Internal Rate of Return
The Internal Rate of Return is the after-tax rate that discounts all of the
after-tax cashflows back to the amount of finance provided upfront.
Another way of looking at the IRR is that it is the rate that is applied to
the lessor's investment balance in each period to give a zero balance at the
end of the transaction.
The IRR method has the advantages of being simple to apply and reasonably
straightforward to understand.
In practice, the calculation of the IRR has a serious drawback.
It is possible for there to be more than one solution to the IRR for a set
of cashflows.
We look at the possibility of multiple solutions by way of an example. The
set of cashflows shown in the table below has three positive solutions for the
IRR, namely 5%, 15% and 40%. This can be seen by calculating the balance of the
cashflows over time using each of these solutions.
| IRR Example |
| Year |
Lessor's
Cashflows |
Balance
using 5% IRR |
Balance
using 15% IRR |
Balance
using 40% IRR |
| 0 |
(53,776) |
53,776 |
53,776 |
53,776 |
| 1 |
134,441 |
(77,976) |
(72,599) |
(59,149) |
| 2 |
(17,612) |
(64,263) |
(65,876) |
(65,203) |
| 3 |
(162,714) |
95,238 |
86,956 |
71,424 |
| 4 |
100,000 |
0 |
0 |
0 |
It is difficult to report the return earned when it is not unique!
The problem of multiple solutions is more likely to occur in a leveraged
lease transaction due to the small amount of equity injected and the large
impact of tax.
The reason that multiple solutions arise is that the IRR method applies the
same rate of return to the lessor's investment balance from time to time
whether the balance is positive or negative.
In the early stages of a tax-based lease the lessor will have equity
invested, but late in the transaction surplus cash is accumulated to pay the
deferred tax. The IRR method assumes that you can earn the same interest rate
on this "sinking fund" as on your investment.
See also:
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