Introduction
The interest rate implicit in the lease is the rate that reflects the lessor’s return on a lease. One can think of it as the lessor's internal rate of return on the lease. This rate is used to discount lease payments to a present value, in order to recognise a lease liability.
When a borrower borrows cash from a lender, the repayments normally exceed the original cash value of the loan. This is because the lender charges the borrower interest on the loan, which the borrower has to pay in addition to the principal amount.
Similarly, when assets are leased, a lessee typically pays, over the course of the lease term, an amount to the lessor that exceeds the fair value of the lease.
ASC 842 and IFRS 16 introduced a new way of accounting for leases, under which this “hidden interest” must be recognised as finance income (for the lessor) and finance cost (for the lessee). The interest rate implicit in the lease helps us measure the lease liability at present value and determine the finance cost and finance income to recognise over the term of the lease.
Definitions:
The definition of the interest rate implicit in the lease is slightly different between IFRS 16 (International Financial Reporting Standards) and ASC 842 (US GAAP).
IFRS 16:
Interest rate implicit in the lease: The rate of interest that causes the present value of
- the lease payments and
- the unguaranteed residual value
to equal the sum of
- the fair value of the underlying asset and
- any initial direct costs of the lessor
ASC 842:
Interest rate implicit in the lease: The rate of interest that at any given date causes the aggregate present value of:
- The lease payments and
- The amount the lessor expects to derive from the underlying asset at the end of the lease term
to equal the sum of both
- The fair value of the underlying asset minus any related investment tax credits retained and expected to be realized by lessor and
- Any deferred initial direct costs of the lessor.
The two definitions describe the same rate. IFRS 16 refers to the unguaranteed residual value while ASC 842 refers to the amount the lessor expects to derive from the asset at the end of the term, and ASC 842 additionally deducts investment tax credits retained by the lessor.
Calculating the Interest Rate Implicit In The Lease
The interest rate implicit in the lease is always calculated from the lessor’s perspective. Therefore, the lessee will use all available information to reasonably estimate the interest rate implicit in the lease. In the cases where the lessee cannot readily determine the rate, they should use their Incremental Borrowing Rate to discount lease payments and determine the lease liability. Shortly, the incremental borrowing rate is the rate the lessee would have to pay to borrow over a similar term, the funds necessary to obtain an asset of similar value and is used only when the implicit rate cannot be readily determined. Due to the inherent uncertainty with regards to the lessor's position, many lessees choose the incremental borrowing rate as the discount rate by default. We recommend however, to always attempt to calculate the interest rate implicit in the lease first, before resorting to the incremental borrowing rate.
The easiest way to think of the calculation of the implicit interest rate is to think of everything the lessor gives (outflows) versus everything the lessor receives (inflows), at different times.
With modern tools, this rate is often calculated with financial calculators or Excel, using the PV, PMT, I and FV parameters.
To calculate the interest rate implicit in the lease, we need to follow the following steps:
- Identify Lease Payments
- Determine Initial Asset Value
- Account for Residual Value
- Set Up Cash Flows
- Solve for the IRR
Did you know?
Use our free calculator to calculate the interest rate implicit in the lease, for your own leases.
Interest Rate Implicit in the Lease Calculator
Example:
- Asset: Vehicle
- Lease term (4 years): 1 January 2021 - 31 December 2024
- An up-front, non-refundable deposit of 4 000
- Payments of 10 000 at the end of each year
- At commencement, the vehicle has a fair value of 50 000
- At the end of the lease, the vehicle is expected to be worth 21 000, of which 12 000 is guaranteed by the lessee
- The lessor paid 1 000 in initial direct costs at commencement date
- As a lease incentive, the lessor gave the lessee 20% discount on the deposit
Lessor’s outflows:
- Fair value of the vehicle at commencement date = 50 000
- Initial direct costs = 1 000
- Lease incentive = 4 000 * 20% = 800
Lessor’s inflows:
- Deposit = 4 000
- Annual payments = 10 000
- Residual value of the vehicle = 21 000
Now it is simply a case of identifying the timing of each inflow and outflow.
Outflows are reflected in negative amounts, while inflows are reflected in positive amounts.
