Jim Bob is a stock picking genius. Every year, based on his system, he has the ability to invest $100 (only) in a security that is expected to earn a 20% return over the next year. That security always has a beta of one. Assume that the risk free rate is 4%, and the market risk premium is 6%. Assume that Jim Bob organized his trading company as a corporation, and has one share of stock outstanding and no debt. The gains from his security trading every year are paid out as dividends, so he always invests $100, and he can pass his techniques on to his kids, so Jim Bob’s firm is expected to last in perpetuity. Ignore taxes.

What is the NPV of his trading opportunity each year? Should he buy the security every year?

To determine the Net Present Value (NPV) of Jim Bob's trading opportunity each year, we need to calculate the present value of the expected future cash flows generated by the investment.

First, let's calculate the expected return from the stock investment:
Expected return = Risk-free rate + Beta * Market risk premium
= 0.04 + 1 * 0.06
= 0.04 + 0.06
= 0.1 or 10%

Next, let's calculate the present value of the expected future cash flows. Since Jim Bob invests $100 every year, the cash flows are constant.

PV of annual cash flows = Cash flow / Discount rate
= $100 / 0.1
= $1000

Now, let's calculate the NPV using the perpetuity formula:
NPV = PV of annual cash flows - Initial investment
= $1000 - $100
= $900

So, the NPV of Jim Bob's trading opportunity each year is $900. This indicates that the investment is worth $900 more than the initial investment of $100. Therefore, Jim Bob should buy the security every year as it provides a positive NPV.

Note: The assumption made here is that the cash flows are paid out as dividends, and there are no other costs or benefits associated with the investment. Additionally, this analysis does not consider the potential risks or volatility associated with the investment.