Question

A company is considering expanding their production capabilities with a new machine that costs $102,000 and has a projected lifespan of 9 years. They estimate the increased production will provide a constant $12,000 per year of additional income. Money can earn 0.6% per year, compounded continuously. Should the company buy the machine?

Select an answer Yes, the present value of the machine is greater than the cost by    $________ over the life of the machine

Answer 1

present value of the machine = sum of present values of each year's additional income

present value of each year's additional income = additional income / ert

where r = continuously compounded rate

n = number of years

present value of the machine = ($12,000 / e0.006*1) + ($12,000 / e0.006*2) + ($12,000 / e0.006*3​​​​​​​) + .......... ..... +  ($12,000 / e0.006*9​​​​​​​)

present value of the machine = $104,820.70

Excess of present value of machine over cost of machine = $104,820.70 - $102,000 = $2,820.70

Yes, the present value of the machine is greater than the cost by $2,820.70 over the life of the machine