Question

Sam is considering purchase of a vending machine to sell sodas. The cost of the vending machine is $3,400. Sam estimates that the vending machine will last for five years and will provide net income of $800 each year for its lifetime.
a. If Sam pays $3,400 for the vending machine today, what is its net present value at 7%? Should Sam purchase the vending machine?
b. If Sam pays $3,400 for the vending machine today, what is its net present value at 5%? Should Sam purchase the vending machine?
c. Suppose the seller of the vending machine allows Sam to defer, without penalty or interest, payment for the vending machine until the end of the first year. What is its net present value at 7%? Should Sam purchase the vending machine?

Answer 1

Initial Cost = $3,400

Revenue per year = $800

Useful life = 5 years

Net Present Value = Revenue per year*PVAF(r%,n) - Initial Cost

a) Interest Rate = 7%

NPV = 800*PVAF(7%,5) - 3400

NPV = 800*[(1-(1+7%)^-5)/7%] - 3400

NPV = 800*4.1002 - 3400

NPV = 3280 - 3400

NPV = -$120 (Sam should not purchase vending machine as NPV is negative, it means revenues will not be able to cover its cost)

b) Interest Rate = 5%

NPV = 800*PVAF(5%,5) - 3400

NPV = 800*[(1-(1+5%)^-5)/5%] - 3400

NPV = 800*4.3294 - 3400

NPV = 3464 - 3400

NPV = $64 (Sam should purchase vending machine as NPV is positive, it means revenues will be able to cover its cost)

c) Interest Rate = 7%, Cost paid at the end of year 1

NPV = 800*PVAF(7%,5) - 3400*PVF(7%,1)

NPV = 800*[(1-(1+7%)^-5)/7%] - 3400*(1.07^-1)

NPV = 800*4.1002 - 3400*0.9345

NPV = 3280 - 3178

NPV = $102 (Sam should purchase vending machine as NPV is positive, it means revenues will be able to cover its cost)