Question

An auto plant that costs $60 million to build can produce a new line of cars that will produce net cash flow of $30 million per year if the line is successful, but only $2.5 million per year it it is unsuccessful. You believe that the probability of success is about 70 percent. The auto plant is expected to have a life of 15 years and the opportunity cost of capital is 5 percent. What is the expected net present value of building the plant?

Answer 1

The expected net present value of building the plant is -$49.318 million. To calculate the expected value, we find the present value of the net cash flows for each year and subtract the initial cost of building the plant.

Step-by-step explanation:

To calculate the expected net present value of building the plant, we need to find the present value of the net cash flows for each year and then calculate the expected value.

For the successful outcome (70% probability), the net cash flow is $30 million per year. For the unsuccessful outcome (30% probability), the net cash flow is $2.5 million per year. We will use the formula for the present value of cash flows:

PV = CF / (1+r)ⁿ

Where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.

Assuming a discount rate of 5% and a plant life of 15 years, the present value of the successful outcome is:

PV(success) = $30 million / (1+0.05)¹⁵ = $30 million / 1.964 = $15.26 million

The present value of the unsuccessful outcome is:

PV(unsuccessful) = $2.5 million / (1+0.05)¹⁵ = $2.5 million / 1.964 = $1.27 million

To calculate the expected net present value, we multiply the probabilities by the present values and subtract the initial cost of building the plant:

Expected NPV = (0.7 × $15.26 million) + (0.3 × $1.27 million) - $60 million = $10.682 million - $60 million = -$49.318 million

Therefore, the expected net present value of building the plant is -$49.318 million.