This article is not intended to replace the textbooks on Financial Mathematics. Our task is a more practical one. Here we will try to bring some clarity into a topic rarely debated, quite confused and suspected by many as a “conspiracy” – the topic of the leasing interest.

**Where does the mystery of leasing interest come from?**

The first reason is the lack of legal requirements, today and in the past, for the disclosure of leasing interest or any other form of profitability by lessors. The logic “if they do not ask, I will not tell,” is popular among lessors around the world. Accordingly, many of the lease agreements do not even mention interest and interest payments at all. Rather they regulate only leasing installments. Some confusion arises from the fact that monthly lease payments include both interest and a part of the principal repayment.

Another reason for the “mystery” around the lease rates comes from the most popular way of leasing distribution – at the point of sale. Imagine how a standard car dealerSee Supplier... More, who can talk for hours about the different cars he sells, comments leasing interest rate, advises on the calculation method and expectations interest rate fluctuations over the next five years. Without wanting to offend the professional car dealers, it is often difficult for them to comment and sometimes even understand a question on leasing interest derived from a lease contract drafted for the asset they sell. This is the starting point of the suspicion that “they are hiding something”.

The third reason for the “mystery” are the lessors themselves. In a fair marketing effort to present their service as the most competitive, which is available on the market, they sometimes openly claim that the lease service has “no interest” or introduces easy-to-use concepts such as “leasing appreciation” / popular in Bulgaria through the first year of the new century / or “leasing factor” / still very popular in the US/. Both concepts, though easy to calculate, are not exactly “leasing interest rates”, although, as numbers, they are presented as similar percentage or decimal values.

The fact is that not all lessees are financially literate and they find it difficult to understand even the most conscious lessorOne of the parties to the... More who tries to explain the floating rate, the interest rate risk, the interest rate index to which the leasing interest is linked and the possibilities for its fluctuation. In parallel, it should be noted that the formula for calculating a monthly annuity installment is not the easiest and is difficult to use without a specialized financial calculator or a computer. Accordingly, “in order not to confuse them” leasing companiesA company whose main activity is... More rarely show the leasing interest to their clients. This again raises doubts about a “conspiracy”.

Last but not least, the reason for the enigma around the leasing interest rates is the competition among the lessors themselves. Leasing interest, as the cost of the leasing service, is an important parameter for comparing one lease offer with another. But when margins are tight, lessors begin to transfer some of their returns to various other non-interest receivables – lesseeThe lessee is the user of... More fees, tax concessions, trade commissions, profits from various additional to the leasing services. With the inclusion of all these different sources of income, the boundaries of the lease rates are greatly diluted. This is how “interest-free” leasing is achieved as well as leasing advertisements for rates significantly lower than the currently prevailing market interest rates /bank loans and other similar services/.

In the absence of information on leasing interest, foul play is possible by lessors and charge of unacceptably high rates. The legislator tries to protect lessees from unethical practices by lessors. In Bulgaria (as well as in most European countries) there is regulated protection for individuals (the logic is that it is the most difficult for them to find their way in the labyrinth of lease rates). The term “Annual Percentage of Costs” is introduced, which somewhat brings together various sources of income for lessors, such as leasing interest and leasing fees. APC is far from perfect because it includes elements such as “insurance premium” and cannot include others such as “trade discounts”. APR rather adds to the “mystery” with diversity among lease rates.

**Who needs leasing interest?**

One of the favorite phrases of Milton Friedman is that “there is no such thing as a free lunch“.

The same is true for leasing too. The use of the leasing assetThe leasing asset is the subject... More by the lesseeThe lessee is the user of... More needs to be compensated.

The payments under the leasing contract always have two component parts:

- Payment of the amortization of the leasing assetThe leasing asset is the subject... More
- Payment of the financial interest

For example, if a lesseeThe lessee is the user of... More receives a vehicle worth 12,000, he pays an initial installment of 2,000, and for the remainder, he contracts for a full payout lease (no residual valueThe residual value is present in... More) for 10 months, then the depreciation component in the monthly installments will be 1,000 / 10,000 divided by 10 /. Thus, the asset will be financially depreciated at the end of the lease – the tenth month in our example. Obviously, the lessorOne of the parties to the... More would have recovered the funds invested at the start of the lease, but that would be a weak motivation for him. He also needs the second component – the payment of the financial costs, ie. payment of interest for the use of the financial resource, which was blocked in the leasing assetThe leasing asset is the subject... More. This is exactly the leasing interest.

