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purchase-money is 84001. and the whole is let to a tenant at 3601. per annum-There is no timber on the estate, subject to valuation.-What are the respective values of the copyhold part, and of the freehold part, supposing 5 years' purchase a just difference between the value of an acre of copyhold, and the value of an acre of freehold land?
The Buildings, if considered distinctly from the land, are estimated to be worth a rental of 201. per annum, and as money vested in buildings should bear a greater interest than when vested in land, I think this part of the freehold property ought to be valued at 4001. (or 5 per cent.) which reduces the purchase-money to 8000l. and the income to 3401. per annum for 230 acres of land of supposed equal yearly value to a tenant: if this income is divided in the same proportion as the freehold and copyhold Land is divided, we shall find that £155.2172 or 155l. 4s. 4d. is the rent for the 105 acres of copyhold land, and 1841. 15s. 8d. is the rent for the 125 acres of freehold land; but as the quit-rent attaches entirely to the copyhold part of the property, 61. must be deducted from the 155l. 4s. 4d. leaving 1491. 4s. 4d. for the rental of the copyhold land; and this reduces the income to 3341. per annum, for which 80001. has been paid. The respective portions of land, acre for acre, are now brought to equality; (except as to the lord's fine, which is admitted to make a difference in value of 5 years' rental), for every other consideration, as Land-Tax, &c. are common to both species of property.'
When the number of years' purchase is known that the copyhold part is worth; by multiplying such income by that number of years we have the whole value of the copyhold land (whether 1 acre or 1000 acres); and if the freehold
'It is my opinion that quit-rents are subject to the Land-Tax, as far as 4s. in the pound, the lord is considered as the first landlord; for fee farm rents of the crown are subject to Land-Tax.
income is multiplied by the same number of years, adding to the product 5 times such yearly income of the freehold part, this will give the whole value of the freehold land (whether 1 acre or1000 acres) which, in this case, must amount together to 8000l. Now if the land was all freehold, or all copyhold, by dividing the 80001. by the annual income, the quotient would express the number of years' purchase; and as the difference to be made, is known, being 5 times 1841. 15s. 8d. or 923l. 18s. 4d.; if this is deducted from 8000l., and the remainder, or 70761. 1s. 8d. is divided by the whole annual income, being 3341.; the quotient will express the number of years' purchase for the copyhold part: then, agreeably to the condition of the question, 5 years added, will express the number of years' purchase for the freehold part: this is easily done by using decimals:-for the sum to be divided is £7076·086; the divisor 3341. ; and the quotient 21-1859, or 21 years and nearly of a year's purchase for the copyhold income; and 26.1859 years' purchase for the freehold income; and this answers the question for if 1491. 4s. 4d. or more correctly its true decimal expression, £149.2172 (the copyhold income) is multiplied by 21-1859 years, the product £3161.3006, or 31611. 6s. Od. is the true value of the copyhold part; and if £184-7828 is multiplied by 26-1859 years' purchase, the product, or 48381. 14s. Od. is the true value of the freehold
Note. In using decimals (but it may be needless to name it to you), the figures on the right hand of the full point signify the decimal parts of 1 or an unit, whether 1 pound, or 1 year, or indeed whatever the figures on the left hand of such full point may stand for: thus, 21-185 years, signify 21 years and 1 tenth part, and 8 hundredth parts, and 5 thousandth parts of ne year; that is, every unit in decimals, is a tenth part of 1 unit that precedes it; and when applied to money, every unit in the first place of a decimal, is equal to 2 shillings, and if every unit in the second place is called 2 pence halfpenny, and every unit in the third place 1 farthing, this will be near enough for common practice.
land ; to this must be added the value of the freehold buildings, or 4001.-making together 52381. 14s. Od. for the value of the freehold part of the property, which, added to the copyhold value, amounts to 84001. being the whole purchase-money, as in the question.
The reasoning on copyhold fines equally applies to disco. ver the present value of the next presentation, or any number of succeeding presentations to a living, or the value of the perpetual advowson, which I will illustrate by the following question.-If a living of £ per annum is worth 2000l. to every incumbent who enters upon it, at 30 years of age; (which we may here suppose will be the age that a person buy. ing such a right, would present), what is the present value of the three next presentations, also each value respectively and the value of the perpetual advowson; supposing the present incumbent to be 70 years of age, and that each succeeding incumbent will enter upon it at 30 years of age?
