You are trying to choose among three investments described below:
• Investment A: Up-front investment of $45,000 and returns $120,000 in six
years.
• Investment B: Up-front investment of $60,000 and returns $8,000 per year
forever.
• Investment C: Invest $10,000 per year for three years starting today and
returns $15,000 each year for 10 years starting at the end of year 8.
Prioritize the investments in the order of return.
To prioritize the investments in terms of return, we need to calculate the total return for each investment. Let's analyze each investment:
Investment A:
Up-front investment: $45,000
Return after six years: $120,000
Investment B:
Up-front investment: $60,000
Returns $8,000 per year forever.
Investment C:
Invest $10,000 per year for three years (years 1-3)
Returns $15,000 each year for ten years (years 8-17)
To calculate the total return for each investment, we will consider the time value of money and use an appropriate method to compare investments known as Net Present Value (NPV). NPV calculates the present value of future cash flows and discounts them to their current value.
For Investment A, we can calculate the NPV using the following formula:
NPV = (Future Value) / (1 + Interest Rate)^n
Where Future Value is $120,000, Interest Rate is the discount rate, and n is the number of years.
Let's assume the discount rate is 5% for now.
NPV for Investment A = (120,000) / (1 + 0.05)^6
For Investment B, we need to calculate the NPV of the infinite cash flows using a perpetuity formula:
NPV = (Cash Flow per period) / (Discount Rate)
NPV for Investment B = 8,000 / 0.05
For Investment C, we need to calculate the NPV of the cash flows over multiple periods. We can use the same formula as Investment A, but for each yearly cash flow:
NPV = (15,000) / (1 + 0.05)^(n - 8)
where n denotes the year of each cash flow.
Once we have the NPV for each investment, we can compare them to determine the prioritization order. The investment with the highest NPV will have the highest return.
It is important to note that the choice of discount rate can significantly impact the NPV calculations. A higher discount rate reduces the present value of future cash flows, making long-term cash flows less significant relative to immediate returns. Therefore, the discount rate should be chosen based on factors such as the investment's risk, opportunity cost, and other considerations.