Hi!
Can I check with you all if it is possible to use this formula for the question below? Thanks!
Formula: Call price = [(initial pr)(1- initial margin)] / (1-maintenance margin)
QUESTION
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Answer = B
The call price formula doesn’t apply here.
If the leverage ratio were 1.6, then the (original) equity investment was:
$22 ÷ 1.6 = $13.75,
so the investor borrowed:
$22.00 – $13.75 = $8.25.
If the total return were 12%, then the total amount in the investor’s account after the sale was:
$13.75 × 1.12 = $15.40.
The total amount in the investor’s account after the sale will be:
sale price + dividend – loan amount – interest
= sale price + $0.60 – $8.25 – $0.33
= sale price – $7.98.
Thus,
$15.40 = sale price – $7.98
sale price = $15.40 + $7.98 = $23.38.
Voilà!
Intuitively…
Since the leverage ratio is 1.6, your equity is $13.75 and the borrowed amount is $8.25 (or 60% of your equity).
I like to lay out a formula that makes sense to me:
X - $8.25 + $0.60 - $0.33 / $13.75 should equal 12%; solve for X and it gives you X = $9.63, and you add that to $13.75 to give you the full ending stock value of $23.38
Another way to calculate:
Return on equity = Leverage ratio x Asset Return - (Leverage ratio-1) x Return on debt
Asset return = (12% + (1.6-1) x 4%) / 1.6 = 9.0%
(selling price + dividend)/purchase price = 1.09
selling price = (1.09x22) - 0.60 = 23.38