# How to Calculate Interest Rate Implicit in the Lease

When you deal with leases in accordance with standard IAS 17 Leases, FAS 13 or any other applicable standard, you know for sure that the lease should be measured, whether initially or subsequently, using interest rate implicit in the lease in the first instance. In other words, when you use interest rate implicit in the lease, you apply actuarial method to apportion individual lease payments between repayment of principal and interest. Well, that’s fine, but what is it and how to calculate it?

To make it simple and clear – the rate implicit in the lease is basically the internal rate of return on all payments or receipts related to the lease in question. So to say, when you add up net amount that you get at the beginning of the lease and then subtract all what you have to pay through the lease duration (or lease term), you’ll find out that you pay definitely more than you get. The difference is the interest that you pay on the lease, because the lease is nothing else than a loan in fact.

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*Special For You!*OK, so you pay an interest on the lease. At what rate? Well – at the rate implicit in the lease, or the internal rate of return on all payments or receipts from the lease. Thus, when you appropriately discount all what you pay as the lease payments by the rate implicit in the lease, you should get exactly the value that you got in the beginning in the lease.

Example: You acquire a new car under the lease. Normal selling price of the same car is EUR 10 000 and you are required to pay a downpayment of EUR 1 000 immediately when you take the car. Then, you will pay EUR 3 500 at the end of each year for 3 years. How should this be understood?

- Amount of your loan is EUR 9 000. You get a car with value of EUR 10 000, but you pay back EUR 1 000 immediately.
- Repayments of your loan are EUR 3 500 each year, for 3 years. Thus you pay 10 500 in total.
- Total interest is EUR 1 500 – that is difference between EUR 10 500 (your repayments) and EUR 9 000 (your loan).

Interest rate of your loan is 8.122%. When you discount all repayments by this rate, the sum of them will give you exactly EUR 9 000:

1st payment | 1/(1+0,08122) * 3 500 | 3 237,08 |

2nd payment | 1/(1+0,08122)^{2} * 3 500 |
2 993,92 |

3rd payment | 1/(1+0,08122)^{3} * 3 500 |
2 769,02 |

Total: | 9 000,02 (0,02 = rounding) |

This was very simple example, when payments are regular, all in arrears (at the end of certain period), with residual value equal to 0. Now you might wonder how the rate of 8.122% was calculated. Let me repeat from above that interest rate implicit in the lease is simply internal rate of return on all payments and receipts from the lease. So using simple MS Excel formula IRR applied to the series of your cash flows would work nicely.

But here might be other complications related to calculation of interest rate implicit in the lease:

- What if the payments are paid monthly and you want annual IRR?
- What if the payments are paid in the beginning of the period?
- What if you have to buy the leased car for some amount at the end of lease term?
- What if the payments are irregular or in varying amounts?

Well, you should check out short video dealing with this topic included in the IFRS Kit. You will not only learn about basic IRR concepts with their examples, but the video shows you how to deal with the trickiest complications or traps in various types of leases. Excel worksheet printed in PDF with all tables and formulas comes with video, so you will get valuable tools to use in your daily job, too.

This is the short clip from the full video:

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Good evening Silvia ! I am reading your publication about IFRS. But I got stuck about interest rate 8,122% could you explain it how you reached 8,122% eventually ,give formula. Is it coumpound interest ? or normal.. From which sum did you get it. in general interest is : Cxtx%/1 or 2/4/12//52 365

Interest rate of your loan is 8.122%. When you discount all repayments by this rate, the sum of them will give you exactly EUR 9 000:(10500-1500)

Explain me please Madame Silvia

Lease a property is just pay rental every month. Why need to implicit interest ? Lease pproperty can geneate right of use in asset column ?

Every term still can use depreciation to make loss in inco.e statement ?

Reduce many tax, but make the account very ugly ?

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Hi silvia, I have a query regarding calculating effective interest rate using IRR.

A company enters into lease or purchase a bond (at say, 10000 for 4 years) during the accounting year (like four months prior to end of financial year), actual interest (say, 8% per annum) is payable (cash flow) thereafter in next accounting periods.

I understand that we calculate effective interest rate based on year 1, year 2, year 3 cash flows, but like in this case, there is no cash flow during the first accounting period and how can we factor 4 months (with no interest) in first accounting period and full yearly interest cash flow in subsequent periods, using excel to derive IRR?

And am I correct in saying that “in first year, the effective interest rate multiplied by initial fair value for four months period will be gross interest income/expense recognized in P & L?”

Hi Shiva, it is difficult to answer shortly in the comments, but I strongly recommend checking out my IFRS Kit – you will find a lot of examples on calculating IRR when payments are irregular, made on different intervals, etc. Thank you!

how do I calculate implicit interest rate using ordinary calculator if fair value is 400,000 annual payment of 110,000 for 4 years

What I do is, I take one random % and calculate p/v for the same. Then I take another % by guess working such that F/V falls between those 2 P/V. Then I use interpolation to calculate the IRR [ Cross multiply ].

After got the implicit interest rate what is the next step? how do i get the yearly interest? Is it (10,500 X 8.122%) 852.81 interest? Then what is the double entries? Thanks.

No, in fact the interest is 9000*8,122%. The double entry is then Debit P/L – finance expenses Credit Liabilities, then Debit Liabilities Credit Cash when repaid. S.

In the ias 17 , it require us to capitalise the lowest between of the fair value of the asset and the present value of the minimum lease payment . However, if we always use the IRR to determine the present value of future lease payment , the present value of minimum lease payment will always equal to the fair value of the assets .

So is that still any chance the fair value of the asset will higher than the minimum lease payment ?

I still don’t get how you got your implicit interest rate

Makalo, it’s written right above in the article. Use the excel formula IRR. I wanted to illustrate that using excel is much easier than calculating it yourself by interpolation. During the exam, you are given IRR. S.

YOUR ARTICLE IS VERY SUPPORTIVE, STRAIGHT TO THE POINT AND EXTREMELY REWARDING. THINK YOU SO MUCH, SO MUCH THANK YOU

IFRS compliance is the key to uniformity in Universal Accounting

Thank you so much for your devoted endeavor!