Question

A firm has two mutually exclusive investment projects to evaluate. The projects have the following cash flows:

Time	Cash Flow X	Cash Flow Y
0	-$90,000	-$75,000
1	35,000	30,000
2	60,000	30,000
3	70,000	30,000
4	-	30,000
5	-	10,000

Projects X and Y are equally risky and may be repeated indefinitely. If the firm’s WACC is 6%, what is the EAA of the project that adds the most value to the firm? Do not round intermediate calculations. Round your answer to the nearest dollar.

A.) Choose Project X , whose EAA = $

Answer 1

Equivalent Annual Annuity (EAA) – Project X

Year	Annual Cash Flow ($)	Present Value factor at 6%	Present Value of Cash Flow ($)
1	35,000	0.943396	33,018.87
2	60,000	0.889996	53,399.79
3	70,000	0.839619	58,773.35
TOTAL		2.673012	1,45,192.00

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $1,45,192.00 - $90,000

= $55,192.00

Equivalent Annual Annuity (EAA) = Net Present Value / [PVIFA 6%, 3 Years]

= $55,192.00 / 2.673012

= $20,647.87

Equivalent Annual Annuity (EAA) – Project Y

Year	Annual Cash Flow ($)	Present Value factor at 6%	Present Value of Cash Flow ($)
1	30,000	0.943396	28,301.89
2	30,000	0.889996	26,699.89
3	30,000	0.839619	25,188.58
4	30,000	0.792094	23,762.81
5	10,000	0.747258	7,472.58
TOTAL		4.212364	1,11,425.75

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $1,11,425.75 / $75,000

= $36,425.75

Equivalent Annual Annuity (EAA) = Net Present Value / [PVIFA 6%, 5 Years]

= $36,425.75 / 4.212364

= $8,647.34

DECISION

If the Projects have unequal lives, then the Project with the higher Equivalent Annual Annuity (EAA) should be selected. Therefore, the firm should Choose Project X, whose EAA = $20,647.87.

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.