IRR, ROI, XIRR, CAGR, TWRR, you must have come across many such acronyms in finance and investing. One common thread through all of them is that they are a rate or % value and each one finds application in different aspects of financial valuation.

However, bear in mind that they are all different from each other. We shall look at the IRR or Internal Rate of Return and a specific type i.e. the XIRR.

## What is IRR? Internal rate of return (IRR), technically speaking, is a rate at which the cash inflows would be equal to the cash outflows. Or in other words the net cash flow would be zero.

This is similar to a parallel concept in economics called break even point whereby the total sales equals the total fixed and variable costs. Thus profits are zero at break-even point.

The emphasis on internal makes it evident that the calculation excludes external factors likes risk-free rate, the rate of inflation, the cost of capital and other financial risk metrics.

The main focal point in IRR analysis is the time factor. Thus before we attempt to understand IRR, let’s get a grasp of the time value of money.

Consider a simple example. Say you had two options- either receive Rs.1,00,000 now or receive Rs.1,00,000 after 6 months. The only difference between the two is the time aspect.

If you are aware of the concept of time value of money, you would promptly choose option 1 i.e. give me the money right away!

This is because you could invest this money in the short term of 6 months and earn a tidy sum as interest income. Or, you could spend the money on a product for Rs.1 lakh, which might get a tad expensive i.e.over Rs.1 lakh, if you were to buy the same product after 6 months.

## How to Calculate IRR? IRR is a discount rate at which the net present value of future cash flows is equal to the initial investment. Let’s consider an example.

Assume you invested Rs. 50,000 in a financial instrument. The expected annuity income is Rs.2000 for Year 1 and Rs 3000 for Year 2. The IRR computation would be as follows:

50000= 2000/(1+IRR)^1 +3000/(1+IRR)^2

Thus the future cash flows are converted to present terms i.e. time 0 or the time of the investment i.e. now to remove the impact of time factor.

### Formula of IRR

0= CF(0)+CF(1)/(1+IRR)^1 +CF(2)/(1+IRR)^2+…………CF(n)/(1+IRR)^n

NPV= CF(1)/(1+IRR)^1 +CF(2)/(1+IRR)^2+…………CF(n)/(1+IRR)^n

CF(0)= Initial investment amount

CF(1), CF(2),….CF(n)= periodic cash flows at future time periods

n = holding period

NPV= net present value

IRR=Internal rate of return

Ceteris Paribus, or other things being equal, a return on investment obtained at a certain time is better than receiving the return at a later point of time. The former would yield a higher IRR than the latter.

## Application of IRR This is a very important concept in corporate finance as business firms are ultimately concerned with earning a rate of return on every investment that is higher than the cost of capital.

This can also be effectively applied in portfolio management whereby only those investment avenues that yield a high IRR can be accepted.

Consider an investment of Rs 10,000 that grows to Rs.11,000 at end of the year. The yield is 10%. This would not be able to compute the impact of varying cash inflows or outflows during the year.

## Drawbacks of CAGR

Compounded annual growth rate or CAGR is far superior to the computation of average returns or simple interest computation. CAGR assumes the capital amount to be compounded over time till maturity, in case of no withdrawal.

However, there are some limitations in CAGR. CAGR assumes steady returns over the time period. Thus, there is no provision to consider varying returns.

### 1.Apt for Low-Risk Investments

In reality, only a very low-risk investment avenue would generate steady returns. Most moderate to high-risk investment options generate varying returns based on market forces and business cycles.

### 2. Does Not Factor Cashflow

It factors in cashflows at only two-time points i.e. the start when the initial investment is made and at the time of maturity when the investment is encashed.

This again is not evident in most cases. In mutual funds, most investors make regular investments. In order to realize returns higher than the risk-free rate, one cannot afford to adopt an invest and forget approach. The portfolio requires constant monitoring and rebalancing.

### 3. Not Useful in Some Cases

In case of multiple investments like SIPs in case of mutual funds or uneven timelines of investment, CAGR becomes redundant in such cases.

For example, say one was to invest after 1 year, then 3 months, followed by 1 month. In such a case IRR works best to compute a realistic return value.

In mutual funds as well, IRR can help evaluate the portfolio returns in case the returns are spread over a time frame. While in case of a single time period, the compounded annual growth rate (CAGR) would work best, in case of multiple time frames, it becomes imperative to remove the effect of time factor.

This is because investments in mutual funds by way of SIPs are made at different points of time.

IRR is useful of the investments or cash flows are at regular intervals. IRR would be able to compute the rate of return for a payout in the form of SIPs at regular period of predefined and equal time periods, once the expected inflow value at the time of sale of the MF units is known.

In case, one invests at irregular intervals or no predefined pattern or makes frequent redemptions of MF units in between, the XIRR, works on the same discounting principle as the IRR would help compute the rate of return.

The advantage is that both these formulae are widely available in most corporate finance and mutual fund calculators, including excel. Thus, one can efficiently calculate the portfolio returns to take a decision to hold, buy or sell units.

So now you know why IRR is better than CAGR and yield in case of inflows and outflows at different points of time. There is another concept of Time Weighted Return. The IRR again beats the TWR in case of evaluation of the fund performance.

### What is Time-Weighted Return? Often fund managers showcase that investing in a fund is a winning proposition based on the time weighted return (TWRR).

This basically gives the performance of single rupee invested at the beginning of a time period till the end of the time period. For example, if you invested for 3 years from 2016-2019, the gains on a single rupee would be considered in TWRR.

However, this is highly unrealistic. Firstly, how many investors would invest a single rupee value at the start of each year?

This is not a popular investing pattern at all! Thus, the returns projected are prone to estimation error. The returns published and the actual returns may show variance.

Thus time factored returns with consideration of annuity inflows and withdrawals or redemptions during different timelines as computed by IRR presents the most accurate results of fund performance.

### IRR Reinforces the Power of Compounding

One can compare the returns generated if one was to invest a lumpsum amount at the start and get the interest and principle at maturity as against investing in regular annuities or SIPs.

In order to generate the same rate of return, one could compute the current investment amount needed. This would help plan one’s investment portfolio and asset allocation strategy.

### Conclusion

In conclusion, IRR is becoming a popular method of computing returns especially in portfolio management and mutual funds where there are several annuities involved with different time periods.

Disclaimer: The views expressed in this post are that of the author and not those of Groww