Question

An investment costs $2,756 today and provides cash flows at the end of each year for 21 years. The investments expected return is 9.6%. The projected cash flows for Years 1, 2, and 3 are $194, $294, and $374, respectively. What is the annual cash flow received for each of Years 4 through 21 (i.e., 18 years)? Assume the same payment for each of these years. (Round answer to 2 decimal places. Do not round intermediate calculations).

Answer 1

Given about an investment,

initial cost = $2756

interest rate r = 9.6%

The projected cash flows for Years 1, 2, and 3 are $194, $294, and $374, respectively.

=> CF1 = $194

CF2 = $294

CF3 = $374

Let annual cash flow received for each of Years 4 through 21 be A.

So, PV of this cash flow at year 3 end using Annuity formula is

PV3 = PMT*(1 - (1+r)^-t)/r = A*(1 - 1.096^-18)/0.096 = 8.42A

So, equal PV of all cash flow today to investment to compute annual payment

=> Co = CF1/(1+r) + CF2/(1+r)^2 + CF3/(1+r)^3 + PV3/(1+r)^3

=> 2756 = 194/1.096 + 294/1.096^2 + 374/1.096^3 + 8.42A/1.096^3

=> Solving for A, we get A = $320.70

So, annual cash flow received for each of Years 4 through 21 = $320.70