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# An office building and its equipment are insured to \$7,100,000 The

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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.

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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 yearsYearCost
(\$)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)01,80,000-1,80,0001.0000-1,80,000-
1,80,00013,60031,95028,3500.892925,313-
1,54,68823,60031,95028,3500.797222,600-
1,32,08733,60031,95028,3500.711820,179-
1,11,90843,60031,95028,3500.635518,017-
93,89153,60031,95028,3500.567416,087-
77,80563,60031,95028,3500.506614,363-
63,44273,60031,95028,3500.452312,824-
50,61883,60031,95028,3500.403911,450-
39,16793,60031,95028,3500.360610,223-
28,944103,60031,95028,3500.32209,128-
19,816113,60031,95028,3500.28758,150-
11,666123,60031,95028,3500.25677,277-
4,389133,60031,95028,3500.22926,4972,108143,60031,95
028,3500.20465,8017,909153,60031,95028,3500.18275,17
913,088163,60031,95028,3500.16314,62417,713173,6003
1,95028,3500.14564,12921,842183,60031,95028,3500.130

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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 ...
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