Question

Problem 1 Suppose there is a series of cashflows that lasts n + 1 periods, {at}t , 0 ≤ t ≤ n, and that is growing at constant rate g, i.e. at = (1 + g) ta0, ∀t. The discount rate is fixed at r and assume g < r. Find an expression for the discounted present value of the cashflows at time 0. Formally, find an expression for S = a0 + a1 1+r + ... + an (1+r) n

Problem 1 Suppose there is a series of cashflows that lasts n + 1 peri- ods, {at}+, 0 <t<n, and that is growing at constant rate g, i.e. Qt = 1 + g'ao, Vt. The discount rate is fized at r and assume g <r. Find an expression for the discounted present value of the cashflows at time 0. Formally, find an expression for S = 20 + 4 + ... + 14mn

Answer 1

discounted value of flon (at) cash at time at cash flon rate s is growing With annually Eill period (h1) cash Aow We have Present valu of all ash fim nts ab(+s) 9 /1t9 a.citg)2 aot (+Y) Cln ao 1 + + 11 1+Y

Arsume i +Y a. +pip'rtpJ Et- p 1 nti

1t9 7 + Y G o As Ro 1Y Sニ Y