The leasing interest is the main source of profit for the leasing companiesA company whose main activity is... More and is an absolute analog to the credit interest with bank credits.

**How to calculate the monthly leasing installment using the leasing interest**

The short answer is – the monthly leasing installment can be computed using the following formula:

Where:

MI is the monthly installment

LA is leasing amount

RV is residual valueThe residual value is present in... More

r is the monthly interest rate of the leasing interest

n in the number of payments

An alternative way for computation has been automated by Microsoft using the built-in formulas in Excel nor net present value /NPV/ and internal rate of return /IRR/.

Now you know from experience why do the lessors often use simpler alternatives for calculation of the monthly installments, such as “leasing appreciation” or “leasing factor”, which were mentioned above.

**Monthly interest explained**

Let us start with the easiest formula for simple interest:

I=P * r * t

Where:

I is the nominal amount of interest

Р is the principal /the amount which was leased, the so-called “leasing amount” /

r is the annual interest rate

t is the number of year of the leasing

This is the formula for the “simple flat rate”.

If interest was paid at the end of the period /hence “simple”/ and the leasing had a tenor of one year with a 5% leasing interest rate and a principal of 10,000, also due in bulk at the end of the period /hence „flat“/, then the leasing interest would be:

I=10000*0.05*1

or

I=500

This formula and the respective calculations would be quite true for a leasing contract, had the leasing period been one year and the lessorOne of the parties to the... More wanted full pay-back of the leased value /principal of 10 000/ and interest for the leased resource /500/ payable on the last day of the year.

It is quite obvious, that in real life there are no such transactions like the one described above. At the same time, the example strongly helps us understand the principles of calculation, which we shall further use.

**Leasing appreciation**

Due to the relatively complex method for calculation of the monthly installments of a lease contract, the lessors in Bulgaria adopted the term “leasing appreciation”. The leasing appreciation is the percent with which the leasing transactions increases the price of the leasing assetThe leasing asset is the subject... More /compared with its purchase price/. If we continue the example from above, the leasing nominal leasing appreciation is 500 or expressed as a percentage: 500/10000 = 5%. In this example, the leasing appreciation is the same as the leasing interest /we should not forget that the leasing interest was calculated as a simple flat rate/.

Should the leasing contract be for a longer than one year period, then the above result is divided by the respective number of years. The formula for calculation of leasing appreciation is:

Where:

I is the amount of interest for the whole leasing period

Р is the principal /the leasing amount/

t is the number of years of the leasing term

The reasons for using the ratio “leasing appreciation” are two. The first is the relative ease of calculation and explanation /to potential lessees/. The second is more a marketing one – this is a relatively low percentage ratio /compared with all others/ which can be advertised, simultaneously hiding the real leasing interest, which is considerably higher.

Why is the leasing interest higher?

In our simplified example, we accepted that the payment of the interest and repayment of the principal to occur with a bullet payment at the end of the leasing contract. In reality, all leasing contracts stipulate repayment in monthly installments, e.g. each month interest and principal is being paid. Therefore with each following payment, the principal decreases and respectively the interest decreases too /in real terms/.

For example, if the principal is 10,000 and the interest is 5%, and the leasing term is divided into ten equal installments, with the first payment of 1500, the lesseeThe lessee is the user of... More will be paying 1000 principal and 500 interest /see the formula for simple interest above/. Therefore for the second payment, the remaining principal will be reduced to 9,000, and the interest for the second payment will decrease to 450. Thus with the second payment of 1500, only 450 will be used for interest payment and the remaining 1050 will be used for principal repayment. In this way, for the third installment, the principal will have dropped to 8,950 and so on. With each installment, the remaining principal decreases progressively, with the decrease of the interest component.

Now, let us bring our example a little closer to reality. Here is how the two ratios will look for 12-month leasing: 10% annual interest, 10,000 principal, 10% initial installment and equal leasing installments with 0 residual valueThe residual value is present in... More:

In order to calculate the leasing amount, we deduct the initial installment. Thus the leasing amount /the principal/ will be 10,000 – (10,000*10%) = 9,000

The monthly installment will be 494.88 payable 12 times

The total interest paid for the whole period will be 494.88

The annual leasing appreciation will be 5.50%, with the leasing interest rate being 10%.

The example emphasizes the second reason /further to the ease of calculation/ for marketing of the leasing appreciation – its value is almost half of the value of the leasing interest rate.

Although it does not carry much information and hinders the comparison with other financial products /e.g. bank credits/, the leasing appreciation is still widely used on the Bulgarian market.

