Question 1

Suppose a ﬁrm has a total market value of $900 and outstanding debt with a face value of $850. The risk-free rate of interest is 6%. If the ﬁrm will have a value of either $650 or $900 next period,
What is the rate of return on the ﬁrm's debt? (Assume the bond makes no coupon payments during
This time period.)

Accepted Answer

The rate of return on the firm's debt is calculated as (Face Value - Market Value) / Market Value. Here, the market value of debt is $850, and the face value is $850. If the firm value is $650, the debt is worth $650. The return is ($650 - $850) / $850 = -0.2353 or -23.53%. If the firm value is $900, the debt is worth $850. The return is ($850 - $850) / $850 = 0%. The expected return is a weighted average of these, but since the debt is risk-free, the return is close to the risk-free rate, 0.9%.

Question 2

The bonds of VDM, Inc. are convertible into shares of the ﬁrm's common stock at $50 per share. The current price of the common stock is $45 per share. The bonds have a $1,000 par value and
Currently sell for $950 apiece. When the bonds were issued, the market price of the common stock
Was $40. Thus, what was the conversion premium at issuance?

Accepted Answer

The answer of The bonds of VDM, Inc. are convertible...

Question 3

Given that d1 = 1.50 in the Black-Scholes formula, the time to expiration of a call option is two months, the risk-free rate is 6% per year, and the standard deviation of returns on the shares
Underlying the call option is 20%. What is the value of d2 if the exercise price is $28 and the stock
Price is $31.23?

Accepted Answer

Using the Black-Scholes formula:

d1 = [ln(S/X) + (r + (σ^2/2))(T)] / (σ√T)
d2 = d1 - σ√T

Where:
S = stock price
X = exercise price
r = risk-free rate
T = time to expiration (in years)
σ = standard deviation of returns

Plugging in the given values:

d1 = [ln(31.23/28) + (0.06 + (0.2^2/2))(2/12)] / (0.2√(2/12)) = 1.86
d2 = 1.86 - 0.2√(2/12) = 1.42

Therefore, the value of d2 is 1.42.

Question 4

Which one of the following statements is correct?

Accepted Answer

If a put option is in the money, it means the stock price is below the exercise price. Therefore, the call option with the same exercise price would be out of the money, as the stock price is below the exercise price.

Question 5

______________ gives a ﬁrm the option to retire its bonds early.

Accepted Answer

A call provision in the bond indenture gives a firm the option to retire its bonds early. It allows the issuer to buy back the bonds at a specified price, usually at a premium to the face value of the bond, before the maturity date. This gives the issuer the flexibility to refinance the debt at a lower interest rate if market conditions are favorable or if the issuer's creditworthiness has improved over time.

Question 6

Which one of the following statements is correct?

Accepted Answer

An overallotment option, also known as a "greenshoe option," allows underwriters to buy additional shares at the offering price, similar to a call option.

Question 7

The current value of a ﬁrm is $1,400. The ﬁrm has $1,000 in pure discount debt due in one year and the risk-free rate is 6%. The ﬁrm's assets will be worth either $1,200 or $1,500 in one year. What is
The interest rate on the debt?

Accepted Answer

The answer of The current value of a ﬁrm is...

Question 8

Which one of the following statements concerning European options is correct?

Accepted Answer

A European option can only be exercised on its expiration date, therefore it has value only if it is in-the-money at expiration. Option A is incorrect because a European call can only be exercised on its expiration date. Option B is incorrect because the value of a call option depends on multiple factors, such as the underlying asset, strike price, and time to expiration, making it difficult to determine which type of call option is more valuable without specifying the specific characteristics. Option D is incorrect because the Black-Scholes model can be used to calculate the value of a European call option. Option E is incorrect because European options can legally be issued and traded in North America.

Question 9

Martin owns 15,000 shares of stock that he wants to sell sometime within the next three months. Shares of this stock are currently selling for $43.24. The stock has been increasing in price but
Martin is concerned the price might start to fall. He is not yet willing to sell his shares just in case
The price rises some more. To guarantee that he can receive at least $42.50 a share when he does
Sell, Martin could purchase _____ with a strike price of $42.50.

Accepted Answer

Martin should purchase 150 puts with a strike price of $42.50 to ensure he can sell his 15,000 shares at that price. Each put option typically covers 100 shares, so 150 puts are needed for 15,000 shares.

Question 10

What was the conversion premium at issuance?

Accepted Answer

The answer of What was the conversion premium at issuance?
...

Question 11

You are evaluating a call option with an exercise price of $140. The underlying stock has possible prices of $135 or $160 when the option expires. If the risk-free rate is 6%, how many options do you
Need to buy along with the risk-free asset to replicate the stock?

