Question

1) You own a tractor that has annual operating costs of $50,000 per year, and no current salvage value. You are considering buying a new, more efficient tractor that would have annual operating costs of only $25,000 per year. You believe that either option could last for three years. If your minimum acceptable rate of return is 10% per year, determine whether the decision of whether to replace the tractor is sensitive to the first cost of the new tractor, if the first cost can range from $40,000 to $60,000.

Answer 1

Annual savings from new tracktor= annual operating cost of old tracktor- annual operating cost of new tracktor= 50000-25000= 25000

Present value of an annuity 'A' is = A*(1-(1+r)^-n)/r

r= Marr

n= 3

Net present value (NPV) of new tracktor= -initial cost+ PV of annual savings

NPV with 40000 initial cost= -40000+25000*(1-1.1^-3)/0.1 =$22171

NPV with 60000 initial cost= -60000+25000*(1-1.1^-3)/0.1 = $2171

NPV is positive for all possible initial costs. Therefore decision is not sensitive to initial cost of new tracktor.