This is a question from sample exam FM. This should be a easy question but I am confused--in the solution provided, what is value of contributions and value of returns? I am not sure how to approach this type of questions. why is the dividend 32 not negative on the left-handside of equation?
Any help is greatly appreciated!!~
Jose and Chris each sell a different stock short for the same price. For each investor,the margin requirement is 50% and interest on the margin debt is paid at an annual effective rate of 6%.Each investor buys back his stock one year later at a price of 760. Jose’s stock paid a dividend of 32 at the end of the year while Chris’s stock paid no dividends. During the 1-year period, Chris’s return on the short sale is i, which is twice the return earned by Jose. Calculate i
Soln:
Chris’ equation of value at end of year:
(Value of contributions) .5 P(1+i) + 760 = P* + .5 P (1.06) (Value of returns), where P = price stock sold for
(*Proceeds received for stock sale at beginning of year are in non-interest bearing account per
government regulations (Kellison top of page 281))
Thus, Chris’ yield i = ((1.03) P – 760)/(.5 P).
Jose’s equation of value at end of year:
(Value of contributions) .5 P(1+j) + 760 + 32 = P* + .5 P (1.06) (Value of returns),
Thus, Jose’s yield j = ((1.03) P - 792)/(.5 P).
It is given that Chris’ yield i = twice Jose’s yield j. So ((1.03) P – 760)/(.5 P) = 2 ((1.03) P - 792)/(.5 P)
or P = 824/(1.03) = 800. Thus, Chris’ yield i = ((1.03) 800 – 760)/400 = 64/400 = .16 or 16%.
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