Question

A company wants to buy one of two machines: machine X or machine Y. The present worth of machine X over a life span of 3 years is $2,200 at an interest rate of 10% per year compounded annually whereas the present worth of machine Y over a life span of 6 years is $ 3,500 at the same interest rate. Based on the present worth criterion, which machine should the company pick?

PLEASE HELP ASAP. dont use excel. solve by hand

Answer 1

As the machines have unequal lives, we will use the Annualised Net Present Value to compare the machines.

Annualized Net Present Value = Net Present Value / Present Value Annuity Factor

Present Value Annuity Factor = {1 - [1/(1+r)ⁿ ] } / r

n = life of machine / project

r = interest rate

For Machine X

PVAF = {1 - [1/(1+0.10)³] } / 0.10 = 2.487

Annualized NPV = 2200 / 2.487 = $884.5999

For Machine Y

PVAF = {1 - [1/(1+0.10)⁶] } / 0.10 = 4.355

Annualized NPV = 3500 / 4.355 = $803.6739

As the machine X has more annualized net present value/worth as compared to machine Y , company will pick machine X.