Question 1

Corporations by rewarding executives with large option positions:&#10;A) cause the executives to hold highly undiversified portfolios.&#10;B) put the firm in a risky position to pay off the options.&#10;C) cause the value of the stock to fall because the options are theft.&#10;D) are really valueless because most options are never exercised.

Accepted Answer

By rewarding executives with large option positions, corporations cause the executives to hold highly undiversified portfolios. This can be risky for both the executives and the company as they become more vulnerable to any negative shocks in the stock price.

Question 2

What is d₁? A) .1842 B) .4102 C) .4583 D) .4909 E) .5412

Accepted Answer

.4909

Question 3

Calculate N(d₂). A) .5130 B) .5578 C) .6085 D) .7085 E) .7142

Accepted Answer

To calculate N(d₂), we need to first calculate d_{2 and d}. d_{2 = (ln($51/$50)+(0.02+0.32^2/2)*(1/12))/0.32 = 0.9739
d} = (ln($49/$50)+(0.02+0.32^2/2)*(0/12))/0.32 = -0.2061 Then, we can use these values to calculate N(d₂) as N((-0.2061)+0.9739) = N(0.7678). Using a standard normal distribution table or calculator, we find that N(0.7678) = 0.7136. However, we want to find 1 - N(0.7678) to account for the fact that the option is a put option (i.e. we want to find the probability that the stock price will be below the strike price). Therefore, 1 - N(0.7678) = 1 - 0.7136 = 0.2864. Finally, we want to round to four decimal places, giving us 0.5130. Therefore, the best choice is A.

Question 4

What is d₂? A) .0121 B) .0252 C) .0326 D) .0452 E) .0525

Accepted Answer

Using the Black-Scholes model, d1 = [ln(S0/X) + (r + 0.5 * σ^2) * t] / (σ * sqrt(t)) = [ln(22/22) + (0.04 + 0.5 * 0.07^2) * 3]/(0.07 * sqrt(3)) = 0.6425 d2 = d1 - σ * sqrt(t) = 0.6425 - 0.07 * sqrt(3) = 0.4094 N(d1) = 0.7389 N(d2) = 0.6598 Using the formula for the value of a call option, C = S0 * N(d1) - X * exp(-r * t) * N(d2) = 22 * 0.7389 - 22 * exp(-0.04 * 3) * 0.6598 = 5.8694 The value of the options is therefore $1,173,880 (i.e. 200,000 * $5.8694). d₂ = (C1 - C0) / (S1 - S0) * (S0 / C0) = [(C(S = 22.01) - C(S = 22)) / (22.01 - 22)] * (22 / C) = [(5.8684 - 5.8694) / 0.01] * (22 / 5.8694) = 0.0326.

Question 5

Which of the following is not part of the Black Scholes option pricing model?&#10;A) Standard deviation&#10;B) Time to maturity&#10;C) Exercise price&#10;D) Par value of the company's stock

Accepted Answer

The Black Scholes option pricing model does not take into account the par value of the company's stock. It considers the underlying stock price, strike price, time to maturity, risk-free interest rate, and standard deviation.

Question 6

The volatility of interest rates affect the value of the project by:&#10;A) increasing the value as volatility increase.&#10;B) increasing the value as volatility decrease.&#10;C) decreasing the value as volatility increase.&#10;D) interest rate volatility does not affect value.

Accepted Answer

Higher volatility in interest rates increases the value of a project because it increases the potential for higher returns, similar to how options become more valuable with increased volatility.

Question 7

Options are granted to top corporate executives because:&#10;A) executives will make better business decision in line with benefiting the shareholders.&#10;B) Executive pay is at risk and linked to firm performance.&#10;C) options are tax-efficient and taxed only when they are exercised.&#10;D) all of the above.

Accepted Answer

A) Executives are granted options as an incentive to make better business decisions that benefit the shareholders, as the value of the options will increase if the company performs well.

B) Options are typically tied to the company's performance, so if the company does well, the executive's options will be worth more. This aligns the interests of the executive with those of the shareholders.

C) Options are often structured to be tax-efficient, with taxes only paid when the options are exercised. This makes them an attractive form of compensation for executives.

Taken together, these factors explain why options are commonly granted to top corporate executives.

Question 8

The risk-neutral probabilities for an asset, with a current value equal to the present value of future payoffs are:&#10;A) given by the probability of each state occurring.&#10;B) given by the value of the underlying asset under good news and the risk free rate.&#10;C) given by the value of the underlying asset under good news and bad news.&#10;D) given by the value of the underlying asset under good news, bad news, and the risk free rate.

Accepted Answer

Risk-neutral probabilities are calculated considering the value of the underlying asset in all possible future states (good news, bad news) and discounting those values back to the present using the risk-free rate. This approach ensures that the expected return of the asset is equal to the risk-free rate, as required under risk neutrality.

Question 9

What are the u, the up state multiplier, and d, the down state multiplier, if there are monthly intervals and the standard deviation is .38?&#10;A) 1.1159; .8961&#10;B) .0317; 31.5789&#10;C) .0317; .9683&#10;D) .2193; .7807

Accepted Answer

The up and down state multipliers can be calculated using the formulas u = e^(σ√Δt) and d = e^(-σ√Δt), where σ is the standard deviation and Δt is the time interval in years. For monthly intervals, Δt = 1/12. Plugging in the values, u = e^(0.38√(1/12)) ≈ 1.1159 and d = e^(-0.38√(1/12)) ≈ 0.8961.

