Question

An auto plant that costs $75 million to build can produce a new line of cars that will produce net cash flow of $40 million per year if the line is successful, but only $4 million per year if it is unsuccessful. You believe that the probability of success is about 25 percent. The auto plant is expected to have a life of 28 years and the opportunity cost of capital is 4 percent. What is the expected net present value of building the plant? Please state your answer in millions and in 2 decimal places. Correct response: 141.62±0.02 million If the plant could be sold for $80 million to another automaker in one year if the auto line is not successful, what is the expected net present value of building the plant?

Answer 1

The expected net present value of building the auto plant is $42.3 million.

Step-by-step explanation:

The expected net present value of building the auto plant can be calculated by multiplying each possible net cash flow by their respective probabilities and discounting them to the present value using the opportunity cost of capital.

For the line to be successful (probability = 0.25):

Expected cash flow = ($40 million × 0.25) + ($4 million × (1-0.25)) = $10 million + $3 million = $13 million

Present value = $13 million / (1+0.04)¹ = $12.5 million

For the line to be unsuccessful (probability = 0.75):

Expected cash flow = ($40 million × 0.75) + ($4 million × (1-0.75)) = $30 million + $1 million = $31 million

Present value = $31 million / (1+0.04)¹ = $29.8 million

Adding up the present values gives: $12.5 million + $29.8 million = $42.3 million

Therefore, the expected net present value of building the plant is $42.3 million.