CHAPTER 20/FINANCING WITH DERIVATIVES 1
CHAPTER 20
FINANCING WITH DERIVATIVES
ANSWERS TO QUESTIONS:
1.a An option is a contract that gives holders the right to buy or sell a commodity (such as 100 shares of a particular stock) at a set price during a specified time period.
b.A call is an option to buy a particular commodity (stock).
c.A put is an option to sell a particular commodity (stock).
d.A contingent claim is a security whose payoffs depend on the value of another security.
2.Call options and warrants are similar in that both securities give holders the right to buy shares of a particular stock at a set price during a specified time perio d. The principal difference is that warrants are issued by firms, and options are written by investors. Most listed call options have relatively short lives (generally 9 months or less), whereas a warrant can have a life of several years or even can be perpetual.
3.The value of a call option is dependent upon four variables:
•The relationship between the option's exercise price and the price of the underlying stock.
•The time remaining until the option expires.
•The level of interest rates.
•The expected volatility of the underlying stock's price.
4.At a time when interest rates are relatively low, option prices in general will be relatively low because the opportunity cost of buying options rather than stocks is also low. On the other hand, when interest rates are high, investors bid up option prices as the opportunity cost of holding stocks increases.
5.The greater the expected stock price volatility, the higher the call option value is, all other things being equal.
6.The major similarities between convertible securities and warrants are:
a.Both convertibles and warrants tend to lower agency costs.
b.The intention is the future issuance of common stock at a price higher than that prevailing at the time of the convertible or warrant issue.
c.Both the convertibility option and the attachment of warrants result in interest expense or preferred dividend savings for the issuing company.
The major differences between convertible securities and warrants are:
a.The company receives additional funds when (and if) the warrants are exercised, whereas no additional funds are received at the time convertibles are exercised.
b.The fixed income security remains on the company's books after exercise of warrants, but in the case of convertibles, the fixed income security is exchanged and taken off the company's books.
7.Companies issue convertible securities for the following reasons:
•To lower agency costs.
•To sell common stock in the future at a higher price than the price prevailing at the time of original issue; and
•To acquire and use low-cost capital for a period of time until the full benefits of the financing can be reflected in the company's earnings.
8.See Figure 20-2 for the relationships.
9.A company effectively can force conversion of a convertible security by exercising the call privilege. This procedure is effective when the conversion value is greater than the call price, because the rational investor will convert.
10.The preemptive right gives common stockholders the right to buy, on a pro rata basis, any new common shares sold by the firm. The preemptive right may be relatively important in a small company with a small number of stockholders and is relatively unimportant in a large corporation where the stock is widely held.
11.An interest rate swap may be used to hedge against the risk associated with fluctuations in interest rates. Swaps are especially effective in hedging against long-term risks. In the case of interest rate swaps, the hedge is often accomplished by exchanging the floating rate interest. payments of one party for the fixed rate interest payments of another.
SOLUTIONS TO PROBLEMS:
1.a.Value of a call option at maturity
= Stock price - Exercise price
= $50 - $40 = $10
b.Its value will be greater than $10.
c.Its value is $0, because the exercise price ($60) is much greater than the stock price ($50).
d.Its value will be greater than zero.
2.a Value of a put option at maturity = Exercise price - Stock price
Because the stock price ($50) is much greater than the exercise price ($40), its value is zero.
b.Its value will be greater than zero.
c.Value of a put option at maturity = Exercise price - Stock price
= $60 - $50 = $10
d.Its value will be greater than $10.
3.a.Conversion ratio = (Par value of security/conversion price)
= 1000/$25
= 40 shares
Conversion value = (conversion ratio)(stock price)
= (40)($25) = $1,000
b.Bond value = $60(PVIFA .09,20) +$1,000(PVIF.09,20)
= $60(9.128) + $1,000(.178)
= $725.68 _ $726
c.A realistic estimate of market value is the $1000-$1100 range. Because the conversion value and bond value are somewhat close together, we can expect the security to sell at a premium above the higher conversion value. The reason is that investors have a high upside conversion value potential (that will be realized if the common stock price moves up) while the bond value represents somewhat of a floor on the value of security and provides some protection from stock price declines.
d.Conversion value = (conversion ratio)(stock price)
= (40)($35) = $1,400
e.A realistic estimate of the market value is $1,400. At this price, the debenture is likely to be called, effectively force conversion. Therefore, the debenture cannot be expected to sell at a premium above conversion value.
f.At $26.75 per share, the conversion value of the bond is equal to the call price ($1,070). A premium of 10-15% above $26.75 (or about $30 per share) would be necessary to assure the success of the call to force conversion.
g.Bond value = $60(PVIFA .10,20) + $1,000(PVIF .10,20)
= $60(8.514) + $1,000(.149)
= $659.84 $660
4.a Conversion ratio = 1000/$83.45 = 11.98 shares
b.Conversion value = (11.98)($67) = $803
c.$83.45 - $67.00 = $16.45
Premium = ($16.45/$67)(100) = 24.6%
5.a. Formula value = (Common stock price - Exercise price) x No. of shares obtainable with each warrant
= ($24 - $20)(1) = $4
Therefore, the premium over formula value = $8 - $4 = $4
6.a. Formula value = ($21.50 - $20.00)(1) = $1.50
b.Premium over formula value = $5.00 - $1.50 = $3.50
c.The principal reason investors are willing to pay more than formula value for these warrants is the potential for higher percentage returns than an equivalent investment in the common stock could yield; that is, leverage . The remaining warrant life influences the amount of premium over formula value.
d.The warrant price would be very close to $1.50, the formula value, because less than one month remains before the expiration date. This short time interval limits the leverage opportunity.
e.Warrant holders do not possess dividend rights and therefore do not receive dividends.