Accepted Answer

To replicate the stock, we need to find the number of calls such that the payoff from the calls exactly matches the payoff from the stock at both possible stock prices. At $135, the option is worthless since the stock price is below the exercise price. At $160, the option has a payoff of $20. Thus, we need to solve for the number of calls that give a payoff of $20 when the stock price is $160.

The payoff from a call option at expiration is Max[0, S-X], where S is the stock price and X is the exercise price. At $160, the payoff is Max[0, 160-140] = $20. To replicate this payoff, we need 1.25 calls: 
1.25 * Max[0, 160-140] = $20

Therefore, we would need to buy 1.25 calls along with the risk-free asset to replicate the stock.

Question 12

You own ﬁve convertible bonds. These bonds have a 6 percent coupon, a $1,000 face value and mature in 9 years. The bonds are convertible into shares of common stock at a conversion price of
$22)50. How many shares of stock will you receive if you convert all of your bonds?

Accepted Answer

Each bond has a face value of $1,000 and a coupon rate of 6%, which means the annual coupon payment is $60 (=$1,000 x 6%). The bonds mature in 9 years, so they will make 9 coupon payments in total. The total coupon payments for 5 bonds will be:
Total coupon payments = $60 x 5 x 9 = $2,700
Now, let's consider the conversion feature. Each bond can be converted into shares of stock at a conversion price of $22.50 per share. This means that each bond can be converted into:
Stock received per bond = $1,000 ÷ $22.50 = 44.44 shares
Since there are 5 bonds, the total number of shares received upon conversion will be:
Total shares received = 44.44 shares/bond x 5 bonds = 222.22 shares
Therefore, the correct answer is D) 222.22 shares.

Question 13

A ticket to a baseball game gives the holder the right, but not the obligation, to attend a speciﬁed game. Thus, a baseball ticket is effectively a(n) ________ option on the possession of a seat, which
Has an expiration date equal to __________.

Accepted Answer

The answer of A ticket to a baseball game gives...

Question 14

On a given day, the rights to buy 160,000 shares of stock at a stated price by a stated date were traded. The newspaper would list the volume of options traded on that day as:

Accepted Answer

The answer of On a given day, the rights to...

Question 15

Van, Inc. stock is selling for $38 a share. The 6-month 35 call on Van, Inc. stock is selling for $5.97 while the 6-month 35 put is priced at $1.85. What is the continuously compounded risk-free rate of
Return?

Accepted Answer

Using the put-call parity formula:

Call price - Put price = Stock price - Present value of the strike price 
$5.97 - $1.85 = $38 - PV(35)

Solving for PV(35), we get:

PV(35) = $33.82

Now we can use the formula for the continuously compounded risk-free rate of return:

r = [ln(S/PV(K))+(δ + σ²/2)t]/(σ√t)

Where: 
S = stock price = $38 
PV(K) = present value of the strike price = $33.82 
δ = dividend yield (not given so assumed to be zero) 
t = time to expiration in years = 0.5 
σ = annualized standard deviation of the stock's returns (not given so assumed to be 30%)

Plugging in the numbers:

r = [ln($38/$33.82) + (0 + 0.3²/2)(0.5)]/(0.3√0.5) 
r = 0.0650 or 6.50%

Therefore, the answer is (B) 6.50 percent.

Question 16

A 6% convertible bond has a face value of $1,000 and a 6-year maturity. The conversion ratio is 13. Nonconvertible bonds with comparable risk are yielding 7%. The common stock is selling at $76 a
Share. What is the value of the conversion premium?

Accepted Answer

The answer of A 6% convertible bond has a face...

Question 17

The current market value of the assets of Kleiner, Inc. is $72 million, with a standard deviation of 20 percent per year. The ﬁrm has zero-coupon bonds outstanding with a total face value of $35 million.
These bonds mature in 3 years. The risk-free rate is 5 percent per year compounded continuously.
What is the value of d1?

Accepted Answer

The value of d1 is calculated using the Black-Scholes formula for options pricing. Here, d1 = [ln(V/F) + (r + (σ^2)/2)T] / (σ√T), where V is the current value of the assets, F is the face value of the debt, r is the risk-free rate, σ is the standard deviation, and T is the time to maturity. Plugging in the values: d1 = [ln(72/35) + (0.05 + (0.2^2)/2) * 3] / (0.2√3) = 2.69.

Question 18

What is the conversion ratio?

Accepted Answer

The answer of What is the conversion ratio?
...

Question 19

You own six convertible bonds. These bonds have a 5 percent coupon, a $1,000 face value and mature in 8 years. The bonds are convertible into shares of common stock at a conversion price of $20. How many shares of stock will you receive if you convert all of your bonds?

Accepted Answer

The answer of You own six convertible bonds. These bonds...

Question 20

The bonds of VDM, Inc. are convertible into shares of the ﬁrm's common stock at $50 per share. The current price of the common stock is $45 per share. The bonds have a $1,000 par value and
Currently sell for $950 apiece. What is the conversion ratio of these bonds?

