Answer:
a) 14.74%.
b) 13 years
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
= = 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
= = 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.