Question

Project A requires an initial investment of $10,000 at t = 0. Project A has an expected life of 3 years with cash inflows of $6,000, $4,500, $6,500 at the end of Years 1, 2, and 3 respectively. The project has a required return of 9%. What is the equivalent annual annuity?

Answer 1

first let us find out the present value of the cash inflows:

present value factor = 1 /(1+r)^n

here,

r = 9%=>0.09

n = number of years =>1,2,3.

year	cash flow	discounting factor (present value factor)	discouted cash flow
1	$6,000	1 / (1.09) =>0.91743	$5,504.5872
2	$4,500	1/(1.09)^2 =>0.841680	$3,787.56
3	$6,500	1/(1.09)^3 =>0.77218	5,019.19
		Total present value	$14,311.33

equivalen annual annuity = total present value of cash inflow / present value of annuity factor

present value of annuity factor = [1- (1+r)^-n] / r

=>[1 - (1.09)^(-3)]/0.09

=>0.2278165/0.09

=>2.53129.

equivalent annual annuity = $14,311.33 / 2.53129

=>$5,653.77....(rounded to two decimals).