SC Ltd$.$ operates under ideal conditions of uncertainty. On January $1,2019,$ it purchased a capital asset that will last for two full years and then will be retired with no salvage. The purchase price was financed with an issue of common stock. SC Ltd$.$ plans to pay no dividends until after the end of $2020.$ The interest rate in the economy is $6$ percent.

SC Ltd$.$ is certain that net cash flow from its only asset will be $$100$ in $2019.$ However, net cash flow in $2020$ is uncertain. Net cash flows in $2020$ will be $$200($the high state$)$ with objective probability $0\mathrm{.}80$ and $$50($the low state$)$ with objective probability $0\mathrm{.}20.$ All cash flows are received at their respective year$-$ends. At the end of year $2$ it becomes known that the high state is realized.

Required

a$.$ How much did SC Ltd$.$ pay for its capital asset at the beginning of $2019?$ Show calculations.

b$.$ Prepare, in good form, a current value$-$based income statement for SC Ltd$.$ for the second year of operations$-$that is$,2020.$

c$.$ Prepare, in good form, a current value$-$based balance sheet for SC Ltd$.$ at the end of $2020($before any dividend payments$).$