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The Worth of Lives








Author of "The Doctrine of Chances.”


The following Letter is published with no other view than that of being useful to those whom the nature of i may interest. With the best recommendation, its own merit, I submit it to public consideration.

Woodbridge, August 31, 1815.




Hasketon, August 4, 1815.

ACCORDING to my promise, I now submit to your judgment some remarks on the comparative value of freehold and copyhold land.

It is always presumed that an acre of freehold and an acre of copyhold land are of equal value to a tenant from year to year. If there are any buildings, or quit-rents, or indeed any outgoing or income not common to both species of property, they should be separately considered and distinctly valued, so as to leave the copyhold land, and the freehold land, subject only to an equal and clear yearly income for each acre. We are then to consider how many years' rental of an acre will be an equivalent to the lord to enfranchise it; but this will be influenced by his mercy as to the fine; however, leaving this attribute out of the calculation, he shall be allowed the utmost that equity will suffer him to take, being two years' rent on every alienation.

If no fine were to be paid, except at death, it must be evident that the older the lives are, when admitted, the more valuable the copyhold will be to the lord, who, like a good christian, makes no distinction of persons,-exacting the same from the man of 80, as from the man of 20 years of age, although one life is worth upwards of 16 years' purchase, and the other not three years and a half.

Let us suppose, that the lives, one with another, when admitted, are each equal in value to a life of 44 years of age, (which supposition, I think, is in favor of the lord), and computing interest of money at 4 per cent. (chancery interest) such a life is worth nearly 12 years and a half's purchase (by the Northampton tables of lives). If the rent is 501. a-year, he will be entitled to 1001. in present money on admitting a life of 44 years of age; and to another 1001. when this life falls, on admitting a 2nd life, then 44; and to another 100l. when the second life falls, on admitting a 3rd life, then 44; and so on ad infinitum.

The present value of all those sums (which will be an equivalent to the lord for enfranchisement) is very easily ascertained, for, the present value of any sum to be received on the death of a person, is found, by merely subtracting the value of the life from the perpetuity.

Now each sum to be received is 100l. which, computing interest at 4 per cent, is equal to, or worth, a perpetuity of 41. per annum, and if the value of a life aged 44 is deducted, (being nearly 12 years' purchase, or 501.), the difference, or 501. in present money, is an equivalent to the lord for 1001. not to be paid until the 1st life drops, or the 2nd life is admitted. Now this value is exactly one half of the 1st fine, (or the 1001. paid down), and as the same sum, or 50l., if it were to be paid when the 2nd life is admitted, would be an equivalent to the lord for the 1001. due when the next, or 3rd life, is admitted,—if half of

that 501. or 251. is paid now, it will be an equivalent for the 1001. fine due on the 3rd life; and reasoning in the same manner, 121. 10s. Od. is the present value of the 1001. fine due on the 4th life, 61. 5s. Od. for the fine due on the 5th life, and so on, taking the half of each value for the succeeding life. But it must appear manifest, that in this manner you will soon arrive at a sum so small as to be considered equal to nothing. By an easy rule in arithmetic, the sum of all the terms in a regular series may be soon found, and all the terms of this series, decreasing in the ratio, 1..

.... &c. &c. until the terms become too small to be noticed, will amount to 2: therefore, as 1 fine (or 100l.) was the first term, and of it the second term, and so on in the same ratio, a full equivalent for all the fines that, in human probability, will ever be received, (computing at 4 per cent. interest) is two fines, or 2001. and the fine, being 2 years' rent, 4 years' purchase is an equivalent to the lord for enfranchising copyhold land: that is, if each fine depend ed on death; and as the 4 years' purchase includes the fine on admission, if a life is already upon it, the value of such life ought to be deducted from the 4 years' purchase; but the quit rents should be computed at 25 years' purchase, and added to the above value of enfranchisement.

This is on the supposition that no fine takes place, except on death, and that each succeeding life is one of 44 years of age, when admitted.

Now 501. in present money, has been shown to be an equivalent for 1001. not to be received until a person now 44 years of age dies; and it also may be seen in the tables of compound interest, that 501. now paid down, is an equivalent for 1001., to be paid certain at the end of 17 years and a half, (in all cases computing at 4 per cent. interest): therefore, a lord would be entitled to the same present sum, or 501., whether as an equivalent for 1001., to be paid

when a Man, aged 44, dies, or for 100l. to be paid certain at the end of 17 years and a half. If we suppose that land changes proprietors every 13 years, (instead of changing on the extinction of a life of 44, or its equivalent, in 17 years) taking Deaths and Sales together, (and I trust you will think this a favourable estimate for the Lords of Manors) in such Case, the Lord is to receive now one fine, or 1001. and will be entitled to the same sum at the end of every 13 succeeding years, for ever; therefore 100l. added to the respective present values of 100l. to be received at the end of 13, 26, 39, 52, 65, 78, &c. years, ad infinitum, will be an equivalent for all the fines that can ever be received by the Lord or his successors: -a few of these Sums are,

100l.601.361.1s. 4d.-211. 13s. 3d.-131. Os. 2d.-71. 16s. 3d. -41. 13s. 10d.-21. 16s. 5d. &c. (as may be seen in the common Interest Tables): and the amount of all these values, if continued until they become so small as to be considered equal to nothing, is, by the same Rule, found to be Two fines and a half': therefore, if the rent is 50l. per Annum, and 2 years' Rent is demanded for a Fine, a Man ought to pay 5 years? Rent to enfranchise the Land, besides 25 years' purchase for the Quit-Rent; but as this 5 years' Rent includes the Fine on Admission; if a Life is upon it, the value of such Life ought to be deducted from the 5 years' purchase. I think therefore, in computing the values of Copyhold and Freehold Land, (after deducting the Quit-Rents, &c. so as to leave an Acre of Copyhold, and an Acre of Freehold, of equal value except as to Fine), if a difference of 5 years' purchase is made between them, such will be an equitable calculation.

On these Principles I have computed the respective values of the Copyhold and Freehold parts of the following Estate, consisting of 230 Acres of Land, whereof 125 Acres, with the House and Buildings, are Freehold, and the remaining 105 Acres are Copyhold, subject to a Quit-Rent of 61. per Annum, and a Fine of 2 years' Rent on Alienation: the

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