Please solve by hand without excel, need to know the process of solving 9. Chris

Question

Please solve by hand without excel, need to know the process of solving

9. Chris sells a stock short for a price of $80. The stock pays a dividend of $5. The margirn requirement is 60% of the short sale price. The margin account earns an annual rate of 6%. The stock is purchased in one year for a price of X. Terry sells a different stock short for a price of $90. The stock pays no dividends. The margin requirement is 50% of the short sale price. The margin account earns an annual rate of 6%. The stock is purchased in one year for a price of X (same price that Chris pays). Terry's rate of return is three times that of Chris' return. Find the price X at which the purchase their respective stock

Explanation / Answer

Return on Short sale=(Selling Price-Purchase Price-Dividends+Margin Requirement*Interest Rate)/Margin Requirement

Chris's return=((80-X)-5+80*60%*6%)/(80*60%)

Terry's return=((90-X)-0+90*50%*6%)/(90*50%)

Given, Terry's return=3*Chris's return
So, (92.7-X)/45=3*(77.88-X)/48

135/48*77.88-135/48X+48/48X=92.7
=>-87X/48=92.7-135/48*77.88
So, x=(-92.7+135/48*77.88)*48/87=69.70345

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