An office building and its equipment are insured to $7,100,000. The present annu
ID: 1257502 • Letter: A
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.
Explanation / Answer
Premium saved for each $100 = $(0.85 - 0.40) = $0.45
Total premium saved per year = $0.45 x $7,100,000 / $100 = $31,950
(a) Rate of return of sprinkler is ensured is found by excel formula =IRR()
IRR = 14.74%
(b) Assuming "Payout period" means discounted payback period (DPBP), we compute the cumulative discounted annual net benefit in above table.
So, DPBP lies between years 12 & 13.
DPBP = 12 + (Absolute value of cumulative discounted annual net benefit of year 12 / Annual net benefit for year 13)
= 12 + $(4,389 / 6,497) = 12 + 0.68 = 12.68 years
Year Cost ($) Annual Benefit ($) Net annual benefit ($) Discount Factor @12% Discounted Net annual benefit ($) Cumulative Discounted Net annual benefit ($) (A) (B) (C) = (B) - (A) (D) (E) = (C) x (D) 0 1,80,000 -1,80,000 1.0000 -1,80,000 -1,80,000 1 3,600 31,950 28,350 0.8929 25,313 -1,54,688 2 3,600 31,950 28,350 0.7972 22,600 -1,32,087 3 3,600 31,950 28,350 0.7118 20,179 -1,11,908 4 3,600 31,950 28,350 0.6355 18,017 -93,891 5 3,600 31,950 28,350 0.5674 16,087 -77,805 6 3,600 31,950 28,350 0.5066 14,363 -63,442 7 3,600 31,950 28,350 0.4523 12,824 -50,618 8 3,600 31,950 28,350 0.4039 11,450 -39,167 9 3,600 31,950 28,350 0.3606 10,223 -28,944 10 3,600 31,950 28,350 0.3220 9,128 -19,816 11 3,600 31,950 28,350 0.2875 8,150 -11,666 12 3,600 31,950 28,350 0.2567 7,277 -4,389 13 3,600 31,950 28,350 0.2292 6,497 2,108 14 3,600 31,950 28,350 0.2046 5,801 7,909 15 3,600 31,950 28,350 0.1827 5,179 13,088 16 3,600 31,950 28,350 0.1631 4,624 17,713 17 3,600 31,950 28,350 0.1456 4,129 21,842 18 3,600 31,950 28,350 0.1300 3,687 25,528 19 3,600 31,950 28,350 0.1161 3,292 28,820 20 3,600 31,950 28,350 0.1037 2,939 31,759 IRR = 14.74%