Light$-$emitting diode $($LED$)$ light bulbs have become required in recent years, but do they make financial sense? Suppose a typical $60-$watt incandescent light bulb costs $$\mathrm{.}45$ and lasts for $1,000$ hours. A $7-$watt LED, which provides the sam$$ light, costs $$2\mathrm{.}25$ and lasts for $40,000$ hours. A kilowatt$-$hour of electricity costs $$\mathrm{.}121,$ which is about the national average. A kilowatt$-$hour is $1,000$ watts for $1$ hour. However, electricity costs actually vary quite a bit depending on location and user type $($you can get information on your rates from your local power company$).$ An industrial user in West Virginia might pay $$\mathrm{.}04$ per kilowatt$-$hour whereas a residential user in Hawaii might pay $$\mathrm{.}25.$

You require a $10$ percent return and use a light fixture $500$ hours per year. What is the break$-$even cost per kilowatt$-$hour? $($ A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to $6$ decimal places, e$.$g$.,32\mathrm{.}16161$