236 ESSAY ON PROBABILITIES. 



prudence of such a step must depend upon the fine 

 demanded for a renewal. In the case>f church leases, 

 I believe it could not often be desirable : and certainly 

 not if they are let so much below their value as has 

 been asserted. But if the fine demanded should be 

 exorbitant, it would then become cheaper to insure the 

 longest of the lives in possession than to pay the demand. 

 The premium for such insurance would be found as in 

 page 214, the value of an annuity on the longest of the 

 lives having been previously found in page 208. 



QUESTION. The average value* of a living is s per 

 annum, and the proper allowance to the incumbent for 

 the performance of the duties is v } the unavoidable 

 expenses at entrance are /for each new incumbent; and 

 the value of the life of the present incumbent is |A, 

 while that of the new incumbent will be |P. What is 

 the value of the perpetual advowson of such living? 



RULE. The value of a reversion of 3 /. per annum 

 after the death of A being found (by subtracting !A 

 from the value of a perpetuity), and multiplied by the 

 excess of s over v, will give the value of the perpetual 

 advowson, as it would be but for the expenses at entry. 

 For these, deduct the present value of a fine/, payable 

 at the end of the year in which each incumbent dies, 

 the value of each pound of which determined by di- 

 viding the reversion aforesaid by one year's purchase 

 more than |P. The difference is the net present value 

 of the advowson required. According to a frequent 

 practice of valuing advowsons, in which the expenses 

 at entrance are neglected, the buyer pays them twice 

 over, 



* This should include all real profits : for instance, the value of the par- 

 sonage house as a residence, considered as taken on a strict repairing lease. 