This table shows the inflows and outflows for each period of the lease:
| Period | Cash Lease Payments | Asset | IDC | Incentives | Total |
|---|---|---|---|---|---|
| 0 | 4,000 | -50,000 | -1,000 | -800 | -47,800 |
| 1 | 10,000 | 10,000 | |||
| 2 | 10,000 | 10,000 | |||
| 3 | 10,000 | 10,000 | |||
| 4 | 10,000 | 21,000 | 31,000 |
Let’s calculate the interest rate implicit in the lease using a financial calculator:
| Parameter | Value |
|---|---|
| N (Number of periods) | 4 |
| PV (Present Value: Commencement Date) | -47,800 |
| PMT (Annual Payment) | 10,000 |
| FV (Future Value: Termination Date) | 21,000 |
| I (Implicit Interest Rate) | 8.59% |
*This amount includes both the guaranteed and unguaranteed portion of the residual value. You might wonder why we include the full residual value, when the definition only requires the unguaranteed portion. The reason is that the definition of lease payments already include the guaranteed portion of the residual value. The guaranteed residual value must therefore also be included as a cash flow at the end of the lease term.
By entering these values into a financial calculator, you will arrive at an interest rate implicit in the lease of 8.59%.
The same result can be achieved by using the Excel IRR function on the Total column, or by using the RATE function.
Why the Full Residual Value Is Used
The single most common query about this calculation is why the future value in the example is the full 21,000 rather than the 9,000 that is unguaranteed. The IFRS 16 definition, after all, refers only to the unguaranteed residual value.
The answer is that the guaranteed portion is already inside the other side of the equation. The definition equates the present value of two things — the lease payments and the unguaranteed residual value — and the definition of lease payments itself includes amounts expected to be payable under a residual value guarantee for lessees, and the full guarantee for lessors..
When the Rate Cannot Be Readily Determined
The rate depends on inputs that belong to the lessor: the fair value of the underlying asset, the lessor's initial direct costs, and the estimated residual value at the end of the term. A lessee that cannot obtain these cannot compute the rate, and IFRS 16 then directs it to its incremental borrowing rate.
"Readily determinable" is the operative phrase. If any single element is unavailable or can only be guessed at, the rate is not readily determinable — one uncertain input is enough, because the rate solves for all of them simultaneously.
Where the information usually comes from
The fair value of the asset is often the most accessible input, since it frequently appears in the contract or can be corroborated against a cash purchase price for the same asset. The residual value assumption is usually the hardest, and it is the one that most often pushes a lessee to the incremental borrowing rate.
The choice is not neutral. A lower discount rate produces a larger lease liability and right-of-use asset, and shifts expense from finance cost towards depreciation. Because the incremental borrowing rate reflects the lessee's own credit standing rather than the pricing of the lease, the two rates can differ materially on the same contract, which is why the standard sets the implicit rate as the primary measure rather than offering a free choice.
Common Pitfalls in the Calculation
| Pitfall | Correct treatment |
|---|---|
| Using only the unguaranteed residual as the future value | Use the total residual value; the guaranteed part sits within lease payments |
| Including the lessee's initial direct costs | Only the lessor's costs enter the rate; the lessee's are added to the right-of-use asset |
| Ignoring a lease incentive | An incentive is a lessor outflow and changes the net amount invested at commencement |
| Mismatching payment timing | Payments in advance and in arrears give different rates on identical amounts |
| Capitalising initial direct costs for a dealer lessor | A manufacturer or dealer lessor expenses them, so they are excluded from the rate |
| Using the carrying amount of the asset | The definition uses fair value, which may differ from the lessor's carrying amount |
Timing deserves particular attention. A deposit or a payment made at commencement belongs at period zero, not period one, and moving a single payment between those two points changes the resulting rate noticeably. Setting the cash flows out on a timeline before solving — as in the table above — avoids most errors of this kind.
Calculating the implicit rate in Excel?
Try our free implicit interest rate calculator, built to the same methodology covered in this article.
Conclusion
Understanding how to use and calculate the interest rate implicit in the lease is crucial for both lessees and lessors.
For additional guidance, please contact insight@leash.co.za.