Question

A new grain combine with a 20 year life can remove seven pounds of rocks from its harvest per hour. Any rocks left in the its output hopper will cause $35,000 damage in subsequent processes. Several investments are available to increase the rock-removal capacity, as listed in the table below. If the effective annual rate of return is 8%, what should be done? Note that the $35,000 damage is on an annual basis. For example, if nothing is done (1^st option), then there is a 20% chance of incurring $35,000 of damage each year.

Rock Removal Rate (RRR)	Probability of exceeding RRR	Required Investment
7 lb/hr	0.20	$0
8 lb/hr	0.10	$12,000
9 lb/hr	0.05	$18,000
10 lb/hr	0.025	$25,000

Answer 1

		A	B=A*$35000	C=7000-B
	OPTION	Probability of exceeding RRR	Expected annual damage	Annual Savings in damages	Present Value (PV)of Savings	(Using PV function of excel with Rate=8%, Nper=20, PMT=-C(annual savings)
	Option 1	0.2	$                     7,000	$0	$0
	Option 2	0.1	$                     3,500	$    3,500	$34,364
	Option 3	0.05	$                     1,750	$    5,250	$51,545
	Option 4	0.025	$                         875	$    6,125	$60,136
	OPTION	Present Value (PV)of Savings	Initial Cash flow	Net Present Value
	Option 1	$0	$0	$0
	Option 2	$34,364	($12,000)	$22,364
	Option 3	$51,545	($18,000)	$33,545
	Option 4	$60,136	($25,000)	$35,136
	Option 4 should be selected with investment of $25,000