An office building and its equipment are insured for $2,500,000. The present ann
ID: 2761231 • 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
1.
Current amount of premium paid = premium payment rate * premium coverage = (1.25/100)*2500000
Current amount of premium paid = $31250
Premium to be paid if sprinkle systems will be installed = new premium payment rate * premium coverage
Premium to be paid if sprinkle systems will be installed =(.6/100)*2500000 = $15000
Thus,
Yearly savings in premium due to new sprinkle system = 31250 – 15000 = $16250
Life of the new sprinkle system (n) = 15 years
Rate of return = R = ?
Installation cost of new sprinkling system = $100000
Annual maintenance cost = $1500
Thus,
Net annual savings = Yearly savings in premium – annual maintenance cost = 16250 – 1500 = $14750
Now, to find the rate of return,
Present value of initial cost = present value of net savings
100000 = 14750*(1-1/(1+R)^n)/R
100000 = 14750*(1-1/(1+R)^15)/R
At R = 13%
PV of net savings = $95320.09
At R = 12%
PV of net savings = $100460.3
As per interpolation,
R = 12% + ((PV of net savings at 12% - 100000)/( PV of net savings at 12% - PV of net savings at 13%))*(13%-12%)
R = 12% + ((100460.3 – 100000)/( 100460.3 - 95320.09))*(13%-12%) = 12.089%
Thus, rate of return for the new sprinkle system is 12.089%
2.
Let, r = 5%
And, payout period = n
100000 = 14750*(1-1/(1+r)^n)/r = 14750*(1-1/1.05^n)/.05
100000*.05/14750 = (1-1/1.05^n)
.33898 = (1-1/1.05^n)
1/(1-.33898) = 1.05^n
1.5128 = 1.05^n
n= log 1.5128 / log 1.05 = 8.4847 years
Thus, payout period at 5% interest rate is 8.4847 years.