### Internal Rate of Return (IRR)

## What is the Internal Rate of Return?

The Internal Rate of Return (IRR) is a metric that allows investors to compare investments with different repayment schedules, tenors and amounts in a standardized manner. The IRR takes into consideration the structure of cash flows from your investment and accommodates for the time value of money. Note however, that the IRR is not an inflation-adjusted rate of return. An investment that pays $100 every month for 10 months will have a greater IRR than an investment that pays $200 every two months for 10 months. This is because, according to the time value of money, $1 today is worth more than $1 tomorrow. For example, earlier cash flows from the first investment can be used to make other investments and earn returns on them.

## Does an IRR of 20% mean I will receive 20% more cash than I invest?

No, because IRR reflects both the amount and the timing of loan repayments (see 'What is the Internal Rate of Return?' above).

## What is the difference between Internal Rate of Return and Annual Rate of Return?

The IRR is different from the Annual Return because it is a metric of time-adjusted returns, not just annual returns. Two investments that have the same annual returns can have different IRRs due to differences in their repayment schedules. Let’s study the case of two separate investments of $100 each that both have an annual return of 10%.

Scenario A | Scenario B | |
---|---|---|

$100 is invested on 1st January 2018, and a lump sum payment of $110 is received on 1st January 2019. | $100 is invested on 1st January 2018, and 12 monthly payments of $9.17 are received. | |

2018-01-01 | -$100 | -$100 |

2018-02-01 | $9.17 | |

2018-03-01 | $9.17 | |

2018-04-01 | $9.17 | |

2018-05-01 | $9.17 | |

2018-06-01 | $9.17 | |

2018-07-01 | $9.17 | |

2018-08-01 | $9.17 | |

2018-09-01 | $9.17 | |

2018-10-01 | $9.17 | |

2018-11-01 | $9.17 | |

2018-12-01 | $9.17 | |

2019-01-01 | $110 | $9.17 |

Internal Rate of Return (IRR) | 10% | 20% |

Annual Rate of Return | 10% | 10% |

Although these investments both have annual returns of 10%, they have different IRRs – which means that they are not equally attractive from an investment standpoint. Since the IRR in scenario B is 20%, twice that of scenario A, scenario B is the better investment opportunity. This is because there is value in getting repaid sooner – you can re-invest this cash and start earning returns on other investments earlier.

## How does liwwa calculate the IRR for a funding campaign?

The first step is to look at the expected cash flow schedule from a campaign. Payment schedules differ from campaign to campaign due to differences in loan tenor, grace period, and the periodicity of payments (e.g. every month vs every 3 months). Below is an example of a $100 pledge to a campaign with a 12 month tenor and 10% annual return, with a monthly repayment schedule.

The first item on the cash flow schedule is the pledge made by investors, which shows as a negative amount (i.e. a cash outflow). The following items on the schedule specify the dates and amounts of payments to be made by the borrower.

**Repayment Schedule**

(can be downloaded from the loan details page after the campaign is funded)

Date | Cashflows | |
---|---|---|

2018-07-05 | -$100.00 | |

2018-07-25 | $10.00 | |

2018-08-25 | $10.00 | |

2018-09-25 | $10.00 | |

2018-10-25 | $10.00 | |

2018-11-25 | $10.00 | |

2018-12-25 | $10.00 | |

2019-01-25 | $10.00 | |

2019-02-25 | $10.00 | |

2019-03-25 | $10.00 | |

2019-04-25 | $10.00 | |

2019-05-25 | $10.00 |

Once we've established the expected cash flow schedule, calculating the IRR is straightforward, and can be done by applying the Internal Rate of Return formula to the cash flow schedule above. Many spreadsheet applications, like Microsoft Excel, offer a function that allows you to calculate the IRR easily. You can copy the schedule above to a Microsoft Excel spreadsheet and apply the XIRR formula on the values and dates above. Using this function, you should get an IRR of 22.67%.

liwwa's internal implementation of the IRR formula replicates the results produced by Excel's XIRR formula. Please note that rounding errors, especially when dealing with smaller numbers, can have drastic effects on IRR calculations. To account for potential rounding errors, liwwa’s backend system calculates return figures up to as many as 12 decimal places thereby providing highly accurate portfolio numbers – even if the investor only sees numbers rounded to 2 decimal places.

## What happens once the borrower starts making repayments?

After the borrower starts making payments, the cash flow schedule will start including both the actual payments made and their dates, as well as the scheduled payments to be made in the future. If a borrower is late on payments, liwwa adjusts the cash flow schedule accordingly.

## How are the risk-adjusted returns different from the unadjusted returns?

The unadjusted returns are calculated assuming that the borrower will make all loan payments on time. This is displayed by default.

The risk-adjusted returns take into account the likelihood that the loan is repaid late or only partially. The risk class and the tenor of the loan both influence the size of the adjustment.

**Example: Returns on a Loan with Risk Class B and 12 Months Tenor:**

Unadjusted Returns | Risk Adjusted Returns | |
---|---|---|

IRR | 15.03% | 11.61% |

Annual Return | 7.41% | 5.77% |

The risk-adjusted returns are lower than the unadjusted returns, because they take into account the probability that a Class-B, twelve-month loan will not be repaid fully or on time.