Final answer:
To determine whether you should remain invested in the firm, you need to calculate the expected return of your investment in comparison to other investment opportunities. The expected return is the weighted sum of the possible returns, where each return is multiplied by its corresponding probability. In this case, the firm claims it can generate $291 per year in perpetuity with your $5,300 investment. However, other long-term investments of similar risk offer an expected return of 8.4%.
Step-by-step explanation:
To determine whether you should remain invested in the firm, you need to calculate the expected return of your investment in comparison to other investment opportunities. The expected return is the weighted sum of the possible returns, where each return is multiplied by its corresponding probability. In this case, the firm claims it can generate $291 per year in perpetuity with your $5,300 investment. However, other long-term investments of similar risk offer an expected return of 8.4%. To calculate the expected return of your investment, you need to calculate the present value of the perpetuity cash flows and compare it to the initial investment.
The formula to calculate the present value of a perpetuity is:
PV = CF / r
Where PV is the present value, CF is the cash flow per period, and r is the discount rate.
In this case, the CF is $291 per year and the discount rate is 8.4%, or 0.084 as a decimal. Plugging in the values, we get:
PV = $291 / 0.084 = $3464.29
Since the present value of the cash flows is less than your initial investment of $5,300, it is not advisable to remain invested in this firm if other similar-risk investments offer an expected return of 8.4%.