Perpetuities and Annuities - Corporate Finance - Ivo Welch
Perpetuities and Annuities - Corporate Finance - Ivo Welch
Perpetuities and Annuities - Corporate Finance - Ivo Welch
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Growing <strong>Perpetuities</strong><br />
A growing perpetuity pays CF , then CF · (1 + g), then CF · (1 + g) 2 , then ... For<br />
example, if CF = $100 <strong>and</strong> g = 0.10 = 10%, then you will receive the following<br />
payments:<br />
CF0 = 0 = $0 (no discount)<br />
CF1 = $100 = $100.00 (then discount with r0,1)<br />
CF2 = $100 · (1 + 10%) = $110.00 (then discount with r0,2)<br />
CF3 = $100 · (1 + 10%) 2 = $121.00 (then discount with r0,3)<br />
CF4 = $100 · (1 + 10%) 3 = $133.10 (then discount with r0,4)<br />
CF5 = $100 · (1 + 10%) 4 = $146.41 (then discount with r0,5)<br />
<strong>and</strong> so on, forever<br />
The PV of a growing perpetuity can be quickly computed as<br />
∞ CF1 · (1 + g)<br />
PV = ∑<br />
t=1<br />
t–1<br />
(1 + r) t = CF1<br />
(r – g)<br />
You must memorize the RHS formula, <strong>and</strong> know what it means!<br />
◮ The growth term acts like a reduction in the interest rate.<br />
◮ The time subscript for the payment matters now, because C1 = C2.<br />
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