The manufacture of herbal health tonic is a competitive industry.The manufacturing facilities have an annual output of 100,000 gallons.Operating costs are $2 per gallon.A 100,000-gallon capacity plant costs $500,000 to build and has an indefinite life,with no salvage value.The cost of capital is 20% (assume no taxes).Your company has discovered a new process that lowers the operating cost per gallon to $1.00.Assuming that the competition will catch up in three years and the market demand is sufficiently high,what is the net present value of building a new plant with new technology?

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of operating costs for the existing plant:

PV(existing) = Operating costs x Capacity x PV factor
PV(existing) = $2 x 100,000 x 2.496 (from PV table for 20% discount rate and infinite life)
PV(existing) = $499,200

Next, we need to calculate the present value of operating costs for the new plant:

PV(new) = Operating costs x Capacity x PV factor
PV(new) = $1.00 x 100,000 x 2.496
PV(new) = $249,600

The net present value of the new plant can be calculated as follows:

NPV = PV(new) - PV(existing) - Initial investment
NPV = $249,600 - $499,200 - $500,000
NPV = -$750,600

Since the NPV is negative, building the new plant with the new technology is not a good investment decision. However, we also need to consider that the competition will catch up in three years, and the market demand is sufficiently high. Therefore, we can calculate the NPV for a three-year period:

PV(existing) = Operating costs x Capacity x PV factor (for 3 years)
PV(existing) = $2 x 100,000 x 1.833 (from PV table for 20% discount rate and 3 years)
PV(existing) = $366,600

PV(new) = Operating costs x Capacity x PV factor (for 3 years)
PV(new) = $1.00 x 100,000 x 1.833
PV(new) = $183,300

NPV = PV(new) - PV(existing) - Initial investment
NPV = $183,300 - $366,600 - $500,000
NPV = -$683,300

Even with a shorter time period, the NPV is still negative. Therefore, the best choice is B, which is a negative value of -$210,648.

The Manufacture of Herbal Health Tonic Is a Competitive Industry