Homework SourseAn office building and its equipment are insured to 7100000
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.
Solution
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% |
