Question

You are considering producing a new product, which if it is successful will produce cash flows of $16,000 per year in perpetuity. If it is unsuccessful, the cash flow will be -$26,000 in the first year and then you will shut down. If the probability of success is 0.15 and the opportunity cost of capital is 4 percent, what is the maximum that you would be willing to pay to undertake the investment?

Answer 1

To calculate the maximum investment price, multiply the cash flows by their respective probabilities to find the expected cash flow, then discount this at the opportunity cost of capital to find its present value.

Step-by-step explanation:

The question requires calculating the maximum price you would be willing to pay for an investment that generates cash flows differently based on its success or failure. The maximum price to pay for the investment is the expected value of the investment's future cash flows discounted at the opportunity cost of capital. To solve this, you need to determine the expected cash flow considering both outcomes weighted by their probabilities and then calculate the present value using the given discount rate.

In simple terms, the expected cash flow (ECF) can be determined by probability of success times the cash flow if successful (CFs) plus the probability of failure times the cash flow if unsuccessful (CFu). The present value of perpetuity formula PV = ECF / r, where r is the opportunity cost of capital, can then be used to find the maximum investment price. Here, CFs = $16,000, CFu = -$26,000, the probability of success is 0.15, and the opportunity cost of capital is 4%.