UCLA finance Questions

You are bullish on Telecom stock. The current market price is $50
per share, and you have $5,000 of your own to invest. You borrow a
additional $5,000 from your broker at an interest rate of 8% per yea
and invest $10,000 in the stock.
a. What will be your rate of return if the price of Telecom stock goe
up by 10% during the next year? (Ignore the expected dividend.)
b. How far does the price of Telecom stock have to fall for you to ge
a margin call if the maintenance margin is 30%? Assume the price
fall happens immediately.
Price per share
Equity invested
Borrowed funds
Interest rate
Total investment
Price change
Margin required
Solution
a.
b.
Shares bought
Value change
Interest payment
Rate of return
𝑅𝑒𝑡𝑢𝑟𝑛 =
𝛥
Margin call price
𝑉𝑎𝑙𝑢𝑒 𝑜𝑓
arket price is $50
vest. You borrow an
rate of 8% per year
Telecom stock goes
ected dividend.)
to fall for you to get
Assume the price
𝛥 𝑖𝑛 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘− 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑒𝑞𝑢𝑖𝑡𝑦 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑
𝐿𝑜𝑎𝑛
𝑜𝑓 𝑠𝑡𝑜𝑐𝑘𝑀𝑎𝑟𝑔𝑖𝑛 𝑐𝑎𝑙𝑙 =
(1 − 𝑀𝑎𝑖𝑛𝑡𝑎𝑖𝑛𝑎𝑛𝑐𝑒 𝑚𝑎𝑟𝑔𝑖𝑛)
You’ve borrowed $20,000 on margin to buy shares in Ixnay, which i
now selling at $40 per share. Your account starts at the initial marg
requirement of 50%. The maintenance margin is 35%. Two days late
the stock price falls to $35 per share.
a. Will you receive a margin call?
b. How low can the price of Ixnay shares fall before you receive a
margin call?
Borrowed funds
Price per share
Initial margin
Maintenance margin
New stock price
Solution
a. Total investment
Shares purchased
New value
Equity value
Margin
𝑀𝑎𝑟𝑔𝑖𝑛
b. Margin call price
𝑉𝑎𝑙𝑢𝑒 𝑜𝑓
s in Ixnay, which is
at the initial margin
5%. Two days later,
re you receive a
𝐸𝑞𝑢𝑖𝑡𝑦
𝑀𝑎𝑟𝑔𝑖𝑛 =
𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑆𝑡𝑜𝑐𝑘
𝑜𝑓 𝑠𝑡𝑜𝑐𝑘𝑀𝑎𝑟𝑔𝑖𝑛 𝑐𝑎𝑙𝑙 =
𝐿𝑜𝑎𝑛
(1 − 𝑀𝑎𝑖𝑛𝑡𝑎𝑖𝑛𝑎𝑛𝑐𝑒 𝑚𝑎𝑟𝑔𝑖𝑛)