In: Finance
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 |
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 | |||||||||||||