Substituting into the pv formula yields pv c1 1 g c1 1

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Unformatted text preview: nity cost of capital Since the cash flow is growing at a constant rate g it implies that C2 = (1+g) · C1, C3 = (1+g)2 · C1, etc. Substituting into the PV formula yields: PV C1 (1  g )C1 (1  g ) 2 C1   " (1  r ) (1  r ) 2 (1  r ) 3 Utilizing that the present value is a geometric series allows for the following simplification for the present value of growing perpetuity: (8) PV of growing perpetituity C1 rg Annuity An asset that pays a fixed sum each year for a specified number of years. The present value of an annuity can be derived by applying the principle of value additivity. By constructing two perpetuities, one with cash flows beginning in year 1 and one beginning in year t+1, the cash flow of the annuity beginning in year 1 and ending in year t is equal to the difference between the two perpetuities. By calculating the present value of the two perpetuities and applying the principle of value additivity, the present value of the annuity is the difference between the present values of the two perpetuities. Asset 0 1 Year of Payment 2….…….t t +1…………... C r Perpetuity 1 (first payment in year 1) Perpetuity 2 (first payment in year t + 1) §C · 1 ¨¸ t © r ¹ (1  r ) § C · § C ·§ 1 ¨ ¸  ¨ ¸¨ t ¨ © r ¹ © r ¹© (1...
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