Jack sells 100 shares of a certain stock short for $60 and buys it back one year

Question

Jack sells 100 shares of a certain stock short for $60 and buys it back one year later for $50. Just before he buys it back, a per share dividend of $X, is paid. Jack is required to make a margin deposit of 50% and the margin interest rate is 5%. Jack's short sale yield is 31.6667%. Jill sells 100 shares of a certain stock short for $65 and buys it back one year later for SB. Just before she buys it back, a per share dividend of $X is paid. Jill is also required to make a margin deposit of 50% and the margin interest rate is 5%. Jill's short sale yield is half of Jack's Determine B A.20 B.40 C.60 D.80 E.100

Explanation / Answer

Margin required =60*100*50%=3000

Interest=3000*5%=150

Equity=3000

Proceeds from shaort sale=60*100=6000

Dividends per share=X

Dividends=X*100

Cost to buy shares=50*100=5000

As dividends would have to be paid by Jack

So, short sale yield=(Sale value-Purchase Value+Interest on Margin-Dividends)/Margin

=6000-5000+150-100X=1150-100X

Return=(1150-100X)/3000

Given this is 31.667%

hence, X=2

Short Sale yield for Jill=(65*100-100*B+65*50%*100*5%-2*100)/(65*100*50%)

Given , Jill's short sale yield is half of Jack's

So, short sale yield for Jill=31.667/2%

=>(65*100-100*B+65*50%*100*5%-2*100)/(65*100*50%)=31.667/2%

hence, (6462.5-100B)/3250=31.667/2%

=>B=60

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