Question

In: Finance

A new grain combine with a 20 year life can remove seven pounds of rocks from...

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 (1st 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

Solutions

Expert Solution

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


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