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Sample Exam 5162 (answers)

IF YOU WANT TO ASK ME A QUESTION RELATED TO THIS EXAM YOU NEED TO GENERALIZE YOUR QUESTION IN SUCH A WAY THAT YOU DO NOT DIRECTLY REFER TO THIS SAMPLE EXAM.

I. FROM CHAPTER 9. SUPPOSE WRS INC. HAD THREE OPERATING DIVISIONS:

DIVISION PERCENTAGE OF FIRM VALUE

Educational supplies 50

Internet Sales & Distribution 40

Medical Research 10

_____________________________ _____

The following companies compete with the WRS divisions:

Reported Fiancials Market Value

COMPANY BETA D/(D+E) D/(D + E) E(ROD)

United Education Products .7 .3 .4 .06

Amazon Sales 1.4 .4 .6 .07 e

Associated Medical Labs 1.1 .2 .3 .05

WRS is financed with 35% debt and 65% equity. The corporate tax rate is 40% and the required return on WRS’s debt is 5%. Treasury bonds are yielding 4% and Treasury bills are yielding 1%. The historical liquidity premium on Treasuries is 1.5%. The expected return on the S&P 500 is 12%.

1. What required return should WRS expect for each of its divisions?

Could use a E(Rf) = treasury bond rate minus Liquidity premium = .04 - .015 = .025

Or

Simply use the treasury bond rate of 4%, which is more typically done in practice.

ROAED = ATWACC of UEP = .4(.06)(1 - .4) + .6 ( .04 + .7(.12 - .04)) = .072

ROAINT = ATWACC of AS = .6(.07)(1 - .4) + .4 (.04 + 1.4(.12 -.04)) = .086

ROAMED = ATWACC of AML = .3(.05)(1-.4) + .7 (.04 + 1.1 (.12 - .04)) = .0986

2. What is WRS's overall cost of capital?

Weighted average of each division’s ATROA

ATROA = .5(.072) + .4(.086) +.10(.0986)

ATROA = .08029

3. What is the required return that WRS stockholders demand on WRS stock?

E(ROE) = ATROA + D/E ((ATROA – ROD(1 – Tc))

ROE = . 08029 + 35/65 (.08029 – (.05)(1-.4))

ROE = .10737

4. Show an alternative calculation of WRS's cost of capital that results in the same answer as #2.

ATROA = ATWACC = .35(ROD)(1 – Tc) + .65(ROE)

= .35(.05)(1-.4) + .65(.10737)

= .08029

II. Efficient Markets - True or False

Indicate first whether the following statement is true or false. Then briefly describe why the statement is true or false. Be sure to specifically address the issue raised in the question.

1. Portfolio managers achieve high returns by identifying over- or underpriced securities. ( 7 pts.)

F – Over or underpriced implies the stock price is mispriced (i.e. has a positive or negative NPV). In efficient markets, there is no mispricing; securities are correctly priced. Portfolio managers can only achieve high expected returns by either selecting a portfolio of high beta stocks or by buying the market portfolio and leveraging up.

2. In efficient markets, anyone can expect to beat the market, that is the S&P 500. ( 7 pts.)

True – You can expect to beat the return on the S&P 500 by buying the S&P 500 with borrowed funds, i.e. leveraging up. You won’t beat the CAPM; you will earn a fair return for the risk (beta) that you have levered up to.

3. If markets are efficient, you cannot predict the future economic direction of an industry on the basis of stock price behavior of firms within that industry. ( 7 pts.)

False - Because markets are efficient the prices of the securities in an industry capture all information (i.e. forecasts) about the company and its industry. Therefore rising stock prices in that industry reflect forecasts that the industry is expected to do well in the future.

4. If markets are efficient, you cannot predict the future direction of stock prices within an industry on the basis of the economic conditions within the industry. (7 pts.)

True - While you can forecast the industry from the stock price, you cannot forecast the stock price from the industry forecast because the stock price already has the very best forecast of the industry imbedded in its stock price.

5. In an efficient market, stocks that pay the highest dividends generate the highest returns for investors. (7 pts.)

False - Stocks provide investors with returns from two sources: capital gains and dividends. Stocks with high dividends simply mean that most of their return will come from dividends rather than capital gains. A high return can only be expected from a stock with a high beta (i.e. high risk class). If a high dividend stock always paid a high return then that would imply inefficiency because a low beta stock with a high dividend would earn a high return. That would be an excess return for that riskclass (i.e. a +NPV, which is an inefficiency!)

III. Derivative Securities

True or False and explain why.

1. If firms issued riskless debt, then stockholders would hold the equivalent of a future on the assets of the firm.

True – stockholder would have to put money into the firm if value of assets fell below value of debt, rather than “walking away.”

2. The greater the exercise price, the greater the call price.

False - in the event of exercise, the call holder would have to pay more (ex price). Therefore, call value goes down.

3. An option is always riskier than the stock it is written on.

True – option is a levered position. It magnifies risk and return.

4. A long risky debt postion can be converted into a long riskless debt position by combining the long risky debt with a short put.

False

G B

long risk debt E St

short put 0 St – E would have to be long a put not short a put

E 2St - E

Problems

The price of Associated Chemical stock on April 20 is $52 per share. Call options and put options maturing on July 20 have an exercise price of $55. The standard deviation of the stock is 35%, treasury bills are yielding 7% and the bonds of the company are yielding 10%.

What is the call option price?

$2.76

What is the put option price?

$4.81

How could you hedge a long stock position with this put. What would be your gains (losses) if the stock

1) increased to $72 2) decreased to $32. Why is this a hedge?

Gain Loss

Long stock 20 -20

Long put (-4.81 + .23) (- 4.81 + 22.05)

Net Gain 15.42 2.76

This is a hedge because your losses are significantly reduced. Of course your gains are also reduced.

1. Suppose only put options are traded on Associated Chemical and they are currently selling for $6. Demostrate how you could synthetically create a call option? What would be its price?

Call = Stock –e-rfTE + Put

= 52 -54.05 + 6

= 3.95

Is it reasonable to expect the call price to be higher than the call price calculated in #2 if the put price is also higher? Why? What does this imply?

Yes, it implies that the variance must be higher than 35% used in #2

2. Suppose American Airlines attaches a double-your-money-back guarantee to every airline ticket it sells. The guarantee can be redeemed if the traveler is "bumped" from a flight. What kind of option is this voucher? Explain in the language of options.

Put - You have the right to put (sell) the old ticket to AA for double the price (exercise price) you paid.

3. A share of stock is currently selling for $25. A three month call option on this stock with an exercise price of $30 currently sells for $3. For every $1 change in the stock price, the call option changes by $.25. At the end of one month the value of the call will fall by $1.50 due to the expiration of time, i.e. without considering the effect of stock price changes.

Construct a riskless hedged equity position with this stock and calls. Show how much equity you would have in the position.

25 - 4(3) = 13

How much would you earn at the end of the month if the stock increased by $4?

New equity positions is: 29 – 4(3 + 1 -1.50) = 19 and 19 -13 = 6

or using ΔS - (ΔS/ ΔC)( ΔC) =

4 - (4) (1 - 1.50) = 6

How much would you earn at the end of the month if the stock decreased by $4?

-4 - (4) (-1 - 1.50) = 6

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