What is an implicit interest rate?

Implicit Rate Overview

An implicit interest rate is an interest rate that is not specifically stated in a transaction. Any transaction that involves a stream of payments that extend over multiple future periods must incorporate an interest rate, even if there is no rate stated in the transaction agreement, because there is a cost associated with delaying payments over a period of time, which is known as interest expense. If a transaction does include an interest rate, but that rate is substantially different from the current market interest rate (such as a stated rate of 1% versus a market rate of 8%) then the implicit rate is still the market rate.

You would then use the implicit interest rate to calculate the present value of the stream of payments, using the formula for either the present value of an annuity due (where payments are due at the beginning of each period) or the present value of an ordinary annuity (where payments are due at the end of each period - which is more common). The difference between the present value of these streams of cash flows and the total payment amount is recorded as the interest component of the transaction.

Implicit Rate Example

Mr. Jones can either buy a refrigerator for $500 in cash or make 12 monthly payments of $130 per year at the end of each of the next five years. There is no stated interest rate in the second option. The market rate of interest for consumer loans for people having roughly the same credit rating as Mr. Jones is 8%. We will consider the 8% rate to be the implicit interest rate for this example, since it is the rate that he would be offered in a similar situation by a different third party.

If Mr. Jones wanted to determine the present value of the second option, he would go to a present value table for an ordinary annuity and extract from it a multiplier factor that relates to the stream of payments (five payments at the end of each year) and the interest rate of 8%.

Mr. Jones goes to the table and finds that the appropriate multiplier rate is 3.9927, which he multiplies by the $130 annual payment to arrive at a present value of $519.05. Thus, at the implicit rate of 8%, the present value of the multi-year payment option is $19.05 more expensive than if he were to pay $500 in cash right now.

Related Topics

Present value of an annuity due table
Present value of an ordinary annuity table
What is an ordinary annuity?
What is the formula for the present value of an annuity due?
What is the formula for the present value of an ordinary annuity?