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Imputed Interest Rate

By Martel PellerinFebruary 12, 2020

The imputed interest rate is an unstated interest rate and it can cover many different scenarios. To calculate an imputed interest rate, you need to input the actual cash flows and then you can solve for the interest rate.

The following are case studies where you would solve for an imputed interest rate:

  • In the leasing industry, they often quote a rate factor versus an interest rate. However, the rate factor is based on the interest rate, the term, and the structure of the lease including payments in advance or arrears and a residual or none.
    TValue is an excellent program to determine the imputed interest rate, yield, or nominal interest rate by inputting the cash flows and then solving for the rate. If you have a rate factor of 0.020 on a $50,000 lease, your structure would include two payments in advance, a 60 month term, and a 10% residual. With these assumptions, it is easy to calculate the interest rate. In TValue, you would put “U” for unknown for the Nominal Annual Rate. Use Lease on line 1 for 50,000. On line 2 you would have 1 Payment for 2,000 representing your two 1,000 payments in advance with the same Date as the Lease on line 1. On line 3, your 58 remaining payments of 1,000, and then on line 4 the Residual of 5,000. You want to be sensitive to the dates for each payment. With these variables, you would have an imputed interest rate of 10.76%.
  • Imputed interest may apply to a family loan whereas parents may lend their son or daughter $100,000 to buy a house at no interest over 20 years. The IRS wants their share and will force you to charge interest using the Applicable Federal Rates (AFRs) as a minimum. To determine the interest, you would do a Present Value calculation at the AFR.
    TValue is an excellent program to do the calculation. In TValue, you would input the AFR rate of let’s say 2% for the Nominal Annual Rate and then put the Loan on line 1 with “U” for the Amount. On line 2, you would put the payments of 416.67 to repay the $100,000 over the 20 year term. When you click Calculate, you will get the Present Value of $82,365 with interest being the difference over the 20 years that you can then calculate on a year by year basis for tax purposes.
  • Another example would be a Zero-Coupon Bond. A zero-coupon bond is a debt security that does not pay interest but instead trades at a deep discount, rendering a profit at maturity when the bond is redeemed for its full face value. You can solve for the imputed interest rate of the bond by inputting the bond at its cost when purchased and then at the full price at maturity.
    In TValue, as an example, you would use Annual compounding and put “U” for the Nominal Annual Rate. Then on line 1 use Invest for the purchase price of an 80,000 bond, and then use Return on line 2 with the maturity Date 5 years later at the full Amount of 100,000. When calculated, your imputed interest rate would be 4.56%.

The bottom line is you can solve for the imputed interest rate by using the cash flows over the term. In TValue, you would just put “U” for the Nominal Annual Rate with the cash flows to solve for the imputed interest rate.

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