Delta Limited plans to acquire Gamma Limited. Delta Limited plans to propose a cash offer by paying the market price of Gamma$$ shares as well as paying $30\%$ of synergy created in the market value of assets. This deal expects to generate synergy of additional $$50,000$ of market value of assets and $$30,000$ of net income. Assume there is no transaction cost, financial and operating risk remain constant.

Share price is $$5$ and $$2$ of Delta Limited and Gamma Limited respectively.

Shares outstanding are $20,000$ and $6,000$ of Delta Limited and Gamma Limited respectively.

Market value of assets are $$250,000$ and $$50,000$ of Delta Limited and Gamma Limited respectively.

Net Income is $$200,000$ and $$60,000$ of Delta Limited and Gamma Limited respectively.

Calculated price$-$earnings ratio of Delta Limited after acquisition.

Option $1$: $0\mathrm{.}50$ times

Option $2$: $0\mathrm{.}20$ times

Option $3.0\mathrm{.}35$ times

Option $4$: $0\mathrm{.}47$ times