler system with life of 20 years and no salvage value can be installed for $18,000.
Annual maintenance and operating costs for the sprinkler is $360. The premium will be reduced to $0.40 per $100 coverage if the sprinkler is installed. Find the payout period for sprinkler system with interest of 12%.
(The payout period is the length of time before the savings due to sprinkler system is equal its cost.)
(Hint: find the time at which the present equivalent value of the cumulative net savings equals its cost $18,000)
Explanation / Answer
Annual Savings = 0.85 - 0.40 per 100 = 0.45 per 100 = (0.45 * 710,000) /100 = 3195 Less: Annual operating Costs =360 Net Savings = 3195-360 =2835 Year Savings PVF PV 1 2835 0.89 2,531.25 2,531.25 2 2835 0.80 2,260.04 4,791.29 3 2835 0.71 2,017.90 6,809.19 4 2835 0.64 1,801.69 8,610.89 5 2835 0.57 1,608.66 10,047.18 6 2835 0.51 1,436.30 11,483.48 7 2835 0.45 1,282.41 12,765.89 8 2835 0.40 1,145.01 13,910.90 9 2835 0.36 1,022.33 14,933.23 10 2835 0.32 912.79 15,846.03 11 2835 0.29 814.99 16,661.02 12 2835 0.26 727.67 17,388.70 Hence Payout period is 17 years approximately. Year Savings PVF PV 1 2835 0.89 2,531.25 2,531.25 2 2835 0.80 2,260.04 4,791.29 3 2835 0.71 2,017.90 6,809.19 4 2835 0.64 1,801.69 8,610.89 5 2835 0.57 1,608.66 10,047.18 6 2835 0.51 1,436.30 11,483.48 7 2835 0.45 1,282.41 12,765.89 8 2835 0.40 1,145.01 13,910.90 9 2835 0.36 1,022.33 14,933.23 10 2835 0.32 912.79 15,846.03 11 2835 0.29 814.99 16,661.02 12 2835 0.26 727.67 17,388.70