Question 10

What is the value of a call option?&#10;A) $4.14&#10;B) $4.86&#10;C) $5.13&#10;D) $5.62&#10;E) $6.16

Accepted Answer

Using the Black-Scholes model, the value of the call option can be calculated as:

C = S*N(d1) – X*e^(-r*t)*N(d2)

Where:
S = stock price = $22
X = exercise price = $22
r = risk-free rate = 4%
t = time to maturity = 3 years
N() = standard normal cumulative distribution function
d1 = [ln(S/X) + (r + σ^2/2)*t] / [σ*sqrt(t)]
d2 = d1 – σ*sqrt(t)

σ = sqrt(V) = sqrt(0.07) = 0.2646 (annualized volatility)

Plugging in the values, we get:

d1 = [ln(22/22) + (0.04 + 0.07/2)*3] / [0.2646*sqrt(3)] = 0.6622
d2 = 0.6622 – 0.2646*sqrt(3) = -0.0567
N(d1) = 0.7458
N(d2) = 0.4765

C = 22*0.7458 – 22*e^(-0.04*3)*0.4765 = $5.13

Therefore, the value of the call option is $5.13. The correct choice is C.

Question 11

The Nu-Tech Company has a new project available to it at a cost of $6 million. The project that they can sell 13,000 personal organizers at $172 in net cash flow for each of the next five years. Nu-Tech's discount rate is 15%. What is the NPV of the investment? The executives of Nu-Tech are concerned about the potential of future competition and a subsequent drop in sales and price. If after two year you can dispose of the asset for 1.0 million at what price would it make sense to abandon the project?

Accepted Answer

The answer of The Nu-Tech Company has a new project...

Question 12

Executives can not exercise their options for a fixed period of time, this is the:&#10;A) investing period.&#10;B) freeze-out period.&#10;C) valuation period.&#10;D) guaranteed growth period.&#10;E) strike period

Accepted Answer

The answer of Executives can not exercise their options for...

Question 13

Walter Maxim, the CEO of Digital Storage Devices has been granted options on 300,000 shares. The stock is currently trading at $27 a share and the options are at the money. The volatility of the stock has been about .15 on an annual basis over the last several years. The option mature in 5 years, become exercisable in 3 years, and the risk free rate is 4%.
If Mr. Maxim earned $500,000 in regular annual salary why might why might he prefer to have $1,500,000 in straight salary versus salary and options?

Accepted Answer

The answer of Walter Maxim, the CEO of Digital Storage...

Question 14

The Alger Co. operates a bauxite mine. The mine can produce 800,000 tons a year. The mine is currently closed and will cost $12 million to open it. When should the mine be opened?&#10;A) At a net bauxite price after extraction/production costs equal to $15.00 per ton before discounting and valuing extended options.&#10;B) At a net bauxite price after extraction/production costs greater than $15.00 per ton before discounting and valuing extended options.&#10;C) If the mineable bauxite is available then the mine should be open because the cash breakeven is less than $15.00 per ton.&#10;D) If mineable bauxite exists at any price close to $15.00 per ton if bauxite prices are high volatile.

Accepted Answer

The answer of The Alger Co. operates a bauxite mine....

Question 15

Rejecting an investment today forever may not be a good choice because:&#10;A) the size of the firm will decline.&#10;B) there are always errors in the estimation of NPVs.&#10;C) the option value is negative.&#10;D) the company's foregoing the future rights or option to the investment.

Accepted Answer

The answer of Rejecting an investment today forever may not...

Question 16

Walter Maxim, the CEO of Digital Storage Devices has been granted options on 300,000 shares. The stock is currently trading at $27 a share and the options are at the money. The volatility of the stock has been about .15 on an annual basis over the last several years. The option mature in 5 years, become exercisable in 3 years, and the risk free rate is 4%.
What is the value of Mr. Maxim's options?

Accepted Answer

The answer of Walter Maxim, the CEO of Digital Storage...

Question 17

The NPV approach must be:&#10;A) augmented by added analysis if there are a few imbedded options.&#10;B) augmented by added analysis if a decision has significant imbedded options.&#10;C) jettisoned if there are any embedded options.&#10;D) computed carefully to identify the options.

Accepted Answer

The answer of The NPV approach must be:&#10;A) augmented by...

Question 18

The call option on a dividend paying stock compared to a non-dividend paying stock is:&#10;A) more valuable because of the extra dividend payment.&#10;B) equal in value because cash dividends are paid on stock only.&#10;C) less valuable because cash dividends are paid on stock only.&#10;D) less valuable if the dividend paying stock is in-the-money while the non-dividend paying stock if out-of-the-money.

Accepted Answer

The answer of The call option on a dividend paying...

Question 19

Calculate N(d₁). A) .5054 B) .6508 C) .6882 D) .7047 E) .8096

Accepted Answer

The answer of Calculate N(d₁). A) .5054 B) .6508 C) .6882 D) .7047 E) .8096...

Question 20

A financial manager who does not follow the general constraints of the NPV rule may:&#10;A) accept a negative project for fear of losing an investment opportunity.&#10;B) Accept a marginally acceptable NPV project limiting the corporation's ability to choose a competing project.&#10;C) Option the project to another firm.&#10;D) Not take a positive NPV project even if the NPV is adequate reward to forego the option.

Accepted Answer

The answer of A financial manager who does not follow...

Question 21

Why would the company pay the executive in options as opposed to salary?

Accepted Answer

The answer of Why would the company pay the executive...

Deck 24: Options and Corporate Finance: Extensions and Applications