5. (20 Marks)

a. If you earn no interest on the funds in your margin account, what will be your rate of return after one year if WN stock is selling at (i) $88; (ii) $80; (iii)$72? Assume that WN pays no dividends.

If WN’s stock sells at price p at the end of the year, you end up with $250(80 − p) + $15, 000.
Hence the return on this investment, rp, is given by

250 X 80-p+ 15,000-15,00015,000 = 80-p60

Thus r88 = −13.33%, r80 = 0% and r72 = 13.33%

b) If the minimum margin is 30 percent, how high can WN’s price rise before you get a margin call?

There a total of $35,000 in the margin account (sale of 250 shares at $80 each plus the $15,000 deposit). Total liabilities are 250p. There’s a margin call when

35,000-250p250p = .3

Which implies that p=107.69

c) Redo parts (a) and (b), now assuming that WN’s dividend (paid at year-end) is $2 per share.

The return on the investment is then, for a price p at the end of the year,

250 X 80-p+ 15,000-15,000-50015,000 = 78-p60

Thus r88= -16.67%. r80= -3.33%, and r72= 10%

Total assets in the margin account at the end of the year are now $35, 000−$500 = $34, 500, thus a margin call occurs if

34,500-250p250p = 0.3

Which implies that p=