Question

You can purchase an optical scanner today for $500. The scanner provides benefits worth $80 a year. The expected life of the scanner is 10 years. Scanners are expected to decrease in price by 20% per year. Suppose the discount rate is 12%. When is the best time to purchase the scanner? (Round your answer to the nearest cent.)

NPV is maximized when you wait ____ (choose from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) years to purchase the scanner. At this date NPV will be equivalent to $____ today.

Answer 1

1:
=(-500*0.8+80/12%*(1-1/1.12^10))/1.12=46.4445020293477

2.
=(-500*0.8^2+80/12%*(1-1/1.12^10))/1.12^2=105.243815587428

3.
=(-500*0.8^3+80/12%*(1-1/1.12^10))/1.12^3=139.521628348833

4.
=(-500*0.8^4+80/12%*(1-1/1.12^10))/1.12^4=157.111408068643

5.
=(-500*0.8^5+80/12%*(1-1/1.12^10))/1.12^5=163.519846928665

6.
=(-500*0.8^6+80/12%*(1-1/1.12^10))/1.12^6=162.601151907903

7.
=(-500*0.8^7+80/12%*(1-1/1.12^10))/1.12^7=157.037663188298

8.
=(-500*0.8^8+80/12%*(1-1/1.12^10))/1.12^8=148.6822444685

9.
=(-500*0.8^9+80/12%*(1-1/1.12^10))/1.12^9=138.802036270614

10.
=(-500*0.8^10+80/12%*(1-1/1.12^10))/1.12^10=128.251841156535

NPV is maximized when you wait 5 years to purchase the scanner. At this date NPV will be equivalent to $163.52 today.