7. a.Pro Forma Balance Sheet
(millions of dollars)
Current assets$200Current liabilities$100
Fixed assets, net400Long-term debt250
$600Common equity250
$600
b.Pro Forma Balance Sheet
(millions of dollars)
Current assets$200Current liabilities$100
Fixed assets, net 400Long-term debt150
_____Common equity350
$600$600
c.No additional funds are raised at the time of conversion.
8.a.Number of additional shares issued =
($75,000,000/$1000/debenture) x (25 warrants/debenture) x
(1 share/warrant) = 1,875,000 shares
Additional funds raised from warrant exercise =
(1,875,000 shares) x ($30/share) = $56,250,000
Capital Structure
Long-term debt$325,000,000
Common stock, $1 par26,875,000
Contributed capital in excess of par value204,375,000
Retained earnings$350,000,000
$906,250,000
b.Common stock price has to be above $30 a share at warrant expiration date.
c.$75 million + $56.25 million = $131.25 million
9.a.Alternatives:
1.Convert, and receive 30 shares of common stock presently selling at $44 a share for a total value of $1,320, or
2. Redeem the debentures for $1,070 cash.
b.Conversion: The reason is obvious (conversion has a greater value to the investor). Thus, as long as conversion value materially exceeds call price, the company can effectively force conversion by exercising the call privilege.
10
10.Issue price = [(interest)(1 - tax rate)] / (1 + kc)t +
t=1 (conversion value at end of year 10) /(1 + kc)10
10
= [$75(1 - 0.4)] / (1 + kc)t + $1,350 / (1 + kc)10
t=1
Using kc = 7.0%:
$1,000 $45(7.024) + $1,350(0.508)
$1,000 $316.08 + $685.8 = $1,001.88
Therefore, kc 7.0%
This calculation is based on the expected conversion value. Hence it probably underestimates the cost of the convertible security because investors may place greater value on the option imbedded in the convertible security than the terminal value as represented by the expected conversion value and date.
11.a.Rights-on case:
R = (Mo - S)/(N + 1) = ($50 - $45)/(10 + 1) = $0.455
Ex-rights case:
R = (Me - S)/N = ($49.545 - $45)/10 = $0.455
b.Stock is expected to drop by the value of the right, because the buyer now no longer receives the right.
c.R = (Mo - S)/(N + 1) = ($52 - $45)/(10 + 1) = $0.636
d.Trend would be for the market price of the right to decrease, reaching its theoretical value immediately prior to expiration.
12.a.Rights on case:
R = (Mo- S)/(N + 1) = ($30 - $25/(12+1) = $0.3846
Ex-rights case:
R = (Me - S)/N = ($29.6154 - $25)/12 = $0.3846
b.Stock is expected to drop by the value of the right, i.e., $0.3846.
c.R = ($40 - $25)/(12+1) = $1.1538 or $1.15
13.a.Formula value = max {$0; ($30 - $32)(0.5)} = $0
Premium = $1.00 - $0 = $1.00
b.Formula value = max {$0; ($32 - $32)(0.5)} = $0
Premium = $2.00 - $0 = $2.00
c.Formula value = max {$0; ($38 - $32)(0.5)} = $3.00
Premium = $3.50 - $3.00 = $0.50
14.a Conversion value = ($1,000/$50)$45 = $900
b.Straight bond value = $90 (PVIFA0.12,18) + $1,000 (PVIF0.12,18)
= $90 (7.250) + $1,000 (0.130)
= 782.5 or $783
c.Conversion premium = $935 - max {$900; $783} = $35
d.Conversion value = ($100/$50)($65) = $1300
e.$1300. There will be no premium because the debentures are callable at $1,030.
15.a.Conversion value = 2.5 shares x $42/share = $105
b.Straight preferred stock value = $10(PVIFA0.09,10) + $100(PVIF0.09,10)
= $106.38, or $106
c.New conversion value = 2.5 shares x $44 = $110
New straight preferred stock value = $10(PVIFA.07,10)
+ $100(PVIF.07,10)
= $121.04 or $121
Because of the threat of a call at 103, the maximum value will be the conversion value, or $110.
16.a.Because the exercise price on the warrant exceeds the stock price, the theoretical value is $0.
b.Warrant values are influenced by the volatility of the stock price, the relationship between the stock price and the exercise price, the level of interest rates and the time remaining until the warrants “must be” exercised -- i.e., the expiration date.
c.HPY (stock) = ($20 - $15)/$15 = 33.33%
HPY (warrant) = ($6.50 - $3)/$3 = 116.67%
d.HPY (stock) = ($25 - $20)/$20 = 25%
HPY (warrant) = ($10.50 - $6.50)/$6.50 = 61.54%
e.As the stock price rises above the exercise price, the rate of return from investing in the warrant declines because of the larger investment required to purchase each warrant.
17.Conversion ratio = $1000 / $40 = 25 shares
a.Bond value = $90 ( PVIFA.11,10) + $1000 (PVIF.11,10) = $882.21
b.Conversion value = 25 shares x $35 per share = $875
c.These debentures will sell for more than $882.21, depending on the valuation of the call option imbedded in the convertible debentures.
d.Accept the call at “105”. The call value likely exceeds the market value prior to the cal l.
18.No recommended solution.