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eddies precision shop is insured for $700,000. The present yearly insurance prem

ID: 1169459 • Letter: E

Question

eddies precision 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 $20,000. Annual maintenance costs for the sprinkler system are $400. If the sprinkler system is installed, the system must be included in shops value for insurance purposes, but the insurance premium will reduce to $0.40 per $100 of coverage. Eddie uses a MARR of 15 percent/year. What's the present worth of this investment? Is the sprinkler system economically justified? eddies precision 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 $20,000. Annual maintenance costs for the sprinkler system are $400. If the sprinkler system is installed, the system must be included in shops value for insurance purposes, but the insurance premium will reduce to $0.40 per $100 of coverage. Eddie uses a MARR of 15 percent/year. What's the present worth of this investment? Is the sprinkler system economically justified? eddies precision 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 $20,000. Annual maintenance costs for the sprinkler system are $400. If the sprinkler system is installed, the system must be included in shops value for insurance purposes, but the insurance premium will reduce to $0.40 per $100 of coverage. Eddie uses a MARR of 15 percent/year. What's the present worth of this investment? Is the sprinkler system economically justified?

Explanation / Answer

Annual maintenance costs for the sprinkler system are $400. 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%/yr.

The insurance would cost $1.00 * $700,000 / $100 = $7,000 per year without the installation of the sprinkler system


The insurance would cost $0.40 * $720,000 / $100 = $2,880 per year after the installation of the sprinkler system

This means that sprinkler will result in savings of 7000-2880=4120 and the cost of installing a sprinkler will be $400 annually for a period of 20 years and the installation costs in the beginning of $20000

Now the benefits after adjusting the costs from savings we will get, for 20 years i.e. the life of sprinkler system


(4120-400)/(1+r)+(4,120-400)/(1+r)2+(4120-400)/(1+r)3 + ... +(4,120-400) / ( 1 + r )20 =20000


Applying the formulae for a geometric sequence

20000 = (4120-400)*((1-1/(1+r)21)/(1-1/(1+r))-1)

Put the equation equal to zero which has degree of 21.

-20000+ ($4,120 - $400 ) * ((1-1/(1+r)21)/(1-1/(1+r))-1) = 0

We use the binary method and get

r = 17.9106%

Note: All figures are in US$.