Implicit Interest Rate

An implicit interest rate is the interest rate that is built into the cash flows of a transaction even though it is not written down as a stated rate. It is found by working backward: it is the discount rate at which the present value of the payments to be made equals the amount being financed today. The concept appears most often in leasing, where accounting standards refer to "the rate implicit in the lease," and in sales on deferred payment terms, where a seller accepts a note or a series of installments instead of cash.

The idea matters because money always has a time value. Paying $10,000 two years from now is not the same as paying $10,000 today, so a contract that charges no visible interest still contains a financing cost hidden in the price. Accounting standards require that cost to be identified and recognized as interest over time rather than included in the price of the goods or the asset.

In general terms, the implicit rate is the value of $r$ that solves:

• $\text{Amount financed}$ is the cash price or fair value of what is acquired today.
• $CF_{t}$ is the payment due in period $t$, including any final balloon or residual amount.
• $n$ is the number of periods and $r$ is the implicit rate per period.

This is the same calculation used to find an internal rate of return, and in practice it is solved with a financial calculator or the RATE or IRR function in a spreadsheet.

A simple case is a non-interest-bearing note. A supplier sells equipment to a customer in exchange for a note promising to pay $10,000 in two years, with no interest stated. The equipment's cash price is $8,573. The implicit rate is the rate at which $10,000 discounted for two years equals $8,573, which is 8 percent a year. The seller records revenue of $8,573 and a note receivable of $10,000 less a discount on notes receivable of $1,427, which it recognizes as interest income over the two years. The buyer mirrors this with a discount on notes payable.

A leasing example is slightly more involved. A lessor leases a machine with a fair value of $50,000 for five annual payments of $11,500, due at the start of each year, with no residual value expected. Solving for the rate that equates the five payments with $50,000 gives an implicit rate of about 7.5 percent. Because the payments are made in advance, the calculation uses an annuity due.

Under ASC 842 in US GAAP and IFRS 16, the rate implicit in the lease is defined as the rate that causes the present value of the lease payments and the unguaranteed residual value to equal the fair value of the leased asset plus any initial direct costs of the lessor. Lessees are required to use this rate to measure their lease liability when it is readily determinable. Often it is not, because the lessee does not know the lessor's residual value assumptions or costs. In that case lessees use their incremental borrowing rate, the rate they would pay to borrow a similar amount over a similar term with similar security. US private companies may also elect to use a risk-free rate. Lessors use the implicit rate to account for sales-type and direct financing leases.

The implicit rate is closely related to imputed interest, the term used when a stated rate is missing or unreasonably low and a market rate must be substituted. US GAAP (ASC 835-30) requires that substitution for many notes so that the transaction is recorded at its economic substance. The resulting interest is then recognized using the effective interest method. Common mistakes include confusing a stated or contractual interest rate with the implicit rate, mixing up payments in advance and in arrears, and forgetting to include residual values or fees in the cash flows. Consumers face the same issue with "zero percent" financing offers, where the true financing cost may be hidden in a higher purchase price.