Imputed Interest

Imputed interest is an estimated interest rate for a debt, rather than the rate contained within the debt agreement. Imputed interest is used when the rate associated with a debt varies markedly from the market rate.

When two parties enter into a business transaction that involves payment with a note, the default assumption is that the interest rate associated with the note will be close to the market rate of interest. However, there are times when no interest rate is stated, or when the stated rate departs significantly from the market rate.

If the stated and market interest rates are substantially different, it is necessary to record the transaction using an interest rate that more closely accords with the market rate. The rate that should be used is one that approximates the rate that would have been used if an independent borrower and lender had entered into a similar arrangement under comparable terms and conditions. This guidance does not apply to the following situations:

  • Receivables and payables using customary trade terms that do not exceed one year
  • Advances, deposits, and security deposits
  • Customer cash lending activities of a financial institution
  • When interest rates are affected by a governmental agency (such as a tax-exempt bond)
  • Transactions between commonly-owned entities (such as between subsidiaries)

If available, the preferred option for deriving imputed interest is to locate the established exchange price of the goods or services involved in the transaction, and use that as the basis for calculating the interest rate. The exchange price is presumed to be the price paid in a cash purchase. In essence, this means that goods or services shall be recorded at their fair value. Any difference between the present value of the note and the fair value of the goods or services shall then be accounted for as a change in interest expense (i.e., as a note discount or premium) over the life of the note.

If it is not possible to determine the established exchange price, an applicable interest rate must be derived at the time the note is issued. The rate selected should be the prevailing rate for similar borrowers with similar credit ratings, which may be further adjusted for the following factors:

  • The credit standing of the borrower
  • Restrictive covenants on the note
  • Collateral on the note
  • Tax consequences to the buyer and seller
  • The rate at which the borrower can obtain similar financing from other sources

Any subsequent changes in the market interest rate shall be ignored for the purposes of this transaction.

Once the correct interest rate has been selected, use it to amortize the difference between the imputed interest rate and the rate on the note over the life of the note, with the difference being charged to the interest expense account. This is called the interest method. The following example illustrates the concept.

Imputed Interest Example

Armadillo Industries issues a $5,000,000 bond at a stated rate of 5% interest, where similar issuances are being purchased by investors at 8% interest. The bonds pay interest annually, and are to be redeemed in six years.

In order to earn the market rate of 8% interest, investors purchase the Armadillo bonds at a discount. The following calculation is used to derive the discount on the bond, which is comprised of the present values of a stream of interest payments and the present value of $5,000,000 payable in six years, with both calculations based on the 8% interest rate:

Present value of 6 payments of $250,000 = $250,000 × 4.62288 $1,155,720
Present value of $5,000,000 = $5,000,000 × 0.63017 3,150,850

Total of present values $4,306,570

Less: Stated bond price $5,000,000

Bond discount $693,430

The controller of Armadillo creates the following table, which shows the derivation of how much of the discount should be charged to interest expense in each of the following years. In essence, the annual amortization of the discount is added back to the present value of the bond, so that the bond’s present value matches its $5,000,000 stated value by the date when the bonds are scheduled for redemption from the bond holders.

Beginning Present Value of Bond Unamortized Discount Interest
Discount Reduction***
1 $4,306,570 $693,430 $344,526 $250,000 $94,526
2 4,401,096 598,904 352,088 250,000 102,088
3 4,503,184 496,816 360,255 250,000 110,255
4 4,613,439 386,561 369,075 250,000 119,075
5 4,732,514 267,486 378,601 250,000 128,601
6 4,861,115 138,885 388,885 250,000 138,885
7 $5,000,000 $0

* Bond present value at the beginning of the period, multiplied by the 8% market rate
** Scheduled annual interest payment for the bond
*** Interest expense, less the cash payment

Armadillo is only obligated to make a cash payment of $250,000 per year, despite the higher 8% implicit interest rate that its investors are earning on the issued bonds. The difference between the actual interest and each cash payment represents an increase in the amount of the bond that the company must eventually pay back to its investors. Thus, by the end of the first year, the present value of Armadillo’s obligation to pay back the bond has increased from $4,306,570 to $4,401,096. By the end of the six-year period, the present value of the amount to be paid back will have increased to $5,000,000.