Question

An office building and its equipment are insured to $7,100,000. The present annual insurance premium is $0.85 per $100 of coverage. A sprinkler system with an estimated life of 20 years and no salvage value can be installed for $180,000. Annual maintenance and operating cost is estimated to be $3,600. The premium will be reduced to $0.40 per $100 coverage if the sprinkler system is installed.

a. Find the rate of return if the sprinkler system is installed.
b. With interest at 12%, find the payout period for the sprinkler system.

Answer 1

a) 14.74%.

b) 13 years

Step-by-step explanation:

a. Find the rate of return if the sprinkler system is installed.

P = -$18,000 - $360(P/A,i,20) + ($0.45)($7,100)(P/A,i,20)

= (P/A,i,20)=18000/2835 = 6.35

=
`((1+i)^(20) -1 )/(i(1+i)^(20))` = 6.35

Solving for i we get,

i =14.74%.

b. With interest at 12%, find the payout period for the sprinkler system.

P = -$18,000 - $360(P/A,12%,n) + ($0.45)($7,100)(P/A,12%,n)

(P/A,12%,n) = 18000/2835 = 6.35

=
`((1+0.12)^(n) -1 )/(0.12(1+0.12)^n)` = 6.35

Using numerical solving to find the real roots of this equation (using a calculator, or Excel), we get n≅12.67 = 13 years. This means the payout period is about 13 years.