FINA2320/2802DE Fall 2015: Homework #1
Solutions
1. Buying on margin case:
(a) The initial value of stock is $75 × 1000 = $75,000.
So investor should using invest:
Equity in account = $75,000 × Initial Margin = $75,000 × 50% = $37,500
And investor should borrow from the broker:
Liability = $75,000 - 37,500 = $37,500
The initial balance sheet looks like this:
Assets
Liabilities and Owner’s Equity
Value of stock
$75,000
Loan from broker
$37,500
Equity
$37,500
(b) (i) If the stock price goes up by 10%, the total value of stock is
$75 × (1 + 10%) × 1000 = $82,500
The liability is $37,500 × (1 + 6%) = $39,750.
Therefore, the equity in account is $82,500 - $39,750 = $42,750.
The balance sheet one year later is:
Assets
Liabilities and Owner’s Equity
Value of stock
$82,500
Loan from broker
$39,750
Equity
$42,750
The dividend payment that the investor received during holding period is $2.5 × 1000 = $2,500.
So investor’s holding period return is
HPR = ($42,750 - 37,500 + 2,500) / $37,500 = 20.67%
(ii) If year-end ex-dividend price of stock does not change, the total value of stock is $75,000.
The liability is $39,750. Therefore, the equity in account is $75,000 - $39,750 = $35,250.
So investor’s holding period return is
HPR = ($35,250 - 37,500 + 2,500) / $37,500 = 0.67%
(iii) If year-end ex-dividend price of stock goes down by 10%, the total value of stock is
$75 × (1 - 10%) × 1000 = $67,500
The liability is $39,750. Therefore, the equity in account is $67,500 - $39,750 = $27,750.
So investor’s holding period return is
HPR = ($27,750 - 37,500 + 2,500) / $37,500 = -19.33%
(c) Assume that the stock price is P when investor receives a margin call. Then the total value of stock is 1000P. The liability is still $39,750. So the equity in account is 1000P – 39,750. The percentage margin is 25% when investor receives a margin call, that is,