In this article, we will learn about calculating IRR backward with writing patterns using a step-by-step approach. IRR, backward, writing patterns, calculate, step-by-step

## Introduction

In this article, we will learn about calculating IRR backward with writing patterns using a step-by-step approach. IRR stands for internal rate of return, and it is a metric used to measure the profitability of an investment. The IRR is the discount rate that makes the net present value of the investment equal to zero. Calculating IRR backward involves finding the discount rate that makes the net present value of the investment equal to the initial investment amount. This is known as the break-even discount rate.

## Step 1: Write down the cash flows of the investment

To calculate IRR backward with writing patterns, we need to write down the cash flows of the investment. These cash flows can be in any order, as long as they are consistent with the timing of the investment. For example, let’s say we have an investment that has the following cash flows:

- Year 1: $2,000
- Year 2: $3,000
- Year 3: $4,000
- Year 4: -$10,000

## Step 2: Calculate the net present value (NPV) of the cash flows using a discount rate of 0%

After writing down the cash flows, we need to calculate the net present value (NPV) of the cash flows using a discount rate of 0%. This will give us the initial investment amount. In this case, the initial investment amount is -$1,000.

## Step 3: Use a trial and error method to find the discount rate that makes the NPV of the cash flows equal to the initial investment amount

To find the break-even discount rate, we need to use a trial and error method. We start with a discount rate of 1%, and then increase or decrease the rate until the NPV equals the initial investment amount.

## Step 4: Use writing patterns to help organize your calculations

To make the calculations easier to read and follow, we can use writing patterns. For example, we could write the following:

- Year 1: $2,000 / (1 + r)^1
- Year 2: $3,000 / (1 + r)^2
- Year 3: $4,000 / (1 + r)^3
- Year 4: -$10,000 / (1 + r)^4

## Step 5: Simplify the writing patterns by calculating the present value of each cash flow

After writing down the cash flows using writing patterns, we need to simplify the patterns by calculating the present value of each cash flow. For example:

- Year 1: $2,000 / (1 + r)^1 = $1,960.78
- Year 2: $3,000 / (1 + r)^2 = $2,783.51
- Year 3: $4,000 / (1 + r)^3 = $3,673.09
- Year 4: -$10,000 / (1 + r)^4 = -$7,955.37

## Step 6: Sum the present values of the cash flows to get the NPV of the investment at the trial discount rate

After calculating the present value of each cash flow, we need to sum the values to get the NPV of the investment at the trial discount rate.

## Step 7: Compare the NPV to the initial investment amount

Next, we need to compare the NPV to the initial investment amount. If the NPV is greater than the initial investment amount, then the trial discount rate is too low. If the NPV is less than the initial investment amount, then the trial discount rate is too high.

## Step 8: Adjust the trial discount rate and repeat steps 4-7 until the NPV equals the initial investment amount

If the NPV is not equal to the initial investment amount, we need to adjust the trial discount rate and repeat steps 4-7 until the NPV equals the initial investment amount. This is the break-even discount rate, which is also the IRR.

## Conclusion

To summarize, calculating IRR backward with writing patterns involves writing down the cash flows, calculating the present value of each cash flow using writing patterns, and using a trial and error method to find the discount rate that makes the NPV of the cash flows equal to the initial investment amount. By following these steps, we can easily calculate the IRR of an investment.