Аннотация и ключевые слова
Аннотация (русский):
This article deals with leasing in general and its two forms, operative leasing and financial leasing, are also compared. The advantages of leasing are also described. Both forms of leasing arecalculated at examples in this article.The use of leasing in practice can be seen there. The results of the examples are seen in the schedule of instalments.

Ключевые слова:
operative leasing, financial leasing, recapitalization price, instalment
Текст
Leasing can be characterized as a financial product that is most frequently used to fund the acquisition of movables, for the most part. It is a method of medium-termand long-term financing, which is based on the lease asset at apre-agreed amount of rent [1]. The base of leasing is a lease agreement; it always has to be written. Part of the lease agreement, between the lessee and the leasing company, is always the agreement on the insurance of the leased asset, which protects the lessor (the leasing company) against losses, which can be caused by the theft or damage of the leased asset. The leasing may be structured according to various aspects. One aspect is the structuring by means of the tax aspect to the financial and operative leasing. In the case of financial leasing, we are talking about an operation that basically substitutes a loan, which the lessee needs to obtain regarding the subject of the leasing.Financial leasing is mostly concluded for the same time, as is the subject of the lease being fully amortized. The leasing company purchases the subject of the leasing from a producer and then it is rented to the lessee; it is the relationship between a producer and a lessee which the leasing company takes part in. The leasing company pays the purchase price to the producer and so it becomes an owner and, at the same time, it also becomes a lessor of the leased subject to the final user (the lessee) [2]. After the lapseof time, (or contract time) for which was the leasing (the lease) was agreed upon, the lessee repurchases the subject of the leasing, usually for a very low price. The lessor remains an owner of the subject of that leasing throughout continuance of lease agreement in the financial leasing. An operative leasing agreement can be agreed upon for a shorter period of time than the amortization of the equipment being leased. The purpose of an operational leasing is the temporary use of the subject, without transferring the majority of the risks associated with the ownership of the subject and also without any contractual entitlement to the possible transfer of ownership of the leased asset to the lessee [3]. Most often, itis this type of leasing which is typically offered directly by the producer, that usually provides the lessee with additional services (such as maintenance, repairs, etc.) throughout the lease. In the case of those provided services by the manufacturer, we are talking about operative leasing or full-service leasing. It is, therefore, outsourcing. Full-service leasing is the most widely used leasing, not only for personal cars and Light Commercial Vehicles, but also in the case of engineering and equipment leasing [4]. Leasing is a financial instrument that allows for the implementation of investment plans. The share of the leasingof the total of tangible fixed assets, which is 1/3 in the Czech Republic and 1/4 in Slovakia, is an important alternative to traditional bank loans [5]. There was an annual decrease in the volume of lease contracts in 2012, due to the stagnation of investment and the restrictions on new viable business projects. During the year, the member companies of the ČLFA (the Czech Leasing and Finance Association) transmitted the use of the engineering equipment and vehicles at a total purchase price (excluding VAT) for CZK 36.3 billion into the lease; that represents an annual decrease of 10.4 %.They concluded with the total 42,026 new contracts for the leasing of engineering equipment and vehicles with business entities. The share of the operative leasing to thetotal leasing of the movable overall investment has increased in the long term; it has already reached 43.5 % in 2012. In terms of the commodities, the representation is dominated by the leasing of personal cars (32.5 %), the leasing of trucks (29.8 %) and the leasing of engineering equipment (25.4 %) [4]. Focus leases movable property CLFA members in the first quarter of 2012, by commodity: 1 - automobiles; 2 - trucks; 3 - motorcycle; 4 - utility vehicles; 5 - buses, trolley; 6 - other heavier road vehicles; 7 - ships, aircraft, railroad cars, locomotives; 8 - information technologies, office and