**Leasing Factor **

The Leasing /or Money/ Factor is a little more complex analog of the leasing appreciation, which is widely used throughout the USA, especially in the car leasing industry. The reasons for its popularity are the same as the ones described above, bringing the popularity of the ration “leasing appreciation”.

Aiming to find an easy way for calculation of the monthly installment or the monthly interest, some unknown, but smart lessorOne of the parties to the... More /or car dealerSee Supplier... More/ from the computer-less-past discovered, that if one calculates the monthly interest on the average outstanding leasing amount /the average principal due under the leasing contract/ he will get an amount which is extremely close to the average leasing interest calculated using the complicated method as described above. Here are the calculations for our example:

The interest rate for one month is the annual interest rate divided by 12 or:

Then the monthly leasing interest is calculated as simple interest on the average outstanding leasing amount /principal/:

or in our example the average monthly interest will be:

and the annual interest will amount to 37.5*12 = 450. This amount is very close to the one as calculated using the complex formula above.

For even greater facility of the car dealers, the leasing companiesA company whose main activity is... More simply forward to them the so-called „leasing factor“ or „money factor“, which is Thus the dealers need just to multiply the leasing amount by the leasing factor, in order to find the amount of the leasing interest for one year. This practice started prior to the computer age, but is still strong today. This allows for the easy calculation of the leasing interest using a simple desktop calculator. The dominant leasing factors in the USA today are about 0.00175, which equals 4,2% annual interest /in order to get the annual interest rate starting from the leasing factor, it is only necessary to multiply it by 2400 – see above to understand why/.

**Leasing Calculators**

With the increased use of computers in our lives, the leasing installments are calculated from specialized leasing programs. Often for the use by future lessees, the leasing companiesA company whose main activity is... More provide online calculators, where the leasing interest rate is seldom mentioned, but the readers know already that it is always present and due with each leasing installment.

In the online leasing calculators instead of quoting the leasing interest rate, it is incorporated in the different leasing programs or is asset-specific – one interest rate for cars, another for equipment, etc.

Here are a few examples of good online leasing calculators:

Leasing calculator of UBB Interlease: https://interlease.bg/calculator.php

Leasing calculator of SoGeLease: http://www.sogelease.bg/bg/instrumenti/kalkulator.html

Leasing calculator of Raiffeisen Leasing: https://www.rlbg.bg/bg/

Leasing calculator of Addventure Leasing: addventure.leasing/calculator

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**Leasing Interest for Operational Leasing**

It is quite clear that all the above methods for calculation of leasing interest are applicable for financial leasingA leasing contract, under which, the... More. Here the lessorOne of the parties to the... More purchases the leasing assetThe leasing asset is the subject... More for a specific purchase price, then grants it to the lesseeThe lessee is the user of... More for a specific term, during which the lesseeThe lessee is the user of... More returns the invested amount /leasing amount or principal/ as well as the interest for the time during which the investment was blocked in the leasing assetThe leasing asset is the subject... More. How then should one calculate the interest for an operational lease contract?

If under financial leasingA leasing contract, under which, the... More the disclosure of the leasing interest is rare, under operational leasing this never occurs. All lessors talk about “rent”, “rent installment”, “additional service packages” and never mention the word “interest”.

Although it seems complicated it really is quite simple. It helps if we review the grading of the different types of leasing:

Under a closed end financial leasingA leasing contract, under which, the... More contract the lessorOne of the parties to the... More invests in an asset and expects the return in full of his investment by the lesseeThe lessee is the user of... More, together with the respective interest due until the full repayment of the investment.

Under the open ended financial leasingA leasing contract, under which, the... More, the lessorOne of the parties to the... More invest in an asset and expects the repayment __only partially__ of the invested amount plus interest by the lesseeThe lessee is the user of... More. The __full return__ of the investment will happen upon the payment of the residual valueThe residual value is present in... More – be it by the lesseeThe lessee is the user of... More (if she should use the purchase option), be it from a third party (should the lesseeThe lessee is the user of... More simply return the leasing assetThe leasing asset is the subject... More).

Under the net operational leasing (without any additional services) the calculations are the same, as with open ended financial leasingA leasing contract, under which, the... More. The difference being that under operational leasing the asset will certainly be remarketed to a third party (the lesseeThe lessee is the user of... More does not have the right to acquire the leasing assetThe leasing asset is the subject... More.

It is rather often when the operational leasing includes some additional services. With cars, for instance, these may include insurance, road fees, taxes, maintenance, consumables, tires, return vehicle and even fuel. How should one calculate the interest on these?

