Problem $10-30$ Break$-$Even Replacement $[$LO$2]$

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 $$\mathrm{.}52$ and lasts for $1,000$ hours. A $15-$watt LED, which provides the same light, costs $$3\mathrm{.}75$ and lasts for $12,000$ hours. A kilowatt$-$hour is $1,000$ watts for $1$ hour. Suppose you have a residence with a lot of incandescent bulbs that are used on average $500$ hours a year. The average bulb will be about halfway through its life, so it will have $500$ hours remaining $($and you can't tell which bulbs are older or newer$).$ If you require a return of $11$ percent, at what cost per kilowatt$-$hour does it make sense to replace your incandescent bulbs today? $($ 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$.,32\mathrm{.}161616.)$

$\backslash$table$[[$Break$-$even cost,$$,0\mathrm{.}006469]]$