A right-turn lane is installed at an intersection at a cost of $450,000. With this new turning lane, each vehicle going through the intersection is expected to

Question

A right-turn lane is installed at an intersection at a cost of $450,000. With this new turning
lane, each vehicle going through the intersection is expected to save an average of $0.01 due to
time savings and reduced accidents costs. The expected traffic for the new lane is estimated at
12,000 vehicles per day -- every day of the year. How many years will it take for the savings to
amortize (i.e. pay off) the cost of the improvement? The interest rate is 6%. (Note that the
amortization costs are the equivalent annual costs necessary to repay the loan.)

Answer 1

Every year, $43,800 will be saved (12,000 * $0.01 * 365).

 

At the end of ever year, the balance will be equal to the cost at the beginning of the year less the amount saved, plus the interest rate. 

 

So after the first year, the balance is:

($450,000 - $43,800) * 1.06 = $406,200.

 

For every year after that, you perform the same equation while using the balance from the previous year. Ie

 

Year 2

($406,200 - $43,800) * 1.06 = $384,144

Year 3

($384,144 - $43,800) * 1.06 = $360, 764

 

And so on. If you plug this into excel, you will find that the saving outweigh the cost after the 14th year. Note, even if you factor in leap year, the answer is unchanged.