# Short Sell and Margin Account

Q1. JLJ Corporation has the following balance sheet:

Assets (2-year average) Debt and Equity (2-year average)

Cash and marketables 2,900 Accounts payable 1,459

Inventories 1,746 Accrued liabilities 1,085

Current Assets 4,646 Current Liabilities 2,544

PPE 4,750 Long-term debt 4,953

Other assets 425 Stockholder's equity 2,324

Total assets 9,821 Total debt + equity 9,821

a) What is JLJ's current ratio?

b) What is JLJ's leverage ratio ?

c) If the aggregate market value of JLJ is $12,635, what is the market to book ratio?

Q2. JJ's Finance Emporium most recent financial statements showed net income of $3.33 per share and the ROE of JJ's was 20%. The dividend payout ratio was 40%.

(a) Find the growth rate (g) of JJ's.

(b) Assuming that today's stock price is $70, what is JJ's capitalization rate (use the dividend discount model)?

Q3. You are considering selling a Treasury bill and observe the following quotes for T-bills in the market:

Maturity (days) Bid Yield Asked Yield

60 4.84 4.75

88 4.83 4.74

116 4.82 4.73

144 4.81 4.72

172 4.80 4.71

Ignore transaction costs...

a) The bill has 116 days left to maturity. At what price can you sell the bill to the dealer?

b) You bought the bill 56 days ago. What is your EAR?

c) Assuming a new investor was to buy the 116-day T-bill today, what would be the EAR if that investor held it to maturity?

Q4. Assume you are a venture capitalist who will make a $5.5 million investment today and will recoup your investment in 8 years. The expected net income of the project in year 8 is $4.7 million and the comparable P/E ratio for the industry is 35. Your required rate of return is 45%.

(a) Compute the future value of your investment .

(b) What is the terminal value of the project ?

(c) What is percentage of the project do you own?

(d) Assume the firm originally had 250,000 shares outstanding, what is the total number of new shares after your investment? What is the price per share that you paid?

Q5. (18 points) Ted Boone is feeling bearish on airline stocks and decides to short sell 1,000 shares of United Airlines (UAL). He posts a 60% initial margin and has a required maintenance margin of 33%. UAL's current market price is $42 per share.

(a) What are Ted's initial sale proceeds and how much margin did he post in dollars? Show the t-accounts.

(b) Assume that the stock price rises instead. At what price would Ted get a margin call?

Formulas: ROE = AU x PM x EM (reduced form)

PM = NI / Sales

AU = Sales / TA

EM = TA/TE

Current Ratio = CA / CL

Acid-Test Ratio = (CA - Inv.) / CL

Turnover = COGS / Inv.

Interest Coverage = EBIT / Int. Exp.

Market to Book = Market Value / Book Value

P/E = Price / Earnings

Dividend Yield = Dividend / Price

HPR = (P1 - P0 + D1)/ P0

g = ROE x plowback ratio

P/E = 1/k x (1 + PVGO/(E/k))

P/E = (1 - plowback) / (k-g)

EAR = (1 + HPR)365/n - 1

rbdy = (Discount/Par) * (360/n)

Price = 10000*[1-(rbdy*(n/360))]

V = (D1)/k - g

FV = (1+k)n x Pmt

Terminal Value = P/E x NI

Percentage Ownership = FV / TV

New shares = [%Ownership/(1-%Ownership)] * Old Shares

Price = Investment / Shares Outstanding

Maintenance margin = (Q*P - Debt) / (Q*P)

Maintenance margin = (Asset - Q*P) / (Q*P)

© BrainMass Inc. brainmass.com October 25, 2018, 9:47 am ad1c9bdddfhttps://brainmass.com/business/discounted-cash-flows-model/short-sell-margin-account-587194

#### Solution Preview

Answer:

We have,

JLJ's Current Ratio:

Current Ratio=(Current Asset)/(Current Liabilities)

Or,

Current Ratio=(4,646/2,544)=1.83

JLJ's leverage ratio:

Leverage Ratio=(Total Debt)/(Total Equity)

Or,

Leverage Ratio=4,953/2,324=2.13

Market to book value ratio:

Market to book value=$12,635/2,324=5.44

We have,

Net income per share=$3.33

ROE=20%

Dividend payout ratio=40%

Growth rate of JJ:

g=20%*(1-40%)=0.12=12%

Capitalization rate:

Capitalization rate=(40%)/($70/$3.33)+20%*(1-40%)=13.9%

We have,

Price at which I will sell the bill to the seller:

Price=$100/(1+4.73%)=$95.48

Effective annual rate:

Effective annual rate=(1+((4.84%)/60))^365-1=34.22%

Effective Annual rate:

Effective annual rate=(1+((4.82%)/116))^365-1=16.37%

We have,

Invested amount today=$5.5 million

Life of investment=8 ...

