PERPETUITIES ďƒ˜ Perpetuities is an annuity whose payments continue forever. ďƒ˜ Present value of a perpetuities-immediate : đ?‘Žâˆž| = đ?‘Ł + đ?‘Ł + đ?‘Ł + . . . = = =
đ?‘Ł −đ?‘Ł đ?‘Ł đ?‘–đ?‘Ł đ?‘–
ďƒ˜ Perpetuity-due can be derived as : đ?‘Žâˆž| =
+đ?‘– = đ?‘– đ?‘‘
ďƒ˜ Accumulated values for perpetuities do not exist.
PERPETUITIES Example 1:
Suppose a company issues a stock that pays a dividend at the end of each year of $10 indeďŹ nitely, and the companies cost of capital is 6%. What is the value of the stock at the beginning of the year? Solution : 10đ?‘Žâˆž|= 10 .
= $166.67
. 6
PERPETUITIES Example 2: What would you be willing to pay for an inďŹ nite stream of $37 annual payments (cash inows) beginning now if the interest rate is 8% per annum?
Solution : 37 đ?‘Žâˆž| = 7 .
. 8 . 8
= $ 99.