A Public Utility Is Planning to Construct a High Head $\$ 3000 \mathrm { USD }$

A public utility is planning to construct a high head hydroelectric facility. The approximate cost for large facilities is $\$ 3000 \mathrm { USD }$ per $\mathrm { kW }$ installed. The utility is considering two options, a $600 \mathrm { MW } _ { \mathrm { e } }$ facility that would operate at a $70 \%$ capacity factor or an $800 \mathrm { MW } _ { \mathrm { e } }$ facility that would operate at a $65 \%$ capacity factor. If electricity is sold for $\$ 0.13$ per $\mathrm { kWh }$ , estimate the payback period for the additional infrastructure costs for the larger facility. Ignore the cost recovery factor and operating costs.