Question

Firm BCD has the opportunity to invest in one of two mutually exclusive machines, which can both produce the same product. Machine A has a life of 9 years, costs $12 million and will produce after-tax inflows of $2.5 million per year at the end of each year. Machine B has a life of 7 years, costs $15 million and will produce after-tax inflows of $3.5 million per year at the end of each year. Assuming that the machines can be replaced indefinitely at constant prices, which machine should BCD choose? Assume a cost of capital of 12%.

Answer 1

In the given Case Life of Both the Machines are Different, therefore first we calculate Net Present Value of each machine, and then its equated annual value, to determine which machine shoud be selected.

Calculation of NPV of Machine A:

NPV = Present Value of Cash Inflow - Present Value of Cash Outflow

Present Value of Cash Inflow = Annual Cash Inflow * PVAF (r%, n year)

PVAF (r%, n year) is the annuity factor where r% is rate of interest and n refers to number of years.

PVAF(12%,9 years) = (1+r%)ⁿ-1/ (r%* (1+r%)ⁿ)

= (1+0.12)⁹-1/ (0.12*(1+0.12)⁹)

= 2.773078757-1/(0.12*2.773078757)

=1.773078757/0.332769451

= 5.3282

Present Value of Cash Inflow = 2.5*5.3282

= $ 13.3205 million

NPV = 13.3205-12

= $ 1.3205 million approx.

Calculation of NPV of Machine B:

NPV = Present Value of Cash Inflow - Present Value of Cash Outflow

Present Value of Cash Inflow = Annual Cash Inflow * PVAF (r%, n year)

PVAF (r%, n year) is the annuity factor where r% is rate of interest and n refers to number of years.

PVAF(12%,7 years) = (1+r%)ⁿ-1/ (r%* (1+r%)ⁿ)

= (1+0.12)⁷-1/ (0.12*(1+0.12)⁷)

= 2.210681407-1/(0.12*2.210681407)

=1.210681407/0.265281769

= 4.5638

Present Value of Cash Inflow = 3.5*4.5638

= $ 15.9733 million

NPV = 15.9733-15

= 0.9733 million

Calculation of Equated Annual Value:

Particular	Machine A	Machine B
NPV (A)	1.3205 million	0.9733 million
PVAF (B)	5.3282	4.5638
Equated Annual Value (A/B)	0.2478 million	0.2133 million

Therefore Machine A should be selected.