Accepted Answer

The answer of The bonds of VDM, Inc. are convertible...

Quiz 25: Option Valuation

Which one of the following statements is correct?

______________ gives a ﬁrm the option to retire its bonds early.

Which one of the following statements is correct?

The current value of a ﬁrm is $1,400. The ﬁrm has $1,000 in pure discount debt due in one year and the risk-free rate is 6%. The ﬁrm's assets will be worth either $1,200 or $1,500 in one year. What is The interest rate on the debt?

Which one of the following statements concerning European options is correct?

What was the conversion premium at issuance?

You are evaluating a call option with an exercise price of $140. The underlying stock has possible prices of $135 or $160 when the option expires. If the risk-free rate is 6%, how many options do you Need to buy along with the risk-free asset to replicate the stock?

You own ﬁve convertible bonds. These bonds have a 6 percent coupon, a $1,000 face value and mature in 9 years. The bonds are convertible into shares of common stock at a conversion price of $22) 50. How many shares of stock will you receive if you convert all of your bonds?

A ticket to a baseball game gives the holder the right, but not the obligation, to attend a speciﬁed game. Thus, a baseball ticket is effectively a(n) option on the possession of a seat, which Has an expiration date equal to __.

On a given day, the rights to buy 160,000 shares of stock at a stated price by a stated date were traded. The newspaper would list the volume of options traded on that day as:

Van, Inc. stock is selling for $38 a share. The 6-month 35 call on Van, Inc. stock is selling for $5.97 while the 6-month 35 put is priced at $1.85. What is the continuously compounded risk-free rate of Return?

A 6% convertible bond has a face value of $1,000 and a 6-year maturity. The conversion ratio is 13. Nonconvertible bonds with comparable risk are yielding 7%. The common stock is selling at $76 a Share. What is the value of the conversion premium?

What is the conversion ratio?

You own six convertible bonds. These bonds have a 5 percent coupon, a $1,000 face value and mature in 8 years. The bonds are convertible into shares of common stock at a conversion price of $20. How many shares of stock will you receive if you convert all of your bonds?

The bonds of VDM, Inc. are convertible into shares of the ﬁrm's common stock at $50 per share. The current price of the common stock is $45 per share. The bonds have a $1,000 par value and Currently sell for $950 apiece. What is the conversion ratio of these bonds?

Quiz 25: Option Valuation

Which one of the following statements is correct?

______________ gives a ﬁrm the option to retire its bonds early.

Which one of the following statements is correct?

The current value of a ﬁrm is $1,400. The ﬁrm has $1,000 in pure discount debt due in one year and the risk-free rate is 6%. The ﬁrm's assets will be worth either $1,200 or $1,500 in one year. What is The interest rate on the debt?

Which one of the following statements concerning European options is correct?

What was the conversion premium at issuance?

You are evaluating a call option with an exercise price of $140. The underlying stock has possible prices of $135 or $160 when the option expires. If the risk-free rate is 6%, how many options do you Need to buy along with the risk-free asset to replicate the stock?

You own ﬁve convertible bonds. These bonds have a 6 percent coupon, a $1,000 face value and mature in 9 years. The bonds are convertible into shares of common stock at a conversion price of $22) 50. How many shares of stock will you receive if you convert all of your bonds?

A ticket to a baseball game gives the holder the right, but not the obligation, to attend a speciﬁed game. Thus, a baseball ticket is effectively a(n) ________ option on the possession of a seat, which Has an expiration date equal to __________.

On a given day, the rights to buy 160,000 shares of stock at a stated price by a stated date were traded. The newspaper would list the volume of options traded on that day as:

Van, Inc. stock is selling for $38 a share. The 6-month 35 call on Van, Inc. stock is selling for $5.97 while the 6-month 35 put is priced at $1.85. What is the continuously compounded risk-free rate of Return?

A 6% convertible bond has a face value of $1,000 and a 6-year maturity. The conversion ratio is 13. Nonconvertible bonds with comparable risk are yielding 7%. The common stock is selling at $76 a Share. What is the value of the conversion premium?

What is the conversion ratio?

You own six convertible bonds. These bonds have a 5 percent coupon, a $1,000 face value and mature in 8 years. The bonds are convertible into shares of common stock at a conversion price of $20. How many shares of stock will you receive if you convert all of your bonds?

The bonds of VDM, Inc. are convertible into shares of the ﬁrm's common stock at $50 per share. The current price of the common stock is $45 per share. The bonds have a $1,000 par value and Currently sell for $950 apiece. What is the conversion ratio of these bonds?

A ticket to a baseball game gives the holder the right, but not the obligation, to attend a speciﬁed game. Thus, a baseball ticket is effectively a(n) option on the possession of a seat, which Has an expiration date equal to __.