Question

Zeta, Inc., has identified the following two mutually exclusive projects:

Year	0	1	2	3	4
Cash Flow A	-$20,500	10,500	15,500
Cash Flow B	-$20,500	5,700	10,500	12,000	15,500

Use both the equal lives method and the equivalent annuity method to determine which project the company should implement.

Discount Rate: 12%

Answer 1

Equivalent Annual Annuity (EAA) for PROJECT A

Period	Annual Cash Flow ($)	Present Value factor at 12%	Present Value of Cash Flow ($)
1	10,500	0.89286	9,375.00
2	15,500	0.79719	12,356.51
TOTAL		1.69005	21,731.51

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

= $21,731.51 - $20,500

= $1,231.51

Equivalent Annual Annuity (EAA)

Equivalent Annual Annuity (EAA) = Net Present Value / (PVIFA 12%, 2 Years)

= $1,231.51 / 1.69005

= $728.68

Equivalent Annual Annuity (EAA) for PROJECT B

Period	Annual Cash Flow ($)	Present Value factor at 12%	Present Value of Cash Flow ($)
1	5,700	0.89286	5,089.29
2	10,500	0.79719	8,370.54
3	12,000	0.71178	8,541.36
4	15,500	0.63552	9,850.53
TOTAL		3.03735	31,851.71

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

= $31,851.71 - $20,500

= $11,351.71

Equivalent Annual Annuity (EAA)

Equivalent Annual Annuity (EAA) = Net Present Value / (PVIFA 12%, 4 Years)

= $11,351.71 / 3.07735

= $3,737.38

DECISION

Zeta Inc. should implement PROJECT-A, since it has the higher Equivalent Annual Annuity of $3,737.38 as compared to the Equivalent Annual Annuity of PROJECT-B.

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.