Question

Bruno's is analyzing two machines to determine which one it should purchase. The company requires a rate of return of 14%. Machine A has a cost of $290,000, annual operating costs of $8,000, and a 3-year life. Machine B costs $180,000, has annual operating costs of $12,000, and has a 2-year life. Whichever machine is purchased will be replaced at the end of its useful life. Which machine should Bruno's purchase and why?

Answer 1

When different machines have different useful life, then equivalent annual cost of each alternative is taken as basis for decision making.

Machine A

Machine B

Cost of Machine

a

$ 2,90,000.00

$ 1,80,000.00

Discount factor

b

2.32163

1.64666

Annual operating costs

c

$       8,000.00

$     12,000.00

Equivalent annual cost

d=c+(a/b)

$ 1,32,912.13

$ 1,21,312.15

Since, annual equivalent cost of Machine B is lower,Machine B should be purchased.

Working:

Cumulative discount factor with 3 years life

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.14)^-3)/0.14

i

14%

=

2.321632027

n

3

Cumulative discount factor with 2 years life

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.14)^-2)/0.14

i

14%

=

1.646660511

n

2