# HELP. NO IDEA HOW TO DO THIS QUESTION

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

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