Question

Machines A and B are mutually exclusive and have the following investment and operating costs. Machine A has a life of 3 years while Machine B has a 2 year life. Year: 0 1 2 3 A $5,000 $800 $900 $1,000 B $6,000 $850 $900 -- Assume the discount rate is 9 percent. The equivalent annual annuity of machine A is ______. The equivalent annual annuity of machine B is ______.

Answer 1

$-1081.01

$-2536.89

Step-by-step explanation:

Equivalent annual cost method is a capital budgeting method used to choose between two projects with an unequal life span

The decision rule is to choose the product with the higher Equivalent annual cost

Equivalent annual annuity method is better for making this decision because if net present value is used, the project with the higher useful life would be chosen. this does not mean it is more profitable

EAA =
`(r(NPV))/(1 - (1)/((1+ r)^(n) ) )`

Net present value is the present value of after-tax cash flows from an investment less the amount invested.

NPV can be calculated using a financial calculator

Machine A

Cash flow in year 0 = - $5,000

Cash flow in year 1 = $800

Cash flow in year 2 = $900

Cash flow in year 3 = $1,000

I = 9%

NPV A = -2736.35

Machine B

Cash flow in year 0 = -$6,000

Cash flow in year 1 = $850

Cash flow in year 2 = $900

I = 9%

NPV B = -4462.67

EAA =

(0.09 x -2736.35) / ( 1 - (1.09)^3) = $-1081.01

(0.09 x -4462.67) / ( 1 - (1.09)^2)= $-2536.89