#### Solution Summary

This solution helps to find margins and creates a t-account.

Complications of the Mixed Processes of Short Sale

See the attached file.

In order to understand clearly the complications of the mixed processes of Short Sale, Aggregate Short Sale and Buying on Margin and the Aggregate of both Short Sale and Buying on Margin I need an elaborate solution to the questions in the two problems as per attached file showing the formulas, writing the formula manually in front of each showing the steps of calculations in order to know and understand clearly the components of the formulas relating to each question so that the solution gives me an elaborate understanding of the concepts of this hybrid stock trading concepts..

Short sale

PROBLEM (1)

First:

Assume that the investor give an order to his broker to sell (short sale) 300 shares from stock (A) which has a price $ 100 per share

1) Prepare a balance sheet for this investor if the initial margin is 60%.

2) Assume that the price of stock (A) declined to $ 60 per share, prepare a balance sheet for this investor.

3) If the Market Price increased to $130 per share, show the investor Balance Sheet and what is the type of his account considering the following cases?

SEE ATTACHED

Do you think that the investor will receive a margin call if the maintenance margin is 30%? Prepare a balance sheet for this investor.

4) How far can the price increase before the investor receives a margin call?

5) Calculate the rate of return if the stock price increased to $120 and the

Aggregate Short Sale:

Assume that the investor gave an order to his broker to sell (short sale) 100 shares from stock (A) that has a price $ 150 per share and another order to sell (short sale) 250 shares from stock (B) with the market price $ 50 per share.

1) Prepare a balance sheet for this investor if the initial margin is 60%.

2) Assume that the price of stock (A) goes up to be $170 per share, and the price of stock (B) increase also to be $60, what is the position of this investor if the maintenance margin is 30%?

Buying on margin and Short Sale:

Assume that another investor asked his broker to sell (short sale) 500 shares from stock (A) that has a price of $ 300 per share and another order to buy on margin 400 shares from stock (B) with the market price of $ 250 per share.

1) Prepare a balance sheet for this investor if the initial margin is 60%.

2) Assume that the price of stock (A) declined to $ 250, and the price of stock (B) increased to $270, do you think that the investor will receive a margin call if the maintenance marging is 30%?

Short sale

PROBLEM (2)

First:

Assume that the investor give an order to his broker to sell (short sale) 500 shares from stock (A) which has a price $ 80 per share

1) Prepare a balance sheet for this investor if the initial margin is 60%.

2) Assume that the price of stock (A) declined to $ 50 per share; prepare a balance sheet for this investor.

3) If the Market Price increased to $110 per share show the investor Balance Sheet and what is the type of his account considering the following cases?

SEE ATTACHED

Do you think that the investor will receive a margin call if the maintenance margin is 30%? Prepare a balance sheet for this investor.

4) How far can the price increase before the investor receives a margin call?

5) Calculate the rate of return if the stock price increased to $90 and the interest

Aggregate Short Sale:

Assume that the investor gave an order to his broker to sell (short sale) 400 shares from stock (A) that has a price $ 150 per share and another order to sell (short sale) 500 shares from stock (B) with the market price $ 70.

1) Prepare a balance sheet for this investor if the initial margin is 60%.

2) Assume that the price of stock (A) goes up to be $170 per share, and the price of stock (B) declined to be $40, what is the position of this investor if the maintenance margin is 30%?

Buying on margin and Short Sale:

Assume that another investor asked his broker to sell (short sale) 300 shares from stock (A) that has a price of $ 120 per share and another order to buy on margin 600 shares from stock (B) with the market price of $ 350 per share.

1) Prepare a balance sheet for this investor if the initial margin is 60%.

Assume that the price of stock (A) goes up to $ 150 and the price of stock (B) also increased to $370, do you think.