Question

You are considering a project that needs $50,000 investment to start. This is a 5 year project and you are expecting that the project generates annual cash flows after taxes of $10,000, $50,000, $90,000, $20,000 and -$30,000 respectively. What is the EAA of this project if the required rate of return is 8%? Round to the penny. Do not include the dollar sign. If there are multiple answers, then type NA.

Answer 1

Solution :-

Equivalent annual annuity (EAA) of project = NPV of Project / Cumulative present value factors for five years at 8 % rate of return.

NPV (Net present value) of the Project = Present value of cash inflows - Present value of cash outflow.

Present value of cash inflows = 10000 / (1 + 0.08)1 + 50000 / (1 + 0.08)2 + 90000 / (1 + 0.08)3 + 20000 / (1 + 0.08)4 + (-) 30000 / (1 + 0.08)5

= 10000 / (1.08)1 + 50000 / (1.08)2 + 90000 / (1.08)3 + 20000 / (1.08)4 - 30000 / (1.08)5

= 10000 / 1.08 + 50000 / 1.1664 + 90000 / 1.2597 + 20000 / 1.3605 - 30000 / 1.4693

= (9259.26 + 42866.94 + 71445.58 + 14700.48) - 20417.89

= 138272.26 - 20417.89

= 117854.37 (approx)

Present value of cash outflow = $ 50,000. (Given in the question).

Accordingly, NPV of Project = 117854.37 - 50000

= $67854.37 (approx)

Cumulative present value factors for five year at 8 % = [ 1 - (1 + r)-T ] / r

= [ 1 - (1 + 0.08)-5 ] / 0.08 (Where r = rate of return and T = Number of years)

= [ 1 - (1.08)-5 ] / 0.08

= (1 - 0.6806) / 0.08

= 0.3194 / 0.08

= 3.9925 (approx)

Accordingly, Equivalent annual annuity (EAA) of project = 67854.34 / 3.9925

= 16995.46 (approx).

Conclusion :- Equivalent annual annuity (EAA) of the project = 16,995.46 (approx).