# Lease Interest Rates

The level of interest rate assets the amount at which a lease liability and associated right of use asset are recognized. There are two types of interest (discount) rates used by lessees and lessors to recognize and unwind their lease liabilities: (a) the interest rate implicit in the lease (also called the implicit interest rate), and (b) the lessee’s incremental borrowing rate.

IFRS 16 requires a lessee to recognize a lease liability by discounting the lease payments at the interest rate implicit in the lease if it is readily determinable, otherwise at the lessee’s incremental borrowing rate. It shows that the interest rate implicit in the lease is preferred interest rate.

## Interest rate implicit in the lease

Interest rate implicit in the lease is the internal rate of return of the lease from the perspective of a lessor. Implicit rate is the interest rate which causes the present value of the lease payments and unguaranteed residual value to equal the sum of the fair value of the underlying asset and the initial direct costs to the lessor.

Lease payments for a lessor include fixed payments (including in-substance fixed payments), variable payments linked to some index or rate and payments related to exercise or non-exercise of options if the lessor is reasonably certain to exercise or not exercise those options.

The unguaranteed residual value is the portion of residual value of the underlying asset which is not guaranteed by the lessee or an unrelated third-party.

Initial direct costs are the incremental costs incurred by the lessee. These are costs that would have been avoided had the lessor not leased the asset out.

The equation for the interest rate implicit in the lease is as follows:

$$\text{A}+\text{I}=\frac{{\text{CF}} _ \text{1}}{{(\text{1}+\text{r})}^\text{1}}+\frac{{\text{CF}} _ \text{2}}{{(\text{1}+\text{r})}^\text{2}}+\ldots+\frac{{\text{CF}} _ \text{n}+\text{U}}{{(\text{1}+\text{r})}^\text{n}}$$

Where A is the fair value of the underlying asset, I is the initial direct costs, CF stands for lease payments occurring on different dates, U is the unguaranteed residual value and r is the interest rate implicit in the lease.

### Implicit rate calculation example

Your company leased out a power plant with 20-year useful life to a municipality for fixed annual rentals of $24 million. The plant cost you$200 million to built and you incurred a cost of $5 million on finalizing the lease and another$10 million on making some modification to the plant at the request of the lessor. If the plant would have zero residual value, what would be your interest rate implicit in the lease.

Interest rate implicit in the lease is the interest at which sum of the present value of lease payments equals the sum of the fair value of the underlying asset and the initial direct costs. Assuming the lease rentals occur at the end of each year, we can create the following expression:

$$\text{\200 million}+\text{\15 million}=\text{\24 million}\times\frac{\text{1}-{(\text{1}+\text{r})}^{-\text{20}}}{\text{r}}$$

We can solve for this using either the hit-and-trial, the financial calculator or the Excel IRR/RATE functions. In this rate, interest rate implicit in the lease r equals 9.27%.

## Incremental borrowing rate

When the interest rate implicit in the lease is not readily determinable, a lessee measures its lease liabilities at its incremental borrowing rate.

The incremental borrowing rate (IBR) is the interest rate at which a lessee can borrow money to obtain an asset similar to the right of use asset obtained on the lease such that the term and security of the loan matches that of the lease.

The incremental borrowing rate may be different for different lessees and it depends, among other things, on the lease term, the value of the underlying asset, the security being provided to the lender, etc. For example, the incremental borrowing rate for a 5-year office space lease will not be the same as a 10-year lease for plant and machinery.

### IBR calculation example

You work as Technical Accounting Manager at a power generation company in Canada. In valuing lease liabilities, your accountant has planned to use the weighted-average interest rate on the following loans as the appropriate interest rate:

• Loan A: 10-year US$400 million loan carrying an interest rate of 3-year LIBOR + 3%. • Loan B: 5-year CAD$100 million loan carrying interest a fixed interest rate of 6%.
• Loan C: 2-year CAD$20 million unsecured loan at 2-year CAD LIBOR + 2%. You company has the following leases: • Lease 1: A 3-year lease for office space denominated in CAD. • Lease 2: A 10-year lease for metering equipment denominated in CAD. The value of the equipment is$10 million.
• Lease 3: A 10-year lease for testing equipment denominated in USD.

#### Solution

Using the weighted-average rate on loans with different maturity, security and currencies to discount lease payments to work out lease liabilities is not a good idea. Here are the different options available for each lease:

• Lease 1: Since Lease 1 is denominated in CAD, we first need to match the currency because we need to find the interest rate applicable to the economic environment in which the lessee operates. Loan B and Loan C are relevant. Next, we match the lease term. Loan C is the closed in maturity to the lease term. It is what we can use as the starting point to determine the incremental borrowing rate. We need to make adjustment for the difference in term. For example, determine the 3-year CAD rate to be a better benchmark.
• Lease 2: The company has no borrowing in CAD with 10-year maturity. Hence, we must estimate the discount rate. One option would be to assume that the 3% spread on Loan A is an appropriate measure of the company’s credit risk and that in order to match currency of the loan with currency of the lease, we replace the benchmark with CAD LIBOR and hence determine the incremental borrowing rate to be CAD LIBOR + 3%. We can also make additional adjustment for the difference in the value of the loan and the underlying asset.
• Lease 3: The interest rate on Loan A is a good starting point because the term and currency of the loan matches with that of the lease. However, adjustment may be needed if the value of the testing equipment (when new) is significantly different from the loan value.