Permian Partners $($PP$)$ produces from aging oil fields in west Texas. Production is $1\mathrm{.}92$ million barrels per year in $2018,$ but production is declining at $9\%$ per year for the foreseeable future. Costs of production, transportation, and administration add up to $$26\mathrm{.}20$ per barrel. The average oil price was $$66\mathrm{.}20$ per barrel in $2018.$

PP has $8\mathrm{.}2$ million shares outstanding. The cost of capital is $11\%.$ All of PP$$s net income is distributed as dividends. For simplicity, assume that the company will stay in business forever and that costs per barrel are constant at $$26\mathrm{.}20.$ Also, ignore taxes.

a$.$ Assume that oil prices are expected to fall to $$61\mathrm{.}20$ per barrel in $2019,$ $$56\mathrm{.}20$ per barrel in $2020,$ and $$51\mathrm{.}20$ per barrel in $2021.$ After $2021,$ assume a long$-$term trend of oil$-$price increases at $7\%$ per year. What is the ending $2018$ value of one PP share?