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# Lease

## rent, value, sum, money, annual, estate and table

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LEASE, a conveyanCe of lands, or tene ments, for a term of years, or during the continuance of a life or lives, in consider ation of a stipulated rent or other recom pense.

The purchaser of a lease may be con sidered as the purchaser of an annuity equal to the rack-rent, for whether he possesses the estate himself, or lets it out to another, he has an interest in the same equal to the annual rent thereof ; there fore, from the principles on which the present value of annuities is ascertained, the value of leases is likewise found. When a certain sum is paid down for the grant of a lease, it may be considered as so much money paid in advance for the annual rents as they may become due; therefore, in order to ascertain what the sum ought to be, it would be necessary to find, separately, the present value of each annual rent, or the sum which, put out to interest at the given rate, would amount to the rent at the time it became due ; and these separate values of each year's rent added together would give the sum to be paid down as the present value of the lease. The rate of interest at which money is supposed to be improveable, affects the value of leases very materially, as the higher the current rate of interest is, the less will any one be disposed to give for payments to be received atfuture periods : thus if 6 per cent interest can be readily obtained for money, no one will give the same sum for a certain year ly rent, as if he could only make 4 per cent. interest of his money. Having then determined on the rate of interest at which money is to be improved, it is only necessary to find, at that rate of interest, the present value of an annuity equal to the net yearly rent of the estate, in order to ascertain the value of the lease. This is given, at 5 per cent. interest, in Table II. article ANNUITIES : but as most per sons in the purchase of leases, particular ly of houses, expect to make rather more than the current interest for money, the following table is better adapted for an swering all practical questions relating tc this subject.

In order to find the value of a lease for any term, the true rack rent of the estate, or the annual value that it may be justly estimated to be worth, must be first ascertained ; otherwise it will be im possible to determine, with any degree of accuracy, the real sum which ought to be given for the purchase of the same ; for :as the values in the Table denote merely the number of years purchase, it is evi dent that the sum deduced therefrom will vary according as the annual rent of the estate varies. On this point, dif ficulties will sometimes arise ; for the value of an estate, depending very often on some real or supposed advantages, or on some local or personal recommen dations, will, in many instances, occa sion a difference of opinion ; and, in most cases, be a matter of some uncertainty. Some annual rent must, however, be fix ed upon as the full sum for which the estate would let, and this rent being multiplied by the sum in the Table, cor responding with the term of years, gives the present value of the lease. Thus, if a house lets for 50/. per ann. to find the value of a lease thereof for 21 years, reckoning interest at 6 per cent. multi ply 50 by 11,764 (the sum in the ta ble corresponding with 21 years) which gives the answer 5881. 48. It frequently happens that the rent of an estate is charged with some annual expense, such as a reserved or quitrent, the payment of an annuity, taxes, and the like ; in such cases, the various charges must be first deducted from the rent received, and the remainder, or nett-rent, only be multiplied by the number of years pur chase in the table.

Example. A person holds a lease, for 35 years, of premises which let for 1201. per annum, out of which he pays 171. 10s. for ground-rent, and 41. 10s. for land.tax ; what should lie require for the lease, allowing the purchaser to make 7 per cent. interest of his money ? The payments to which the rent is subject be ing deducted,leave a nett-rent of 98/. which multiplied by 12,948 (the sum in the ta ble corresponding with 35 years) gives 1268/ 18s.

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