Question

1. Davis Industries is considering two alternative machines. Machine A has an expected life of 4 years, will cost $10 million, and will produce net cash flows of $3 million per year. Machine B has a life of 10 years, will cost $13 million, and will produce net cash flows of $2.5 million per year. Inflation in operation costs, machine costs is expected to be zero, and the company’s cost of capital is 10. Which machine should Davis Industries select?

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.

Net Present Value (NPV) of MACHINE-A

Year	Annual Cash flow ($ in Million)	Present Value factor at 10%	Present Value of Annual Cash flow ($ in Million)
1	3.00	0.90909	2.73
2	3.00	0.82645	2.48
3	3.00	0.75131	2.25
TOTAL		3.16987	9.51

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

= $9.51 Million - $10 Million

= -$0.49 Million (Negative NPV)

Equivalent Annual Annuity (EAA) of MACHINE-A

Equivalent Annual Annuity (EAA) = Net Present Value / (PVIFA 10%, 4 Years)

= -$0.49 Million / 3.16987

= -$0.15 Million

Net Present Value (NPV) of MACHINE-B

Year	Annual Cash flow ($ in Million)	Present Value factor at 10%	Present Value of Annual Cash flow ($ in Million)
1	2.50	0.90909	2.27
2	2.50	0.82645	2.07
3	2.50	0.75131	1.88
4	2.50	0.68301	1.71
5	2.50	0.62092	1.55
6	2.50	0.56447	1.41
7	2.50	0.51316	1.28
8	2.50	0.46651	1.17
9	2.50	0.42410	1.06
10	2.50	0.38554	0.96
TOTAL		6.14457	15.36

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

= $15.36 Million - $13 Million

= $2.36 Million

Equivalent Annual Annuity (EAA) of MACHINE-B

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

= $2.36 Million / 6.14457

= $0.38 Million

DECISION

David Should select MACHINE-B, since it has the higher Equivalent Annual Annuity of $0.38 Million as compared to the Equivalent Annual Annuity of Machine-A.

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.