Computing the interest of money at 4 per cent. per an num, 20001, is equal to, or worth, a perpetual income of 801. per annum; but this sum will not be due until a life, now 70 years of age, is extinct; therefore, deducting the value of the incumbent's life, at the same rate of interest, which is 6.361 years' purchase of 801. or 5081. 17s. 7d.— the difference, being 14911. 2s. 5d. is the present value of the first presentation; for this is an equivalent for 2000l. to be paid, when a person, now 70 years of age, dies. Reasoning in the same manner, when the present incumbent dies, we shall have to pay an equivalent for 2000l. that will be due, when the then incumbent of 30 dies; therefore we ought now only to pay what will amount to such an equiva ent, when the present life of 70 drops. If this life be supposed extinct, and the first incumbent of 30 presented, an equivalent for the 2nd presentation of 30 would be found by merely deducting the value of the then
incumbent's life of 30, being 14-781 years' purchase of sol. from the perpetuity, or its worth, 20001.: but as the above difference 14911. 2s. 5d. or its decimal, ₤1491.12 now paid in money, is an equivalent for 2000l. to be paid when a life of 70 drops; if we now deduct the value of a life of 30 from a perpetual income, worth £1491∙12 (and which at 4 per cent. is found by dividing the sum by 25, the number of years' purchase for a perpetuity), it will be the same as deducting the value of a life of 30, from a perpetual income, worth 2000l. when a life of 70 dies. Now part of £1491.12 is £59.645; and 14-781 times this sum, or £881.6127, is the present value of 801. a-year during a life that will be 30 years of age when a life now 70 is extinct, but the annuity not to take place until that period. And this value deducted from £1491·12 the difference, being £609-5073, is the present value of the second presentation of a life to be then 30 years of age. Thus reasoning on part of this £609.5073 (which is the remainder of the 2000l. after the values of a present life of 70 and a future life of 30 are deducted), or £24.38029, being a perpetual income of present enjoyment, equal in value to a perpetual income of 801. a-year, which is not to be entered upon until the extinction of two successive lives, the first now 70, and the second will be 30 when the first dies; therefore 14.781 times £24.38029 or £360.36278 is the present worth of 801. a-year during a life that will be 30 years of age when the above two successive lives are extinct; and this value, deducted from 609.5073, (the above remainder), being £249.1445, is the present value of the 3rd presentation of a life, to be then 30 years of age. And the present values of the 3 next presentations, to begin at the death of the incumbent, now 70 years of age, and according to the question, that each of the 3 lives shall be so years of age when presented, are as follow:
Present value of the first presentation . 1491.. 2.. 5
Total present value of the 3 presentations, l. 2349.. 15.. 4
Thus we see, that in successive lives, the present value of each, (or of an annuity to continue during each respectively) is found to be the number of years' purchase (answering to the life) of a perpetual income, corresponding to each remainder of 20001., (or any other sum) respectively; and each remainder is the present value of the 2000l. to be paid when all preceding lives are extinct; for example, £24.38029 is the perpetual income corresponding with the remainder £609.5073, and 14-781 times £24.3829 has been found equal in value to so many times 801. if it is not to be paid until two successive lives, (one now 70 and the other that will be 30, when the first dies), are both extinct and this remainder, or the worth of the perpetual income of £24.38029 per annum, being £609•5073 now paid in money, is an equivalent for 2000l. to be paid, when the same two successive lives are extinct.
If all the successive incumbents are supposed of equal ages at the times of presentation respectively, the present values of their lives in succession, and the present values of their respective presentations, will each form a regular geometrical series, (one being deduced from the other) and the sum of each series is very easily found. The sum of the present values of the respective presentations, ad infinitum, will be the present value of the perpetual advowson ; and the sum of the present values of annuities of 801. during the lives of each in succession, ad infinitum, will be the present value of a perpetual income of 801. or amount to its worth, that is 20001. This will appear plain by each of the following series £1491 12-£609:5073--