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How to analyze an investment project with multiple rates of return?

In the world of finance, evaluating investment projects with different rates of return may seem challenging, but it is an essential skill for any investor. In this guide, you will learn how to manage variable cash flow and use opportunity rates to determine net present value (NPV) and make informed investment decisions.

How do you determine cash flow and initial investment?

Before getting into the detailed analysis of a project, it is essential to understand how cash flow is structured:

• Initial Investment (Year Zero): A capital outlay, which in our example is $1,000.
• Annual Cash Flow: Expected returns on investment as income, for example, $350 in the first year, $380 in the second year, $400 in the third year and $500 in the fourth year.

To calculate the return, the net cash flow obtained should be compared against the initial investment, taking into account that the value of money changes over time.

What is the impact of the time value of money?

Money has a different value depending on when it is received; that is why it is crucial to adjust each operating flow to reflect its present value. In our case:

1. Sum of periodic flows: simply add up each year's flows and subtract the initial investment. However, this technique ignores opportunity rates.
2. Opportunity Rate: This is the criterion that sets the minimum expected return to compensate for the risk of investing. In case A it is 20% and in case B it is 30%.

How to calculate the net present value with different rates?

This is where the math comes in! We must bring each cash flow to its present value based on the respective interest rate. The process is as follows:

• For Investor A (Rate 20%):

  • Present value of 350 = 291,
  • Present value of 380 = 263,
  • Present value of 400 = 231,
  • Present value of 500 = 241.
  • Total NPV: 1,028.16 (income) - 1,000 (expenses) = 28.16

• For investor B (Rate 30%):

  • Present value of 350 = 269,
  • Present value of 380 = 224,
  • Present value of 400 = 182,
  • Present value of 500 = 175.
  • Total NPV: 851.21 (income) - 1,000 (outgoings) = -148.79

How to perform calculations in Excel?

Microsoft Excel is an invaluable tool for these calculations:

1. Organize your cash flow: List all income and initial outlay.
2. NPV formulas: Use available financial formulas such as "Net Present Value" to calculate the present value of your income.

The correct use of rates and accurate data analysis will allow you to choose optimal options for your investment, preferably the one that yields a positive NPV, such as investor A in our example.

Which alternative is better according to the NPV?

Technology brings clarity to finance. In our situation, with a positive NPV of 28.16, Investment A is preferable as it is above the expected opportunity rate. The fundamental concept is that the NPV reflects the ability to cover the initial investment despite the timely cost of capital.

Avoid those projects that, after this evaluation, result in negative values such as case B, as the results show. This indicates that the expected return does not compensate the risk assumed according to the opportunity rate. Work consistently on improving your evaluation skills and keep exploring additional examples to master everything about net present value. Practice makes perfect!