In this article, we will explain the discount rate used to calculate the lease obligation. A lease liability is calculated by discounting the total amount of payments for the entire lease term (Lease Payment – to be explained in the next article) to the present value (Present Value – PV), and it is necessary to determine what the discount rate to use.

**Type of discount rate**

The new leasing standard ASC 842 presents the following two discount rates

- Implicit rate
- Incremental borrowing rate

Although simplified, each can be explained as follows.

Implicit rate:

PV of lease payments + PV of residual assets = Fair value of assets + Deferred initial direct costs

Implicit rate: Such discount rate that leads to a present value (PV) on the left-hand side equal to the right-hand side above.

At first glance, this may seem difficult to understand, but to simplify, you can say that lessors are making decisions so that the __lease payments__ and the __residual value of the asset discounted to th__e present value (PV) will recover the current __fair value of the ____asset__ and the __initial direct cost of executing the__ lease. The discount rate that satisfies the equation is called the implicit rate.

Incremental borrowing rate:

This is the discount rate from the lessee’s perspective and is defined as the rate of interest a lessee would have to pay to borrow an amount equal to the total lease payments on a collateralized basis over a similar term in a similar economic environment.

In other words, it is the additional borrowing rate that would be required if lessee had to borrow the total lease payment. Note that we assume a secured loan with a similar lease term and economic situation.

**Order of application of discount rates**

ASC 842 provides for the order of application of the implicit rate and incremental borrowing rate. In principle, the implicit rate is applied. However, as explained above, this rate is calculated from the lessor’s perspective, and such information may be difficult to obtain for lessees, especially for operating lease lessees.

Therefore, ASC 842 specifies that if the implicit rate is not readily determinable, the incremental borrowing rate is used.

**Use of ****risk-free discount rate ****(simplified method)**

However, the actual calculation of the incremental borrowing rate by lessees is quite complicated. In other words, it is not an easy task, as it requires taking into account the credit rating of the lessee, the liquidity of the collateral assets (including the assets borrowed under the lease), the lease term, and the economic situation. In practice, it may be possible to obtain a written quote from the bank, assuming that the lease payments are to be borrowed, but this is also considered to be a hurdle.

In light of the above issues, __private companies__ can choose to use the risk-free rate as a discount rate as a practical expedient. A risk-free rate is not specifically defined in ASC 842, but an example of a risk-free rate is the zero-coupon U.S. Treasury instrument.

When selecting a risk-free rate, the following points should be kept in mind

- If the implicit rate from the lessor’s perspective mentioned above is readily determinable, it should be used.
- The choice to use the risk-free rate can be made for each class of underlying assets. Here, the underlying assets are the assets subject to the lease. However, it is not clear in ASC 842 what this class means. Therefore, it seems that there are two types of discussions: one is to divide the leased asset by its physical nature (land, building, machinery, etc.), and the other is to divide the leased asset by the degree of risk (intended use, environment, etc.) to the leased asset.
- Since the risk-free rate is usually lower than the incremental borrowing rate, the ROU asset and liability increase as a result of the lower discount rate.

**Discount rate of consolidated subsidiaries (****incremental borrowing rate****)**

By the way, when using incremental borrowing rates in a consolidated subsidiary, it can be problematic at what level the interest rate on the additional borrowing is used.

Although this point is not explicitly stated in ASC 842, Basis of Conclusions (BC) 201, which accompanies ASC 842, provides the following discussion.

Depending on the terms and conditions of the lease and the corresponding negotiations, the parent entity’s incremental borrowing rate may be the most appropriate rate to use as a practical means of reflecting the interest rate in the contract.

In other words, in some cases it may be optimal to use the incremental borrowing rate of the parent company. The following are some specific examples of such cases.

For example, this might be appropriate when the subsidiary does not have its own treasury function (all funding for the group is managed centrally by the parent entity) and, consequently, the negotiations with the lessor result in the parent entity providing a guarantee of the lease payments to the lessor. Therefore, the pricing of the lease is more significantly influenced by the credit standing of the parent than that of the subsidiary.

To summarize, if the lessor’s lease pricing is based on the parent company’s credit rather than the subsidiary’s, it is appropriate to use the parent company’s incremental borrowing rate.

In the next article, we will touch on lease payments subject to discount calculations.