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 five 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

To calculate the net present value (NPV) of building a new plant with the new technology, we need to calculate the present value of the cash flows associated with the project.

The initial investment is the cost of building the new plant, which is $500,000. The annual operating cost per gallon is $2.00 without the new technology and $1.00 with the new technology. The annual output is 100,000 gallons.

The cash flows associated with the project can be summarized as follows:

Year 0: - $500,000 (initial investment)
Year 1-5: $100,000 savings per year ($2.00-$1.00 x 100,000 gallons)
Year 6-indefinite: $200,000 savings per year ($2.00-$1.00 x 100,000 gallons)

We can calculate the present value of these cash flows using a discount rate of 20%. Using the formula for the present value of an annuity, we get:

NPV = - $500,000 + $100,000 x (1-1/(1+0.20)^5)/0.20 + $200,000/(1+0.20)^5 x (1/(0.20-0.05))

NPV = $299,061

Therefore, the net present value of building a new plant with new technology is positive, and the best choice is C, +$299,061.

The Manufacture of Herbal Health Tonic Is a Competitive Industry