IRR

Let's get a deeper understanding of Internal Rate of Return

Definition

IRR is a concept which is used to find out how much have we earned out of our investments distributed over uniform intervals in time.

Unlike ROI ( Return on investment ), IRR accounts for the time factor of money and investments.

Uses

Calculation

We can use the following formula for calculating IRR:

$$\sum_{n=1}^N \frac{C_n}{(1+r)^n} - Initial\, Investment = 0 = NPV$$ Where,
  • N : total number of periods
  • n : serial number of transaction (1, 2, 3, ....)
  • C : cash flow or transaction value (negative or positive)
  • r : Internal Rate of Return
  • NPV : Net present value

Evaluating the above formula, the formula for n number of cash flows can be written in simple terms as:

$$0 = \frac{C_n}{(1+r)} + \frac{C_n}{(1+r)^2} + \frac{C_n}{(1+r)^3} + ... + \frac{C_n}{(1+r)^n} - Initial\, Investment$$

By calculating IRR for various investment patterns, we can determine which pattern of investment is more likely to provide a better return.

Example

Let us say Mr. X is planning on investing ₹10000 in a project that is expected to produce cash flow ₹3500, ₹4000 and ₹5000 for three consecutive years. Let us calculate IRR for this investment.

After putting value in above formula, the IRR equation is going to look like below:

$$0 = \frac{3500}{(1+r)} + \frac{4000}{(1+r)^2} + \frac{5000}{(1+r)^3} - 10000$$

We can obtain the IRR only with trial and error method. Obtaining the exact IRR value is a cumbersome task. So, our goal must be to provide r (IRR) which can be used in above equation that would make it equal (or at least close) to zero (NPV). Let's take the r as 0.10 (10%).

$$0 = \frac{3500}{(1+0.10)} + \frac{4000}{(1+0.10)^2} + \frac{5000}{(1+0.10)^3} - 10000$$

In order to get NPV = 0, following must satisfy

$$0 = 3181.81 + 3305.78 + 3759.39 - 10000$$
$$0 = 10196.98 - 10000$$

As you can see in the above example, the equation is not equal to zero.

Again using the trail-error method, we will repeat the process with value or r as 0.11 (11%).

$$0 = \frac{3500}{(1+0.11)} + \frac{4000}{(1+0.11)^2} + \frac{5000}{(1+0.11)^3} - 10000$$

In order to get NPV = 0, following must satisfy

$$0 = 3153.15 + 3252.03 + 3649.63 - 10000$$
$$0 = 10054.82 - 10000$$

So at r = 0.11 the value of equation approaching near zero.

So, we can say the IRR of the above investment is 0.11 * 100 = 11 % (approx.)

This is how you can apply the formula for calculating the IRR value manually which can be a difficult task.

IRR vs XIRR

But here is the interesting part, investments are not as evenly distributed across periodic intervals.

In those cases, we can use the XIRR.

IRR vs CAGR

IRR can have multiple cash inflows (investments) and outflows (withdrawals).

In contrast, CAGR has only a single cash inflow (initial investment) and only one cash outflow (final amount).

IRR vs Absolute return (RoR)

IRR calculates the returns that can be expected over a certain time period, while simple ROI gives you the actual return on the investment, without factoring in timing and taking compounding into consideration.