How to approximate IRR with simple formula for two loans of different terms

[Aidie1]

I am trying to make a simple formula to approximate the IRR using the IRR of each loan, their respective term and loan size.

i.e.

loan one is $\$1,000,$ has a term of $10$ years and an IRR of $5\%$.

loan two is $\$100$ has a term of $1$ year and an IRR of $15\%$.

Using a simple weighted does not capture the difference of term - this would show an IRR of $5.91\%$, while the real IRR is $5.12\%$.

Any help is appreciated!

 

[Aaron Bex]

The best way to approximate the IRR in this case is to use the internal rate of return formula, which takes into account both the size and duration of the loans. The formula is:

IRR = (PV1 + PV2 + ...) / (FV1 + FV2 + ...)

where PV stands for present value (the amount borrowed) and FV stands for future value (the amount repaid).

For example, for loan one:

PV1 = 1000
FV1 = 1000 * (1 + 0.05)^10

For loan two:

PV2 = 100
FV2 = 100 * (1 + 0.15)^1

Plugging these values into the formula gives us an estimate of the IRR of 5.12%.