Again this is not very complicated. If in all examples above the initial investment was a single upfront payment in the beginning of the leasing period, under operational leasing with additional services, the investment will be made more or less although the life of the leasing contract. Further to the purchase of the leasing assetThe leasing asset is the subject... More in the beginning of the leasing transaction, the lessorOne of the parties to the... More will make additional payments through the leasing period – for insurance, for repairs, for consumables, for tires, etc. The latter smaller investments, just like the main investment in the leasing assetThe leasing asset is the subject... More, also need to be compensated to the lessorOne of the parties to the... More in the leasing installments, including the respective interest upon them for the respective holding period.

Since the lessorOne of the parties to the... More needs to determine a specific rent installment upfront, for the operational leasing contract, he will have to make educated assumptions for all service expenses based on the millage of the car, the price of the insurance, etc. Now you know why operational leasing contracts have limits on the allowed annual millage.

The calculation of the leasing interest for operational lease contracts with additional services /without the use of specialized software/ can be made easily in Excel, using the function for Internal Rate of Return /which in this case is the leasing interest/.

**Other Sources of Revenue for Lessors**

The leasing market is strongly competitive. Further to many competing lessors, the interest rates are curbed also by competing products, such as the bank credits. This intense competition usually leads to the decrease of the interest margins for the leasing companiesA company whose main activity is... More. Aiming at being profitable, lessors seek other alternative sources of revenue, which are circumstantial to the leasing transactions.

The most obvious are the captiveCaptive Leasing Company is a company... More leasing companiesA company whose main activity is... More. Their main purpose is not so much a financial profit, as support to the mother-dealer and his sales. Here one can often come across a lesing company, which is selling its service at interest rate levels equal to, and sometimes bellow, the price of funding. captiveCaptive Leasing Company is a company... More leasing companiesA company whose main activity is... More often offer “interest free leasing” or package additional free services in the leasing transaction. As anyone can guess, the price of these services is subsidized by the mother-dealer, who decreases part of his profit for the respective promotion. The leasing interest exist in the interest-free leasing too. The only difference is the party which will pay it.

Another, very easy to spot alternative source of revenue for the lessors are the various fees, which they charge for various “services” – „fee for document handling“, „leasing administration fee“, „fee for the registration of the leasing assetThe leasing asset is the subject... More“, „fee for …“. All these fees increase the positive cash flow to the leasing companiesA company whose main activity is... More and compliment the revenues from the interest rate margin.

Another serious source of revenue is the management of the market risk of the residual valueThe residual value is present in... More in leasing transactions which have a residual valueThe residual value is present in... More. For example /from an actual leasing deal/ if a new car has been leased for 3 years with allowed annual 15,000 km. mileage, full insurance cover and residual valueThe residual value is present in... More of 30%, it should be clear to everyone that the lessorOne of the parties to the... More is ready to make an additional revenue of at least 10% from the purchase price of the car upon remarketing of the residual valueThe residual value is present in... More. If the lesseeThe lessee is the user of... More accepts this – the transaction and the additional revenue will happen.

One very popular in the world, but not often found in Bulgaria, additional source of revenue for the leasing companiesA company whose main activity is... More are tax allowances. Not that the legal framework is unfavorable in Bulgaria, the reason is that the local leasing market is still immature for their utilization.

Yet another additional source of additional income are the various penalty fees and interest. Some of these are so high, that they belittle the revenue generated by the leasing interest. For example, the penalty for exceeding the allowed mileage under an operational leasing contract can reach BGN 1.00 for each kilometer above the contracted limit – a penalty which exceeds the price for taxi services. The penalty annual interest rates often reach a three digit number /even with today’s low interest rate levels/.

Other additional sources of revenue for lessors may include trade discounts from the vendors of the leasing assets, insurance commissions from the insurance companies, commissions from various sub-contractors for services linked with the leasing transaction. leasing companiesA company whose main activity is... More should not be deemed as greedy. These additional revenue streams help the leasing companiesA company whose main activity is... More to:

- Exist on the market /even with negligible interest margins/;
- To offer better terms than bank credits;
- To underwrite bigger client risk than banks;
- To offer various promotions to the lessees;
- To invest in better customer service for their clients.

If need be, all these additional revenue streams to the leasing transactions may also be calculated as “leasing interest” or “leasing return”. All which is necessary is to add the respective positive cash payments on their respective dates in the life of the leasing contract /similar to the negative cash payments for the services under operational leasing, as described above/.

We do hope that we have shed some light on the leasing interest topic which should now be a bit less “mysterious”.

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