Question

Faleye Consulting is deciding which of two computer systems to purchase. It can purchase state-of-the-art equipment (System A) for $22,000, which will generate cash flows of $6,000 at the end of each of the next 6 years. Alternatively, the company can spend $14,000 for equipment that can be used for 3 years and will generate cash flows of $6,000 at the end of each year (System B). If the company’s WACC is 10% and both “projects” can be repeated indefinitely, which system should be chosen, and what is its EAA? Do not round intermediate calculations. Round your answer to the nearest cent.

Choose Project (A or B), whose EAA = $_____  

Answer 1

Evaluation of Investment proposal using Equivalent Annual Annuity (EAA) Rule

-Here, the both Projects have different useful lives and therefore, the decision can be made on the basis of Equivalent Annual Annuity (EAA)

-The Equivalent Annual Annuity (EAA) should be always preferred if the Projects has the different lives or unequal lives. Since, the EAA gives the exact annual net worth of the project whereas the NPV shows the total worth to the shareholders.

Equivalent Annual Annuity (EAA) of PROJECT-A

Net Present Value (NPV) of Project-A

Year	Annual Cash flow ($)	Present Value factor at 10.00%	Present Value of Annual Cash flow ($)
1	6,000	0.909091	5,454.55
2	6,000	0.826446	4,958.68
3	6,000	0.751315	4,507.89
4	6,000	0.683013	4,098.08
5	6,000	0.620921	3,725.53
6	6,000	0.564474	3,386.84
TOTAL		4.355261	26,131.56

Net Present Value (NPV) = Present value of annual cash inflows – Initial investment costs

= $26,131.56 - $22,000

= $4,131.56

Equivalent Annual Annuity (EAA) of PROJECT-A

Equivalent Annual Annuity (EAA) = Net Present Value / (PVIFA 10%, 6 Years)

= $4,131.56 / 4.355261

= $948.64

Equivalent Annual Annuity (EAA) of PROJECT-B

Net Present Value (NPV) of Project-B

Year	Annual Cash flow ($)	Present Value factor at 10.00%	Present Value of Annual Cash flow ($)
1	6,000	0.909091	5,454.55
2	6,000	0.826446	4,958.68
3	6,000	0.751315	4,507.89
TOTAL		2.486852	14,921.11

Net Present Value (NPV) = Present value of annual cash inflows – Initial investment costs

= $14,921.11 - $14,000

= $921.11

Equivalent Annual Annuity (EAA) of PROJECT-B

Equivalent Annual Annuity (EAA) = Net Present Value / (PVIFA 10%, 3 Years)

= $921.11 / 2.486852

= $370.39

DECISION

Choose Project A, whose EAA = $948.64

We should select PROJECT-A, since it has the higher Equivalent Annual Annuity of $948.64 as compared to the Equivalent Annual Annuity of Project-B.

NOTE

The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Discount Rate/Cost of capital and “n” is the number of years.