communications equipment; 9 - machinery and equipment; 10 - photovoltaic systems; 11 - other commodities In the Figure, we can see the focus of the leasing of movable objects as given by the ČLFA (Česká leasingová a finanční asociace/the Czech Leasing and Finance Association) in the first quarter of 2012, according to the commodity. It is apparent that two-fifths of the leasing of movables that are directed into private sector services (that is the leasing of movable assets in industry and construction) is roughly half. During this period, businessmen concluded 9.955 new contracts of the leasing of engineering, equipment and vehicles; 3.827 were financed leases and 6.128 were operating leases. There were 198.834 active lease contracts (the leasing of machinery, equipment and vehicles for businessmen) in progress at the end of the first quarter of 2012, which the ČLFA member companies had concluded; 125.004 contracts were for financial leasing and 73.830 were for the operative leasing contracts [5]. The advantages of using lease financing are: - It allows you to finance up to 100 % of the value of the leased asset from other sources; - leasing fees are usually paid after commissioning, at that time when the subject of leasing company is already used; therefore is possible to better temporally coordinate the costs and yields; - the leasing fees are usually pre-fixed; - that leasing is a balancing neutral. The disadvantages of the use of lease financing are: - that it is anexpensive form of acquisition of property; - that the termination of contract by the lessee is not possible; - that it becomes a lessee's propertylike an almost amortized after termination of the leasing; - that theleasing agreement restricts the use of the lessee's rights; - that the property risks are transferred to the lessee. The subject of almost half of the lease contracts in the Czech Republic are in the case of the lease of movables, cars and other important items are the other vehicles and enginery and equipment [3]. The total leasing price represents the total instalments paid during the lease term. It is the sum of the input price of the property, the interest of the loan (if the refinancing of the loan lease transactions) and the leasing lessor's margin. The proportion of the total lease price (including VAT and the purchase price the leased item including VAT) expresses the leasing coefficient. The leasing coefficient is an increase in the total cost of leasing compared to the purchase of the leased asset for cash. As was already mentioned in the article, the lessee may purchase the leased item for the selling priceafter the expiration of the lease in the case of the financed lease. The selling price is that price for which the leasing company sales are subject to the existinglessee after its completion, for further distinguishing the lease residual value, which is formed as the difference between the purchase price of the asset and its depreciation [6]. In the calculation of the examples in the article, we have proceeded according to the following formulas, which are necessary for the calculation of the prices and lease instalments that the lessee pays for the leased assets. The Operative Leasing: For the calculation of the operative leasing, we need the following formulas: LP = PC + LM. This formula shows the calculation of the total price of the lease (the leasing price) where: LP = lease price; PP = purchase price; LM = leasing margin. We also need to know the calculation of the increase of the first lease paymentsformula: the increase of the instalment = PC × % increase. The increased payment is calculated by multiplying the purchase price with the percentage increase in the first lease payment, because the increase of the first instalment is calculated from the purchase price. The formula for the calculation of periodic lease payments is: PLP = (LP - the first increased instalment) / t; PLP = the periodical lease payment; LP = the lease price; t = the number of months for which the leasing closed. Financial Leasing: The calculation of the recapitalized price depends on the following formula: RPL = PP xadvance × RP × t; RPL = the recapitalized price of leasing; PP = the purchase price; RP = the recapitalized percent; t = the time ofadvance. The calculation of the lease payments paid at the beginning of the year: The lease payments at the beginning of the year = RPL × the reduction of the interest rate. The calculation of the lease payments paid at the end of the year: The lease payments paid into year-end × RPL = the amortization. The reduction of the interest rate = 1 / (1 + i) n, i = the interest rate the amortization = (1 + i) n × i / (1 + i) n - 1. Operative Leasing Example 1: the Leasing of a Truck. The leasing company finances the subject of the lease (a Tatra truck - a highly versatile mobile heavy truck 8 × 8.1 R) from own sources. We will calculate the amount of the regular lease payments, provided the following. The cost of the truck is 217.984.70 EUR; the leasing company assumes the regular monthly instalments for a period of 6 years; the increase in the first instalment is 20 % of the purchase price and a 10 % leasing margin of the purchase price. First, we will calculate the total cost of leasing: The total cost of leasing = 217.984.70 EUR + 21.798.50 EUR = 239.783.20 EUR. The total cost of leasing is calculated by the cost of the truck (217.984.70 EUR) and leasing margin (10 %). The leasing margin is 10 % of the purchase price of the truck (0.10 × 217.984.70 EUR), so 21.798.50 EUR. The increase of the first lease payment: The increase of the instalment = 217.984.70 EUR × 0.20 = 43.596.90 EUR. The increase of the first lease paymentis 20 % of the purchase price of the truck (217.984.70 EUR × 0.20). The first lease payment will increaseby 43.596.90 EUR. The regular monthly lease payment: The periodic payment 239.783.20 EUR - 43.596.90 EUR = 196.186.30 EUR (which is the amount attributable to regular instalments). In the calculation of a monthly lease payments, we will subtract from the lease price (6.239.783.20 EUR) the increase of lease payment (43.596.90 EUR); then we will get the amount that falls on the regular monthly lease payments (196.186.30 EUR). 196.186.30 EUR / 72 = 2.724.80 EUR (the regular monthly lease payment). To calculate the periodic lease payments, we have to divide the amount we will get after first payment, deducting the increase in lease payments (196.186.30 EUR) by the number of months that the lease is finalized (6 years = 6 × 12 = 72 months). The regular lease payment is 2.724.80 EUR. The calculation of the first (increased) lease payment: 43.596.90 EUR + 2.724.80 EUR = 46.321.70 EUR. The first increased lease payment we will get by the sum of the regular monthly lease payments (2.724.80 EUR) and an increase in the first lease payment (43.596.90 EUR). The first increase of lease payment is 46 321.70 EUR. In the Tabl. 1 we can see that the total lease price is 239.783.20 EUR. The total lease term is 6 years, 72 months with regular monthly leasing instalments 2.724.80 EUR. The total amount of payments for each year is 32.697.60 EUR, except for the first year in which the total sum of instalments for 79.019.30 EUR. Table 1 The Leasing Plan Lease term (years) Number of months Regular monthly instalment (EUR) Increase of the first instalment (EUR) Total lease price (EUR) 1 12 2.724.80 43.596.90 79.019.30 2 12 2.724.80 0 32.697.60 3 12 2.724.80 0 32.697.60 4 12 2.724.80 0 32.697.60 5 12 2.724.80 0 32.697.60 6 12 2.724.80 0 32.697.60 Total 72 16.348.80 43.596.90 239.783.20 Here we have to increase first regular lease payments by 20 % of the purchase price of the truck, at 43.596.90 EUR. Finally, we can determine the leasing coefficient, which we calculate by dividing the lease price (239.783.20 EUR) cost (217.984.70 EUR). Leasing coefficient is 1.1. Financial Leasing Example 2: the Leasing of a Construction Machine. The leasing company finances the subject of the lease (a Tatra three - way tipper construction machine) through the credit company loan. We will calculate the amount of the lease payments, provided that we consider instalment: - it is paid at the end of the year; - it is paid at the beginning of the year. The leasing company provided construction machine with a purchase price 108.991.80 EUR to its lessee by finance leases. The leasing was closed with four annual instalments. The supplier requires an advance payment of 10.899.20 EUR which is to be paid four months before the machine is delivered. The recapitalized percentage is 10 %. The interest rate on the credit company is 15 %, while the leasing company requires a margin of 5 %. The redemption price at the end of the lease is assumed to be zero. Under certain circumstances, the leasing price can be still reduced by de-capitalization or increased by the recapitalization. The recapitalization applies when a leasing company has to e. g. back up the payment to producer for the purchase of property. The recapitalization percentage is derived from interest on loans for refinancing. The total amount of lease price is then given by the sum of the individual lease payments. The lease price includes: - the gradual repayment of the purchase price of the property; - the lessor's costs associated with the leased property (administrative costs associated with the lease); - the leasing lessor's margin. The calculation of the recapitalized price: The recapitalized price = 108.991.80 EUR + 10.899.20 EUR × 0.10 × (4/12) = 109.355.10 EUR. In the calculation of the recapitalized price we multiplied backup supplier (10.899.20 EUR) by recapitalized percentage (10 %) and the number of months during which the backup will take place before the delivery of construction machinery (4 months). The calculation of the lease payments paid at the end of the year: Lease payments = recapitalized price × the reduction of the interest rate (5 % + 15 %) = = 109.355.10 EUR × 0.38628912 = 42.242.70 EUR the reduction of the interest rate = (1 + i)n xi / (1 + + i)n - 1 = (1 + 0.2)4 × 0.2 / (1 + 0.2)4 - 1 = 0.38628912. In the Tabl. 2, we can see that the total lease price with payments paid at the end of the year is 16.897.80 EUR. For four years, we will pay each year at the end of the year payment of 42.242.70 EUR. Table 2 The Leasing Plan - Lease Payments Paid at the End of the Year Lease term (years) Number of payments Payment (EUR) Total lease price (EUR) 1 1 42.242.70 42.242.70 2 1 42.242.70 42.242.70 3 1 42.242.70 42.242.70 4 1 42.242.70 42.242.70 Total 4 168.970.80 168.970.80 The leasing coefficient is calculated by dividing the total lease price (168.970.80 EUR) the recapitalized price (109.355.10 EUR), which is 1.55. The calculation of the lease payments paid at the beginning of the year: The calculation of the instalment is the same like in the previous example - the recapitalized purchase price x payer (5 % + 15 %). Because we have started to pay off in the beginning of the year we must fix the reduction of the interest rate for one year. 42.242.70 EUR × the reduction of the interest rate = 42.242.70 EUR × 0.833 333 333 = 35.202.20 EUR the reduction of the interest rate = 1 / (1 + i) n = 1 / (1 + 0.2) 1 = 0.83 333 333. Tabl. 3 shows the leasing plan, which captures the instalments paid at the beginning of the year. Table 3 The Leasing Plan - the payment paid at the beginning of the year Lease term (year) Number of payments Payment (EUR) Total lease price (EUR) 1 1 35.202.20 35.202.20 2 1 35.202.20 35.202.20 3 1 35.202.20 35.202.20 4 1 35.202.20 35.202.20 Total 4 140.808.80 140.808.80 Here is the total leasing price 140.808.80 EUR. After a period of four at the beginning of the year will the payment be 35. 202.20 EUR. The leasing rate will be 1.29 (140.808.80 EUR / 109.355.10 EUR). The purpose of an operative leasing is to provide those services that are not an acquisition of the investment. It can include theservice of the leased asset at pre-agreed limits. The operative leasing contract is concluded for a relatively short period of time, which is usually much shorter than the useful life or amortization period. After the end of the lease, the subject of the lease remains as the property of the leasing company, unless otherwise agreed upon in advance. The calculation of instalments is in the fixedform, which shows an example 1. There is theleasing of a truck, which is determined by the periodic lease payments of 2.724.80 EUR for six years. The total cost of the lease is here 239.783.20 EUR. The total cost of leasing can be calculated as the difference between the total leasing price and the cost of the leased asset. The total cost of leasing a truck is 21.798.50 EUR. A financed lease is a standard financial lease with an option or obligation to purchase a leased thing. The product allows for the fast and simple acquisition of movable assets with a minimum of required documents with the distribution of payments over a longer period of time. We have shown financial leasing in example 2, where we can determine whether we want to pay the instalments at the beginning or at the end of the year. In example 2, we can see that it is better for the lessee to choose instalments that have to be paidat the beginning of the year. The instalment at the beginning of the year is 35.202.20 EUR, compared to the instalment of 42.242.70 EUR at the end of the year. The instalments are paid over four years, after which the lessee has the option or obligation to purchase the subject of lease, according to the predetermined conditions. As can be seen in the Figure, the leasing of movable objects has the largest representation of the commodity machines and equipment in the form of 27.8 %, 32.1 % for personal cars and 26.7 % for trucks. It is evident that even heavy equipment has its representation, whether it will be construction equipement, tractors, trucks and other machines, which are financed by leasing.
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