In most cases, you look at financial leasing, from its merely theoretical point of view, but sometimes it is necessary to show its mathematical-financial connotation, which is of great importance for decision-making.
As is known, one of the forms of financing that the company can use is financial leasing, which allows them to use capital goods that are not owned by them, but have been leased to them, with the option of purchase upon expiration of the lease.
Normally, in a leasing contract, capital goods that are required by third parties are acquired and delivered at a cost, which is paid periodically by a rental fee.
Functionality
In many cases it is much better to obtain capital goods through the lease than to acquire them in their entirety
It is customary to include the following clauses in favor of the lessee in the lease:
- The option of acquiring the capital asset object of the contract upon its expiration, for a price that is almost always defined prior to the signing of the contract and for a value lower than market value. Extending the contract for an additional time, with a lease fee lower than the one initially agreed.Return the capital asset to the lessor at the expiration of the contract.Dispose the asset, in favor of a third party.
The lease can be paid overdue period or early period, therefore there are two ways from the mathematical-financial point of view that will be analyzed below.
Leasing paid in past due periods
If a financial leasing contract is carried out, in which the cost of the property is determined by $ C and by which the lessee agrees to pay a monthly rental fee of $ R, for n months and at the expiration of the contract, the lessee has the option to acquire the property for $ S. If the landlord wants to earn a rate i. The value equation will be mathematically:
C = R an¬i + S (1 + i) -n
The above can be clearly seen by preparing a table for a leasing for such a situation.
Example
The cost of a capital asset of $ 800,000, with a duration of six months and with a purchase option value at the expiration of the contract, equivalent to 10% of the cost value. Assume a rate of 4% effective monthly and that the lease fee is past due.
Solution
The value equation is given by:
800,000 = R a6¬4% + 80,000 (1 + 0.04) -6
R = 140,548.57
The payment made by the company for the financial leasing of assets represents an expense and is therefore tax deductible, producing a tax benefit
The leasing table is equal to an amortization table:
|
n |
Option to buy |
Interest |
Canyon |
Amortization |
|
0 |
800,000 |
|||
|
one |
691,451.43 |
32,000 |
140,548.57 |
108,548.57 |
|
two |
578,560.92 |
27,658.06 |
140,548.57 |
112,890.51 |
|
3 |
461,154.79 |
23,142.44 |
140,548.57 |
117,406.13 |
|
4 |
339,052.41 |
18,446.19 |
140,548.57 |
122,102.38 |
|
5 |
212,065.94 |
13,562.10 |
140,548.57 |
126,986.47 |
|
6 |
80,000 |
8,482.64 |
140,548.57 |
132,065.93 |
Leasing paid in advance periods
If a financial leasing contract is made, in which the cost of the property is determined by $ C and by which the lessee agrees to pay a monthly rental fee of $ R, for n months payable at the beginning of each month. Upon expiration of the contract, the lessor has the option of acquiring the property for $ S. If the landlord wants to earn a rate i.
it must be taken into account that, if the lease fee is advanced, the first payment will be made in period zero; that is, it covers the period from 0 to 1 and the last payment is made in n - 1 and corresponds to the period that begins in n - 1 and ends in n. Furthermore, since n corresponds to the expiration of the contract, this is where the purchase option for $ S is.
Then the value equation will be mathematically:
C = R än¬i + S (1 + i) -n
C = R an¬i (1 + i) + S (1 + i) -n
Faced with this type of leasing payment and applying it to the previous example, the lease fee will be:
800,000 = R a6¬4% (1 + 0.04) + 80,000 (1 + 0.04) -6
R = 135,142.86
In period zero, the table starts with a purchase option of:
S = 800,000 - 135,142.86
S = 664,857.14
Therefore, only five leases remain to be paid, plus the final purchase option:
|
n |
Option to buy |
Interest |
Canyon |
Amortization |
|
0 |
664,857.14 |
|||
|
one |
556,308.57 |
26,594.29 |
135,142.86 |
108,548.57 |
|
two |
443,418.05 |
22,252.34 |
135,142.86 |
112,890.52 |
|
3 |
326,011.91 |
17,736.72 |
135,142.86 |
117,406.14 |
|
4 |
203,909.53 |
13,040.48 |
135,142.86 |
122,102.38 |
|
5 |
76,923.05 |
8,156.38 |
135,142.86 |
126,986.47 |
|
6 |
0 |
3,076.95 |
80,000 |
76,923.05 |
The lessee cannot calculate the IRR in a leasing contract, since the calculation of a IRR requires that there be income and expenses and the lessee only has expenses; however, if the income generated by such a good is taken into account, then it is feasible to calculate an IRR.
In the case of the lessor, if a IRR of the leasing can be calculated, since his expense is the cost of the good that is purchased and his income is the rental lease that he receives, plus the purchase option.
From the above it follows that, if the lessee wishes to evaluate investment alternatives, where one of them is a leasing, the use of the VPN may be more advisable than the IRR.
