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 percent (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), we need to determine the initial investment and the present value of cash flows.

Initial investment:
The cost of building the new plant is $500,000.

Present value of cash flows:
We will assume a projected cash flow of $1 per gallon for the first five years, and $2 per gallon for the remaining life of the plant (since the technology will eventually become obsolete and the operating cost will return to $2 per gallon). The total cash flow for the project is:

(100,000 gallons x $1/gallon x 5 years) + (100,000 gallons x $2/gallon x 95 years) = $19,000,000

To calculate the present value of the cash flows, we need to discount them back to their present value using the cost of capital. The present value factor can be calculated from the formula:

PV factor = 1 / (1 + r)^n

where r = cost of capital and n = number of years.

Using a discount rate of 20%, the present value factor for each year is:

Year 0: 1.000
Year 1: 0.833
Year 2: 0.694
Year 3: 0.579
Year 4: 0.482
Year 5: 0.402
Year 6-100: 0.097

The present value of the cash flows is:

Year 0: $0
Year 1: $166,596
Year 2: $131,219
Year 3: $103,182
Year 4: $81,766
Year 5: $7,840
Year 6-100: $7,243,826

NPV = Present value of cash flows – Initial investment
NPV = ($166,596 + $131,219 + $103,182 + $81,766 + $7,840 + $7,243,826) - $500,000
NPV = $299,061

Therefore, the net present value of building a new plant with the new technology is +$299,061, which means it is a good investment.

The Manufacture of Herbal Health Tonic Is a Competitive Industry