Investment Practice Problems for Exam 2

Corporate Fund started the year with a net asset value of $12.50. By year-end, its NAV equaled $12.10. The fund paid year-end distributions of income and capital gains of $1.50. What was the (pretax) rate of return to an investor in the fund?

NAV1 - NAV0 + Distributions / NAV0 = 12.10 - 12.50 + 1.50 / 12.50 = .088 or 8.8%

Suppose that the inflation rate is expected to be 3% in the near future and the average real rate from the table is .38%. Using the historical data provided in this chapter, what would be your predictions for: a. The T-bill rate?

From Table 5.3, the average real rate on T-bills has been 0.38%. a. T-bills: 0.38% real rate + 3% inflation = 3.38%

a. Suppose the real rate of interest is 3% per year and the expected inflation rate is 8%. According to the Fisher hypothesis, what is the nominal interest rate? b. Suppose the expected inflation rate rises to 10%, but the real rate is unchanged. what happens to the nominal interest rate?

a) 1 + rnom = (1 + Rreal)(1 + i) = (1.03)(1.08) = 1.1124 - 1 = .1124 = 11.24% b) 1 + rnom = (1.03)(1.10) = 1.133 - 1 = 13.3%

Solving for Maintenance Margin: Continuing the scenario presented in Example 3.1, suppose the maintenance margin is 30%. How far could the stock price fall before the investor would get a margin call?

100p - 4000/ 100p = .3 --> 57.14 or below

Solve for NAV: Consider a mutual fund that manages a portfolio of securities worth $120 million. Suppose the fund owes $4 million to its investment advisers and another $1 million for rent, wages due, and miscellaneous expenses. The fund has 5 million shares outstanding.

120 mill - 5 mill / 5 mill = 23 per share

To Illustrate the mechanics of short-selling, suppose you are bearish(pessimistic) on Dot Bomb stock, and its market price is $100 per share.You tell your broker to sell short 1.000 shares. The broker borrows 1,000shares either from another customer's account or from another broker.The $100,000 cash proceeds from the short sale are credited to youraccount. Suppose the broker has a 50% margin requirement on shortsales. This means you must have other cash or securities in your accountworth at least $50,000 that can serve as margin on the short sale. Let'ssay that you have $50,000 in Treasury bills. Your account with the brokerafter the short sale will then be Suppose the broker has a maintenance margin of 30% on short sales.This means the equity in your account must be at least 30% of the valueof your short position at all times. How much can the price of Dot Bomb stock rise before you get a margin call?

150,000 - 1,000p / 1,000p = .3 --> p = 115.38 if it rise above that you will get margin call

Consider these data from the October 2021 annual report of Fidelity's Focused Stock Fund. (All values are in millions.) What was the net asset value of the fund? Assets: $4,034.4 Liabilities: $ 81.8 Shares: 101.1

4,034.4 - 81.8 / 101.1 = 39.10

Solving for buying on margin or margin: Suppose an investor initially pays $6,000 toward the purchase:of $10,000 worth of stock (100 shares at $100 per share), borrowing the remaining $4,000 from a broker.

Margin = Equity in account / Value of Stock = 6000/10,000 = 60%

Solving for percent margin: Suppose you are bearish(pessimistic) on Dot Bomb stock, and its market price is $100 per share.You tell your broker to sell short 1,000 shares. The broker borrows 1,000 shares either from another customer's account or from another broker.The $100,000 cash proceeds from the short sale are credited to your account. Suppose the broker has a 50% margin requirement on short sales. This means you must have other cash or securities in your account worth at least $50,000 that can serve as margin on the short sale. Let's say that you have $50,000 in Treasury bills.

Percent Margin = Equity / value of stock owned = 50,000/100,000 = .50

Stock Shares, Price [A 200,000 $35] [B 300,000 40] [C 400,000 20] [D 600,000 25] The fund has not borrowed any funds, but its accrued management fee with the portfolio manager currently totals $30,000. There are 4 million shares outstanding. What is the net asset value of the fund?

Stock Value Held by Fund A $ 7,000,000. (200,000 x 35) B 12,000,000 C 8,000,000 D 15,000,000 Total $42,000,000 Net Asset Value = 42,000,000 - 30,000 / 4,000,000 = 10.49

Suppose that you sell short 1,000 shares of Xtel, currently selling for $20 per share, and give your broker $15,000 to establish your margin account. a. If you earn no interest on the funds in your margin account, what will be your rate of return after one year if Xtel stock is selling at: (i) $22; (ii) $20; (iii) $18? Assume that Xtel pays no dividends. b. If the maintenance margin is 25%, how high can Xtel's price rise before you get a margin call?

The gain or loss on the short position is: (-1,000 ́ ΔP)Invested funds = $15,000 Therefore: rate of return = (-1,000 ́ ΔP)/15,000 The rate of return in each of the three scenarios is: (i) Rate of return = (-1,000 x $2)/$15,000 = -0.1333, or-13.33% (ii) Rate of return = (-1,000 x $0)/$15,000 = 0% (iii) Rate of return = [-1,000 x (-$2)]/$15,000 = +0.1333, or+13.33% b. Total assets in the margin account equal: $20,000 (from the sale of the stock) + $15,000 (the initial margin) = $35,000, Liabilities are 1,000P. You will receive a margin call when: 35,000 - 1000p/ 1,000p = 0.25 --> when P = $28 or higher

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 an additional $5,000 from your broker at an interest rate of 8% per year and invest $10,000 in the stock. a. What will be your rate of return if the price of Telecom stock goes up by 10% during the next year? The stock currently pays no dividends. b. How far does the price of Telecom stock have to fall for you to get a margin call if the maintenance margin is 30%? Assume the price fall happens immediately.

a) You buy 200 shares at $50.00 per share of Telecom for $10,000. These shares increase in value by 10%, or $1,000. You pay interest of: 0.08 x $5,000 = $400The rate of return will be: 1,000 - 400/5,000 = .12 = 12% b)The value of the 200 shares is 200P. Equity is (200P - $5,000). You will receive a margin call when: 200p - 5000/ 200p = 0.30 --> when P= $35.71 or lower

You are bearish on Telecom and decide to sell short 100 shares at the current market price of $50 per share. a. How much in cash or securities must you put into your brokerage account if the broker's initial margin requirement is 50% of the value of the short position? b. How high can the price of the stock go before you get a margin call if the maintenance margin is 30% of the value of the short position?

a) You short 100 shares at $50.00 per share for a total of $5,000. Initial margin is50% of $5,000, or $2,500. b) Total assets are $7,500 ($5,000 from the sale of the stock and $2,500 put up formargin). Liabilities are 100P. Therefore, equity is ($7,500 - 100P). A margin call will be issued when: 7,500 - 100p/100p = .30 --> when P = 57.69 or higher

During a period of severe inflation, a bond offered a nominal HPR of 80% per year. The inflation rate was 70% per year. a. What was the real HPR on the bond over the year? b. Compare this real HPR to the approximation r ≈ r − i. real nom

a) r real = r nominal - i / 1+i r real = .80 - .70 / 1.70 = 5.88% b) Approximation = r - i = .80 - .70 = .10 Approximate give real HPR that is to high

Solving for EAR: A bank offers two alternative schedules for a savings account of $100,000 locked in for 3 years: (a) a monthly rate of 1% and (b) an annually, continuously compounded rate, rcc, of 12%. Which alternative should you choose?

a. EAR = (1 + .01)^12 − 1 = .1268 = 12.68% b. EAR = e^.12 − 1 = .1275 = 12.75% Choose which EAR is higher